[{"data":1,"prerenderedAt":6983},["ShallowReactive",2],{"lesson:\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures":3,"course-wordcounts":1252,"ref-card-index":2164,"nav:artificial-intelligence":6842,"tikz:c26310028ead1984a843b7de005b0ac7b17883eb4e526dc42c96f4795ff0b74a":6975,"tikz:ad770ff37a70201dfadc6213ca9ce49e22ecf1d59cbc89a8835fd4f66752ad94":6976,"tikz:c5156b374498d4ca1ab53909849162f8c1697c44e8896a316306932b6fc83d23":6977,"tikz:fa909f8f909109615a6c171fcf0758752e9e454e273c37d978cc3d2b1651d096":6978,"tikz:0cf97ca3884219d89c4846c9f121ff3a2f999b7b0edde079a3fa9e632728ce98":6979,"tikz:c349b016c91ccce86ec144152a70bf21f2c9962bf9bae79430e82b54a32c798c":6980,"tikz:0a7524e2b188070f65e98bba6c06e2429ad3ee9cc08f02660ef37cbd7e0b015e":6981,"tikz:15057735ea9a3ac099d18aa40754acd3549c9fc29beb7eb3fe21394c6f5ce455":6982},{"id":4,"title":5,"blurb":6,"body":7,"brief":1222,"category":1223,"description":1224,"draft":1225,"extension":1226,"meta":1227,"module":1231,"navigation":1232,"path":1233,"practice":1234,"rawbody":1235,"readingTime":1236,"seo":1241,"sources":1242,"status":1247,"stem":1248,"summary":1249,"topics":1250,"__hash__":1251},"course\u002F08.artificial-intelligence\u002F01.foundations\u002F04.agent-architectures.md","Agent Architectures","",{"type":8,"value":9,"toc":1207},"minimark",[10,37,42,140,410,415,477,481,603,607,631,634,653,657,668,671,691,695,710,713,728,954,970,974,985,988,1011,1023,1027,1080,1083,1087,1102,1133,1136,1152,1156,1159,1162],[11,12,13,14,19,20,24,25,28,29,32,33,36],"p",{},"This builds on ",[15,16,18],"a",{"href":17},"\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents","Intelligent Agents",",\nwhich fixed what an agent ",[21,22,23],"em",{},"is"," (a percept-to-action loop, captured by an agent\nfunction), what makes one ",[21,26,27],{},"good"," (rationality — maximizing expected performance),\nand how to ",[21,30,31],{},"specify"," the problem it faces (PEAS and the six environment axes). This\nlesson takes up the remaining question: how do you actually ",[21,34,35],{},"build"," a program that\ncomputes a good agent function? The answer is not one design but a ladder of four,\neach adding machinery the one below it lacked.",[38,39,41],"h2",{"id":40},"the-structure-of-agents","The structure of agents",[11,43,44,45,49,50,53,54,135,136,139],{},"The job of AI is to design an ",[46,47,48],"strong",{},"agent program"," that implements the agent\nfunction, running on an ",[46,51,52],{},"architecture"," — a device with physical sensors and\nactuators. In short, ",[55,56,59],"span",{"className":57},[58],"katex",[55,60,64,96,121],{"className":61,"ariaHidden":63},[62],"katex-html","true",[55,65,68,73,83,88,93],{"className":66},[67],"base",[55,69],{"className":70,"style":72},[71],"strut","height:0.8095em;vertical-align:-0.1944em;",[55,74,78],{"className":75},[76,77],"mord","text",[55,79,82],{"className":80},[76,81],"textit","agent",[55,84],{"className":85,"style":87},[86],"mspace","margin-right:0.2778em;",[55,89,92],{"className":90},[91],"mrel","=",[55,94],{"className":95,"style":87},[86],[55,97,99,103,109,113,118],{"className":98},[67],[55,100],{"className":101,"style":102},[71],"height:0.7778em;vertical-align:-0.0833em;",[55,104,106],{"className":105},[76,77],[55,107,52],{"className":108},[76,81],[55,110],{"className":111,"style":112},[86],"margin-right:0.2222em;",[55,114,117],{"className":115},[116],"mbin","+",[55,119],{"className":120,"style":112},[86],[55,122,124,128],{"className":123},[67],[55,125],{"className":126,"style":127},[71],"height:0.625em;vertical-align:-0.1944em;",[55,129,131],{"className":130},[76,77],[55,132,134],{"className":133},[76,81],"program",".\nThe agent program takes just the ",[21,137,138],{},"current"," percept as input (that is all the\nsensors offer at any instant) and returns an action; if the agent's behavior must\ndepend on the whole history, the program has to remember the percepts itself.",[11,141,142,143,162,163,181,182,324,325,405,406,409],{},"Why not implement the agent function as a literal lookup table? Because it is\nastronomically too big. Let ",[55,144,146],{"className":145},[58],[55,147,149],{"className":148,"ariaHidden":63},[62],[55,150,152,156],{"className":151},[67],[55,153],{"className":154,"style":155},[71],"height:0.6833em;",[55,157,161],{"className":158,"style":160},[76,159],"mathcal","margin-right:0.0822em;","P"," be the set of percepts and ",[55,164,166],{"className":165},[58],[55,167,169],{"className":168,"ariaHidden":63},[62],[55,170,172,175],{"className":171},[67],[55,173],{"className":174,"style":155},[71],[55,176,180],{"className":177,"style":179},[76,178],"mathnormal","margin-right:0.1389em;","T"," the\nagent's lifetime; the table needs ",[55,183,185],{"className":184},[58],[55,186,188],{"className":187,"ariaHidden":63},[62],[55,189,191,195,282,286,290,293],{"className":190},[67],[55,192],{"className":193,"style":194},[71],"height:1.2809em;vertical-align:-0.2997em;",[55,196,199,206],{"className":197},[198],"mop",[55,200,205],{"className":201,"style":204},[198,202,203],"op-symbol","small-op","position:relative;top:0em;","∑",[55,207,210],{"className":208},[209],"msupsub",[55,211,215,273],{"className":212},[213,214],"vlist-t","vlist-t2",[55,216,219,268],{"className":217},[218],"vlist-r",[55,220,224,253],{"className":221,"style":223},[222],"vlist","height:0.9812em;",[55,225,227,232],{"style":226},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[55,228],{"className":229,"style":231},[230],"pstrut","height:2.7em;",[55,233,239],{"className":234},[235,236,237,238],"sizing","reset-size6","size3","mtight",[55,240,242,246,249],{"className":241},[76,238],[55,243,245],{"className":244},[76,178,238],"t",[55,247,92],{"className":248},[91,238],[55,250,252],{"className":251},[76,238],"1",[55,254,256,259],{"style":255},"top:-3.2029em;margin-right:0.05em;",[55,257],{"className":258,"style":231},[230],[55,260,262],{"className":261},[235,236,237,238],[55,263,265],{"className":264},[76,238],[55,266,180],{"className":267,"style":179},[76,178,238],[55,269,272],{"className":270},[271],"vlist-s","​",[55,274,276],{"className":275},[218],[55,277,280],{"className":278,"style":279},[222],"height:0.2997em;",[55,281],{},[55,283],{"className":284,"style":285},[86],"margin-right:0.1667em;",[55,287,289],{"className":288},[76],"∣",[55,291,161],{"className":292,"style":160},[76,159],[55,294,296,299],{"className":295},[76],[55,297,289],{"className":298},[76],[55,300,302],{"className":301},[209],[55,303,305],{"className":304},[213],[55,306,308],{"className":307},[218],[55,309,312],{"className":310,"style":311},[222],"height:0.7936em;",[55,313,315,318],{"style":314},"top:-3.063em;margin-right:0.05em;",[55,316],{"className":317,"style":231},[230],[55,319,321],{"className":320},[235,236,237,238],[55,322,245],{"className":323},[76,178,238]," entries. For an\nautomated taxi with a single camera, that is on the order of ",[55,326,328],{"className":327},[58],[55,329,331],{"className":330,"ariaHidden":63},[62],[55,332,334,338,341],{"className":333},[67],[55,335],{"className":336,"style":337},[71],"height:0.8141em;",[55,339,252],{"className":340},[76],[55,342,344,348],{"className":343},[76],[55,345,347],{"className":346},[76],"0",[55,349,351],{"className":350},[209],[55,352,354],{"className":353},[213],[55,355,357],{"className":356},[218],[55,358,360],{"className":359,"style":337},[222],[55,361,362,365],{"style":314},[55,363],{"className":364,"style":231},[230],[55,366,368],{"className":367},[235,236,237,238],[55,369,371,375,383,387,393,396,402],{"className":370},[76,238],[55,372,374],{"className":373},[76,238],"250",[55,376,378],{"className":377},[76,238],[55,379,382],{"className":380},[381,238],"mpunct",",",[55,384,386],{"className":385},[76,238],"000",[55,388,390],{"className":389},[76,238],[55,391,382],{"className":392},[381,238],[55,394,386],{"className":395},[76,238],[55,397,399],{"className":398},[76,238],[55,400,382],{"className":401},[381,238],[55,403,386],{"className":404},[76,238],"\nentries for an hour's driving — no physical agent could store it, no designer\ncould fill it, no learner could ever populate it. The challenge of AI is to\nproduce rational behavior from a ",[21,407,408],{},"small program"," rather than a vast table, just\nas a five-line Newton's-method routine replaced the printed tables of square\nroots. Four program skeletons underlie almost every intelligent system, in order\nof increasing sophistication.",[411,412,414],"h3",{"id":413},"simple-reflex-agents","Simple reflex agents",[11,416,417,418,420,421,424,425,428,429,432,433,476],{},"The simplest agent selects an action from the ",[21,419,138],{}," percept alone, ignoring\nthe rest of the history. It works by ",[46,422,423],{},"condition–action rules"," (also called\nsituation–action rules or if–then rules): ",[21,426,427],{},"if car-in-front-is-braking then\ninitiate-braking",". For the vacuum world the entire program is three rules — ",[21,430,431],{},"if\ndirty then suck; else if in A then go right; else go left"," — a dramatic reduction\nfrom the ",[55,434,436],{"className":435},[58],[55,437,439],{"className":438,"ariaHidden":63},[62],[55,440,442,446],{"className":441},[67],[55,443],{"className":444,"style":445},[71],"height:0.8413em;",[55,447,449,453],{"className":448},[76],[55,450,452],{"className":451},[76],"4",[55,454,456],{"className":455},[209],[55,457,459],{"className":458},[213],[55,460,462],{"className":461},[218],[55,463,465],{"className":464,"style":445},[222],[55,466,467,470],{"style":314},[55,468],{"className":469,"style":231},[230],[55,471,473],{"className":472},[235,236,237,238],[55,474,180],{"className":475,"style":179},[76,178,238]," table.",[478,479],"tikz-figure",{"hash":480},"c26310028ead1984a843b7de005b0ac7b17883eb4e526dc42c96f4795ff0b74a",[11,482,483,484,487,488,518,519,544,545,549,550,566,567,570,571,595,596,598,599,602],{},"Simple reflex agents are admirably compact but of limited intelligence: they work\n",[21,485,486],{},"only if the correct action can be decided from the current percept alone — only\nif the environment is fully observable",". A little unobservability causes trouble.\nA vacuum agent stripped of its location sensor, perceiving only ",[55,489,491],{"className":490},[58],[55,492,494],{"className":493,"ariaHidden":63},[62],[55,495,497,501,506,513],{"className":496},[67],[55,498],{"className":499,"style":500},[71],"height:1em;vertical-align:-0.25em;",[55,502,505],{"className":503},[504],"mopen","[",[55,507,509],{"className":508},[76,77],[55,510,512],{"className":511},[76,81],"Dirty",[55,514,517],{"className":515},[516],"mclose","]","\nor ",[55,520,522],{"className":521},[58],[55,523,525],{"className":524,"ariaHidden":63},[62],[55,526,528,531,534,541],{"className":527},[67],[55,529],{"className":530,"style":500},[71],[55,532,505],{"className":533},[504],[55,535,537],{"className":536},[76,77],[55,538,540],{"className":539},[76,81],"Clean",[55,542,517],{"className":543},[516],", has no rule that can reliably progress — moving ",[546,547,548],"code",{},"Left","\nloops forever if it starts in ",[55,551,553],{"className":552},[58],[55,554,556],{"className":555,"ariaHidden":63},[62],[55,557,559,562],{"className":558},[67],[55,560],{"className":561,"style":155},[71],[55,563,565],{"className":564},[76,178],"A",". Escaping such loops sometimes requires\n",[46,568,569],{},"randomization",": perceiving ",[55,572,574],{"className":573},[58],[55,575,577],{"className":576,"ariaHidden":63},[62],[55,578,580,583,586,592],{"className":579},[67],[55,581],{"className":582,"style":500},[71],[55,584,505],{"className":585},[504],[55,587,589],{"className":588},[76,77],[55,590,540],{"className":591},[76,81],[55,593,517],{"className":594},[516],", flip a coin between ",[546,597,548],{}," and\n",[546,600,601],{},"Right",". A randomized simple reflex agent can outperform a deterministic one in\npartially observable worlds — though in single-agent settings, a better\ndeterministic agent with memory usually does better still.",[411,604,606],{"id":605},"model-based-reflex-agents","Model-based reflex agents",[11,608,609,610,613,614,617,618,622,623,626,627,630],{},"The way to handle partial observability is to ",[21,611,612],{},"keep track of the part of the\nworld the agent can't currently see"," — to maintain ",[46,615,616],{},"internal state"," that depends\non the percept history and reflects the unobserved aspects of the current state.\nUpdating that state requires two pieces of knowledge encoded in the program: how\nthe world evolves independently of the agent (an overtaking car will be closer a\nmoment later), and how the agent's own actions affect the world (turning the\nwheel clockwise turns the car right). This knowledge — ",[619,620,621],"q",{},"how the world works"," — is\na ",[46,624,625],{},"model"," of the world, and an agent that uses one is a ",[46,628,629],{},"model-based agent",".",[478,632],{"hash":633},"ad770ff37a70201dfadc6213ca9ce49e22ecf1d59cbc89a8835fd4f66752ad94",[11,635,636,637,640,641,644,645,648,649,652],{},"Even a model-based agent seldom knows the current state ",[21,638,639],{},"exactly"," in a\npartially observable world; the box ",[619,642,643],{},"what the world is like now"," holds its best\nguess. The taxi may not see around the truck stalled ahead of it and can only\nguess at the hold-up — but it must still decide. Internal state need not describe\nthe world literally, either: ",[619,646,647],{},"driving home"," is really a fact about the taxi's\n",[21,650,651],{},"destination",", an aspect of the agent's own intended state, not the world's.",[411,654,656],{"id":655},"goal-based-agents","Goal-based agents",[11,658,659,660,663,664,667],{},"Knowing the current state is not always enough to decide what to do. At a junction\nthe taxi can turn left, turn right, or go straight — and the right choice depends\non ",[21,661,662],{},"where the taxi is trying to get to",". Beyond a current-state description, the\nagent needs ",[46,665,666],{},"goal"," information describing desirable situations, and it combines\nthe goal with its model to choose actions that (eventually) achieve the goal.",[478,669],{"hash":670},"c5156b374498d4ca1ab53909849162f8c1697c44e8896a316306932b6fc83d23",[11,672,673,674,677,678,681,682,598,686,690],{},"This differs sharply from reflex rules, because it involves\nconsideration of the future — ",[619,675,676],{},"what will happen if I do this?"," and ",[619,679,680],{},"will that make me happy?"," — information a reflex agent never represents explicitly. When\ngoal satisfaction takes a single action it is easy; when it needs a long sequence\nof twists and turns, finding one is the province of\n",[15,683,685],{"href":684},"\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search","search",[15,687,689],{"href":688},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning","planning",". The\ngoal-based agent looks less efficient than a reflex agent, but it is far more\nflexible: its knowledge is explicit and modifiable. Tell it a new destination and\nits whole behavior adapts; the reflex agent would need every rule rewritten.",[411,692,694],{"id":693},"utility-based-agents","Utility-based agents",[11,696,697,698,701,702,705,706,709],{},"Goals are only a crude binary — ",[619,699,700],{},"happy"," or ",[619,703,704],{},"unhappy."," Most environments offer\nmany action sequences that reach the goal, some quicker, safer, or cheaper than\nothers, and goals alone cannot choose among them. A ",[46,707,708],{},"utility function"," maps a\nstate (or sequence of states) to a real number capturing how desirable it is; it\nis essentially an internalization of the performance measure. When the internal\nutility function agrees with the external performance measure, an agent that\nchooses actions to maximize utility is rational by the external standard.",[478,711],{"hash":712},"fa909f8f909109615a6c171fcf0758752e9e454e273c37d978cc3d2b1651d096",[11,714,715,716,719,720,723,724,727],{},"A utility function is indispensable in two cases goals cannot handle. When goals\n",[21,717,718],{},"conflict"," — speed against safety — utility specifies the right tradeoff. When\nseveral goals are all ",[21,721,722],{},"uncertain",", utility weighs the likelihood of success\nagainst the importance of each goal. Because partial observability and\nstochasticity are everywhere, a rational utility-based agent chooses the action\nthat maximizes ",[46,725,726],{},"expected utility",": the utility it expects on average, given the\nprobabilities and utilities of each outcome.",[729,730,732],"callout",{"type":731},"definition",[11,733,734,737,738,953],{},[46,735,736],{},"Definition (Expected utility)."," Given a probability distribution over the\npossible outcomes of an action, its expected utility is ",[55,739,741],{"className":740},[58],[55,742,744,775],{"className":743,"ariaHidden":63},[62],[55,745,747,750,755,758,763,766,769,772],{"className":746},[67],[55,748],{"className":749,"style":500},[71],[55,751,754],{"className":752},[76,753],"mathbb","E",[55,756,505],{"className":757},[504],[55,759,762],{"className":760,"style":761},[76,178],"margin-right:0.109em;","U",[55,764,517],{"className":765},[516],[55,767],{"className":768,"style":87},[86],[55,770,92],{"className":771},[91],[55,773],{"className":774,"style":87},[86],[55,776,778,782,862,865,868,872,905,909,912,915,918,950],{"className":777},[67],[55,779],{"className":780,"style":781},[71],"height:1.0516em;vertical-align:-0.2997em;",[55,783,785,788],{"className":784},[198],[55,786,205],{"className":787,"style":204},[198,202,203],[55,789,791],{"className":790},[209],[55,792,794,854],{"className":793},[213,214],[55,795,797,851],{"className":796},[218],[55,798,801],{"className":799,"style":800},[222],"height:0.1783em;",[55,802,803,806],{"style":226},[55,804],{"className":805,"style":231},[230],[55,807,809],{"className":808},[235,236,237,238],[55,810,812],{"className":811},[76,238],[55,813,815,819],{"className":814},[76,238],[55,816,818],{"className":817},[76,178,238],"s",[55,820,822],{"className":821},[209],[55,823,825],{"className":824},[213],[55,826,828],{"className":827},[218],[55,829,832],{"className":830,"style":831},[222],"height:0.6828em;",[55,833,835,839],{"style":834},"top:-2.786em;margin-right:0.0714em;",[55,836],{"className":837,"style":838},[230],"height:2.5em;",[55,840,844],{"className":841},[235,842,843,238],"reset-size3","size1",[55,845,847],{"className":846},[76,238],[55,848,850],{"className":849},[76,238],"′",[55,852,272],{"className":853},[271],[55,855,857],{"className":856},[218],[55,858,860],{"className":859,"style":279},[222],[55,861],{},[55,863],{"className":864,"style":285},[86],[55,866,161],{"className":867,"style":179},[76,178],[55,869,871],{"className":870},[504],"(",[55,873,875,878],{"className":874},[76],[55,876,818],{"className":877},[76,178],[55,879,881],{"className":880},[209],[55,882,884],{"className":883},[213],[55,885,887],{"className":886},[218],[55,888,891],{"className":889,"style":890},[222],"height:0.7519em;",[55,892,893,896],{"style":314},[55,894],{"className":895,"style":231},[230],[55,897,899],{"className":898},[235,236,237,238],[55,900,902],{"className":901},[76,238],[55,903,850],{"className":904},[76,238],[55,906,908],{"className":907},[516],")",[55,910],{"className":911,"style":285},[86],[55,913,762],{"className":914,"style":761},[76,178],[55,916,871],{"className":917},[504],[55,919,921,924],{"className":920},[76],[55,922,818],{"className":923},[76,178],[55,925,927],{"className":926},[209],[55,928,930],{"className":929},[213],[55,931,933],{"className":932},[218],[55,934,936],{"className":935,"style":890},[222],[55,937,938,941],{"style":314},[55,939],{"className":940,"style":231},[230],[55,942,944],{"className":943},[235,236,237,238],[55,945,947],{"className":946},[76,238],[55,948,850],{"className":949},[76,238],[55,951,908],{"className":952},[516],",\nthe utility of each outcome state weighted by its probability. A rational agent\nin an uncertain environment chooses the action of maximum expected utility.",[11,955,956,957,960,961,965,966,969],{},"Any rational agent can be shown to behave ",[21,958,959],{},"as if"," it possesses a utility function\nit is trying to maximize; making that function explicit lets the agent make\nrational decisions with a general-purpose algorithm. This is the thread the\n",[15,962,964],{"href":963},"\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions","uncertainty"," chapters pick\nup. Building such an agent is not simple — it must model and track its\nenvironment, tasks that draw on perception, representation, reasoning, and\nlearning — but the ",[21,967,968],{},"principle"," is clean: maximize expected utility.",[411,971,973],{"id":972},"learning-agents","Learning agents",[11,975,976,977,980,981,984],{},"None of the four architectures explains how an agent's program ",[21,978,979],{},"comes into being",".\nTuring's answer, now the state of the art, was to build a ",[46,982,983],{},"learning agent"," and\nteach it. Learning also lets an agent operate in an initially unknown environment\nand become more competent than its starting knowledge allows. A learning agent has\nfour conceptual components.",[478,986],{"hash":987},"0cf97ca3884219d89c4846c9f121ff3a2f999b7b0edde079a3fa9e632728ce98",[11,989,990,991,994,995,998,999,1002,1003,1006,1007,1010],{},"The ",[46,992,993],{},"performance element"," is what we previously called the whole agent — it\ntakes percepts and chooses actions. The ",[46,996,997],{},"learning element"," improves it. The\n",[46,1000,1001],{},"critic"," tells the learning element how well the agent is doing against a\n",[21,1004,1005],{},"fixed"," performance standard; the standard must be fixed and external, or the\nagent could satisfy it by lowering its own bar. The ",[46,1008,1009],{},"problem generator"," suggests\nexploratory actions: the performance element left alone would keep doing what it\nalready knows is best, but a suboptimal exploratory action now may reveal a much\nbetter one later. This is what a scientist does — Galileo dropped rocks not to\nbreak them but to improve his own theory.",[11,1012,1013,1014,1017,1018,1022],{},"The performance element can be any of the four architectures, and learning can\nimprove any of its knowledge components — how the world evolves, what actions do,\nthe utility of states. In this sense the performance standard supplies a ",[46,1015,1016],{},"reward","\n(or penalty) about the quality of the agent's behavior, the seed of the framework\nthat ",[15,1019,1021],{"href":1020},"\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning","reinforcement learning","\ndevelops in full. Learning in intelligent agents is, in one line, the process of\nmodifying each component to bring it into closer agreement with the available\nfeedback, improving overall performance.",[38,1024,1026],{"id":1025},"representing-the-world","Representing the world",[11,1028,1029,1030,1033,1034,1033,1037,1040,1041,1044,1045,1048,1049,1051,1052,1055,1056,1060,1061,1065,1066,1070,1071,1074,1075,1079],{},"Every box in the diagrams above — ",[619,1031,1032],{},"what the world is like now,"," ",[619,1035,1036],{},"goals,",[619,1038,1039],{},"utility"," —\nholds a description of the world, and how detailed that description is turns out to\nmatter as much as the architecture wrapped around it. That question of ",[21,1042,1043],{},"how"," a\ncomponent represents the world runs across all these designs, along a scale of\nincreasing expressive power. An ",[46,1046,1047],{},"atomic","\nrepresentation treats each state as an indivisible black box, distinguishable only\nas same-or-different from another — enough for the route-finding of\n",[15,1050,685],{"href":684}," and the states of a\nMarkov decision process. A ",[46,1053,1054],{},"factored"," representation splits each state into a\nfixed set of variables or attributes, each with a value, so two states can share\nsome attributes and differ on others — the substrate of\n",[15,1057,1059],{"href":1058},"\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction","constraint satisfaction",",\n",[15,1062,1064],{"href":1063},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic","propositional logic",",\nand ",[15,1067,1069],{"href":1068},"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks","Bayesian networks",". A\n",[46,1072,1073],{},"structured"," representation describes objects and the relationships among them,\nthe expressiveness underlying\n",[15,1076,1078],{"href":1077},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic","first-order logic",".\nEach step up the scale can say, at least as concisely, everything the level below\ncan, and more — at the cost of harder reasoning and learning.",[478,1081],{"hash":1082},"c349b016c91ccce86ec144152a70bf21f2c9962bf9bae79430e82b54a32c798c",[38,1084,1086],{"id":1085},"the-language-model-agent","The language-model agent",[11,1088,1089,1090,1093,1094,1097,1098,1101],{},"The four architectures were written for agents whose program a human designs\ncomponent by component: the model, the goals, the utility function are explicit\ndata structures. A different construction became prominent after ",[21,1091,1092],{},"AIMA","'s third\nedition, and it fits the same skeleton without changing it. A large language model\ntrained on text can be placed inside the perceive-act loop directly: its ",[46,1095,1096],{},"percept","\nis a text context (the user's request plus any results it has seen), and its\n",[46,1099,1100],{},"action"," is the next text it emits. Wrapped in a loop that feeds its output back\nas new input, an off-the-shelf model becomes an agent in the exact sense of this\nlesson.",[11,1103,1104,1105,1108,1109,1112,1113,1116,1117,1120,1121,1124,1125,1128,1129,1132],{},"The four internal components reappear, but as\n",[21,1106,1107],{},"learned or prompted"," structure rather than hand-coded modules. The ",[46,1110,1111],{},"ReAct","\npattern (Yao et al., ",[619,1114,1115],{},"ReAct: Synergizing Reasoning and Acting in Language Models,","\nICLR 2023) interleaves a reasoning trace with actions: the model writes a thought,\ntakes an action (often a tool call), observes the result, and repeats — a\ngoal-based agent whose ",[619,1118,1119],{},"what will happen if I do A"," step is the model's own\npredicted continuation. ",[46,1122,1123],{},"Tool use"," gives it actuators beyond text: Toolformer\n(Schick et al., NeurIPS 2023) showed a model can learn to call external tools —\na calculator, a search engine, a database — and splice the results back into its\nreasoning, exactly the actuator\u002Fsensor extension the PEAS frame anticipates.\n",[46,1126,1127],{},"Memory"," supplies the internal state a model-based agent needs, since a raw model\nis stateless past its context window: retrieval over a store of past interactions\n(the retrieval-augmented pattern of Lewis et al., ",[619,1130,1131],{},"Retrieval-Augmented Generation,","\nNeurIPS 2020) reintroduces persistence across a long task.",[478,1134],{"hash":1135},"0a7524e2b188070f65e98bba6c06e2429ad3ee9cc08f02660ef37cbd7e0b015e",[11,1137,1138,1139,1142,1143],{},"The honest reading keeps the frame in charge, not the technique. A language-model\nagent is a new and capable way of ",[21,1140,1141],{},"computing the agent function",", but it is subject\nto the same analysis: it has a performance measure (often implicit and\nmis-specified, which is the source of much of its unreliability), it operates in a\npartially observable, non-deterministic, sequential environment, and it is rational\nonly to the extent that its emitted action maximizes expected performance given its\ncontext. The concerns this lesson raised — designing the measure around what you\nwant in the environment rather than what you imagine the agent should do, and\ndistinguishing the agent function from the program that realizes it — apply to it\nunchanged. It is the four architectures seen again, with a learned program in the\nbox.",[1144,1145,1146],"sup",{},[15,1147,252],{"href":1148,"ariaDescribedBy":1149,"dataFootnoteRef":6,"id":1151},"#user-content-fn-llm-agents",[1150],"footnote-label","user-content-fnref-llm-agents",[38,1153,1155],{"id":1154},"the-ladder-of-architectures","The ladder of architectures",[11,1157,1158],{},"Each architecture answers the same question — what action should I take now? — with\nmore machinery than the last. The reflex agent maps percept straight to action; the\nmodel-based agent adds memory; the goal-based agent adds foresight; the\nutility-based agent adds a scale of preference; and the learning agent improves any\nof them from experience.",[478,1160],{"hash":1161},"15057735ea9a3ac099d18aa40754acd3549c9fc29beb7eb3fe21394c6f5ce455",[1163,1164,1167,1172],"section",{"className":1165,"dataFootnotes":6},[1166],"footnotes",[38,1168,1171],{"className":1169,"id":1150},[1170],"sr-only","Footnotes",[1173,1174,1175],"ol",{},[1176,1177,1179,1182,1183,1185,1186,1182,1189,1192,1193,1182,1196,1199,1200],"li",{"id":1178},"user-content-fn-llm-agents",[46,1180,1181],{},"S. Yao et al.",", ",[619,1184,1115],{}," ICLR 2023 (interleaved reasoning and action); ",[46,1187,1188],{},"T. Schick et al.",[619,1190,1191],{},"Toolformer: Language Models Can Teach Themselves to Use Tools,"," NeurIPS 2023 (learned tool use as actuators); and ",[46,1194,1195],{},"P. Lewis et al.",[619,1197,1198],{},"Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks,"," NeurIPS 2020 (retrieval as external memory \u002F internal state). These place a language model inside the perceive-act loop of §2.1 without altering the agent framework. ",[15,1201,1206],{"href":1202,"ariaLabel":1203,"className":1204,"dataFootnoteBackref":6},"#user-content-fnref-llm-agents","Back to reference 1",[1205],"data-footnote-backref","↩",{"title":6,"searchDepth":1208,"depth":1208,"links":1209},2,[1210,1218,1219,1220,1221],{"id":40,"depth":1208,"text":41,"children":1211},[1212,1214,1215,1216,1217],{"id":413,"depth":1213,"text":414},3,{"id":605,"depth":1213,"text":606},{"id":655,"depth":1213,"text":656},{"id":693,"depth":1213,"text":694},{"id":972,"depth":1213,"text":973},{"id":1025,"depth":1208,"text":1026},{"id":1085,"depth":1208,"text":1086},{"id":1154,"depth":1208,"text":1155},{"id":1150,"depth":1208,"text":1171},[],"computer-science","This builds on Intelligent Agents,\nwhich fixed what an agent is (a percept-to-action loop, captured by an agent\nfunction), what makes one good (rationality — maximizing expected performance),\nand how to specify the problem it faces (PEAS and the six environment axes). This\nlesson takes up the remaining question: how do you actually build a program that\ncomputes a good agent function? The answer is not one design but a ladder of four,\neach adding machinery the one below it lacked.",false,"md",{"moduleNumber":1228,"lessonNumber":1229,"order":1230},1,4,104,"Foundations",true,"\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures",[],"---\ntitle: Agent Architectures\nmodule: Foundations\nmoduleNumber: 1\nlessonNumber: 4\norder: 104\nsummary: >\n  How to build a program that computes a good agent function without storing an\n  astronomically large lookup table. Four skeleton architectures in order of\n  increasing power — simple reflex, model-based, goal-based, and utility-based —\n  plus the learning agent that improves any of them, the scale of world\n  representations (atomic, factored, structured) they rest on, and how a modern\n  language-model agent fits the same frame.\ntopics: [Foundations]\nsources:\n  - book: AIMA\n    ref: \"Ch. 2 — Intelligent Agents; §2.4 The Structure of Agents\"\n  - book: AIMA\n    ref: \"§2.4.6 How the Components of Agent Programs Work\"\n---\n\nThis builds on [Intelligent Agents](\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents),\nwhich fixed what an agent _is_ (a percept-to-action loop, captured by an agent\nfunction), what makes one _good_ (rationality — maximizing expected performance),\nand how to _specify_ the problem it faces (PEAS and the six environment axes). This\nlesson takes up the remaining question: how do you actually _build_ a program that\ncomputes a good agent function? The answer is not one design but a ladder of four,\neach adding machinery the one below it lacked.\n\n## The structure of agents\n\nThe job of AI is to design an **agent program** that implements the agent\nfunction, running on an **architecture** — a device with physical sensors and\nactuators. In short, $\\textit{agent} = \\textit{architecture} + \\textit{program}$.\nThe agent program takes just the _current_ percept as input (that is all the\nsensors offer at any instant) and returns an action; if the agent's behavior must\ndepend on the whole history, the program has to remember the percepts itself.\n\nWhy not implement the agent function as a literal lookup table? Because it is\nastronomically too big. Let $\\mathcal{P}$ be the set of percepts and $T$ the\nagent's lifetime; the table needs $\\sum_{t=1}^{T} |\\mathcal{P}|^t$ entries. For an\nautomated taxi with a single camera, that is on the order of $10^{250{,}000{,}000{,}000}$\nentries for an hour's driving — no physical agent could store it, no designer\ncould fill it, no learner could ever populate it. The challenge of AI is to\nproduce rational behavior from a _small program_ rather than a vast table, just\nas a five-line Newton's-method routine replaced the printed tables of square\nroots. Four program skeletons underlie almost every intelligent system, in order\nof increasing sophistication.\n\n### Simple reflex agents\n\nThe simplest agent selects an action from the _current_ percept alone, ignoring\nthe rest of the history. It works by **condition–action rules** (also called\nsituation–action rules or if–then rules): _if car-in-front-is-braking then\ninitiate-braking_. For the vacuum world the entire program is three rules — _if\ndirty then suck; else if in A then go right; else go left_ — a dramatic reduction\nfrom the $4^T$ table.\n\n$$\n% caption: A simple reflex agent. The current percept is abstracted into a\n% description of the world now; a matching condition-action rule selects the\n% action. There is no memory of past percepts.\n\\begin{tikzpicture}[>=stealth, font=\\small,\n  ag\u002F.style={draw, thick, minimum width=72mm, minimum height=42mm},\n  env\u002F.style={draw, minimum width=16mm, minimum height=42mm, align=center, fill=black!5},\n  bx\u002F.style={draw, minimum width=26mm, minimum height=10mm, align=center, font=\\footnotesize},\n  ov\u002F.style={draw, ellipse, minimum width=32mm, minimum height=9mm, align=center, font=\\scriptsize}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[ag] (agent) at (0,0) {};\n  \\node[anchor=north west, font=\\footnotesize] at (agent.north west) {Agent};\n  \\node[env] (env) at (5.6,0) {Environment};\n  \\node[font=\\scriptsize, anchor=south east] at (2.55,2.18) {Sensors};\n  \\node[font=\\scriptsize, anchor=north east] at (2.55,-2.18) {Actuators};\n  \\node[bx] (world) at (1.1,1.1) {what the world\\\\is like now};\n  \\node[ov] (rules) at (-2.15,-1.1) {condition-action rules};\n  \\node[bx] (act)   at (1.1,-1.1) {what action I\\\\should do now};\n  % percept in\n  \\draw[->, acc, thick] (env.north west) ++(0,-0.4) -| (world.north);\n  \\draw[->, acc, thick] (world) -- (act);\n  \\draw[->, acc, thick] (rules) -- (act);\n  \\draw[->, acc, thick] (act.south) |- ++(0,-0.5) -| (env.south west);\n\\end{tikzpicture}\n$$\n\nSimple reflex agents are admirably compact but of limited intelligence: they work\n_only if the correct action can be decided from the current percept alone — only\nif the environment is fully observable_. A little unobservability causes trouble.\nA vacuum agent stripped of its location sensor, perceiving only $[\\textit{Dirty}]$\nor $[\\textit{Clean}]$, has no rule that can reliably progress — moving `Left`\nloops forever if it starts in $A$. Escaping such loops sometimes requires\n**randomization**: perceiving $[\\textit{Clean}]$, flip a coin between `Left` and\n`Right`. A randomized simple reflex agent can outperform a deterministic one in\npartially observable worlds — though in single-agent settings, a better\ndeterministic agent with memory usually does better still.\n\n### Model-based reflex agents\n\nThe way to handle partial observability is to _keep track of the part of the\nworld the agent can't currently see_ — to maintain **internal state** that depends\non the percept history and reflects the unobserved aspects of the current state.\nUpdating that state requires two pieces of knowledge encoded in the program: how\nthe world evolves independently of the agent (an overtaking car will be closer a\nmoment later), and how the agent's own actions affect the world (turning the\nwheel clockwise turns the car right). This knowledge — \"how the world works\" — is\na **model** of the world, and an agent that uses one is a **model-based agent**.\n\n$$\n% caption: A model-based reflex agent. It combines the current percept with the\n% previous internal state, using its model of how the world evolves and what its\n% actions do, to update its best estimate of the world now, then applies\n% condition-action rules as before.\n\\begin{tikzpicture}[>=stealth, font=\\small,\n  ag\u002F.style={draw, thick, minimum width=80mm, minimum height=46mm},\n  env\u002F.style={draw, minimum width=16mm, minimum height=46mm, align=center, fill=black!5},\n  bx\u002F.style={draw, minimum width=24mm, minimum height=10mm, align=center, font=\\footnotesize},\n  ov\u002F.style={draw, ellipse, minimum width=30mm, minimum height=8mm, align=center, font=\\scriptsize}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[ag] (agent) at (0,0) {};\n  \\node[anchor=south west, font=\\footnotesize] at (agent.south west) {Agent};\n  \\node[env] (env) at (6.0,0) {Environment};\n  \\node[font=\\scriptsize, anchor=south east] at (2.95,2.38) {Sensors};\n  \\node[font=\\scriptsize, anchor=north east] at (2.95,-2.38) {Actuators};\n  \\node[bx] (world)  at (1.4,1.2) {what the world\\\\is like now};\n  \\node[ov] (evolve) at (-2.4,0.7) {how the world evolves};\n  \\node[ov] (actions) at (-2.4,-0.35) {what my actions do};\n  \\node[ov] (rules)  at (-2.4,-1.4) {condition-action rules};\n  \\node[bx] (act)    at (1.4,-1.4) {what action I\\\\should do now};\n  % percept in\n  \\draw[->, acc, thick] (env.north west) ++(0,-0.4) -| (world.north);\n  \\draw[->, acc, thick] (evolve.east) -- (world.west);\n  \\draw[->, acc, thick] (actions.east) -- ++(0.5,0) |- (world.west);\n  \\draw[->, acc, thick] (world) -- (act);\n  \\draw[->, acc, thick] (rules.east) -- (act.west);\n  \\draw[->, acc, thick] (act.south) |- ++(0,-0.5) -| (env.south west);\n\\end{tikzpicture}\n$$\n\nEven a model-based agent seldom knows the current state _exactly_ in a\npartially observable world; the box \"what the world is like now\" holds its best\nguess. The taxi may not see around the truck stalled ahead of it and can only\nguess at the hold-up — but it must still decide. Internal state need not describe\nthe world literally, either: \"driving home\" is really a fact about the taxi's\n_destination_, an aspect of the agent's own intended state, not the world's.\n\n### Goal-based agents\n\nKnowing the current state is not always enough to decide what to do. At a junction\nthe taxi can turn left, turn right, or go straight — and the right choice depends\non _where the taxi is trying to get to_. Beyond a current-state description, the\nagent needs **goal** information describing desirable situations, and it combines\nthe goal with its model to choose actions that (eventually) achieve the goal.\n\n$$\n% caption: A goal-based agent. On top of the model it keeps a goal, and it\n% predicts what the world will be like if it takes an action A, choosing the\n% action that leads toward the goal. This requires reasoning about the future.\n\\begin{tikzpicture}[>=stealth, font=\\small,\n  ag\u002F.style={draw, thick, minimum width=82mm, minimum height=50mm},\n  env\u002F.style={draw, minimum width=16mm, minimum height=50mm, align=center, fill=black!5},\n  bx\u002F.style={draw, minimum width=26mm, minimum height=10mm, align=center, font=\\footnotesize},\n  ov\u002F.style={draw, ellipse, minimum width=30mm, minimum height=8mm, align=center, font=\\scriptsize}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[ag] (agent) at (0,0) {};\n  \\node[anchor=south west, font=\\footnotesize] at (agent.south west) {Agent};\n  \\node[env] (env) at (6.1,0) {Environment};\n  \\node[font=\\scriptsize, anchor=south east] at (3.05,2.58) {Sensors};\n  \\node[font=\\scriptsize, anchor=north east] at (3.05,-2.58) {Actuators};\n  \\node[bx] (world)  at (1.5,1.6) {what the world\\\\is like now};\n  \\node[bx] (pred)   at (1.5,0.05) {what it will be like\\\\if I do action A};\n  \\node[ov] (evolve) at (-2.5,1.35) {how the world evolves};\n  \\node[ov] (actions) at (-2.5,0.3) {what my actions do};\n  \\node[ov] (goals)  at (-2.5,-1.4) {goals};\n  \\node[bx] (act)    at (1.5,-1.6) {what action I\\\\should do now};\n  \\draw[->, acc, thick] (env.north west) ++(0,-0.4) -| (world.north);\n  \\draw[->, acc, thick] (evolve.east) -- (world.west);\n  \\draw[->, acc, thick] (actions.east) -- (pred.west);\n  \\draw[->, acc, thick] (world) -- (pred);\n  \\draw[->, acc, thick] (pred) -- (act);\n  \\draw[->, acc, thick] (goals.east) -- (act.west);\n  \\draw[->, acc, thick] (act.south) |- ++(0,-0.5) -| (env.south west);\n\\end{tikzpicture}\n$$\n\nThis differs sharply from reflex rules, because it involves\nconsideration of the future — \"what will happen if I do this?\" and \"will that\nmake me happy?\" — information a reflex agent never represents explicitly. When\ngoal satisfaction takes a single action it is easy; when it needs a long sequence\nof twists and turns, finding one is the province of\n[search](\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search) and\n[planning](\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning). The\ngoal-based agent looks less efficient than a reflex agent, but it is far more\nflexible: its knowledge is explicit and modifiable. Tell it a new destination and\nits whole behavior adapts; the reflex agent would need every rule rewritten.\n\n### Utility-based agents\n\nGoals are only a crude binary — \"happy\" or \"unhappy.\" Most environments offer\nmany action sequences that reach the goal, some quicker, safer, or cheaper than\nothers, and goals alone cannot choose among them. A **utility function** maps a\nstate (or sequence of states) to a real number capturing how desirable it is; it\nis essentially an internalization of the performance measure. When the internal\nutility function agrees with the external performance measure, an agent that\nchooses actions to maximize utility is rational by the external standard.\n\n$$\n% caption: A utility-based agent. It predicts the outcome of each action and\n% scores how desirable the resulting state is by a utility function, choosing the\n% action of highest expected utility — the average utility over possible outcomes,\n% weighted by their probability.\n\\begin{tikzpicture}[>=stealth, font=\\small,\n  ag\u002F.style={draw, thick, minimum width=82mm, minimum height=56mm},\n  env\u002F.style={draw, minimum width=16mm, minimum height=56mm, align=center, fill=black!5},\n  bx\u002F.style={draw, minimum width=26mm, minimum height=10mm, align=center, font=\\footnotesize},\n  ov\u002F.style={draw, ellipse, minimum width=30mm, minimum height=8mm, align=center, font=\\scriptsize}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[ag] (agent) at (0,0) {};\n  \\node[anchor=south west, font=\\footnotesize] at (agent.south west) {Agent};\n  \\node[env] (env) at (6.1,0) {Environment};\n  \\node[font=\\scriptsize, anchor=south east] at (3.05,2.88) {Sensors};\n  \\node[font=\\scriptsize, anchor=east] at (3.95,-2.5) {Actuators};\n  \\node[bx] (world)  at (1.5,1.95) {what the world\\\\is like now};\n  \\node[bx] (pred)   at (1.5,0.55) {what it will be like\\\\if I do action A};\n  \\node[bx] (happy)  at (1.5,-0.85) {how happy I will be\\\\in such a state};\n  \\node[ov] (evolve) at (-2.5,1.7) {how the world evolves};\n  \\node[ov] (actions) at (-2.5,0.65) {what my actions do};\n  \\node[ov] (util)   at (-2.5,-0.9) {utility};\n  \\node[bx] (act)    at (1.5,-2.1) {what action I\\\\should do now};\n  \\draw[->, acc, thick] (env.north west) ++(0,-0.4) -| (world.north);\n  \\draw[->, acc, thick] (evolve.east) -- (world.west);\n  \\draw[->, acc, thick] (actions.east) -- (pred.west);\n  \\draw[->, acc, thick] (world) -- (pred);\n  \\draw[->, acc, thick] (pred) -- (happy);\n  \\draw[->, acc, thick] (util.east) -- (happy.west);\n  \\draw[->, acc, thick] (happy) -- (act);\n  \\draw[->, acc, thick] (act.south) |- ++(0,-0.5) -| (env.south west);\n\\end{tikzpicture}\n$$\n\nA utility function is indispensable in two cases goals cannot handle. When goals\n_conflict_ — speed against safety — utility specifies the right tradeoff. When\nseveral goals are all _uncertain_, utility weighs the likelihood of success\nagainst the importance of each goal. Because partial observability and\nstochasticity are everywhere, a rational utility-based agent chooses the action\nthat maximizes **expected utility**: the utility it expects on average, given the\nprobabilities and utilities of each outcome.\n\n> **Definition (Expected utility).** Given a probability distribution over the\n> possible outcomes of an action, its expected utility is $\\mathbb{E}[U] = \\sum_{s'} P(s') \\, U(s')$,\n> the utility of each outcome state weighted by its probability. A rational agent\n> in an uncertain environment chooses the action of maximum expected utility.\n\nAny rational agent can be shown to behave _as if_ it possesses a utility function\nit is trying to maximize; making that function explicit lets the agent make\nrational decisions with a general-purpose algorithm. This is the thread the\n[uncertainty](\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions) chapters pick\nup. Building such an agent is not simple — it must model and track its\nenvironment, tasks that draw on perception, representation, reasoning, and\nlearning — but the _principle_ is clean: maximize expected utility.\n\n### Learning agents\n\nNone of the four architectures explains how an agent's program _comes into being_.\nTuring's answer, now the state of the art, was to build a **learning agent** and\nteach it. Learning also lets an agent operate in an initially unknown environment\nand become more competent than its starting knowledge allows. A learning agent has\nfour conceptual components.\n\n$$\n% caption: A general learning agent. The performance element (a whole agent of\n% one of the earlier kinds) selects actions; the critic judges results against a\n% fixed performance standard; the learning element uses that feedback to improve\n% the performance element; the problem generator suggests exploratory actions.\n\\begin{tikzpicture}[>=stealth, font=\\small,\n  ag\u002F.style={draw, thick, minimum width=84mm, minimum height=56mm},\n  env\u002F.style={draw, minimum width=15mm, minimum height=56mm, align=center, fill=black!5},\n  bx\u002F.style={draw, minimum width=24mm, minimum height=11mm, align=center, font=\\footnotesize}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[ag] (agent) at (0,0) {};\n  \\node[anchor=south west, font=\\footnotesize] at (agent.south west) {Agent};\n  \\node[env] (env) at (6.2,0) {Environment};\n  \\node[font=\\scriptsize] at (-0.5,2.95) {Performance standard};\n  \\node[font=\\scriptsize, anchor=east] at (3.05,1.6) {Sensors};\n  \\node[font=\\scriptsize, anchor=east] at (3.05,-2.45) {Actuators};\n  \\node[bx] (critic)  at (-0.5,1.5) {Critic};\n  \\node[bx] (learn)   at (-2.0,-0.45) {Learning\\\\element};\n  \\node[bx] (perf)    at (1.6,-0.45) {Performance\\\\element};\n  \\node[bx] (probgen) at (-2.0,-2.0) {Problem\\\\generator};\n  % percept in to critic\n  \\draw[->, acc, thick] (env.north west) ++(0,-0.5) -- (critic.east);\n  % performance standard in to critic\n  \\draw[->, acc, thick] (-0.5,2.7) -- (critic.north);\n  \\draw[->, acc, thick] (critic) -- node[right, font=\\scriptsize, text=black] {feedback} (learn);\n  \\draw[->, acc, thick] (learn) -- node[above, font=\\scriptsize, text=black] {changes} (perf);\n  \\draw[->, acc, thick] (perf) -- node[below, font=\\scriptsize, text=black] {knowledge} (learn);\n  \\draw[->, acc, thick] (learn) -- node[left, font=\\scriptsize, text=black] {goals} (probgen);\n  \\draw[->, acc, thick] (probgen.east) -- (perf.south west);\n  \\draw[->, acc, thick] (perf.south) |- ++(0,-0.6) -| (env.south west);\n\\end{tikzpicture}\n$$\n\nThe **performance element** is what we previously called the whole agent — it\ntakes percepts and chooses actions. The **learning element** improves it. The\n**critic** tells the learning element how well the agent is doing against a\n_fixed_ performance standard; the standard must be fixed and external, or the\nagent could satisfy it by lowering its own bar. The **problem generator** suggests\nexploratory actions: the performance element left alone would keep doing what it\nalready knows is best, but a suboptimal exploratory action now may reveal a much\nbetter one later. This is what a scientist does — Galileo dropped rocks not to\nbreak them but to improve his own theory.\n\nThe performance element can be any of the four architectures, and learning can\nimprove any of its knowledge components — how the world evolves, what actions do,\nthe utility of states. In this sense the performance standard supplies a **reward**\n(or penalty) about the quality of the agent's behavior, the seed of the framework\nthat [reinforcement learning](\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning)\ndevelops in full. Learning in intelligent agents is, in one line, the process of\nmodifying each component to bring it into closer agreement with the available\nfeedback, improving overall performance.\n\n## Representing the world\n\nEvery box in the diagrams above — \"what the world is like now,\" \"goals,\" \"utility\" —\nholds a description of the world, and how detailed that description is turns out to\nmatter as much as the architecture wrapped around it. That question of _how_ a\ncomponent represents the world runs across all these designs, along a scale of\nincreasing expressive power. An **atomic**\nrepresentation treats each state as an indivisible black box, distinguishable only\nas same-or-different from another — enough for the route-finding of\n[search](\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search) and the states of a\nMarkov decision process. A **factored** representation splits each state into a\nfixed set of variables or attributes, each with a value, so two states can share\nsome attributes and differ on others — the substrate of\n[constraint satisfaction](\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction),\n[propositional logic](\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic),\nand [Bayesian networks](\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks). A\n**structured** representation describes objects and the relationships among them,\nthe expressiveness underlying\n[first-order logic](\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic).\nEach step up the scale can say, at least as concisely, everything the level below\ncan, and more — at the cost of harder reasoning and learning.\n\n$$\n% caption: Three ways to represent a state, in order of increasing expressive\n% power: atomic (an indivisible label), factored (a vector of attribute values),\n% and structured (objects with attributes and relations among them).\n\\begin{tikzpicture}[>=stealth, font=\\small,\n  cell\u002F.style={draw, minimum width=8mm, minimum height=8mm, align=center, font=\\footnotesize}]\n  \\definecolor{acc}{HTML}{2348F2}\n  % atomic\n  \\node[cell] (b) at (0,0) {B};\n  \\node[cell] (c) at (1.4,0) {C};\n  \\draw[->, acc, thick] (b) -- (c);\n  \\node[font=\\scriptsize, anchor=north] at (0.7,-0.9) {atomic};\n  % factored\n  \\begin{scope}[xshift=42mm]\n    \\draw (0,-0.55) rectangle (1.5,0.95);\n    \\node[font=\\scriptsize] at (0.35,0.65) {oil};\n    \\node[font=\\scriptsize] at (0.4,0.25) {gas};\n    \\node[font=\\scriptsize] at (0.5,-0.15) {city};\n    \\node[draw, minimum width=6mm, minimum height=3mm, font=\\tiny, anchor=west] at (0.75,-0.15) {B};\n    \\node[font=\\scriptsize, anchor=north] at (0.75,-0.9) {factored};\n  \\end{scope}\n  % structured\n  \\begin{scope}[xshift=82mm]\n    \\node[cell, minimum width=6mm, minimum height=6mm] (o1) at (0,0.35) {};\n    \\node[cell, minimum width=6mm, minimum height=6mm] (o2) at (1.5,0.35) {};\n    \\node[cell, minimum width=6mm, minimum height=6mm] (o3) at (0.75,-0.5) {};\n    \\draw[->, acc] (o1) -- (o2);\n    \\draw[->, acc] (o1) -- (o3);\n    \\draw[->, acc] (o3) -- (o2);\n    \\node[font=\\scriptsize, anchor=north] at (0.75,-1.25) {structured};\n  \\end{scope}\n\\end{tikzpicture}\n$$\n\n## The language-model agent\n\nThe four architectures were written for agents whose program a human designs\ncomponent by component: the model, the goals, the utility function are explicit\ndata structures. A different construction became prominent after _AIMA_'s third\nedition, and it fits the same skeleton without changing it. A large language model\ntrained on text can be placed inside the perceive-act loop directly: its **percept**\nis a text context (the user's request plus any results it has seen), and its\n**action** is the next text it emits. Wrapped in a loop that feeds its output back\nas new input, an off-the-shelf model becomes an agent in the exact sense of this\nlesson.\n\nThe four internal components reappear, but as\n_learned or prompted_ structure rather than hand-coded modules. The **ReAct**\npattern (Yao et al., \"ReAct: Synergizing Reasoning and Acting in Language Models,\"\nICLR 2023) interleaves a reasoning trace with actions: the model writes a thought,\ntakes an action (often a tool call), observes the result, and repeats — a\ngoal-based agent whose \"what will happen if I do A\" step is the model's own\npredicted continuation. **Tool use** gives it actuators beyond text: Toolformer\n(Schick et al., NeurIPS 2023) showed a model can learn to call external tools —\na calculator, a search engine, a database — and splice the results back into its\nreasoning, exactly the actuator\u002Fsensor extension the PEAS frame anticipates.\n**Memory** supplies the internal state a model-based agent needs, since a raw model\nis stateless past its context window: retrieval over a store of past interactions\n(the retrieval-augmented pattern of Lewis et al., \"Retrieval-Augmented Generation,\"\nNeurIPS 2020) reintroduces persistence across a long task.\n\n$$\n% caption: A language-model agent in the ReAct loop, mapped onto the goal-based\n% skeleton. The model reasons (predicts an outcome), acts (emits text or a tool\n% call), and observes the result, which becomes the next percept. Tools are\n% actuators and sensors; a memory store supplies internal state.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize,\n  bx\u002F.style={draw, minimum width=26mm, minimum height=10mm, align=center},\n  bxa\u002F.style={draw=acc, text=acc, thick, minimum width=26mm, minimum height=10mm, align=center}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[bxa] (think) at (0,1.4)   {reason (thought)};\n  \\node[bxa] (act)   at (0,-0.4)  {act (text \u002F tool call)};\n  \\node[bx]  (obs)   at (5.6,-0.4) {observe result};\n  \\node[bx]  (mem)   at (5.6,1.4)  {memory store};\n  \\draw[->, acc, thick] (think) -- (act);\n  \\draw[->, thick] (act) -- (obs);\n  \\draw[->, thick] (obs) -- ++(0,1.0) -| (think.east);\n  \\node[font=\\scriptsize, anchor=south] at (2.8,-0.35) {tool = actuator};\n  \\draw[->, black] (mem) -- (think);\n  \\node[font=\\scriptsize, text=black, anchor=west] at (6.9,1.4) {internal state};\n\\end{tikzpicture}\n$$\n\nThe honest reading keeps the frame in charge, not the technique. A language-model\nagent is a new and capable way of _computing the agent function_, but it is subject\nto the same analysis: it has a performance measure (often implicit and\nmis-specified, which is the source of much of its unreliability), it operates in a\npartially observable, non-deterministic, sequential environment, and it is rational\nonly to the extent that its emitted action maximizes expected performance given its\ncontext. The concerns this lesson raised — designing the measure around what you\nwant in the environment rather than what you imagine the agent should do, and\ndistinguishing the agent function from the program that realizes it — apply to it\nunchanged. It is the four architectures seen again, with a learned program in the\nbox.[^llm-agents]\n\n## The ladder of architectures\n\nEach architecture answers the same question — what action should I take now? — with\nmore machinery than the last. The reflex agent maps percept straight to action; the\nmodel-based agent adds memory; the goal-based agent adds foresight; the\nutility-based agent adds a scale of preference; and the learning agent improves any\nof them from experience.\n\n$$\n% caption: The four architectures as a ladder of added machinery, each keeping\n% everything below it. Reflex maps percept to action; model-based adds memory of\n% the unseen world; goal-based adds prediction toward a goal; utility-based adds a\n% preference scale; and a learning agent can wrap any of them.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize,\n  rung\u002F.style={draw, minimum width=44mm, minimum height=10mm, align=center}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[rung] (r1) at (0,0)    {simple re\\\u002Ff\\\u002Flex\\\\percept to action};\n  \\node[rung] (r2) at (0,1.3)  {model-based\\\\add internal state};\n  \\node[rung] (r3) at (0,2.6)  {goal-based\\\\add foresight to a goal};\n  \\node[rung, draw=acc, text=acc, thick] (r4) at (0,3.9) {utility-based\\\\add a preference scale};\n  \\draw[->, black] (r1) -- (r2);\n  \\draw[->, black] (r2) -- (r3);\n  \\draw[->, black] (r3) -- (r4);\n  \\node[rung, minimum height=52mm, minimum width=6mm] (learn) at (3.6,1.95) {};\n  \\node[text=acc, rotate=90, font=\\scriptsize] at (3.6,1.95) {learning wraps any};\n\\end{tikzpicture}\n$$\n\n[^llm-agents]: **S. Yao et al.**, \"ReAct: Synergizing Reasoning and Acting in Language Models,\" ICLR 2023 (interleaved reasoning and action); **T. Schick et al.**, \"Toolformer: Language Models Can Teach Themselves to Use Tools,\" NeurIPS 2023 (learned tool use as actuators); and **P. Lewis et al.**, \"Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks,\" NeurIPS 2020 (retrieval as external memory \u002F internal state). These place a language model inside the perceive-act loop of §2.1 without altering the agent framework.\n",{"text":1237,"minutes":1238,"time":1239,"words":1240},"11 min read",10.22,613200,2044,{"title":5,"description":1224},[1243,1245],{"book":1092,"ref":1244},"Ch. 2 — Intelligent Agents; §2.4 The Structure of Agents",{"book":1092,"ref":1246},"§2.4.6 How the Components of Agent Programs Work","available","08.artificial-intelligence\u002F01.foundations\u002F04.agent-architectures","How to build a program that computes a good agent function without storing an astronomically large lookup table. Four skeleton architectures in order of increasing power — simple reflex, model-based, goal-based, and utility-based — plus the learning agent that improves any of them, the scale of world representations (atomic, factored, structured) they rest on, and how a modern language-model agent fits the same frame.\n",[1231],"73KYkbks-nXPyoSQaE-fjnF9CP9BgfIhay5rp4B1jNE",{"\u002Falgorithms\u002Ffoundations\u002Fwhat-is-an-algorithm":1253,"\u002Falgorithms\u002Ffoundations\u002Fproof-techniques":1254,"\u002Falgorithms\u002Ffoundations\u002Fasymptotic-analysis":1255,"\u002Falgorithms\u002Ffoundations\u002Fgrowth-rates-and-loop-analysis":1256,"\u002Falgorithms\u002Ffoundations\u002Frecurrences":1257,"\u002Falgorithms\u002Ffoundations\u002Famortized-analysis":1258,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fmergesort":1259,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fquicksort":1260,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fselection":1261,"\u002Falgorithms\u002Fdivide-and-conquer\u002Ffast-multiplication":1262,"\u002Falgorithms\u002Fsorting\u002Fheaps-and-heapsort":1263,"\u002Falgorithms\u002Fsorting\u002Fsorting-lower-bounds":1264,"\u002Falgorithms\u002Fsorting\u002Flinear-time-sorting":1265,"\u002Falgorithms\u002Fsorting\u002Fexternal-sorting":1266,"\u002Falgorithms\u002Fdata-structures\u002Felementary-structures":1267,"\u002Falgorithms\u002Fdata-structures\u002Fhash-tables":1268,"\u002Falgorithms\u002Fdata-structures\u002Fbinary-search-trees":1269,"\u002Falgorithms\u002Fdata-structures\u002Favl-trees":1270,"\u002Falgorithms\u002Fdata-structures\u002Fbalanced-trees":1271,"\u002Falgorithms\u002Fdata-structures\u002Funion-find":1272,"\u002Falgorithms\u002Fdata-structures\u002Ffenwick-and-segment-trees":1273,"\u002Falgorithms\u002Fdata-structures\u002Fspatial-data-structures":1274,"\u002Falgorithms\u002Fdata-structures\u002Fskip-lists-and-probabilistic-structures":1275,"\u002Falgorithms\u002Fdata-structures\u002Fb-trees":1276,"\u002Falgorithms\u002Fdata-structures\u002Fdata-stream-algorithms":1277,"\u002Falgorithms\u002Fdata-structures\u002Fstreaming-sketches":1278,"\u002Falgorithms\u002Fsequences\u002Ftwo-pointers-and-windows":1279,"\u002Falgorithms\u002Fsequences\u002Fprefix-sums":1280,"\u002Falgorithms\u002Fsequences\u002Fmonotonic-stacks":1281,"\u002Falgorithms\u002Fsequences\u002Fbinary-search-on-the-answer":1282,"\u002Falgorithms\u002Fsequences\u002Fstring-matching":1283,"\u002Falgorithms\u002Fsequences\u002Fkmp-and-z-function":1284,"\u002Falgorithms\u002Fsequences\u002Ftries":1285,"\u002Falgorithms\u002Fsequences\u002Fsuffix-arrays-and-aho-corasick":1286,"\u002Falgorithms\u002Fgraphs\u002Frepresentations-and-traversal":1287,"\u002Falgorithms\u002Fgraphs\u002Fdepth-first-search":1288,"\u002Falgorithms\u002Fgraphs\u002Ftopological-sort-and-scc":1289,"\u002Falgorithms\u002Fgraphs\u002Fminimum-spanning-trees":1290,"\u002Falgorithms\u002Fgraphs\u002Fkruskal-and-prim":1291,"\u002Falgorithms\u002Fgraphs\u002Fshortest-paths":1292,"\u002Falgorithms\u002Fgraphs\u002Fall-pairs-and-negative-weights":1293,"\u002Falgorithms\u002Fgraphs\u002Fnetwork-flow":1294,"\u002Falgorithms\u002Fgraphs\u002Fmax-flow-min-cut":1295,"\u002Falgorithms\u002Fgraphs\u002Fbridges-and-articulation-points":1296,"\u002Falgorithms\u002Fgraphs\u002Flowest-common-ancestor":1297,"\u002Falgorithms\u002Fgraphs\u002Ftwo-sat":1298,"\u002Falgorithms\u002Fgraphs\u002Feulerian-tours":1299,"\u002Falgorithms\u002Fgraphs\u002Fbipartite-matching":1300,"\u002Falgorithms\u002Fgreedy\u002Fthe-greedy-method":1301,"\u002Falgorithms\u002Fgreedy\u002Fscheduling-and-intervals":1302,"\u002Falgorithms\u002Fgreedy\u002Fhuffman-codes":1303,"\u002Falgorithms\u002Fgreedy\u002Fmatroids":1304,"\u002Falgorithms\u002Fgreedy\u002Fstable-matching":1305,"\u002Falgorithms\u002Fdynamic-programming\u002Fprinciples":1306,"\u002Falgorithms\u002Fdynamic-programming\u002Fsequence-dp":1307,"\u002Falgorithms\u002Fdynamic-programming\u002Flongest-increasing-subsequence":1308,"\u002Falgorithms\u002Fdynamic-programming\u002Fknapsack":1309,"\u002Falgorithms\u002Fdynamic-programming\u002Fcoin-change-and-unbounded":1310,"\u002Falgorithms\u002Fdynamic-programming\u002Finterval-dp":1311,"\u002Falgorithms\u002Fdynamic-programming\u002Ftree-dp":1312,"\u002Falgorithms\u002Fdynamic-programming\u002Fbitmask-dp":1313,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-optimizations":1314,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-on-graphs":1315,"\u002Falgorithms\u002Fdynamic-programming\u002Fdigit-and-probability-dp":1316,"\u002Falgorithms\u002Fbacktracking\u002Fbacktracking-fundamentals":1317,"\u002Falgorithms\u002Fbacktracking\u002Fconstraint-search":1318,"\u002Falgorithms\u002Fbacktracking\u002Fbranch-and-bound":1319,"\u002Falgorithms\u002Fbacktracking\u002Fgraph-backtracking":1320,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fnumber-theory-basics":1321,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmodular-exponentiation-and-primality":1322,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fsieve-and-factorization":1323,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fcombinatorics":1324,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmatrix-exponentiation":1325,"\u002Falgorithms\u002Fmathematical-algorithms\u002Ffast-fourier-transform":1326,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fgradient-descent":1327,"\u002Falgorithms\u002Fcomputational-geometry\u002Fgeometric-primitives":1328,"\u002Falgorithms\u002Fcomputational-geometry\u002Fconvex-hull":1329,"\u002Falgorithms\u002Fcomputational-geometry\u002Fsweep-line":1330,"\u002Falgorithms\u002Fcomputational-geometry\u002Fpolygons-and-proximity":1331,"\u002Falgorithms\u002Fintractability\u002Fp-np-reductions":1332,"\u002Falgorithms\u002Fintractability\u002Fnp-completeness":1333,"\u002Falgorithms\u002Fintractability\u002Fcoping-with-hardness":1334,"\u002Falgorithms\u002Fintractability\u002Fapproximation-algorithms":1335,"\u002Falgorithms":1336,"\u002Fcalculus\u002Flimits-and-continuity\u002Ffunctions-and-models":1337,"\u002Fcalculus\u002Flimits-and-continuity\u002Fthe-limit-of-a-function":1338,"\u002Fcalculus\u002Flimits-and-continuity\u002Flimit-laws-and-the-precise-definition":1339,"\u002Fcalculus\u002Flimits-and-continuity\u002Fcontinuity":1340,"\u002Fcalculus\u002Fderivatives\u002Fthe-derivative-and-rates-of-change":1341,"\u002Fcalculus\u002Fderivatives\u002Fdifferentiation-rules-and-the-chain-rule":1342,"\u002Fcalculus\u002Fderivatives\u002Fimplicit-differentiation-and-related-rates":1343,"\u002Fcalculus\u002Fderivatives\u002Flinear-approximations-and-differentials":1344,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fextrema-and-the-mean-value-theorem":1345,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fhow-derivatives-shape-a-graph":1346,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fcurve-sketching-and-optimization":1347,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fnewtons-method-and-antiderivatives":1348,"\u002Fcalculus\u002Fintegrals\u002Farea-and-the-definite-integral":1349,"\u002Fcalculus\u002Fintegrals\u002Fthe-fundamental-theorem-of-calculus":1350,"\u002Fcalculus\u002Fintegrals\u002Fthe-substitution-rule":1351,"\u002Fcalculus\u002Fapplications-of-integration\u002Fareas-and-volumes":1352,"\u002Fcalculus\u002Fapplications-of-integration\u002Fwork-average-value-and-arc-length":1353,"\u002Fcalculus\u002Fapplications-of-integration\u002Fphysics-economics-and-probability":1354,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Finverse-functions-logarithms-and-exponentials":1355,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Fgrowth-decay-inverse-trig-and-hyperbolic-functions":1356,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Flhospitals-rule":1357,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fintegration-by-parts":1358,"\u002Fcalculus\u002Ftechniques-of-integration\u002Ftrigonometric-integrals-and-substitution":1359,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fpartial-fractions-and-integration-strategy":1360,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fapproximate-and-improper-integrals":1361,"\u002Fcalculus\u002Fparametric-and-polar\u002Fparametric-curves-and-their-calculus":1362,"\u002Fcalculus\u002Fparametric-and-polar\u002Fpolar-coordinates":1363,"\u002Fcalculus\u002Fparametric-and-polar\u002Fconic-sections":1364,"\u002Fcalculus\u002Fsequences-and-series\u002Fsequences":1365,"\u002Fcalculus\u002Fsequences-and-series\u002Fseries-and-the-integral-test":1366,"\u002Fcalculus\u002Fsequences-and-series\u002Fthe-convergence-tests":1367,"\u002Fcalculus\u002Fsequences-and-series\u002Fpower-series":1368,"\u002Fcalculus\u002Fsequences-and-series\u002Ftaylor-and-maclaurin-series":1369,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvectors-and-the-dot-product":1370,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fthe-cross-product-lines-and-planes":1351,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fcylinders-and-quadric-surfaces":1371,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvector-functions-and-space-curves":1372,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Farc-length-curvature-and-motion":1373,"\u002Fcalculus\u002Fpartial-derivatives\u002Ffunctions-of-several-variables":1341,"\u002Fcalculus\u002Fpartial-derivatives\u002Fpartial-derivatives":1374,"\u002Fcalculus\u002Fpartial-derivatives\u002Ftangent-planes-and-the-chain-rule":1375,"\u002Fcalculus\u002Fpartial-derivatives\u002Fdirectional-derivatives-and-the-gradient":1376,"\u002Fcalculus\u002Fpartial-derivatives\u002Foptimization-and-lagrange-multipliers":1377,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fdouble-integrals":1378,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Ftriple-integrals-and-coordinate-systems":1379,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fvector-fields-and-line-integrals":1380,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fgreens-theorem-curl-and-divergence":1381,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fsurface-integrals":1382,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fstokes-and-the-divergence-theorem":1383,"\u002Fcalculus":1384,"\u002Fmechanics\u002Ffoundations\u002Fmeasurement-and-dimensions":1385,"\u002Fmechanics\u002Ffoundations\u002Fvector-algebra":1386,"\u002Fmechanics\u002Fkinematics\u002Fone-dimensional-motion":1387,"\u002Fmechanics\u002Fkinematics\u002Fmotion-graphs":1388,"\u002Fmechanics\u002Fkinematics\u002Fprojectile-motion":1389,"\u002Fmechanics\u002Fkinematics\u002Frelative-motion":1390,"\u002Fmechanics\u002Fkinematics\u002Fcircular-motion":1391,"\u002Fmechanics\u002Fdynamics\u002Fnewtons-laws":1392,"\u002Fmechanics\u002Fdynamics\u002Ffree-body-diagrams":1393,"\u002Fmechanics\u002Fdynamics\u002Ffriction-and-curved-motion":1394,"\u002Fmechanics\u002Fdynamics\u002Fnumerical-dynamics":1395,"\u002Fmechanics\u002Fdynamics\u002Fcenter-of-mass-systems":1396,"\u002Fmechanics\u002Fenergy\u002Fwork-and-kinetic-energy":1397,"\u002Fmechanics\u002Fenergy\u002Fpotential-energy":1398,"\u002Fmechanics\u002Fenergy\u002Fmultiparticle-work":1399,"\u002Fmechanics\u002Fenergy\u002Fmass-energy-and-binding":1400,"\u002Fmechanics\u002Fenergy\u002Fphotons-and-quantization":1401,"\u002Fmechanics\u002Fmomentum\u002Fmomentum-and-collisions":1402,"\u002Fmechanics\u002Fmomentum\u002Fcenter-of-mass-collisions":1403,"\u002Fmechanics\u002Fmomentum\u002Frocket-propulsion":1404,"\u002Fmechanics\u002Frotation\u002Frotational-inertia":1405,"\u002Fmechanics\u002Frotation\u002Frotational-dynamics":1406,"\u002Fmechanics\u002Frotation\u002Frolling-motion":1407,"\u002Fmechanics\u002Frotation\u002Fangular-momentum":1408,"\u002Fmechanics\u002Frotation\u002Frolling-resistance":1409,"\u002Fmechanics\u002Frotation\u002Fgyroscopic-precession":1410,"\u002Fmechanics\u002Fgravity-and-matter\u002Fkeplerian-orbits":1411,"\u002Fmechanics\u002Fgravity-and-matter\u002Fgravitational-fields":1412,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstatic-equilibrium":1413,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-statics":1414,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-flow":1415,"\u002Fmechanics\u002Fgravity-and-matter\u002Forbital-motion":1416,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstress-and-elasticity":1417,"\u002Fmechanics\u002Foscillations-waves\u002Fdamped-oscillators":1418,"\u002Fmechanics\u002Foscillations-waves\u002Ftravelling-waves":1419,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-superposition":1420,"\u002Fmechanics\u002Foscillations-waves\u002Fstanding-waves":1421,"\u002Fmechanics\u002Foscillations-waves\u002Fsound-waves":1422,"\u002Fmechanics\u002Foscillations-waves\u002Fdoppler-effect":1423,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-packets":1424,"\u002Fmechanics\u002Foscillations-waves\u002Fbeats-and-coupling":1425,"\u002Fmechanics\u002Foscillations-waves\u002Fsimple-harmonic-motion":1426,"\u002Fmechanics\u002Foscillations-waves\u002Fpendulum-motion":1427,"\u002Fmechanics\u002Foscillations-waves\u002Fdriven-oscillators":1428,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-boundaries":1429,"\u002Fmechanics\u002Fthermodynamics\u002Fkinetic-theory-of-ideal-gases":1430,"\u002Fmechanics\u002Fthermodynamics\u002Ffirst-law-of-thermodynamics":1431,"\u002Fmechanics\u002Fthermodynamics\u002Fentropy-and-the-second-law":1432,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-processes":1433,"\u002Fmechanics\u002Fthermodynamics\u002Fphase-changes":1434,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-machines":1435,"\u002Fmechanics":1436,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcharge-and-conductors":1437,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcoulombs-law":1438,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-and-force":1439,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-maps":1440,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-dipoles":1441,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fcontinuous-charge-fields":1442,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fgauss-law-and-conductors":1443,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpoint-charge-potential":1444,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpotential-gradients-and-equipotentials":1445,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Felectrostatic-energy-and-pressure":1446,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Flaplace-boundary-problems":1447,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fcontinuous-charge-potentials":1448,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitance-fundamentals":1425,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-networks":1449,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-energy-and-force":1450,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fdielectric-polarization-and-breakdown":1451,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fcurrent-and-resistance":1421,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fkirchhoff-network-analysis":1286,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Frc-transients":1452,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-trajectories":1412,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fhall-effect":1453,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-force-on-conductors":1454,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-dipoles":1455,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmass-spectrometry":1456,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmoving-charge-fields":1457,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fbiot-savart-law":1458,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fcircular-current-loops":1459,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Famperes-law":1460,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fgauss-law-for-magnetism":1461,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmagnetic-materials":1386,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-flux":1462,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Ffaradays-law":1463,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Flenzs-law":1464,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmotional-emf":1465,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Feddy-currents":1466,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fself-inductance":1467,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-energy":1468,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Frl-circuits":1469,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-fundamentals":1404,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Freactance":1403,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Frlc-resonance":1470,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-power":1471,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Ftransformers":1472,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdisplacement-current":1473,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-waves":1474,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-momentum":1475,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdipole-radiation":1476,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fpolarization":1477,"\u002Felectricity-and-magnetism\u002Foptics\u002Freflection-and-refraction":1478,"\u002Felectricity-and-magnetism\u002Foptics\u002Fthin-lenses":1430,"\u002Felectricity-and-magnetism\u002Foptics\u002Fspherical-mirrors":1428,"\u002Felectricity-and-magnetism":1479,"\u002Flinear-algebra\u002Flinear-systems\u002Fsystems-and-echelon-forms":1480,"\u002Flinear-algebra\u002Flinear-systems\u002Fvector-and-matrix-equations":1481,"\u002Flinear-algebra\u002Flinear-systems\u002Fsolution-sets-and-applications":1482,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-independence":1483,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-transformations":1484,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-operations":1485,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-inverse-and-invertibility":1486,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fpartitioned-matrices-and-lu":1487,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fsubspaces-dimension-rank":1488,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fapplications-leontief-and-graphics":1338,"\u002Flinear-algebra\u002Fdeterminants\u002Fdeterminants-and-cofactors":1489,"\u002Flinear-algebra\u002Fdeterminants\u002Fproperties-of-determinants":1490,"\u002Flinear-algebra\u002Fdeterminants\u002Fcramer-volume-and-area":1342,"\u002Flinear-algebra\u002Fvector-spaces\u002Fvector-spaces-and-subspaces":1491,"\u002Flinear-algebra\u002Fvector-spaces\u002Fnull-and-column-spaces":1492,"\u002Flinear-algebra\u002Fvector-spaces\u002Fbases-and-independent-sets":1493,"\u002Flinear-algebra\u002Fvector-spaces\u002Fcoordinate-systems":1494,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdimension-and-rank":1495,"\u002Flinear-algebra\u002Fvector-spaces\u002Fchange-of-basis":1496,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdifference-equations-and-markov":1497,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-eigenvalues":1498,"\u002Flinear-algebra\u002Feigenvalues\u002Fthe-characteristic-equation":1499,"\u002Flinear-algebra\u002Feigenvalues\u002Fdiagonalization":1500,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-linear-transformations":1501,"\u002Flinear-algebra\u002Feigenvalues\u002Fcomplex-eigenvalues":1502,"\u002Flinear-algebra\u002Feigenvalues\u002Fdynamical-systems":1503,"\u002Flinear-algebra\u002Feigenvalues\u002Fpower-method":1504,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-length-orthogonality":1505,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Forthogonal-sets-and-projections":1506,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fgram-schmidt-and-qr":1507,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-problems":1508,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-applications":1509,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-spaces":1510,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fdiagonalizing-symmetric-matrices":1377,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fquadratic-forms":1511,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fconstrained-optimization":1512,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsingular-value-decomposition":1513,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsvd-applications-pca-imaging":1514,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-thinking-and-matrix-computation":1515,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Flu-and-cholesky":1516,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fconditioning-and-floating-point":1517,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fstability-and-error-analysis":1518,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fqr-and-numerical-least-squares":1519,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-eigenvalues-and-svd":1520,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-combinations":1521,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-independence-and-barycentric-coordinates":1522,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fconvex-combinations-and-convex-sets":1523,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fhyperplanes-and-polytopes":1524,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fcurves-and-surfaces":1525,"\u002Flinear-algebra":1526,"\u002Ftheory-of-computation":1527,"\u002Fcomputer-architecture\u002Ffoundations\u002Fbits-bytes-and-words":1528,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-representation":1529,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-arithmetic":1530,"\u002Fcomputer-architecture\u002Ffoundations\u002Ffloating-point":1531,"\u002Fcomputer-architecture\u002Ffoundations\u002Fboolean-algebra-and-bit-manipulation":1532,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fthe-machines-view":1533,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fdata-movement":1534,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farithmetic-and-logic":1535,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fcontrol-flow":1536,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fprocedures":1537,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farrays-structs-and-alignment":1538,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fmemory-layout-and-buffer-overflows":1539,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fwhat-an-isa-is":1540,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Finstruction-formats-and-operands":1541,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Faddressing-modes":1542,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fthe-y86-64-instruction-set":1543,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fy86-64-programming":1544,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Ftransistors-gates-and-boolean-functions":1545,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fcombinational-logic-and-hcl":1546,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmultiplexers-decoders-and-the-alu":1547,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmemory-elements-latches-flip-flops-and-clocking":1548,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fregister-files-and-random-access-memory":1549,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-fetch-decode-execute-cycle":1550,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-seq-stages":1551,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fcontrol-logic-and-sequencing":1552,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fassembling-seq":1553,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Ftracing-a-program":1554,"\u002Fcomputer-architecture\u002Fpipelining\u002Fpipelining-principles":1555,"\u002Fcomputer-architecture\u002Fpipelining\u002Ffrom-seq-to-pipe":1556,"\u002Fcomputer-architecture\u002Fpipelining\u002Fdata-hazards-stalling-and-forwarding":1557,"\u002Fcomputer-architecture\u002Fpipelining\u002Fcontrol-hazards-and-branch-prediction":1558,"\u002Fcomputer-architecture\u002Fpipelining\u002Fthe-complete-pipe-processor":1559,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fstorage-technologies-and-the-latency-gap":1560,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Flocality":1561,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-memories-direct-mapped":1562,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fset-associative-and-write-policies":1563,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-performance-and-cache-friendly-code":1564,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Faddress-spaces-and-translation":1565,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fpage-tables-and-page-faults":1566,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fthe-tlb-and-multi-level-page-tables":1567,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Fexceptional-control-flow":1568,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Finterrupts-and-the-kernel":1569,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fprocesses-threads-and-parallelism":1570,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fhardware-multithreading":1571,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fcache-coherence":1572,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmemory-consistency-and-synchronization":1573,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmulticore-organization":1574,"\u002Fcomputer-architecture\u002Fcapstone\u002Fthe-whole-machine":1575,"\u002Fcomputer-architecture\u002Fcapstone\u002Fassembling-a-complete-cpu":1576,"\u002Fcomputer-architecture":1527,"\u002Fdifferential-equations\u002Ffoundations\u002Fmodels-and-direction-fields":1577,"\u002Fdifferential-equations\u002Ffoundations\u002Fclassification-and-terminology":1578,"\u002Fdifferential-equations\u002Ffirst-order\u002Flinear-first-order-integrating-factors":1579,"\u002Fdifferential-equations\u002Ffirst-order\u002Fseparable-and-exact":1342,"\u002Fdifferential-equations\u002Ffirst-order\u002Fmodeling-first-order":1580,"\u002Fdifferential-equations\u002Ffirst-order\u002Fautonomous-and-population-dynamics":1341,"\u002Fdifferential-equations\u002Ffirst-order\u002Fexistence-uniqueness-euler":1348,"\u002Fdifferential-equations\u002Ffirst-order\u002Ffirst-order-difference-equations":1581,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhomogeneous-constant-coefficients":1582,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fcomplex-and-repeated-roots":1382,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fnonhomogeneous-undetermined-coefficients":1583,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fvariation-of-parameters":1584,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fmechanical-electrical-vibrations":1585,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhigher-order-linear":1586,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fpower-series-ordinary-points":1587,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fregular-singular-frobenius":1588,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fbessel-and-special-functions":1589,"\u002Fdifferential-equations\u002Flaplace\u002Flaplace-definition-ivps":1590,"\u002Fdifferential-equations\u002Flaplace\u002Fstep-impulse-convolution":1591,"\u002Fdifferential-equations\u002Fsystems\u002Fmatrices-eigenvalues-review":1592,"\u002Fdifferential-equations\u002Fsystems\u002Fconstant-coefficient-systems-phase-portraits":1593,"\u002Fdifferential-equations\u002Fsystems\u002Frepeated-eigenvalues-fundamental-matrices":1594,"\u002Fdifferential-equations\u002Fnumerical\u002Feuler-and-runge-kutta":1589,"\u002Fdifferential-equations\u002Fnumerical\u002Fmultistep-systems-stability":1595,"\u002Fdifferential-equations\u002Fnonlinear\u002Fphase-plane-autonomous-stability":1596,"\u002Fdifferential-equations\u002Fnonlinear\u002Flocally-linear-and-liapunov":1597,"\u002Fdifferential-equations\u002Fnonlinear\u002Fcompeting-species-predator-prey-limit-cycles":1598,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Ffourier-series":1599,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fheat-wave-laplace-equations":1600,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fsturm-liouville":1601,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fcalculus-of-variations":1602,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fhistorical-notes":1603,"\u002Fdifferential-equations":1604,"\u002Frelativity\u002Ffoundations\u002Fspecial-relativity-postulates":1605,"\u002Frelativity\u002Ffoundations\u002Florentz-transformation-spacetime":1606,"\u002Frelativity\u002Ffoundations\u002Ftime-dilation-length-contraction":1607,"\u002Frelativity\u002Ffoundations\u002Frelativistic-momentum-energy":1608,"\u002Frelativity\u002Ffoundations\u002Fgeneral-relativity":1487,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fminkowski-spacetime-and-the-interval":1609,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Ffour-vectors-and-index-notation":1610,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fthe-lorentz-group-and-rapidity":1611,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fdoppler-aberration-and-appearance":1612,"\u002Frelativity\u002Frelativistic-dynamics\u002Ffour-momentum-force-and-accelerated-motion":1613,"\u002Frelativity\u002Frelativistic-dynamics\u002Fparticle-decays-and-two-body-kinematics":1614,"\u002Frelativity\u002Frelativistic-dynamics\u002Fcollisions-thresholds-and-the-cm-frame":1357,"\u002Frelativity\u002Frelativistic-dynamics\u002Fmandelstam-variables-and-invariants":1615,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ffour-current-and-the-four-potential":1616,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fthe-electromagnetic-field-tensor":1617,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ftransformation-of-electric-and-magnetic-fields":1618,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fcovariant-maxwell-and-the-stress-energy-tensor":1619,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-equivalence-principle-formalized":1620,"\u002Frelativity\u002Fcurved-spacetime\u002Fmanifolds-vectors-and-the-metric":1621,"\u002Frelativity\u002Fcurved-spacetime\u002Fcovariant-derivative-and-christoffel-symbols":1622,"\u002Frelativity\u002Fcurved-spacetime\u002Fgeodesics-and-the-geodesic-equation":1623,"\u002Frelativity\u002Fcurved-spacetime\u002Fcurvature-riemann-and-geodesic-deviation":1624,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-einstein-field-equations":1579,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fthe-schwarzschild-metric":1625,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fgeodesics-and-orbits-in-schwarzschild":1626,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Flight-bending-and-null-geodesics":1627,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fperihelion-precession-of-mercury":1628,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fdeflection-of-light-and-gravitational-lensing":1629,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fgravitational-redshift-and-shapiro-delay":1508,"\u002Frelativity\u002Ftests-of-general-relativity\u002Frelativity-in-technology-gps":1630,"\u002Frelativity\u002Fblack-holes\u002Fhorizons-and-coordinate-singularities":1631,"\u002Frelativity\u002Fblack-holes\u002Frotating-and-charged-black-holes":1518,"\u002Frelativity\u002Fblack-holes\u002Fblack-hole-thermodynamics":1632,"\u002Frelativity\u002Fgravitational-waves\u002Flinearized-gravity-and-wave-solutions":1633,"\u002Frelativity\u002Fgravitational-waves\u002Fgeneration-and-the-quadrupole-formula":1634,"\u002Frelativity\u002Fgravitational-waves\u002Fdetection-ligo-and-the-first-events":1635,"\u002Frelativity\u002Fcosmological-bridge\u002Fthe-cosmological-principle-and-flrw-metric":1636,"\u002Frelativity\u002Fcosmological-bridge\u002Ffriedmann-equations-and-cosmic-dynamics":1637,"\u002Frelativity":1638,"\u002Fphysical-computing":1527,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fblackbody-radiation-and-the-planck-quantum":1639,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-photoelectric-effect-and-the-photon":1618,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fx-rays-and-the-compton-effect":1640,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-old-quantum-theory-bohr-and-sommerfeld":1641,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fde-broglie-waves-and-electron-diffraction":1642,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fwave-packets-and-the-probability-interpretation":1643,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fthe-uncertainty-principle":1644,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-schrodinger-equation-in-one-dimension":1645,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-free-particle-and-wave-packet-dynamics":1646,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fparticle-in-infinite-and-finite-square-wells":1594,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Foperators-expectation-values-and-the-harmonic-oscillator":1518,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-dirac-delta-potential":1647,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fbarrier-penetration-and-quantum-tunneling":1648,"\u002Fquantum-mechanics\u002Fformalism\u002Fhilbert-space-and-dirac-notation":1649,"\u002Fquantum-mechanics\u002Fformalism\u002Fobservables-hermitian-operators-and-eigenvalues":1650,"\u002Fquantum-mechanics\u002Fformalism\u002Fthe-postulates-and-quantum-measurement":1646,"\u002Fquantum-mechanics\u002Fformalism\u002Fposition-momentum-and-continuous-spectra":1651,"\u002Fquantum-mechanics\u002Fformalism\u002Fcommutators-and-the-generalized-uncertainty-principle":1626,"\u002Fquantum-mechanics\u002Fformalism\u002Ftime-evolution-schrodinger-and-heisenberg-pictures":1379,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fladder-operators-and-the-number-states":1652,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fcoherent-and-squeezed-states":1653,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fsymmetries-generators-and-conservation-laws":1359,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fparity-time-reversal-and-discrete-symmetries":1654,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Forbital-angular-momentum-and-spherical-harmonics":1655,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Fthe-angular-momentum-algebra":1656,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Faddition-of-angular-momenta-and-clebsch-gordan":1657,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-schrodinger-equation-in-three-dimensions":1658,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-hydrogen-atom":1659,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-isotropic-oscillator-and-hidden-symmetry":1660,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-half-pauli-matrices-and-stern-gerlach":1661,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-in-a-magnetic-field-precession-and-resonance":1662,"\u002Fquantum-mechanics\u002Fspin\u002Ftwo-level-systems-and-the-bloch-sphere":1618,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fidentical-particles-and-exchange-symmetry":1663,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fthe-pauli-principle-atoms-and-the-periodic-table":1664,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ftime-independent-perturbation-theory":1665,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ffine-structure-and-the-real-hydrogen-atom":1652,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-zeeman-and-stark-effects":1340,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-variational-method":1666,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-wkb-approximation":1667,"\u002Fquantum-mechanics":1668,"\u002Freal-analysis\u002Ffoundations\u002Fsets-logic-functions":1602,"\u002Freal-analysis\u002Ffoundations\u002Fordered-fields-completeness":1669,"\u002Freal-analysis\u002Ffoundations\u002Fabsolute-value-bounds":1670,"\u002Freal-analysis\u002Ffoundations\u002Fintervals-uncountability":1491,"\u002Freal-analysis\u002Fsequences-series\u002Fsequences-limits":1671,"\u002Freal-analysis\u002Fsequences-series\u002Flimit-laws-monotone":1377,"\u002Freal-analysis\u002Fsequences-series\u002Flimsup-bolzano-weierstrass":1672,"\u002Freal-analysis\u002Fsequences-series\u002Fcauchy-completeness":1673,"\u002Freal-analysis\u002Fsequences-series\u002Fseries-convergence":1514,"\u002Freal-analysis\u002Fsequences-series\u002Fabsolute-conditional-rearrangement":1624,"\u002Freal-analysis\u002Fmetric-spaces\u002Fmetric-spaces-norms":1674,"\u002Freal-analysis\u002Fmetric-spaces\u002Fopen-closed-sets":1675,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconvergence-completeness":1676,"\u002Freal-analysis\u002Fmetric-spaces\u002Fcompactness":1677,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconnectedness":1678,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-of-functions":1651,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuous-functions":1679,"\u002Freal-analysis\u002Fcontinuity\u002Fevt-ivt":1484,"\u002Freal-analysis\u002Fcontinuity\u002Funiform-continuity":1680,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuity-metric-spaces":1681,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-infinity-monotone":1338,"\u002Freal-analysis\u002Fdifferentiation\u002Fthe-derivative":1682,"\u002Freal-analysis\u002Fdifferentiation\u002Fmean-value-theorem":1683,"\u002Freal-analysis\u002Fdifferentiation\u002Ftaylors-theorem":1640,"\u002Freal-analysis\u002Fdifferentiation\u002Finverse-function-1d":1367,"\u002Freal-analysis\u002Friemann-integration\u002Fdarboux-integral":1518,"\u002Freal-analysis\u002Friemann-integration\u002Fintegrability-classes":1684,"\u002Freal-analysis\u002Friemann-integration\u002Fproperties-of-the-integral":1685,"\u002Freal-analysis\u002Friemann-integration\u002Ffundamental-theorem":1503,"\u002Freal-analysis\u002Friemann-integration\u002Flog-exp-improper":1628,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpointwise-uniform-convergence":1686,"\u002Freal-analysis\u002Ffunction-sequences\u002Finterchange-of-limits":1687,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpower-series-weierstrass":1688,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpicard-ode":1523,"\u002Freal-analysis\u002Fseveral-variables\u002Fdifferentiability-rn":1689,"\u002Freal-analysis\u002Fseveral-variables\u002Fgradient-chain-rule":1690,"\u002Freal-analysis\u002Fseveral-variables\u002Fhigher-derivatives-taylor-extrema":1691,"\u002Freal-analysis\u002Fseveral-variables\u002Finverse-implicit-theorems":1691,"\u002Freal-analysis\u002Fseveral-variables\u002Fmultiple-integrals":1692,"\u002Freal-analysis":1693,"\u002Fabstract-algebra\u002Ffoundations\u002Fsets-functions-relations":1694,"\u002Fabstract-algebra\u002Ffoundations\u002Fintegers-and-modular-arithmetic":1695,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fgroup-axioms-and-first-examples":1696,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fdihedral-and-symmetric-groups":1697,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fmatrix-and-quaternion-groups":1698,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fhomomorphisms-and-group-actions":1699,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fsubgroups-and-substructures":1700,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcyclic-groups":1701,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fgeneration-and-subgroup-lattices":1702,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcosets-lagrange-and-normal-subgroups":1703,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fisomorphism-theorems":1667,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcomposition-series-and-the-alternating-group":1704,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Factions-and-cayleys-theorem":1696,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fconjugation-and-the-class-equation":1613,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fsylow-theorems":1705,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fautomorphisms-and-simple-groups":1706,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fdirect-products-and-finite-abelian-groups":1707,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fsemidirect-products":1708,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fnilpotent-and-solvable-groups":1709,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fclassifying-small-groups":1710,"\u002Fabstract-algebra\u002Fring-theory\u002Frings-definitions-and-examples":1711,"\u002Fabstract-algebra\u002Fring-theory\u002Fideals-quotients-and-homomorphisms":1712,"\u002Fabstract-algebra\u002Fring-theory\u002Ffractions-and-the-chinese-remainder-theorem":1706,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Feuclidean-domains-pids-ufds":1713,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fpolynomial-rings-over-fields":1682,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fgauss-lemma-and-unique-factorization":1714,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Firreducibility-criteria-and-groebner":1715,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fintroduction-to-modules":1716,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ffree-modules-and-direct-sums":1717,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ftensor-products-and-exact-sequences":1718,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fvector-spaces-and-linear-maps":1719,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fstructure-theorem-over-pids":1720,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Frational-canonical-form":1721,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fjordan-canonical-form":1722,"\u002Fabstract-algebra\u002Ffield-theory\u002Ffield-extensions-and-algebraic-elements":1723,"\u002Fabstract-algebra\u002Ffield-theory\u002Fstraightedge-and-compass-constructions":1356,"\u002Fabstract-algebra\u002Ffield-theory\u002Fsplitting-fields-and-algebraic-closure":1724,"\u002Fabstract-algebra\u002Ffield-theory\u002Fseparable-and-cyclotomic-extensions":1725,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fthe-galois-correspondence":1598,"\u002Fabstract-algebra\u002Fgalois-theory\u002Ffinite-fields":1726,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fcyclotomic-and-abelian-extensions":1727,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fgalois-groups-of-polynomials":1655,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fsolvability-by-radicals-and-the-quintic":1727,"\u002Fabstract-algebra\u002Fcapstone\u002Fcommutative-algebra-and-algebraic-geometry":1728,"\u002Fabstract-algebra\u002Fcapstone\u002Frepresentation-and-character-theory":1729,"\u002Fabstract-algebra":1730,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fatomic-spectra-rutherford":1731,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-model-hydrogen":1732,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fx-ray-spectra-franck-hertz":1733,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-sommerfeld-old-quantum-theory":1734,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fold-quantum-theory-limits-wkb":1735,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fschrodinger-3d-hydrogen":1647,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fhydrogen-wave-functions":1736,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fradial-equation-in-full":1737,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fsymmetry-degeneracy-runge-lenz":1738,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fexpectation-values-virial":1739,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fquantum-defects-alkali-spectra":1740,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Frydberg-atoms":1741,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Frelativistic-kinetic-correction":1742,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fspin-orbit-thomas-precession":1481,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdarwin-term-fine-structure-formula":1610,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdirac-equation-hydrogen":1356,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Flamb-shift-qed":1743,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fhyperfine-structure-21cm":1340,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fnuclear-effects-isotope-shift":1744,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fperiodic-table-atomic-spectra":1745,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fcentral-field-self-consistent":1378,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fidentical-particles-hartree-fock":1672,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhelium-two-electron-atom":1746,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fls-jj-coupling-term-symbols":1747,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhund-rules-ground-terms":1748,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fzeeman-effect":1749,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fpaschen-back-intermediate":1750,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fstark-effect-polarizability":1751,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Ftime-dependent-perturbation-golden-rule":1752,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fdipole-approximation-einstein-coefficients":1753,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fselection-rules-forbidden-transitions":1754,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Flifetimes-and-line-shapes":1755,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Flaser-principles":1756,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fspectroscopy-techniques":1757,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fline-catalog-nist-asd":1758,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Flaser-cooling-doppler":1759,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fsub-doppler-trapping":1703,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fbose-einstein-condensation":1760,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Foptical-clocks-precision":1761,"\u002Fatomic-physics":1762,"\u002Fdatabases":1527,"\u002Fcategory-theory\u002Ffoundations\u002Fwhat-is-a-category":1763,"\u002Fcategory-theory\u002Ffoundations\u002Fexamples-of-categories":1764,"\u002Fcategory-theory\u002Ffoundations\u002Fspecial-morphisms":1765,"\u002Fcategory-theory\u002Ffoundations\u002Ffunctors":1694,"\u002Fcategory-theory\u002Ffoundations\u002Fnatural-transformations":1766,"\u002Fcategory-theory\u002Ffoundations\u002Fsize-and-set-theory":1767,"\u002Fcategory-theory\u002Funiversal-properties\u002Funiversal-properties":1768,"\u002Fcategory-theory\u002Funiversal-properties\u002Fproducts-and-coproducts":1769,"\u002Fcategory-theory\u002Funiversal-properties\u002Fconstructions-on-categories":1770,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Frepresentable-functors":1771,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-lemma":1772,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-consequences":1773,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits":1774,"\u002Fcategory-theory\u002Flimits-colimits\u002Fproducts-equalizers-pullbacks":1775,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcolimits":1776,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcomputing-limits":1777,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits-and-functors":1778,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions":1779,"\u002Fcategory-theory\u002Fadjunctions\u002Funits-and-counits":1780,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions-via-universal-arrows":1781,"\u002Fcategory-theory\u002Fadjunctions\u002Ffree-forgetful-adjunctions":1782,"\u002Fcategory-theory\u002Fadjoints-limits\u002Flimits-via-adjoints":1783,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fpresheaf-limits-colimits":1784,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoints-preserve-limits":1785,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoint-functor-theorem":1776,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fmonads":1786,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-eilenberg-moore":1787,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fkleisli-and-programming":1788,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-for-endofunctors":1789,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Fcartesian-closed-categories":1790,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Flambda-calculus-correspondence":1735,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Ffixed-points-and-recursion":1791,"\u002Fcategory-theory":1792,"\u002Fdeep-learning\u002Fmathematical-background\u002Flinear-algebra-for-deep-learning":1793,"\u002Fdeep-learning\u002Fmathematical-background\u002Fprobability-and-information-theory":1794,"\u002Fdeep-learning\u002Fmathematical-background\u002Fnumerical-computation":1795,"\u002Fdeep-learning\u002Fmathematical-background\u002Fcalculus":1796,"\u002Fdeep-learning\u002Ffoundations\u002Fwhat-is-deep-learning":1797,"\u002Fdeep-learning\u002Ffoundations\u002Fmachine-learning-refresher":1798,"\u002Fdeep-learning\u002Ffoundations\u002Flinear-models-and-the-perceptron":1757,"\u002Fdeep-learning\u002Fneural-networks\u002Fthe-multilayer-perceptron":1799,"\u002Fdeep-learning\u002Fneural-networks\u002Factivation-functions":1800,"\u002Fdeep-learning\u002Fneural-networks\u002Funiversal-approximation":1801,"\u002Fdeep-learning\u002Fneural-networks\u002Fbackpropagation":1802,"\u002Fdeep-learning\u002Fneural-networks\u002Floss-functions-and-output-units":1803,"\u002Fdeep-learning\u002Foptimization\u002Fgradient-descent-and-sgd":1804,"\u002Fdeep-learning\u002Foptimization\u002Fmomentum-and-adaptive-methods":1805,"\u002Fdeep-learning\u002Foptimization\u002Finitialization":1806,"\u002Fdeep-learning\u002Foptimization\u002Fthe-optimization-landscape":1807,"\u002Fdeep-learning\u002Foptimization\u002Fsecond-order-and-approximate-methods":1808,"\u002Fdeep-learning\u002Fregularization\u002Fregularization-overview":1809,"\u002Fdeep-learning\u002Fregularization\u002Fdropout-and-data-augmentation":1810,"\u002Fdeep-learning\u002Fregularization\u002Fearly-stopping-and-parameter-sharing":1811,"\u002Fdeep-learning\u002Fregularization\u002Fnormalization":1812,"\u002Fdeep-learning\u002Farchitectures\u002Fconvolutional-networks":1813,"\u002Fdeep-learning\u002Farchitectures\u002Fcnn-architectures":1814,"\u002Fdeep-learning\u002Farchitectures\u002Frecurrent-networks":1815,"\u002Fdeep-learning\u002Farchitectures\u002Flstm-and-gru":1816,"\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers":1817,"\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture":1818,"\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice":1819,"\u002Fdeep-learning\u002Farchitectures\u002Fgraph-neural-networks":1820,"\u002Fdeep-learning\u002Farchitectures\u002Fstate-space-models":1821,"\u002Fdeep-learning\u002Ftheory\u002Fgeneralization-theory":1822,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-robustness":1823,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-defenses":1824,"\u002Fdeep-learning\u002Ftheory\u002Fbayesian-and-ensemble-methods":1825,"\u002Fdeep-learning\u002Ftheory\u002Fdeep-equilibrium-models":1769,"\u002Fdeep-learning\u002Fgenerative-models\u002Flinear-factor-models":1826,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoencoders":1827,"\u002Fdeep-learning\u002Fgenerative-models\u002Fvariational-autoencoders":1828,"\u002Fdeep-learning\u002Fgenerative-models\u002Fgenerative-adversarial-networks":1829,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoregressive-and-normalizing-flows":1830,"\u002Fdeep-learning\u002Fgenerative-models\u002Fenergy-based-and-boltzmann-machines":1831,"\u002Fdeep-learning\u002Fgenerative-models\u002Fdiffusion-and-score-based-models":1832,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fstructured-probabilistic-models":1321,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fmonte-carlo-and-mcmc":1833,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fapproximate-inference":1834,"\u002Fdeep-learning\u002Fpractical\u002Fpractical-methodology":1557,"\u002Fdeep-learning\u002Fpractical\u002Fhyperparameters-and-debugging":1835,"\u002Fdeep-learning\u002Fpractical\u002Frepresentation-learning":1836,"\u002Fdeep-learning\u002Fpractical\u002Ftransfer-learning":1837,"\u002Fdeep-learning\u002Fpractical\u002Fapplications":1838,"\u002Fdeep-learning\u002Fpractical\u002Fmodel-compression-and-distillation":1839,"\u002Fdeep-learning\u002Fpractical\u002Fmeta-learning-and-few-shot":1840,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Flarge-language-models":1841,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fscaling-inference-and-alignment":1842,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fseq2seq-pretraining-and-bart":1843,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ftext-to-text-transfer-and-conditional-generation":1844,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fspeech-and-audio-models":1845,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fself-supervised-speech-and-synthesis":1846,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fai-agents":1530,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fagent-memory-retrieval-and-orchestration":1847,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmixture-of-experts":1848,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmultimodal-models":1849,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ffusion-and-vision-language-models":1850,"\u002Fdeep-learning\u002Freinforcement-learning\u002Ffoundations-of-reinforcement-learning":1567,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fmodel-free-prediction-and-control":1851,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fdeep-q-networks":1852,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fpolicy-gradients-and-actor-critic":1853,"\u002Fdeep-learning\u002Freinforcement-learning\u002Frl-from-human-feedback":1854,"\u002Fdeep-learning":1527,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fequilibrium-state-variables-zeroth-law":1855,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Ffirst-law-heat-and-work":1652,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fsecond-law-entropy-and-the-carnot-bound":1856,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fthermodynamic-potentials-and-maxwell-relations":1857,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fstability-response-functions-and-the-third-law":1858,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fclassical-statistics-and-equipartition":1859,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fphase-space-and-liouvilles-theorem":1860,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fensembles-and-the-equal-probability-postulate":1861,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fstatistical-entropy-boltzmann-and-gibbs":1862,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fmicrocanonical-ensemble-and-entropy":1863,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fequilibrium-conditions-temperature-pressure-chemical-potential":1699,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fideal-gas-phase-space-and-the-sackur-tetrode-entropy":1864,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Ftwo-state-systems-paramagnets-and-negative-temperature":1865,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fcanonical-ensemble-and-the-boltzmann-distribution":1866,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fpartition-function-and-the-helmholtz-free-energy":1586,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fenergy-fluctuations-and-ensemble-equivalence":1379,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fthe-einstein-solid-and-harmonic-systems":1867,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fparamagnetism-and-the-schottky-anomaly":1868,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fideal-gas-partition-function-and-the-gibbs-paradox":1869,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fequipartition-and-the-virial-theorem":1513,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fmolecular-gases-rotation-and-vibration":1870,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fgrand-canonical-ensemble-and-the-grand-partition-function":1871,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fchemical-potential-fugacity-and-number-fluctuations":1591,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fensemble-summary-and-the-thermodynamic-web":1518,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fquantum-statistics-bose-einstein-and-fermi-dirac":1872,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fderiving-the-quantum-distributions":1487,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fthe-classical-limit-and-quantum-concentration":1357,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fideal-quantum-gases-general-framework":1373,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-and-the-fermion-gas":1873,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthe-photon-gas-and-plancks-radiation-law":1874,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fblackbody-thermodynamics-and-radiation-pressure":1875,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fphonons-and-the-debye-model":1505,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-derived":1876,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthermodynamics-of-the-bose-gas-and-superfluidity":1367,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fthe-ideal-fermi-gas-at-zero-temperature":1877,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fsommerfeld-expansion-and-electrons-in-metals":1878,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":1879,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fneutron-stars-and-nuclear-matter":1880,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-cluster-expansion-and-virial-coefficients":1701,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-van-der-waals-gas-and-liquid-gas-coexistence":1881,"\u002Fstatistical-mechanics\u002Finteractions\u002Fquantum-gases-with-interactions-and-exchange":1882,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fphases-coexistence-and-classification":1883,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-ising-model-and-exact-solutions":1884,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fmean-field-theory-and-the-weiss-model":1647,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fcritical-exponents-and-landau-theory":1885,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-renormalization-group-idea":1625,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fthermodynamic-fluctuations-and-response":1886,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fbrownian-motion-and-the-langevin-equation":1486,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Flinear-response-and-the-fluctuation-dissipation-theorem":1887,"\u002Fstatistical-mechanics":1888,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fbonding-mechanisms":1889,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fmolecular-orbitals-and-h2-plus":1352,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fhydrogen-molecule-and-exchange":1612,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fvan-der-waals-forces":1890,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Frotational-vibrational-spectra":1891,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Fanharmonicity-and-rovibrational-structure":1892,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Framan-and-electronic-bands":1893,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Flasers-and-masers":1894,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fstructure-of-solids":1895,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fbravais-lattices-and-crystal-systems":1485,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Freciprocal-lattice-and-brillouin-zones":1896,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fdiffraction-and-structure-factors":1897,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonon-dispersion":1898,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonons-quantization-and-dos":1899,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fdebye-einstein-heat-capacity":1628,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fanharmonicity-and-thermal-transport":1900,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ffree-electron-gas-and-conduction":1901,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fsommerfeld-model-and-heat-capacity":1902,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ftransport-and-the-hall-effect":1903,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fscreening-and-plasmons":1904,"\u002Fcondensed-matter\u002Fband-theory\u002Fblochs-theorem-and-energy-bands":1683,"\u002Fcondensed-matter\u002Fband-theory\u002Fnearly-free-electron-model":1627,"\u002Fcondensed-matter\u002Fband-theory\u002Ftight-binding-method":1905,"\u002Fcondensed-matter\u002Fband-theory\u002Ffermi-surfaces-and-semiclassical-dynamics":1906,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fsemiconductor-bands-and-junctions":1907,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fintrinsic-and-extrinsic-semiconductors":1908,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fcarrier-transport-and-recombination":1618,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fthe-pn-junction":1909,"\u002Fcondensed-matter\u002Fsemiconductors\u002Ftransistors-and-optoelectronics":1910,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fdielectrics-and-polarization":1855,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fferroelectrics-and-piezoelectrics":1755,"\u002Fcondensed-matter\u002Fmagnetism\u002Fdiamagnetism-and-paramagnetism":1482,"\u002Fcondensed-matter\u002Fmagnetism\u002Fexchange-and-ferromagnetism":1911,"\u002Fcondensed-matter\u002Fmagnetism\u002Fantiferromagnetism-and-domains":1348,"\u002Fcondensed-matter\u002Fmagnetism\u002Fspin-waves-and-magnons":1912,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fsuperconductivity-phenomenology":1913,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Flondon-theory-and-the-meissner-effect":1493,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fginzburg-landau-theory":1914,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fbcs-theory":1748,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fjosephson-and-high-tc":1915,"\u002Fcondensed-matter\u002Fnanostructures\u002Fquantum-wells-wires-and-dots":1340,"\u002Fcondensed-matter\u002Fnanostructures\u002Finteger-quantum-hall-effect":1916,"\u002Fcondensed-matter\u002Fnanostructures\u002Ffractional-quantum-hall-and-topology":1351,"\u002Fcondensed-matter\u002Fnanostructures\u002Fgraphene-and-dirac-materials":1917,"\u002Fcondensed-matter":1668,"\u002Flogic\u002Ffoundations\u002Flogic-as-a-mathematical-model":1918,"\u002Flogic\u002Fsentential-logic\u002Fformal-languages-and-well-formed-formulas":1919,"\u002Flogic\u002Fsentential-logic\u002Ftruth-assignments-and-tautologies":1920,"\u002Flogic\u002Fsentential-logic\u002Funique-readability-and-parsing":1921,"\u002Flogic\u002Fsentential-logic\u002Finduction-and-recursion":1365,"\u002Flogic\u002Fsentential-logic\u002Fexpressive-completeness-and-normal-forms":1922,"\u002Flogic\u002Fsentential-logic\u002Fboolean-circuits":1923,"\u002Flogic\u002Fsentential-logic\u002Fcompactness-and-effectiveness":1365,"\u002Flogic\u002Ffirst-order-languages\u002Ffirst-order-languages":1924,"\u002Flogic\u002Ffirst-order-languages\u002Fstructures-truth-and-satisfaction":1778,"\u002Flogic\u002Ffirst-order-languages\u002Fdefinability-and-elementary-equivalence":1925,"\u002Flogic\u002Ffirst-order-languages\u002Fterms-substitution-and-parsing":1926,"\u002Flogic\u002Fdeductive-calculus\u002Fa-deductive-calculus":1927,"\u002Flogic\u002Fdeductive-calculus\u002Fdeduction-theorem-and-derived-rules":1925,"\u002Flogic\u002Fdeductive-calculus\u002Fsoundness":1928,"\u002Flogic\u002Fdeductive-calculus\u002Fcompleteness-and-consistency":1929,"\u002Flogic\u002Fmodels-and-theories\u002Fcompactness-and-lowenheim-skolem":1930,"\u002Flogic\u002Fmodels-and-theories\u002Ftheories-elementary-classes-and-categoricity":1931,"\u002Flogic\u002Fmodels-and-theories\u002Finterpretations-between-theories":1932,"\u002Flogic\u002Fmodels-and-theories\u002Fnonstandard-analysis":1933,"\u002Flogic\u002Farithmetic-and-definability\u002Fdefinability-in-arithmetic":1934,"\u002Flogic\u002Farithmetic-and-definability\u002Fnatural-numbers-with-successor":1935,"\u002Flogic\u002Farithmetic-and-definability\u002Fpresburger-and-reducts":1856,"\u002Flogic\u002Farithmetic-and-definability\u002Fa-subtheory-and-representability":1936,"\u002Flogic\u002Fincompleteness\u002Farithmetization-of-syntax":1929,"\u002Flogic\u002Fincompleteness\u002Fincompleteness-and-undecidability":1937,"\u002Flogic\u002Fincompleteness\u002Fsecond-incompleteness-theorem":1938,"\u002Flogic\u002Fcomputability-and-representability\u002Frecursive-functions":1571,"\u002Flogic\u002Fcomputability-and-representability\u002Frepresenting-exponentiation":1939,"\u002Flogic\u002Fsecond-order-logic\u002Fsecond-order-languages":1756,"\u002Flogic\u002Fsecond-order-logic\u002Fskolem-functions-and-many-sorted-logic":1940,"\u002Flogic\u002Fsecond-order-logic\u002Fgeneral-structures":1941,"\u002Flogic":1942,"\u002Freinforcement-learning\u002Ffoundations\u002Fwhat-is-reinforcement-learning":1943,"\u002Freinforcement-learning\u002Ffoundations\u002Fa-brief-history-of-rl":1944,"\u002Freinforcement-learning\u002Ffoundations\u002Fmulti-armed-bandits":1557,"\u002Freinforcement-learning\u002Ffoundations\u002Fbandit-exploration-algorithms":1945,"\u002Freinforcement-learning\u002Ffoundations\u002Fmarkov-decision-processes":1946,"\u002Freinforcement-learning\u002Ffoundations\u002Fvalue-functions-and-optimality":1947,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdynamic-programming":1948,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdp-async-and-gpi":1938,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-methods":1949,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-off-policy":1950,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftemporal-difference-learning":1951,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftd-control-sarsa-and-q-learning":1849,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-bootstrapping":1952,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-off-policy-methods":1953,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-and-learning":1954,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-focusing-and-decision-time":1955,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdecision-time-planning":1956,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-tree-search":1574,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-prediction":1957,"\u002Freinforcement-learning\u002Fapproximation\u002Ffeature-construction-and-nonlinear":1958,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-control":1959,"\u002Freinforcement-learning\u002Fapproximation\u002Faverage-reward-control":1960,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-and-the-deadly-triad":1765,"\u002Freinforcement-learning\u002Fapproximation\u002Fbellman-error-and-gradient-td":1961,"\u002Freinforcement-learning\u002Fapproximation\u002Feligibility-traces":1937,"\u002Freinforcement-learning\u002Fapproximation\u002Ftrue-online-and-sarsa-lambda":1962,"\u002Freinforcement-learning\u002Fapproximation\u002Fpolicy-gradient-methods":1963,"\u002Freinforcement-learning\u002Fapproximation\u002Factor-critic-and-continuous-actions":1964,"\u002Freinforcement-learning\u002Fapproximation\u002Fleast-squares-and-memory-based-methods":1585,"\u002Freinforcement-learning\u002Fapproximation\u002Fmemory-and-kernel-methods":1965,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-eligibility-traces":1715,"\u002Freinforcement-learning\u002Fapproximation\u002Fstable-off-policy-traces":1966,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdeep-q-networks":1967,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdqn-improvements":1547,"\u002Freinforcement-learning\u002Fdeep-rl\u002Factor-critic-and-ppo":1968,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fppo-and-continuous-control":1969,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fcase-studies":1970,"\u002Freinforcement-learning\u002Fdeep-rl\u002Frl-beyond-games":1971,"\u002Freinforcement-learning\u002Fdeep-rl\u002Ffrontiers":1972,"\u002Freinforcement-learning\u002Fdeep-rl\u002Freward-design-and-open-problems":1825,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow":1973,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow-part-2":1974,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control":1975,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control-part-2":1860,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl":1976,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl-part-2":1977,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration":1978,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration-part-2":1574,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl":1641,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl-part-2":1979,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl":1980,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl-part-2":1981,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl":1982,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl-part-2":1983,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl":1984,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl-part-2":1985,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Frlhf-and-language-models":1986,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps":1987,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps-part-2":1988,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl":1989,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl-part-2":1990,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmeta-rl-and-generalization":1991,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fpsychology-of-reinforcement":1992,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Finstrumental-conditioning-and-control":1993,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-and-td-error":1994,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-in-the-brain":1995,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fanimal-learning-and-cognition":1996,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fcognitive-maps-and-planning":1997,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fneuroscience-of-reinforcement":1998,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fseveral-learning-systems":1999,"\u002Freinforcement-learning":1527,"\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai":2000,"\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai":2001,"\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents":2002,"\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures":1240,"\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search":2003,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared":2004,"\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search":2005,"\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions":2006,"\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search":2007,"\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search":2008,"\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search":2009,"\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information":2010,"\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction":2011,"\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure":1854,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty":1709,"\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search":2012,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic":2013,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference":2014,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic":2015,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use":2016,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution":2017,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution":1836,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning":2018,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan":2019,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world":2020,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty":2021,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation":2022,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults":2023,"\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes":2024,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes":2025,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks":2026,"\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks":2027,"\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time":2028,"\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association":2029,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions":1768,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes":2019,"\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory":2030,"\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design":1308,"\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples":2031,"\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families":2032,"\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning":2033,"\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization":2034,"\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning":2035,"\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search":1817,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning":2036,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods":2037,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception":2038,"\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world":2039,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics":2040,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control":2041,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai":2042,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech":2043,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future":2044,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future":2045,"\u002Fartificial-intelligence":1527,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart":1784,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions":2046,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy":1344,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula":1342,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles":1878,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview":2047,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron":1370,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering":1680,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin":2048,"\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model":2049,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates":2050,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle":1740,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations":2051,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes":2052,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium":2053,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory":1939,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance":2054,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino":2055,"\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay":1354,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation":1583,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass":2056,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation":1684,"\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers":2057,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer":2058,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections":1579,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances":1667,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model":2059,"\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics":2060,"\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics":2061,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement":1349,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis":1724,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis":1586,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power":2062,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions":1634,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors":1698,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology":2063,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine":2064,"\u002Fnuclear-physics":2065,"\u002Fnatural-language-processing\u002Ffoundations\u002Fwhat-is-nlp":2066,"\u002Fnatural-language-processing\u002Ffoundations\u002Fregex-and-text-normalization":2067,"\u002Fnatural-language-processing\u002Ffoundations\u002Fminimum-edit-distance":1705,"\u002Fnatural-language-processing\u002Ffoundations\u002Fn-gram-language-models":2068,"\u002Fnatural-language-processing\u002Ffoundations\u002Fsmoothing-and-backoff":2069,"\u002Fnatural-language-processing\u002Fclassification\u002Fnaive-bayes-and-sentiment":2070,"\u002Fnatural-language-processing\u002Fclassification\u002Fevaluating-classifiers":1553,"\u002Fnatural-language-processing\u002Fclassification\u002Flogistic-regression":2071,"\u002Fnatural-language-processing\u002Fclassification\u002Fsentiment-and-affect-lexicons":2072,"\u002Fnatural-language-processing\u002Fsemantics\u002Fvector-semantics-and-embeddings":1850,"\u002Fnatural-language-processing\u002Fsemantics\u002Fstatic-word-embeddings":2073,"\u002Fnatural-language-processing\u002Fsemantics\u002Fneural-language-models":2018,"\u002Fnatural-language-processing\u002Fsequences\u002Fsequence-labeling":2074,"\u002Fnatural-language-processing\u002Fsequences\u002Fcrfs-and-neural-taggers":2075,"\u002Fnatural-language-processing\u002Fsequences\u002Frnns-and-lstms":2076,"\u002Fnatural-language-processing\u002Ftransformers\u002Ftransformers-and-attention":2077,"\u002Fnatural-language-processing\u002Ftransformers\u002Fthe-transformer-architecture":2078,"\u002Fnatural-language-processing\u002Ftransformers\u002Flarge-language-models":2079,"\u002Fnatural-language-processing\u002Ftransformers\u002Fllm-pretraining-and-scaling":2080,"\u002Fnatural-language-processing\u002Ftransformers\u002Ffine-tuning-and-prompting":1531,"\u002Fnatural-language-processing\u002Ftransformers\u002Fprompting-and-alignment":2081,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-parsing":2082,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcky-scoring-and-evaluation":2024,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdependency-parsing":2083,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fgraph-based-and-neural-dependency-parsing":2084,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fword-senses-and-wsd":2085,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fwsd-in-practice-and-induction":2086,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-roles-and-information-extraction":2087,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Frelations-events-and-templates":2088,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoreference-and-discourse":2089,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoherence-and-discourse-structure":2090,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Flogical-semantics":1949,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcompositional-semantics-and-description-logics":2091,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-parsing":2092,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fneural-semantic-parsing":2093,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Finformation-extraction":2094,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftimes-events-and-templates":2095,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdiscourse-coherence":2096,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fentity-based-and-global-coherence":2097,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-grammars":2098,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftreebanks-and-lexicalized-grammars":2099,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation":2100,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation-decoding-and-evaluation":2101,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering":2102,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering-knowledge-and-llms":1803,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-and-chatbots":1970,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-systems-and-assistants":1559,"\u002Fnatural-language-processing\u002Fapplications\u002Ftext-summarization":2103,"\u002Fnatural-language-processing\u002Fapplications\u002Fabstractive-summarization-and-evaluation":2104,"\u002Fnatural-language-processing\u002Fspeech\u002Fphonetics":2105,"\u002Fnatural-language-processing\u002Fspeech\u002Facoustic-phonetics":2106,"\u002Fnatural-language-processing\u002Fspeech\u002Fautomatic-speech-recognition":1817,"\u002Fnatural-language-processing\u002Fspeech\u002Fasr-evaluation-and-applications":2107,"\u002Fnatural-language-processing":1527,"\u002Fparticle-physics\u002Ffoundations\u002Fhistorical-overview-particle-zoo":2108,"\u002Fparticle-physics\u002Ffoundations\u002Fparticle-physics-basic-concepts":1725,"\u002Fparticle-physics\u002Ffoundations\u002Ffundamental-interactions-force-carriers":2109,"\u002Fparticle-physics\u002Funits-kinematics\u002Fnatural-units-and-scales":1870,"\u002Fparticle-physics\u002Funits-kinematics\u002Ffour-vectors-invariant-mass":2110,"\u002Fparticle-physics\u002Funits-kinematics\u002Fdecay-scattering-kinematics-mandelstam":2111,"\u002Fparticle-physics\u002Funits-kinematics\u002Fcross-sections-golden-rule":2059,"\u002Fparticle-physics\u002Fsymmetries\u002Fconservation-laws-symmetries":2112,"\u002Fparticle-physics\u002Fsymmetries\u002Fdiscrete-symmetries-cpt":2113,"\u002Fparticle-physics\u002Fsymmetries\u002Fparity-violation-weak":1675,"\u002Fparticle-physics\u002Fsymmetries\u002Fsu2-su3-flavor-symmetry":1377,"\u002Fparticle-physics\u002Fquark-model\u002Feightfold-way-su3":2114,"\u002Fparticle-physics\u002Fquark-model\u002Fmeson-spectroscopy":1629,"\u002Fparticle-physics\u002Fquark-model\u002Fbaryon-spectroscopy":2115,"\u002Fparticle-physics\u002Fquark-model\u002Fcolor-confinement-exotics":1662,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fklein-gordon-equation":2116,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fdirac-equation-spinors":1916,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fantiparticles-hole-theory":2117,"\u002Fparticle-physics\u002Fqed\u002Ffeynman-rules-qed":2118,"\u002Fparticle-physics\u002Fqed\u002Fqed-tree-processes":1885,"\u002Fparticle-physics\u002Fqed\u002Frenormalization-running-coupling":2119,"\u002Fparticle-physics\u002Fqed\u002Felectron-g-2":1348,"\u002Fparticle-physics\u002Fweak-interaction\u002Fva-structure-weak":2120,"\u002Fparticle-physics\u002Fweak-interaction\u002Fw-z-bosons-decays":2121,"\u002Fparticle-physics\u002Fweak-interaction\u002Fckm-matrix":2122,"\u002Fparticle-physics\u002Fweak-interaction\u002Fcp-violation-kaons-b-mesons":1666,"\u002Fparticle-physics\u002Fqcd\u002Fcolor-su3-gluons":1882,"\u002Fparticle-physics\u002Fqcd\u002Fasymptotic-freedom-confinement":2123,"\u002Fparticle-physics\u002Fqcd\u002Fdeep-inelastic-scattering-partons":2124,"\u002Fparticle-physics\u002Fqcd\u002Fjets-hadronization":1741,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Felectroweak-su2-u1":2125,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fspontaneous-symmetry-breaking":1786,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-mechanism":2126,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-boson-discovery":2127,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fstandard-model":1675,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-oscillations":1708,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-mass-pmns":2128,"\u002Fparticle-physics\u002Fneutrinos\u002Fdirac-majorana-experiments":2129,"\u002Fparticle-physics\u002Fexperiment\u002Faccelerators-luminosity":2130,"\u002Fparticle-physics\u002Fexperiment\u002Fdetectors-subsystems":1764,"\u002Fparticle-physics\u002Fexperiment\u002Fhow-discoveries-are-made":2131,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fbeyond-standard-model":1505,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fgrand-unified-theories":2132,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fsupersymmetry":1608,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fhierarchy-problem-naturalness":2133,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fdark-matter-candidates":2134,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fmatter-antimatter-open-questions":1932,"\u002Fparticle-physics":2135,"\u002Fastrophysics-cosmology\u002Forientation\u002Fthe-sun-and-stars":1726,"\u002Fastrophysics-cosmology\u002Forientation\u002Fstellar-death-final-states":1880,"\u002Fastrophysics-cosmology\u002Forientation\u002Fgalaxies-and-cosmology":2136,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fmagnitudes-fluxes-and-the-distance-modulus":1665,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fstellar-spectra-and-spectral-classification":2137,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Ftelescopes-and-detectors-across-the-spectrum":1725,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fthe-cosmic-distance-ladder":1637,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fblackbody-radiation-and-specific-intensity":2138,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fradiative-transfer-and-the-transfer-equation":2139,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fspectral-line-formation-and-broadening":2140,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fopacity-and-the-rosseland-mean":2141,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fhydrostatic-equilibrium-and-the-virial-theorem":2142,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equations-of-stellar-structure":1931,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equation-of-state-and-polytropes":1862,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-standard-solar-model":2143,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fthermonuclear-reaction-rates-and-the-gamow-peak":2144,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhydrogen-burning-pp-chains-and-cno":2145,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhelium-burning-and-the-triple-alpha-process":2146,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fadvanced-burning-and-neutron-capture-nucleosynthesis":2058,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fphases-of-the-interstellar-medium":2147,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fmolecular-clouds-and-gravitational-collapse":1621,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fprotostars-and-the-pre-main-sequence":1684,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-main-sequence-and-its-structure":1666,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fpost-main-sequence-low-mass-evolution":2148,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-evolution-of-massive-stars":1750,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fstellar-pulsation-and-the-instability-strip":1366,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":2149,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fcore-collapse-supernovae":2150,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fthermonuclear-supernovae-type-ia":1881,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fneutron-stars-and-pulsars":2151,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fblack-holes-schwarzschild-and-kerr":2152,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fbinary-systems-and-mass-transfer":2153,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Faccreting-compact-objects":2154,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fgravitational-waves-from-inspiraling-binaries":1347,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fmultimessenger-astronomy-and-gamma-ray-bursts":2155,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fthe-milky-way":2156,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-morphology-and-classification":1608,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-rotation-curves-and-dark-matter":2157,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Factive-galactic-nuclei-and-supermassive-black-holes":2158,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-clusters-and-large-scale-structure":1874,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-expanding-universe-and-hubbles-law":1529,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-frw-metric-and-cosmological-redshift":2159,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-friedmann-equations-and-cosmic-dynamics":2160,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fcosmological-models-and-distances":1786,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fdark-energy-and-the-accelerating-universe":1772,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fthe-thermal-history-of-the-universe":1784,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fbig-bang-nucleosynthesis":1881,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Frecombination-and-the-cosmic-microwave-background":2161,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcmb-anisotropies-and-cosmological-parameters":1346,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcosmic-inflation":1538,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fstructure-formation-and-the-growth-of-perturbations":2162,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fdark-matter-dark-energy-and-open-questions":1625,"\u002Fastrophysics-cosmology":1730,"\u002Fcolophon":2163,"\u002F":1527},4250,4808,3626,2682,4109,4786,3878,3875,3751,3415,4067,3153,3000,4042,5461,5808,3961,3749,4327,5067,4246,4655,4154,5436,2640,4003,3601,2158,4331,4189,2273,3252,4633,4964,4172,3131,5524,3160,4031,2309,4207,3226,2648,4842,5340,3307,5701,4977,4039,2615,3472,4460,3848,4075,4400,3382,3010,3602,3737,3740,3707,3922,5191,4043,3804,4542,4214,5062,2850,4361,3443,3627,4044,3766,4140,3860,4006,5199,4334,5234,3651,5509,5680,153,1375,1073,1093,1125,1146,1014,1132,876,1541,1189,1173,984,1402,1301,950,1268,1063,1107,1408,1161,925,1012,866,964,1090,1142,1085,1020,1207,973,980,728,764,1225,1329,796,929,801,878,774,1044,1488,1175,1130,890,814,870,154,4073,5140,4961,5127,4870,5382,5195,4955,5369,4501,5576,3824,4132,4289,4307,4570,3403,5084,5105,5201,5116,5341,5175,5368,5188,5211,5499,5155,4981,5125,5415,5255,5304,5130,5167,5552,5164,5094,5239,5036,5190,5004,5099,5035,5159,5088,5026,4937,5023,5264,5244,133,5114,5078,5043,5312,5170,5342,5139,5151,5049,5212,5013,5068,5079,5102,5121,5081,5029,5379,5854,5110,2139,3798,5055,5364,4984,4935,4895,4972,5289,5112,5156,4987,5031,5025,5149,5302,5042,5002,4979,4922,4960,5279,126,1877,1180,1129,907,958,1112,1300,1053,1250,1181,1241,1234,966,1050,734,1190,484,1082,926,733,761,571,607,798,804,952,977,731,784,645,771,1017,742,1004,1000,1562,1254,1288,1101,1011,1486,1061,856,992,1169,988,137,0,2037,1782,2384,2254,2123,2332,1643,1714,2089,1751,1367,1660,2511,1998,1892,1854,1791,2438,2487,1917,2375,2525,2266,1845,2275,1810,1631,2310,2166,2233,2113,2505,2347,2672,2112,2473,2592,2380,3013,2513,3256,3218,2194,2173,2205,2326,2081,3342,3152,1799,1670,1027,960,1095,1291,986,897,1209,1055,1817,1801,1593,1465,1196,1464,1201,1230,1435,1684,1461,1926,1500,1409,1284,1774,1869,162,1487,1122,1188,1001,1351,982,1005,979,1325,1046,943,1279,824,1008,989,1798,1277,1025,987,1043,1211,1074,981,939,1002,739,1139,1108,1013,1070,978,1458,1317,157,1357,1077,2355,1116,1037,1178,1637,1314,1109,1056,1702,1474,1071,1158,832,993,1404,1024,1068,1339,1106,1264,1248,913,1848,1328,1633,1224,1143,135,1378,959,1028,998,911,1527,1203,1266,1483,1165,990,938,965,1257,1418,1099,942,1352,956,1035,1398,1003,1094,1292,138,1721,1827,1449,1354,1148,1184,1285,1281,1213,1290,1271,1252,1274,1778,1591,1503,1437,1571,1584,1957,1117,1781,1648,1342,1667,1510,1965,1607,1365,1849,1259,1303,1356,1238,2208,1564,173,1671,1286,1227,1638,1529,668,1078,918,709,865,880,940,1534,1015,874,922,841,794,1194,822,1105,1658,1359,1296,1438,1921,1844,1570,1429,1324,1400,140,1787,1558,1654,1492,1747,2224,2002,2009,1323,1349,1785,1573,1722,1829,1353,1548,1552,1583,1624,1585,1245,1364,1514,1343,1397,1355,2211,1481,1770,160,2388,2293,2256,2552,2569,2478,2039,2496,2578,2814,2519,2461,2587,2492,2714,3278,2654,3050,2447,2849,2238,2369,2061,2214,2602,2563,2186,2985,2749,3364,2038,2282,2409,2126,2573,2206,2176,2268,2182,2402,2705,2633,2414,2213,2801,3313,3410,3195,1952,2017,1509,2537,2645,2027,2415,2838,2356,1906,3184,2950,2807,2954,1683,1316,1034,1138,1763,1822,1705,1246,1701,1097,1104,1187,1032,1083,1228,916,1489,1033,1652,997,692,837,1023,888,864,1089,1231,1214,1675,1156,1075,1520,1309,139,1205,1051,735,1123,1072,915,567,768,825,1253,983,1007,762,1058,861,862,971,1208,1149,1145,1029,1084,927,810,838,857,807,936,949,2321,1622,1069,1113,1057,854,1958,1528,1618,2049,1432,1679,1796,1685,1346,1275,1476,1505,1610,2018,1599,1215,1838,1909,132,3902,2215,2240,3266,3208,3073,2454,2969,2451,1875,2728,1884,2371,2516,2842,1690,1904,2346,3146,1386,2607,1966,2668,1665,2885,1606,2577,3074,2869,2403,2433,2082,1939,1587,2460,2747,2032,2642,1619,3123,1993,2090,2339,3829,1737,2622,2340,2322,3828,4409,2305,3411,2510,4527,3030,3569,3043,2457,1946,2277,2909,1693,1945,2093,2399,2115,2898,2742,2242,3895,3378,3376,2769,2223,3062,3262,2651,2949,2768,3128,2423,1977,2087,2866,3388,2830,2210,2489,2884,3945,2099,2713,3402,1692,2931,4195,3989,3206,4391,3004,3704,3494,2902,999,881,901,919,748,869,1018,1045,1049,1333,954,1092,1019,976,1771,1480,1396,953,1026,161,3533,2495,1818,3007,2595,3427,3537,2216,1895,2304,3396,1739,2073,1962,2203,1767,2666,2264,2276,2852,1807,3735,1560,4144,1669,1676,1972,2418,3291,1525,2040,2766,2337,2220,2800,3001,2078,1759,2836,1896,2026,1758,1543,1047,896,946,1060,1384,1482,815,1414,1322,1440,1240,1468,1098,1133,847,1009,1381,1052,1191,1258,1370,1712,1441,1199,957,1079,150,1262,1417,1368,1219,1136,1064,1463,1636,1059,931,1115,1736,1174,1376,1363,1411,1247,1746,1313,1299,1617,1102,1076,1495,1265,1193,1263,80,{"\u002Falgorithms\u002Ffoundations\u002Fwhat-is-an-algorithm":2165,"\u002Falgorithms\u002Ffoundations\u002Fproof-techniques":2169,"\u002Falgorithms\u002Ffoundations\u002Fasymptotic-analysis":2173,"\u002Falgorithms\u002Ffoundations\u002Fgrowth-rates-and-loop-analysis":2177,"\u002Falgorithms\u002Ffoundations\u002Frecurrences":2181,"\u002Falgorithms\u002Ffoundations\u002Famortized-analysis":2185,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fmergesort":2189,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fquicksort":2194,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fselection":2198,"\u002Falgorithms\u002Fdivide-and-conquer\u002Ffast-multiplication":2202,"\u002Falgorithms\u002Fsorting\u002Fheaps-and-heapsort":2206,"\u002Falgorithms\u002Fsorting\u002Fsorting-lower-bounds":2211,"\u002Falgorithms\u002Fsorting\u002Flinear-time-sorting":2215,"\u002Falgorithms\u002Fsorting\u002Fexternal-sorting":2219,"\u002Falgorithms\u002Fdata-structures\u002Felementary-structures":2223,"\u002Falgorithms\u002Fdata-structures\u002Fhash-tables":2228,"\u002Falgorithms\u002Fdata-structures\u002Fbinary-search-trees":2232,"\u002Falgorithms\u002Fdata-structures\u002Favl-trees":2236,"\u002Falgorithms\u002Fdata-structures\u002Fbalanced-trees":2240,"\u002Falgorithms\u002Fdata-structures\u002Funion-find":2244,"\u002Falgorithms\u002Fdata-structures\u002Ffenwick-and-segment-trees":2248,"\u002Falgorithms\u002Fdata-structures\u002Fspatial-data-structures":2252,"\u002Falgorithms\u002Fdata-structures\u002Fskip-lists-and-probabilistic-structures":2256,"\u002Falgorithms\u002Fdata-structures\u002Fb-trees":2260,"\u002Falgorithms\u002Fdata-structures\u002Fdata-stream-algorithms":2264,"\u002Falgorithms\u002Fdata-structures\u002Fstreaming-sketches":2268,"\u002Falgorithms\u002Fsequences\u002Ftwo-pointers-and-windows":2272,"\u002Falgorithms\u002Fsequences\u002Fprefix-sums":2277,"\u002Falgorithms\u002Fsequences\u002Fmonotonic-stacks":2281,"\u002Falgorithms\u002Fsequences\u002Fbinary-search-on-the-answer":2285,"\u002Falgorithms\u002Fsequences\u002Fstring-matching":2289,"\u002Falgorithms\u002Fsequences\u002Fkmp-and-z-function":2293,"\u002Falgorithms\u002Fsequences\u002Ftries":2297,"\u002Falgorithms\u002Fsequences\u002Fsuffix-arrays-and-aho-corasick":2301,"\u002Falgorithms\u002Fgraphs\u002Frepresentations-and-traversal":2305,"\u002Falgorithms\u002Fgraphs\u002Fdepth-first-search":2310,"\u002Falgorithms\u002Fgraphs\u002Ftopological-sort-and-scc":2314,"\u002Falgorithms\u002Fgraphs\u002Fminimum-spanning-trees":2318,"\u002Falgorithms\u002Fgraphs\u002Fkruskal-and-prim":2322,"\u002Falgorithms\u002Fgraphs\u002Fshortest-paths":2326,"\u002Falgorithms\u002Fgraphs\u002Fall-pairs-and-negative-weights":2330,"\u002Falgorithms\u002Fgraphs\u002Fnetwork-flow":2334,"\u002Falgorithms\u002Fgraphs\u002Fmax-flow-min-cut":2338,"\u002Falgorithms\u002Fgraphs\u002Fbridges-and-articulation-points":2342,"\u002Falgorithms\u002Fgraphs\u002Flowest-common-ancestor":2346,"\u002Falgorithms\u002Fgraphs\u002Ftwo-sat":2350,"\u002Falgorithms\u002Fgraphs\u002Feulerian-tours":2354,"\u002Falgorithms\u002Fgraphs\u002Fbipartite-matching":2358,"\u002Falgorithms\u002Fgreedy\u002Fthe-greedy-method":2362,"\u002Falgorithms\u002Fgreedy\u002Fscheduling-and-intervals":2367,"\u002Falgorithms\u002Fgreedy\u002Fhuffman-codes":2371,"\u002Falgorithms\u002Fgreedy\u002Fmatroids":2375,"\u002Falgorithms\u002Fgreedy\u002Fstable-matching":2379,"\u002Falgorithms\u002Fdynamic-programming\u002Fprinciples":2383,"\u002Falgorithms\u002Fdynamic-programming\u002Fsequence-dp":2388,"\u002Falgorithms\u002Fdynamic-programming\u002Flongest-increasing-subsequence":2392,"\u002Falgorithms\u002Fdynamic-programming\u002Fknapsack":2396,"\u002Falgorithms\u002Fdynamic-programming\u002Fcoin-change-and-unbounded":2400,"\u002Falgorithms\u002Fdynamic-programming\u002Finterval-dp":2404,"\u002Falgorithms\u002Fdynamic-programming\u002Ftree-dp":2408,"\u002Falgorithms\u002Fdynamic-programming\u002Fbitmask-dp":2412,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-optimizations":2416,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-on-graphs":2420,"\u002Falgorithms\u002Fdynamic-programming\u002Fdigit-and-probability-dp":2424,"\u002Falgorithms\u002Fbacktracking\u002Fbacktracking-fundamentals":2428,"\u002Falgorithms\u002Fbacktracking\u002Fconstraint-search":2433,"\u002Falgorithms\u002Fbacktracking\u002Fbranch-and-bound":2437,"\u002Falgorithms\u002Fbacktracking\u002Fgraph-backtracking":2441,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fnumber-theory-basics":2445,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmodular-exponentiation-and-primality":2450,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fsieve-and-factorization":2454,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fcombinatorics":2458,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmatrix-exponentiation":2462,"\u002Falgorithms\u002Fmathematical-algorithms\u002Ffast-fourier-transform":2466,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fgradient-descent":2470,"\u002Falgorithms\u002Fcomputational-geometry\u002Fgeometric-primitives":2474,"\u002Falgorithms\u002Fcomputational-geometry\u002Fconvex-hull":2479,"\u002Falgorithms\u002Fcomputational-geometry\u002Fsweep-line":2483,"\u002Falgorithms\u002Fcomputational-geometry\u002Fpolygons-and-proximity":2487,"\u002Falgorithms\u002Fintractability\u002Fp-np-reductions":2491,"\u002Falgorithms\u002Fintractability\u002Fnp-completeness":2496,"\u002Falgorithms\u002Fintractability\u002Fcoping-with-hardness":2500,"\u002Falgorithms\u002Fintractability\u002Fapproximation-algorithms":2504,"\u002Falgorithms":2508,"\u002Fcalculus\u002Flimits-and-continuity\u002Ffunctions-and-models":2511,"\u002Fcalculus\u002Flimits-and-continuity\u002Fthe-limit-of-a-function":2516,"\u002Fcalculus\u002Flimits-and-continuity\u002Flimit-laws-and-the-precise-definition":2520,"\u002Fcalculus\u002Flimits-and-continuity\u002Fcontinuity":2524,"\u002Fcalculus\u002Fderivatives\u002Fthe-derivative-and-rates-of-change":2528,"\u002Fcalculus\u002Fderivatives\u002Fdifferentiation-rules-and-the-chain-rule":2533,"\u002Fcalculus\u002Fderivatives\u002Fimplicit-differentiation-and-related-rates":2537,"\u002Fcalculus\u002Fderivatives\u002Flinear-approximations-and-differentials":2541,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fextrema-and-the-mean-value-theorem":2545,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fhow-derivatives-shape-a-graph":2550,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fcurve-sketching-and-optimization":2554,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fnewtons-method-and-antiderivatives":2558,"\u002Fcalculus\u002Fintegrals\u002Farea-and-the-definite-integral":2562,"\u002Fcalculus\u002Fintegrals\u002Fthe-fundamental-theorem-of-calculus":2567,"\u002Fcalculus\u002Fintegrals\u002Fthe-substitution-rule":2571,"\u002Fcalculus\u002Fapplications-of-integration\u002Fareas-and-volumes":2575,"\u002Fcalculus\u002Fapplications-of-integration\u002Fwork-average-value-and-arc-length":2580,"\u002Fcalculus\u002Fapplications-of-integration\u002Fphysics-economics-and-probability":2584,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Finverse-functions-logarithms-and-exponentials":2588,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Fgrowth-decay-inverse-trig-and-hyperbolic-functions":2593,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Flhospitals-rule":2597,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fintegration-by-parts":2601,"\u002Fcalculus\u002Ftechniques-of-integration\u002Ftrigonometric-integrals-and-substitution":2606,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fpartial-fractions-and-integration-strategy":2610,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fapproximate-and-improper-integrals":2614,"\u002Fcalculus\u002Fparametric-and-polar\u002Fparametric-curves-and-their-calculus":2618,"\u002Fcalculus\u002Fparametric-and-polar\u002Fpolar-coordinates":2623,"\u002Fcalculus\u002Fparametric-and-polar\u002Fconic-sections":2627,"\u002Fcalculus\u002Fsequences-and-series\u002Fsequences":2631,"\u002Fcalculus\u002Fsequences-and-series\u002Fseries-and-the-integral-test":2636,"\u002Fcalculus\u002Fsequences-and-series\u002Fthe-convergence-tests":2640,"\u002Fcalculus\u002Fsequences-and-series\u002Fpower-series":2644,"\u002Fcalculus\u002Fsequences-and-series\u002Ftaylor-and-maclaurin-series":2648,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvectors-and-the-dot-product":2652,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fthe-cross-product-lines-and-planes":2657,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fcylinders-and-quadric-surfaces":2661,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvector-functions-and-space-curves":2665,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Farc-length-curvature-and-motion":2669,"\u002Fcalculus\u002Fpartial-derivatives\u002Ffunctions-of-several-variables":2673,"\u002Fcalculus\u002Fpartial-derivatives\u002Fpartial-derivatives":2678,"\u002Fcalculus\u002Fpartial-derivatives\u002Ftangent-planes-and-the-chain-rule":2681,"\u002Fcalculus\u002Fpartial-derivatives\u002Fdirectional-derivatives-and-the-gradient":2685,"\u002Fcalculus\u002Fpartial-derivatives\u002Foptimization-and-lagrange-multipliers":2689,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fdouble-integrals":2693,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Ftriple-integrals-and-coordinate-systems":2698,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fvector-fields-and-line-integrals":2702,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fgreens-theorem-curl-and-divergence":2706,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fsurface-integrals":2710,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fstokes-and-the-divergence-theorem":2714,"\u002Fcalculus":2718,"\u002Fmechanics\u002Ffoundations\u002Fmeasurement-and-dimensions":2721,"\u002Fmechanics\u002Ffoundations\u002Fvector-algebra":2725,"\u002Fmechanics\u002Fkinematics\u002Fone-dimensional-motion":2729,"\u002Fmechanics\u002Fkinematics\u002Fmotion-graphs":2734,"\u002Fmechanics\u002Fkinematics\u002Fprojectile-motion":2738,"\u002Fmechanics\u002Fkinematics\u002Frelative-motion":2742,"\u002Fmechanics\u002Fkinematics\u002Fcircular-motion":2746,"\u002Fmechanics\u002Fdynamics\u002Fnewtons-laws":2750,"\u002Fmechanics\u002Fdynamics\u002Ffree-body-diagrams":2755,"\u002Fmechanics\u002Fdynamics\u002Ffriction-and-curved-motion":2759,"\u002Fmechanics\u002Fdynamics\u002Fnumerical-dynamics":2763,"\u002Fmechanics\u002Fdynamics\u002Fcenter-of-mass-systems":2767,"\u002Fmechanics\u002Fenergy\u002Fwork-and-kinetic-energy":2771,"\u002Fmechanics\u002Fenergy\u002Fpotential-energy":2776,"\u002Fmechanics\u002Fenergy\u002Fmultiparticle-work":2780,"\u002Fmechanics\u002Fenergy\u002Fmass-energy-and-binding":2784,"\u002Fmechanics\u002Fenergy\u002Fphotons-and-quantization":2788,"\u002Fmechanics\u002Fmomentum\u002Fmomentum-and-collisions":2792,"\u002Fmechanics\u002Fmomentum\u002Fcenter-of-mass-collisions":2797,"\u002Fmechanics\u002Fmomentum\u002Frocket-propulsion":2801,"\u002Fmechanics\u002Frotation\u002Frotational-inertia":2805,"\u002Fmechanics\u002Frotation\u002Frotational-dynamics":2810,"\u002Fmechanics\u002Frotation\u002Frolling-motion":2814,"\u002Fmechanics\u002Frotation\u002Fangular-momentum":2818,"\u002Fmechanics\u002Frotation\u002Frolling-resistance":2822,"\u002Fmechanics\u002Frotation\u002Fgyroscopic-precession":2826,"\u002Fmechanics\u002Fgravity-and-matter\u002Fkeplerian-orbits":2830,"\u002Fmechanics\u002Fgravity-and-matter\u002Fgravitational-fields":2835,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstatic-equilibrium":2839,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-statics":2843,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-flow":2847,"\u002Fmechanics\u002Fgravity-and-matter\u002Forbital-motion":2851,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstress-and-elasticity":2855,"\u002Fmechanics\u002Foscillations-waves\u002Fdamped-oscillators":2859,"\u002Fmechanics\u002Foscillations-waves\u002Ftravelling-waves":2864,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-superposition":2868,"\u002Fmechanics\u002Foscillations-waves\u002Fstanding-waves":2872,"\u002Fmechanics\u002Foscillations-waves\u002Fsound-waves":2876,"\u002Fmechanics\u002Foscillations-waves\u002Fdoppler-effect":2880,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-packets":2884,"\u002Fmechanics\u002Foscillations-waves\u002Fbeats-and-coupling":2888,"\u002Fmechanics\u002Foscillations-waves\u002Fsimple-harmonic-motion":2892,"\u002Fmechanics\u002Foscillations-waves\u002Fpendulum-motion":2896,"\u002Fmechanics\u002Foscillations-waves\u002Fdriven-oscillators":2900,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-boundaries":2904,"\u002Fmechanics\u002Fthermodynamics\u002Fkinetic-theory-of-ideal-gases":2908,"\u002Fmechanics\u002Fthermodynamics\u002Ffirst-law-of-thermodynamics":2913,"\u002Fmechanics\u002Fthermodynamics\u002Fentropy-and-the-second-law":2917,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-processes":2921,"\u002Fmechanics\u002Fthermodynamics\u002Fphase-changes":2925,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-machines":2929,"\u002Fmechanics":2933,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcharge-and-conductors":2936,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcoulombs-law":2941,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-and-force":2945,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-maps":2949,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-dipoles":2953,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fcontinuous-charge-fields":2957,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fgauss-law-and-conductors":2962,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpoint-charge-potential":2966,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpotential-gradients-and-equipotentials":2971,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Felectrostatic-energy-and-pressure":2975,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Flaplace-boundary-problems":2979,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fcontinuous-charge-potentials":2983,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitance-fundamentals":2987,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-networks":2992,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-energy-and-force":2996,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fdielectric-polarization-and-breakdown":3000,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fcurrent-and-resistance":3004,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fkirchhoff-network-analysis":3009,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Frc-transients":3013,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-trajectories":3017,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fhall-effect":3022,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-force-on-conductors":3026,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-dipoles":3030,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmass-spectrometry":3034,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmoving-charge-fields":3038,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fbiot-savart-law":3043,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fcircular-current-loops":3047,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Famperes-law":3051,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fgauss-law-for-magnetism":3055,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmagnetic-materials":3059,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-flux":3063,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Ffaradays-law":3068,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Flenzs-law":3072,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmotional-emf":3076,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Feddy-currents":3080,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fself-inductance":3084,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-energy":3088,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Frl-circuits":3092,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-fundamentals":3096,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Freactance":3101,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Frlc-resonance":3105,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-power":3109,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Ftransformers":3113,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdisplacement-current":3117,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-waves":3122,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-momentum":3126,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdipole-radiation":3130,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fpolarization":3134,"\u002Felectricity-and-magnetism\u002Foptics\u002Freflection-and-refraction":3138,"\u002Felectricity-and-magnetism\u002Foptics\u002Fthin-lenses":3143,"\u002Felectricity-and-magnetism\u002Foptics\u002Fspherical-mirrors":3147,"\u002Felectricity-and-magnetism":3151,"\u002Flinear-algebra\u002Flinear-systems\u002Fsystems-and-echelon-forms":3154,"\u002Flinear-algebra\u002Flinear-systems\u002Fvector-and-matrix-equations":3159,"\u002Flinear-algebra\u002Flinear-systems\u002Fsolution-sets-and-applications":3163,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-independence":3167,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-transformations":3171,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-operations":3175,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-inverse-and-invertibility":3180,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fpartitioned-matrices-and-lu":3184,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fsubspaces-dimension-rank":3188,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fapplications-leontief-and-graphics":3192,"\u002Flinear-algebra\u002Fdeterminants\u002Fdeterminants-and-cofactors":3196,"\u002Flinear-algebra\u002Fdeterminants\u002Fproperties-of-determinants":3201,"\u002Flinear-algebra\u002Fdeterminants\u002Fcramer-volume-and-area":3205,"\u002Flinear-algebra\u002Fvector-spaces\u002Fvector-spaces-and-subspaces":3209,"\u002Flinear-algebra\u002Fvector-spaces\u002Fnull-and-column-spaces":3214,"\u002Flinear-algebra\u002Fvector-spaces\u002Fbases-and-independent-sets":3218,"\u002Flinear-algebra\u002Fvector-spaces\u002Fcoordinate-systems":3222,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdimension-and-rank":3226,"\u002Flinear-algebra\u002Fvector-spaces\u002Fchange-of-basis":3230,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdifference-equations-and-markov":3234,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-eigenvalues":3238,"\u002Flinear-algebra\u002Feigenvalues\u002Fthe-characteristic-equation":3243,"\u002Flinear-algebra\u002Feigenvalues\u002Fdiagonalization":3247,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-linear-transformations":3251,"\u002Flinear-algebra\u002Feigenvalues\u002Fcomplex-eigenvalues":3255,"\u002Flinear-algebra\u002Feigenvalues\u002Fdynamical-systems":3259,"\u002Flinear-algebra\u002Feigenvalues\u002Fpower-method":3263,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-length-orthogonality":3267,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Forthogonal-sets-and-projections":3272,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fgram-schmidt-and-qr":3276,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-problems":3280,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-applications":3284,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-spaces":3288,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fdiagonalizing-symmetric-matrices":3292,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fquadratic-forms":3297,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fconstrained-optimization":3301,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsingular-value-decomposition":3305,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsvd-applications-pca-imaging":3309,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-thinking-and-matrix-computation":3313,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Flu-and-cholesky":3318,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fconditioning-and-floating-point":3322,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fstability-and-error-analysis":3326,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fqr-and-numerical-least-squares":3330,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-eigenvalues-and-svd":3334,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-combinations":3338,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-independence-and-barycentric-coordinates":3343,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fconvex-combinations-and-convex-sets":3347,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fhyperplanes-and-polytopes":3351,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fcurves-and-surfaces":3355,"\u002Flinear-algebra":3359,"\u002Ftheory-of-computation":3362,"\u002Fcomputer-architecture\u002Ffoundations\u002Fbits-bytes-and-words":3365,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-representation":3369,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-arithmetic":3373,"\u002Fcomputer-architecture\u002Ffoundations\u002Ffloating-point":3377,"\u002Fcomputer-architecture\u002Ffoundations\u002Fboolean-algebra-and-bit-manipulation":3381,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fthe-machines-view":3385,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fdata-movement":3390,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farithmetic-and-logic":3394,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fcontrol-flow":3398,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fprocedures":3402,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farrays-structs-and-alignment":3406,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fmemory-layout-and-buffer-overflows":3410,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fwhat-an-isa-is":3414,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Finstruction-formats-and-operands":3419,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Faddressing-modes":3423,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fthe-y86-64-instruction-set":3427,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fy86-64-programming":3431,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Ftransistors-gates-and-boolean-functions":3435,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fcombinational-logic-and-hcl":3440,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmultiplexers-decoders-and-the-alu":3444,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmemory-elements-latches-flip-flops-and-clocking":3448,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fregister-files-and-random-access-memory":3452,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-fetch-decode-execute-cycle":3456,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-seq-stages":3461,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fcontrol-logic-and-sequencing":3465,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fassembling-seq":3469,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Ftracing-a-program":3473,"\u002Fcomputer-architecture\u002Fpipelining\u002Fpipelining-principles":3477,"\u002Fcomputer-architecture\u002Fpipelining\u002Ffrom-seq-to-pipe":3482,"\u002Fcomputer-architecture\u002Fpipelining\u002Fdata-hazards-stalling-and-forwarding":3486,"\u002Fcomputer-architecture\u002Fpipelining\u002Fcontrol-hazards-and-branch-prediction":3490,"\u002Fcomputer-architecture\u002Fpipelining\u002Fthe-complete-pipe-processor":3494,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fstorage-technologies-and-the-latency-gap":3498,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Flocality":3503,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-memories-direct-mapped":3507,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fset-associative-and-write-policies":3511,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-performance-and-cache-friendly-code":3515,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Faddress-spaces-and-translation":3519,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fpage-tables-and-page-faults":3524,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fthe-tlb-and-multi-level-page-tables":3528,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Fexceptional-control-flow":3532,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Finterrupts-and-the-kernel":3537,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fprocesses-threads-and-parallelism":3541,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fhardware-multithreading":3546,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fcache-coherence":3550,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmemory-consistency-and-synchronization":3554,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmulticore-organization":3558,"\u002Fcomputer-architecture\u002Fcapstone\u002Fthe-whole-machine":3562,"\u002Fcomputer-architecture\u002Fcapstone\u002Fassembling-a-complete-cpu":3567,"\u002Fcomputer-architecture":3571,"\u002Fdifferential-equations\u002Ffoundations\u002Fmodels-and-direction-fields":3574,"\u002Fdifferential-equations\u002Ffoundations\u002Fclassification-and-terminology":3578,"\u002Fdifferential-equations\u002Ffirst-order\u002Flinear-first-order-integrating-factors":3582,"\u002Fdifferential-equations\u002Ffirst-order\u002Fseparable-and-exact":3587,"\u002Fdifferential-equations\u002Ffirst-order\u002Fmodeling-first-order":3591,"\u002Fdifferential-equations\u002Ffirst-order\u002Fautonomous-and-population-dynamics":3595,"\u002Fdifferential-equations\u002Ffirst-order\u002Fexistence-uniqueness-euler":3599,"\u002Fdifferential-equations\u002Ffirst-order\u002Ffirst-order-difference-equations":3603,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhomogeneous-constant-coefficients":3607,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fcomplex-and-repeated-roots":3612,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fnonhomogeneous-undetermined-coefficients":3616,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fvariation-of-parameters":3620,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fmechanical-electrical-vibrations":3624,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhigher-order-linear":3628,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fpower-series-ordinary-points":3632,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fregular-singular-frobenius":3637,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fbessel-and-special-functions":3641,"\u002Fdifferential-equations\u002Flaplace\u002Flaplace-definition-ivps":3645,"\u002Fdifferential-equations\u002Flaplace\u002Fstep-impulse-convolution":3650,"\u002Fdifferential-equations\u002Fsystems\u002Fmatrices-eigenvalues-review":3654,"\u002Fdifferential-equations\u002Fsystems\u002Fconstant-coefficient-systems-phase-portraits":3659,"\u002Fdifferential-equations\u002Fsystems\u002Frepeated-eigenvalues-fundamental-matrices":3663,"\u002Fdifferential-equations\u002Fnumerical\u002Feuler-and-runge-kutta":3667,"\u002Fdifferential-equations\u002Fnumerical\u002Fmultistep-systems-stability":3672,"\u002Fdifferential-equations\u002Fnonlinear\u002Fphase-plane-autonomous-stability":3676,"\u002Fdifferential-equations\u002Fnonlinear\u002Flocally-linear-and-liapunov":3681,"\u002Fdifferential-equations\u002Fnonlinear\u002Fcompeting-species-predator-prey-limit-cycles":3685,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Ffourier-series":3689,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fheat-wave-laplace-equations":3694,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fsturm-liouville":3698,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fcalculus-of-variations":3702,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fhistorical-notes":3707,"\u002Fdifferential-equations":3711,"\u002Frelativity\u002Ffoundations\u002Fspecial-relativity-postulates":3714,"\u002Frelativity\u002Ffoundations\u002Florentz-transformation-spacetime":3719,"\u002Frelativity\u002Ffoundations\u002Ftime-dilation-length-contraction":3723,"\u002Frelativity\u002Ffoundations\u002Frelativistic-momentum-energy":3727,"\u002Frelativity\u002Ffoundations\u002Fgeneral-relativity":3731,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fminkowski-spacetime-and-the-interval":3735,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Ffour-vectors-and-index-notation":3740,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fthe-lorentz-group-and-rapidity":3744,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fdoppler-aberration-and-appearance":3748,"\u002Frelativity\u002Frelativistic-dynamics\u002Ffour-momentum-force-and-accelerated-motion":3752,"\u002Frelativity\u002Frelativistic-dynamics\u002Fparticle-decays-and-two-body-kinematics":3757,"\u002Frelativity\u002Frelativistic-dynamics\u002Fcollisions-thresholds-and-the-cm-frame":3761,"\u002Frelativity\u002Frelativistic-dynamics\u002Fmandelstam-variables-and-invariants":3765,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ffour-current-and-the-four-potential":3769,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fthe-electromagnetic-field-tensor":3774,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ftransformation-of-electric-and-magnetic-fields":3778,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fcovariant-maxwell-and-the-stress-energy-tensor":3782,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-equivalence-principle-formalized":3786,"\u002Frelativity\u002Fcurved-spacetime\u002Fmanifolds-vectors-and-the-metric":3791,"\u002Frelativity\u002Fcurved-spacetime\u002Fcovariant-derivative-and-christoffel-symbols":3795,"\u002Frelativity\u002Fcurved-spacetime\u002Fgeodesics-and-the-geodesic-equation":3799,"\u002Frelativity\u002Fcurved-spacetime\u002Fcurvature-riemann-and-geodesic-deviation":3803,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-einstein-field-equations":3807,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fthe-schwarzschild-metric":3811,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fgeodesics-and-orbits-in-schwarzschild":3816,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Flight-bending-and-null-geodesics":3820,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fperihelion-precession-of-mercury":3824,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fdeflection-of-light-and-gravitational-lensing":3829,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fgravitational-redshift-and-shapiro-delay":3833,"\u002Frelativity\u002Ftests-of-general-relativity\u002Frelativity-in-technology-gps":3837,"\u002Frelativity\u002Fblack-holes\u002Fhorizons-and-coordinate-singularities":3841,"\u002Frelativity\u002Fblack-holes\u002Frotating-and-charged-black-holes":3846,"\u002Frelativity\u002Fblack-holes\u002Fblack-hole-thermodynamics":3850,"\u002Frelativity\u002Fgravitational-waves\u002Flinearized-gravity-and-wave-solutions":3854,"\u002Frelativity\u002Fgravitational-waves\u002Fgeneration-and-the-quadrupole-formula":3859,"\u002Frelativity\u002Fgravitational-waves\u002Fdetection-ligo-and-the-first-events":3863,"\u002Frelativity\u002Fcosmological-bridge\u002Fthe-cosmological-principle-and-flrw-metric":3867,"\u002Frelativity\u002Fcosmological-bridge\u002Ffriedmann-equations-and-cosmic-dynamics":3872,"\u002Frelativity":3876,"\u002Fphysical-computing":3879,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fblackbody-radiation-and-the-planck-quantum":3882,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-photoelectric-effect-and-the-photon":3887,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fx-rays-and-the-compton-effect":3891,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-old-quantum-theory-bohr-and-sommerfeld":3895,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fde-broglie-waves-and-electron-diffraction":3899,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fwave-packets-and-the-probability-interpretation":3904,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fthe-uncertainty-principle":3908,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-schrodinger-equation-in-one-dimension":3912,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-free-particle-and-wave-packet-dynamics":3917,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fparticle-in-infinite-and-finite-square-wells":3921,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Foperators-expectation-values-and-the-harmonic-oscillator":3925,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-dirac-delta-potential":3929,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fbarrier-penetration-and-quantum-tunneling":3933,"\u002Fquantum-mechanics\u002Fformalism\u002Fhilbert-space-and-dirac-notation":3937,"\u002Fquantum-mechanics\u002Fformalism\u002Fobservables-hermitian-operators-and-eigenvalues":3942,"\u002Fquantum-mechanics\u002Fformalism\u002Fthe-postulates-and-quantum-measurement":3946,"\u002Fquantum-mechanics\u002Fformalism\u002Fposition-momentum-and-continuous-spectra":3950,"\u002Fquantum-mechanics\u002Fformalism\u002Fcommutators-and-the-generalized-uncertainty-principle":3954,"\u002Fquantum-mechanics\u002Fformalism\u002Ftime-evolution-schrodinger-and-heisenberg-pictures":3958,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fladder-operators-and-the-number-states":3962,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fcoherent-and-squeezed-states":3967,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fsymmetries-generators-and-conservation-laws":3971,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fparity-time-reversal-and-discrete-symmetries":3975,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Forbital-angular-momentum-and-spherical-harmonics":3979,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Fthe-angular-momentum-algebra":3983,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Faddition-of-angular-momenta-and-clebsch-gordan":3987,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-schrodinger-equation-in-three-dimensions":3991,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-hydrogen-atom":3996,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-isotropic-oscillator-and-hidden-symmetry":4000,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-half-pauli-matrices-and-stern-gerlach":4004,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-in-a-magnetic-field-precession-and-resonance":4009,"\u002Fquantum-mechanics\u002Fspin\u002Ftwo-level-systems-and-the-bloch-sphere":4013,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fidentical-particles-and-exchange-symmetry":4017,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fthe-pauli-principle-atoms-and-the-periodic-table":4022,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ftime-independent-perturbation-theory":4026,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ffine-structure-and-the-real-hydrogen-atom":4031,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-zeeman-and-stark-effects":4035,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-variational-method":4039,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-wkb-approximation":4043,"\u002Fquantum-mechanics":4047,"\u002Freal-analysis\u002Ffoundations\u002Fsets-logic-functions":4050,"\u002Freal-analysis\u002Ffoundations\u002Fordered-fields-completeness":4055,"\u002Freal-analysis\u002Ffoundations\u002Fabsolute-value-bounds":4059,"\u002Freal-analysis\u002Ffoundations\u002Fintervals-uncountability":4063,"\u002Freal-analysis\u002Fsequences-series\u002Fsequences-limits":4067,"\u002Freal-analysis\u002Fsequences-series\u002Flimit-laws-monotone":4072,"\u002Freal-analysis\u002Fsequences-series\u002Flimsup-bolzano-weierstrass":4076,"\u002Freal-analysis\u002Fsequences-series\u002Fcauchy-completeness":4080,"\u002Freal-analysis\u002Fsequences-series\u002Fseries-convergence":4084,"\u002Freal-analysis\u002Fsequences-series\u002Fabsolute-conditional-rearrangement":4088,"\u002Freal-analysis\u002Fmetric-spaces\u002Fmetric-spaces-norms":4092,"\u002Freal-analysis\u002Fmetric-spaces\u002Fopen-closed-sets":4097,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconvergence-completeness":4101,"\u002Freal-analysis\u002Fmetric-spaces\u002Fcompactness":4105,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconnectedness":4109,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-of-functions":4113,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuous-functions":4117,"\u002Freal-analysis\u002Fcontinuity\u002Fevt-ivt":4121,"\u002Freal-analysis\u002Fcontinuity\u002Funiform-continuity":4125,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuity-metric-spaces":4129,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-infinity-monotone":4133,"\u002Freal-analysis\u002Fdifferentiation\u002Fthe-derivative":4137,"\u002Freal-analysis\u002Fdifferentiation\u002Fmean-value-theorem":4142,"\u002Freal-analysis\u002Fdifferentiation\u002Ftaylors-theorem":4146,"\u002Freal-analysis\u002Fdifferentiation\u002Finverse-function-1d":4150,"\u002Freal-analysis\u002Friemann-integration\u002Fdarboux-integral":4154,"\u002Freal-analysis\u002Friemann-integration\u002Fintegrability-classes":4159,"\u002Freal-analysis\u002Friemann-integration\u002Fproperties-of-the-integral":4163,"\u002Freal-analysis\u002Friemann-integration\u002Ffundamental-theorem":4167,"\u002Freal-analysis\u002Friemann-integration\u002Flog-exp-improper":4170,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpointwise-uniform-convergence":4174,"\u002Freal-analysis\u002Ffunction-sequences\u002Finterchange-of-limits":4179,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpower-series-weierstrass":4183,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpicard-ode":4187,"\u002Freal-analysis\u002Fseveral-variables\u002Fdifferentiability-rn":4191,"\u002Freal-analysis\u002Fseveral-variables\u002Fgradient-chain-rule":4196,"\u002Freal-analysis\u002Fseveral-variables\u002Fhigher-derivatives-taylor-extrema":4200,"\u002Freal-analysis\u002Fseveral-variables\u002Finverse-implicit-theorems":4204,"\u002Freal-analysis\u002Fseveral-variables\u002Fmultiple-integrals":4208,"\u002Freal-analysis":4212,"\u002Fabstract-algebra\u002Ffoundations\u002Fsets-functions-relations":4215,"\u002Fabstract-algebra\u002Ffoundations\u002Fintegers-and-modular-arithmetic":4219,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fgroup-axioms-and-first-examples":4223,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fdihedral-and-symmetric-groups":4228,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fmatrix-and-quaternion-groups":4232,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fhomomorphisms-and-group-actions":4236,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fsubgroups-and-substructures":4240,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcyclic-groups":4245,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fgeneration-and-subgroup-lattices":4249,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcosets-lagrange-and-normal-subgroups":4253,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fisomorphism-theorems":4257,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcomposition-series-and-the-alternating-group":4261,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Factions-and-cayleys-theorem":4265,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fconjugation-and-the-class-equation":4270,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fsylow-theorems":4274,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fautomorphisms-and-simple-groups":4278,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fdirect-products-and-finite-abelian-groups":4282,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fsemidirect-products":4287,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fnilpotent-and-solvable-groups":4291,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fclassifying-small-groups":4295,"\u002Fabstract-algebra\u002Fring-theory\u002Frings-definitions-and-examples":4299,"\u002Fabstract-algebra\u002Fring-theory\u002Fideals-quotients-and-homomorphisms":4304,"\u002Fabstract-algebra\u002Fring-theory\u002Ffractions-and-the-chinese-remainder-theorem":4308,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Feuclidean-domains-pids-ufds":4312,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fpolynomial-rings-over-fields":4317,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fgauss-lemma-and-unique-factorization":4321,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Firreducibility-criteria-and-groebner":4325,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fintroduction-to-modules":4329,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ffree-modules-and-direct-sums":4334,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ftensor-products-and-exact-sequences":4338,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fvector-spaces-and-linear-maps":4342,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fstructure-theorem-over-pids":4346,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Frational-canonical-form":4351,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fjordan-canonical-form":4355,"\u002Fabstract-algebra\u002Ffield-theory\u002Ffield-extensions-and-algebraic-elements":4359,"\u002Fabstract-algebra\u002Ffield-theory\u002Fstraightedge-and-compass-constructions":4364,"\u002Fabstract-algebra\u002Ffield-theory\u002Fsplitting-fields-and-algebraic-closure":4368,"\u002Fabstract-algebra\u002Ffield-theory\u002Fseparable-and-cyclotomic-extensions":4372,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fthe-galois-correspondence":4376,"\u002Fabstract-algebra\u002Fgalois-theory\u002Ffinite-fields":4381,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fcyclotomic-and-abelian-extensions":4385,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fgalois-groups-of-polynomials":4389,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fsolvability-by-radicals-and-the-quintic":4393,"\u002Fabstract-algebra\u002Fcapstone\u002Fcommutative-algebra-and-algebraic-geometry":4397,"\u002Fabstract-algebra\u002Fcapstone\u002Frepresentation-and-character-theory":4402,"\u002Fabstract-algebra":4406,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fatomic-spectra-rutherford":4409,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-model-hydrogen":4414,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fx-ray-spectra-franck-hertz":4418,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-sommerfeld-old-quantum-theory":4422,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fold-quantum-theory-limits-wkb":4426,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fschrodinger-3d-hydrogen":4430,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fhydrogen-wave-functions":4435,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fradial-equation-in-full":4439,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fsymmetry-degeneracy-runge-lenz":4443,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fexpectation-values-virial":4447,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fquantum-defects-alkali-spectra":4451,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Frydberg-atoms":4455,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Frelativistic-kinetic-correction":4459,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fspin-orbit-thomas-precession":4464,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdarwin-term-fine-structure-formula":4468,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdirac-equation-hydrogen":4472,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Flamb-shift-qed":4476,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fhyperfine-structure-21cm":4481,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fnuclear-effects-isotope-shift":4485,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fperiodic-table-atomic-spectra":4489,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fcentral-field-self-consistent":4494,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fidentical-particles-hartree-fock":4498,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhelium-two-electron-atom":4502,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fls-jj-coupling-term-symbols":4506,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhund-rules-ground-terms":4510,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fzeeman-effect":4514,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fpaschen-back-intermediate":4519,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fstark-effect-polarizability":4523,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Ftime-dependent-perturbation-golden-rule":4527,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fdipole-approximation-einstein-coefficients":4532,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fselection-rules-forbidden-transitions":4536,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Flifetimes-and-line-shapes":4540,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Flaser-principles":4544,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fspectroscopy-techniques":4549,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fline-catalog-nist-asd":4553,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Flaser-cooling-doppler":4557,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fsub-doppler-trapping":4562,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fbose-einstein-condensation":4566,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Foptical-clocks-precision":4570,"\u002Fatomic-physics":4574,"\u002Fdatabases":4577,"\u002Fcategory-theory\u002Ffoundations\u002Fwhat-is-a-category":4580,"\u002Fcategory-theory\u002Ffoundations\u002Fexamples-of-categories":4584,"\u002Fcategory-theory\u002Ffoundations\u002Fspecial-morphisms":4588,"\u002Fcategory-theory\u002Ffoundations\u002Ffunctors":4592,"\u002Fcategory-theory\u002Ffoundations\u002Fnatural-transformations":4596,"\u002Fcategory-theory\u002Ffoundations\u002Fsize-and-set-theory":4600,"\u002Fcategory-theory\u002Funiversal-properties\u002Funiversal-properties":4604,"\u002Fcategory-theory\u002Funiversal-properties\u002Fproducts-and-coproducts":4609,"\u002Fcategory-theory\u002Funiversal-properties\u002Fconstructions-on-categories":4613,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Frepresentable-functors":4617,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-lemma":4622,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-consequences":4626,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits":4630,"\u002Fcategory-theory\u002Flimits-colimits\u002Fproducts-equalizers-pullbacks":4635,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcolimits":4639,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcomputing-limits":4643,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits-and-functors":4647,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions":4651,"\u002Fcategory-theory\u002Fadjunctions\u002Funits-and-counits":4656,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions-via-universal-arrows":4660,"\u002Fcategory-theory\u002Fadjunctions\u002Ffree-forgetful-adjunctions":4664,"\u002Fcategory-theory\u002Fadjoints-limits\u002Flimits-via-adjoints":4668,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fpresheaf-limits-colimits":4673,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoints-preserve-limits":4677,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoint-functor-theorem":4681,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fmonads":4685,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-eilenberg-moore":4690,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fkleisli-and-programming":4694,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-for-endofunctors":4698,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Fcartesian-closed-categories":4702,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Flambda-calculus-correspondence":4707,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Ffixed-points-and-recursion":4711,"\u002Fcategory-theory":4715,"\u002Fdeep-learning\u002Fmathematical-background\u002Flinear-algebra-for-deep-learning":4718,"\u002Fdeep-learning\u002Fmathematical-background\u002Fprobability-and-information-theory":4722,"\u002Fdeep-learning\u002Fmathematical-background\u002Fnumerical-computation":4726,"\u002Fdeep-learning\u002Fmathematical-background\u002Fcalculus":4730,"\u002Fdeep-learning\u002Ffoundations\u002Fwhat-is-deep-learning":4733,"\u002Fdeep-learning\u002Ffoundations\u002Fmachine-learning-refresher":4737,"\u002Fdeep-learning\u002Ffoundations\u002Flinear-models-and-the-perceptron":4741,"\u002Fdeep-learning\u002Fneural-networks\u002Fthe-multilayer-perceptron":4745,"\u002Fdeep-learning\u002Fneural-networks\u002Factivation-functions":4750,"\u002Fdeep-learning\u002Fneural-networks\u002Funiversal-approximation":4754,"\u002Fdeep-learning\u002Fneural-networks\u002Fbackpropagation":4758,"\u002Fdeep-learning\u002Fneural-networks\u002Floss-functions-and-output-units":4762,"\u002Fdeep-learning\u002Foptimization\u002Fgradient-descent-and-sgd":4766,"\u002Fdeep-learning\u002Foptimization\u002Fmomentum-and-adaptive-methods":4771,"\u002Fdeep-learning\u002Foptimization\u002Finitialization":4775,"\u002Fdeep-learning\u002Foptimization\u002Fthe-optimization-landscape":4779,"\u002Fdeep-learning\u002Foptimization\u002Fsecond-order-and-approximate-methods":4783,"\u002Fdeep-learning\u002Fregularization\u002Fregularization-overview":4787,"\u002Fdeep-learning\u002Fregularization\u002Fdropout-and-data-augmentation":4792,"\u002Fdeep-learning\u002Fregularization\u002Fearly-stopping-and-parameter-sharing":4796,"\u002Fdeep-learning\u002Fregularization\u002Fnormalization":4800,"\u002Fdeep-learning\u002Farchitectures\u002Fconvolutional-networks":4804,"\u002Fdeep-learning\u002Farchitectures\u002Fcnn-architectures":4809,"\u002Fdeep-learning\u002Farchitectures\u002Frecurrent-networks":4813,"\u002Fdeep-learning\u002Farchitectures\u002Flstm-and-gru":4817,"\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers":4821,"\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture":4825,"\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice":4829,"\u002Fdeep-learning\u002Farchitectures\u002Fgraph-neural-networks":4833,"\u002Fdeep-learning\u002Farchitectures\u002Fstate-space-models":4837,"\u002Fdeep-learning\u002Ftheory\u002Fgeneralization-theory":4841,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-robustness":4846,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-defenses":4850,"\u002Fdeep-learning\u002Ftheory\u002Fbayesian-and-ensemble-methods":4854,"\u002Fdeep-learning\u002Ftheory\u002Fdeep-equilibrium-models":4858,"\u002Fdeep-learning\u002Fgenerative-models\u002Flinear-factor-models":4862,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoencoders":4867,"\u002Fdeep-learning\u002Fgenerative-models\u002Fvariational-autoencoders":4871,"\u002Fdeep-learning\u002Fgenerative-models\u002Fgenerative-adversarial-networks":4875,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoregressive-and-normalizing-flows":4879,"\u002Fdeep-learning\u002Fgenerative-models\u002Fenergy-based-and-boltzmann-machines":4883,"\u002Fdeep-learning\u002Fgenerative-models\u002Fdiffusion-and-score-based-models":4887,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fstructured-probabilistic-models":4891,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fmonte-carlo-and-mcmc":4896,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fapproximate-inference":4900,"\u002Fdeep-learning\u002Fpractical\u002Fpractical-methodology":4904,"\u002Fdeep-learning\u002Fpractical\u002Fhyperparameters-and-debugging":4909,"\u002Fdeep-learning\u002Fpractical\u002Frepresentation-learning":4913,"\u002Fdeep-learning\u002Fpractical\u002Ftransfer-learning":4917,"\u002Fdeep-learning\u002Fpractical\u002Fapplications":4921,"\u002Fdeep-learning\u002Fpractical\u002Fmodel-compression-and-distillation":4925,"\u002Fdeep-learning\u002Fpractical\u002Fmeta-learning-and-few-shot":4929,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Flarge-language-models":4933,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fscaling-inference-and-alignment":4938,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fseq2seq-pretraining-and-bart":4942,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ftext-to-text-transfer-and-conditional-generation":4946,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fspeech-and-audio-models":4950,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fself-supervised-speech-and-synthesis":4954,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fai-agents":4958,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fagent-memory-retrieval-and-orchestration":4962,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmixture-of-experts":4966,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmultimodal-models":4970,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ffusion-and-vision-language-models":4974,"\u002Fdeep-learning\u002Freinforcement-learning\u002Ffoundations-of-reinforcement-learning":4978,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fmodel-free-prediction-and-control":4983,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fdeep-q-networks":4987,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fpolicy-gradients-and-actor-critic":4991,"\u002Fdeep-learning\u002Freinforcement-learning\u002Frl-from-human-feedback":4995,"\u002Fdeep-learning":4999,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fequilibrium-state-variables-zeroth-law":5002,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Ffirst-law-heat-and-work":5006,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fsecond-law-entropy-and-the-carnot-bound":5010,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fthermodynamic-potentials-and-maxwell-relations":5014,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fstability-response-functions-and-the-third-law":5018,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fclassical-statistics-and-equipartition":5022,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fphase-space-and-liouvilles-theorem":5027,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fensembles-and-the-equal-probability-postulate":5031,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fstatistical-entropy-boltzmann-and-gibbs":5035,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fmicrocanonical-ensemble-and-entropy":5039,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fequilibrium-conditions-temperature-pressure-chemical-potential":5044,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fideal-gas-phase-space-and-the-sackur-tetrode-entropy":5048,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Ftwo-state-systems-paramagnets-and-negative-temperature":5052,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fcanonical-ensemble-and-the-boltzmann-distribution":5056,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fpartition-function-and-the-helmholtz-free-energy":5061,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fenergy-fluctuations-and-ensemble-equivalence":5065,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fthe-einstein-solid-and-harmonic-systems":5069,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fparamagnetism-and-the-schottky-anomaly":5073,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fideal-gas-partition-function-and-the-gibbs-paradox":5077,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fequipartition-and-the-virial-theorem":5082,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fmolecular-gases-rotation-and-vibration":5086,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fgrand-canonical-ensemble-and-the-grand-partition-function":5090,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fchemical-potential-fugacity-and-number-fluctuations":5095,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fensemble-summary-and-the-thermodynamic-web":5099,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fquantum-statistics-bose-einstein-and-fermi-dirac":5103,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fderiving-the-quantum-distributions":5108,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fthe-classical-limit-and-quantum-concentration":5112,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fideal-quantum-gases-general-framework":5116,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-and-the-fermion-gas":5120,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthe-photon-gas-and-plancks-radiation-law":5125,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fblackbody-thermodynamics-and-radiation-pressure":5129,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fphonons-and-the-debye-model":5133,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-derived":5137,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthermodynamics-of-the-bose-gas-and-superfluidity":5141,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fthe-ideal-fermi-gas-at-zero-temperature":5145,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fsommerfeld-expansion-and-electrons-in-metals":5150,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":5154,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fneutron-stars-and-nuclear-matter":5158,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-cluster-expansion-and-virial-coefficients":5162,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-van-der-waals-gas-and-liquid-gas-coexistence":5167,"\u002Fstatistical-mechanics\u002Finteractions\u002Fquantum-gases-with-interactions-and-exchange":5171,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fphases-coexistence-and-classification":5175,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-ising-model-and-exact-solutions":5180,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fmean-field-theory-and-the-weiss-model":5184,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fcritical-exponents-and-landau-theory":5188,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-renormalization-group-idea":5192,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fthermodynamic-fluctuations-and-response":5196,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fbrownian-motion-and-the-langevin-equation":5201,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Flinear-response-and-the-fluctuation-dissipation-theorem":5205,"\u002Fstatistical-mechanics":5209,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fbonding-mechanisms":5212,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fmolecular-orbitals-and-h2-plus":5217,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fhydrogen-molecule-and-exchange":5221,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fvan-der-waals-forces":5225,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Frotational-vibrational-spectra":5229,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Fanharmonicity-and-rovibrational-structure":5234,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Framan-and-electronic-bands":5238,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Flasers-and-masers":5242,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fstructure-of-solids":5246,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fbravais-lattices-and-crystal-systems":5251,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Freciprocal-lattice-and-brillouin-zones":5255,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fdiffraction-and-structure-factors":5259,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonon-dispersion":5263,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonons-quantization-and-dos":5268,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fdebye-einstein-heat-capacity":5272,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fanharmonicity-and-thermal-transport":5276,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ffree-electron-gas-and-conduction":5280,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fsommerfeld-model-and-heat-capacity":5285,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ftransport-and-the-hall-effect":5289,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fscreening-and-plasmons":5293,"\u002Fcondensed-matter\u002Fband-theory\u002Fblochs-theorem-and-energy-bands":5297,"\u002Fcondensed-matter\u002Fband-theory\u002Fnearly-free-electron-model":5302,"\u002Fcondensed-matter\u002Fband-theory\u002Ftight-binding-method":5306,"\u002Fcondensed-matter\u002Fband-theory\u002Ffermi-surfaces-and-semiclassical-dynamics":5310,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fsemiconductor-bands-and-junctions":5314,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fintrinsic-and-extrinsic-semiconductors":5319,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fcarrier-transport-and-recombination":5323,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fthe-pn-junction":5327,"\u002Fcondensed-matter\u002Fsemiconductors\u002Ftransistors-and-optoelectronics":5331,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fdielectrics-and-polarization":5335,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fferroelectrics-and-piezoelectrics":5340,"\u002Fcondensed-matter\u002Fmagnetism\u002Fdiamagnetism-and-paramagnetism":5344,"\u002Fcondensed-matter\u002Fmagnetism\u002Fexchange-and-ferromagnetism":5349,"\u002Fcondensed-matter\u002Fmagnetism\u002Fantiferromagnetism-and-domains":5353,"\u002Fcondensed-matter\u002Fmagnetism\u002Fspin-waves-and-magnons":5357,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fsuperconductivity-phenomenology":5361,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Flondon-theory-and-the-meissner-effect":5366,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fginzburg-landau-theory":5370,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fbcs-theory":5374,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fjosephson-and-high-tc":5378,"\u002Fcondensed-matter\u002Fnanostructures\u002Fquantum-wells-wires-and-dots":5382,"\u002Fcondensed-matter\u002Fnanostructures\u002Finteger-quantum-hall-effect":5387,"\u002Fcondensed-matter\u002Fnanostructures\u002Ffractional-quantum-hall-and-topology":5391,"\u002Fcondensed-matter\u002Fnanostructures\u002Fgraphene-and-dirac-materials":5395,"\u002Fcondensed-matter":5399,"\u002Flogic\u002Ffoundations\u002Flogic-as-a-mathematical-model":5402,"\u002Flogic\u002Fsentential-logic\u002Fformal-languages-and-well-formed-formulas":5406,"\u002Flogic\u002Fsentential-logic\u002Ftruth-assignments-and-tautologies":5411,"\u002Flogic\u002Fsentential-logic\u002Funique-readability-and-parsing":5415,"\u002Flogic\u002Fsentential-logic\u002Finduction-and-recursion":5419,"\u002Flogic\u002Fsentential-logic\u002Fexpressive-completeness-and-normal-forms":5423,"\u002Flogic\u002Fsentential-logic\u002Fboolean-circuits":5427,"\u002Flogic\u002Fsentential-logic\u002Fcompactness-and-effectiveness":5431,"\u002Flogic\u002Ffirst-order-languages\u002Ffirst-order-languages":5435,"\u002Flogic\u002Ffirst-order-languages\u002Fstructures-truth-and-satisfaction":5440,"\u002Flogic\u002Ffirst-order-languages\u002Fdefinability-and-elementary-equivalence":5444,"\u002Flogic\u002Ffirst-order-languages\u002Fterms-substitution-and-parsing":5448,"\u002Flogic\u002Fdeductive-calculus\u002Fa-deductive-calculus":5452,"\u002Flogic\u002Fdeductive-calculus\u002Fdeduction-theorem-and-derived-rules":5457,"\u002Flogic\u002Fdeductive-calculus\u002Fsoundness":5461,"\u002Flogic\u002Fdeductive-calculus\u002Fcompleteness-and-consistency":5465,"\u002Flogic\u002Fmodels-and-theories\u002Fcompactness-and-lowenheim-skolem":5469,"\u002Flogic\u002Fmodels-and-theories\u002Ftheories-elementary-classes-and-categoricity":5474,"\u002Flogic\u002Fmodels-and-theories\u002Finterpretations-between-theories":5478,"\u002Flogic\u002Fmodels-and-theories\u002Fnonstandard-analysis":5482,"\u002Flogic\u002Farithmetic-and-definability\u002Fdefinability-in-arithmetic":5486,"\u002Flogic\u002Farithmetic-and-definability\u002Fnatural-numbers-with-successor":5491,"\u002Flogic\u002Farithmetic-and-definability\u002Fpresburger-and-reducts":5495,"\u002Flogic\u002Farithmetic-and-definability\u002Fa-subtheory-and-representability":5499,"\u002Flogic\u002Fincompleteness\u002Farithmetization-of-syntax":5503,"\u002Flogic\u002Fincompleteness\u002Fincompleteness-and-undecidability":5508,"\u002Flogic\u002Fincompleteness\u002Fsecond-incompleteness-theorem":5512,"\u002Flogic\u002Fcomputability-and-representability\u002Frecursive-functions":5516,"\u002Flogic\u002Fcomputability-and-representability\u002Frepresenting-exponentiation":5521,"\u002Flogic\u002Fsecond-order-logic\u002Fsecond-order-languages":5525,"\u002Flogic\u002Fsecond-order-logic\u002Fskolem-functions-and-many-sorted-logic":5530,"\u002Flogic\u002Fsecond-order-logic\u002Fgeneral-structures":5534,"\u002Flogic":5538,"\u002Freinforcement-learning\u002Ffoundations\u002Fwhat-is-reinforcement-learning":5541,"\u002Freinforcement-learning\u002Ffoundations\u002Fa-brief-history-of-rl":5545,"\u002Freinforcement-learning\u002Ffoundations\u002Fmulti-armed-bandits":5549,"\u002Freinforcement-learning\u002Ffoundations\u002Fbandit-exploration-algorithms":5553,"\u002Freinforcement-learning\u002Ffoundations\u002Fmarkov-decision-processes":5557,"\u002Freinforcement-learning\u002Ffoundations\u002Fvalue-functions-and-optimality":5561,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdynamic-programming":5565,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdp-async-and-gpi":5569,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-methods":5573,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-off-policy":5577,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftemporal-difference-learning":5581,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftd-control-sarsa-and-q-learning":5585,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-bootstrapping":5589,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-off-policy-methods":5593,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-and-learning":5597,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-focusing-and-decision-time":5601,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdecision-time-planning":5605,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-tree-search":5609,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-prediction":5613,"\u002Freinforcement-learning\u002Fapproximation\u002Ffeature-construction-and-nonlinear":5618,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-control":5622,"\u002Freinforcement-learning\u002Fapproximation\u002Faverage-reward-control":5626,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-and-the-deadly-triad":5630,"\u002Freinforcement-learning\u002Fapproximation\u002Fbellman-error-and-gradient-td":5634,"\u002Freinforcement-learning\u002Fapproximation\u002Feligibility-traces":5638,"\u002Freinforcement-learning\u002Fapproximation\u002Ftrue-online-and-sarsa-lambda":5642,"\u002Freinforcement-learning\u002Fapproximation\u002Fpolicy-gradient-methods":5646,"\u002Freinforcement-learning\u002Fapproximation\u002Factor-critic-and-continuous-actions":5650,"\u002Freinforcement-learning\u002Fapproximation\u002Fleast-squares-and-memory-based-methods":5654,"\u002Freinforcement-learning\u002Fapproximation\u002Fmemory-and-kernel-methods":5658,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-eligibility-traces":5662,"\u002Freinforcement-learning\u002Fapproximation\u002Fstable-off-policy-traces":5666,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdeep-q-networks":5670,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdqn-improvements":5674,"\u002Freinforcement-learning\u002Fdeep-rl\u002Factor-critic-and-ppo":5678,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fppo-and-continuous-control":5682,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fcase-studies":5686,"\u002Freinforcement-learning\u002Fdeep-rl\u002Frl-beyond-games":5690,"\u002Freinforcement-learning\u002Fdeep-rl\u002Ffrontiers":5694,"\u002Freinforcement-learning\u002Fdeep-rl\u002Freward-design-and-open-problems":5698,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow":5702,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow-part-2":5707,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control":5711,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control-part-2":5715,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl":5719,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl-part-2":5723,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration":5727,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration-part-2":5731,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl":5735,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl-part-2":5739,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl":5743,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl-part-2":5747,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl":5751,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl-part-2":5755,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl":5759,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl-part-2":5763,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Frlhf-and-language-models":5767,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps":5771,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps-part-2":5775,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl":5779,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl-part-2":5783,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmeta-rl-and-generalization":5787,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fpsychology-of-reinforcement":5791,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Finstrumental-conditioning-and-control":5796,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-and-td-error":5800,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-in-the-brain":5804,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fanimal-learning-and-cognition":5808,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fcognitive-maps-and-planning":5812,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fneuroscience-of-reinforcement":5816,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fseveral-learning-systems":5820,"\u002Freinforcement-learning":5824,"\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai":5826,"\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai":5830,"\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents":5834,"\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures":5836,"\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search":5837,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared":5841,"\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search":5845,"\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions":5849,"\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search":5853,"\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search":5857,"\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search":5861,"\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information":5865,"\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction":5869,"\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure":5872,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty":5876,"\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search":5880,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic":5884,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference":5888,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic":5892,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use":5895,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution":5899,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution":5903,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning":5907,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan":5910,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world":5914,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty":5918,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation":5922,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults":5926,"\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes":5930,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes":5935,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks":5939,"\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks":5942,"\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time":5946,"\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association":5950,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions":5954,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes":5957,"\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory":5960,"\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design":5964,"\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples":5968,"\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families":5973,"\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning":5977,"\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization":5981,"\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning":5985,"\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search":5987,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning":5991,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods":5995,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception":5999,"\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world":6004,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics":6008,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control":6012,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai":6016,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech":6020,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future":6024,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future":6028,"\u002Fartificial-intelligence":6032,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart":6035,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions":6040,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy":6044,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula":6048,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles":6052,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview":6056,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron":6061,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering":6065,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin":6069,"\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model":6073,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates":6078,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle":6082,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations":6086,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes":6090,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium":6095,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory":6099,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance":6104,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino":6108,"\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay":6113,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation":6117,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass":6121,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation":6125,"\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers":6130,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer":6134,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections":6138,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances":6143,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model":6147,"\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics":6151,"\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics":6156,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement":6160,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis":6165,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis":6169,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power":6173,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions":6178,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors":6182,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology":6186,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine":6190,"\u002Fnuclear-physics":6194,"\u002Fnatural-language-processing\u002Ffoundations\u002Fwhat-is-nlp":6197,"\u002Fnatural-language-processing\u002Ffoundations\u002Fregex-and-text-normalization":6201,"\u002Fnatural-language-processing\u002Ffoundations\u002Fminimum-edit-distance":6205,"\u002Fnatural-language-processing\u002Ffoundations\u002Fn-gram-language-models":6209,"\u002Fnatural-language-processing\u002Ffoundations\u002Fsmoothing-and-backoff":6213,"\u002Fnatural-language-processing\u002Fclassification\u002Fnaive-bayes-and-sentiment":6217,"\u002Fnatural-language-processing\u002Fclassification\u002Fevaluating-classifiers":6222,"\u002Fnatural-language-processing\u002Fclassification\u002Flogistic-regression":6226,"\u002Fnatural-language-processing\u002Fclassification\u002Fsentiment-and-affect-lexicons":6230,"\u002Fnatural-language-processing\u002Fsemantics\u002Fvector-semantics-and-embeddings":6234,"\u002Fnatural-language-processing\u002Fsemantics\u002Fstatic-word-embeddings":6239,"\u002Fnatural-language-processing\u002Fsemantics\u002Fneural-language-models":6243,"\u002Fnatural-language-processing\u002Fsequences\u002Fsequence-labeling":6247,"\u002Fnatural-language-processing\u002Fsequences\u002Fcrfs-and-neural-taggers":6251,"\u002Fnatural-language-processing\u002Fsequences\u002Frnns-and-lstms":6255,"\u002Fnatural-language-processing\u002Ftransformers\u002Ftransformers-and-attention":6259,"\u002Fnatural-language-processing\u002Ftransformers\u002Fthe-transformer-architecture":6263,"\u002Fnatural-language-processing\u002Ftransformers\u002Flarge-language-models":6266,"\u002Fnatural-language-processing\u002Ftransformers\u002Fllm-pretraining-and-scaling":6269,"\u002Fnatural-language-processing\u002Ftransformers\u002Ffine-tuning-and-prompting":6273,"\u002Fnatural-language-processing\u002Ftransformers\u002Fprompting-and-alignment":6277,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-parsing":6281,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcky-scoring-and-evaluation":6286,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdependency-parsing":6290,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fgraph-based-and-neural-dependency-parsing":6294,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fword-senses-and-wsd":6298,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fwsd-in-practice-and-induction":6302,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-roles-and-information-extraction":6306,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Frelations-events-and-templates":6310,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoreference-and-discourse":6314,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoherence-and-discourse-structure":6318,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Flogical-semantics":6322,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcompositional-semantics-and-description-logics":6326,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-parsing":6330,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fneural-semantic-parsing":6334,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Finformation-extraction":6338,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftimes-events-and-templates":6342,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdiscourse-coherence":6346,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fentity-based-and-global-coherence":6350,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-grammars":6354,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftreebanks-and-lexicalized-grammars":6358,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation":6362,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation-decoding-and-evaluation":6366,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering":6370,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering-knowledge-and-llms":6374,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-and-chatbots":6378,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-systems-and-assistants":6382,"\u002Fnatural-language-processing\u002Fapplications\u002Ftext-summarization":6386,"\u002Fnatural-language-processing\u002Fapplications\u002Fabstractive-summarization-and-evaluation":6390,"\u002Fnatural-language-processing\u002Fspeech\u002Fphonetics":6394,"\u002Fnatural-language-processing\u002Fspeech\u002Facoustic-phonetics":6399,"\u002Fnatural-language-processing\u002Fspeech\u002Fautomatic-speech-recognition":6403,"\u002Fnatural-language-processing\u002Fspeech\u002Fasr-evaluation-and-applications":6407,"\u002Fnatural-language-processing":6411,"\u002Fparticle-physics\u002Ffoundations\u002Fhistorical-overview-particle-zoo":6414,"\u002Fparticle-physics\u002Ffoundations\u002Fparticle-physics-basic-concepts":6418,"\u002Fparticle-physics\u002Ffoundations\u002Ffundamental-interactions-force-carriers":6422,"\u002Fparticle-physics\u002Funits-kinematics\u002Fnatural-units-and-scales":6426,"\u002Fparticle-physics\u002Funits-kinematics\u002Ffour-vectors-invariant-mass":6431,"\u002Fparticle-physics\u002Funits-kinematics\u002Fdecay-scattering-kinematics-mandelstam":6435,"\u002Fparticle-physics\u002Funits-kinematics\u002Fcross-sections-golden-rule":6439,"\u002Fparticle-physics\u002Fsymmetries\u002Fconservation-laws-symmetries":6443,"\u002Fparticle-physics\u002Fsymmetries\u002Fdiscrete-symmetries-cpt":6448,"\u002Fparticle-physics\u002Fsymmetries\u002Fparity-violation-weak":6452,"\u002Fparticle-physics\u002Fsymmetries\u002Fsu2-su3-flavor-symmetry":6456,"\u002Fparticle-physics\u002Fquark-model\u002Feightfold-way-su3":6460,"\u002Fparticle-physics\u002Fquark-model\u002Fmeson-spectroscopy":6465,"\u002Fparticle-physics\u002Fquark-model\u002Fbaryon-spectroscopy":6469,"\u002Fparticle-physics\u002Fquark-model\u002Fcolor-confinement-exotics":6473,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fklein-gordon-equation":6477,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fdirac-equation-spinors":6482,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fantiparticles-hole-theory":6486,"\u002Fparticle-physics\u002Fqed\u002Ffeynman-rules-qed":6490,"\u002Fparticle-physics\u002Fqed\u002Fqed-tree-processes":6495,"\u002Fparticle-physics\u002Fqed\u002Frenormalization-running-coupling":6499,"\u002Fparticle-physics\u002Fqed\u002Felectron-g-2":6503,"\u002Fparticle-physics\u002Fweak-interaction\u002Fva-structure-weak":6507,"\u002Fparticle-physics\u002Fweak-interaction\u002Fw-z-bosons-decays":6512,"\u002Fparticle-physics\u002Fweak-interaction\u002Fckm-matrix":6516,"\u002Fparticle-physics\u002Fweak-interaction\u002Fcp-violation-kaons-b-mesons":6520,"\u002Fparticle-physics\u002Fqcd\u002Fcolor-su3-gluons":6524,"\u002Fparticle-physics\u002Fqcd\u002Fasymptotic-freedom-confinement":6529,"\u002Fparticle-physics\u002Fqcd\u002Fdeep-inelastic-scattering-partons":6533,"\u002Fparticle-physics\u002Fqcd\u002Fjets-hadronization":6537,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Felectroweak-su2-u1":6541,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fspontaneous-symmetry-breaking":6546,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-mechanism":6550,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-boson-discovery":6554,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fstandard-model":6558,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-oscillations":6562,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-mass-pmns":6567,"\u002Fparticle-physics\u002Fneutrinos\u002Fdirac-majorana-experiments":6571,"\u002Fparticle-physics\u002Fexperiment\u002Faccelerators-luminosity":6575,"\u002Fparticle-physics\u002Fexperiment\u002Fdetectors-subsystems":6580,"\u002Fparticle-physics\u002Fexperiment\u002Fhow-discoveries-are-made":6584,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fbeyond-standard-model":6588,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fgrand-unified-theories":6592,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fsupersymmetry":6596,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fhierarchy-problem-naturalness":6600,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fdark-matter-candidates":6604,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fmatter-antimatter-open-questions":6608,"\u002Fparticle-physics":6612,"\u002Fastrophysics-cosmology\u002Forientation\u002Fthe-sun-and-stars":6615,"\u002Fastrophysics-cosmology\u002Forientation\u002Fstellar-death-final-states":6620,"\u002Fastrophysics-cosmology\u002Forientation\u002Fgalaxies-and-cosmology":6624,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fmagnitudes-fluxes-and-the-distance-modulus":6628,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fstellar-spectra-and-spectral-classification":6633,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Ftelescopes-and-detectors-across-the-spectrum":6637,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fthe-cosmic-distance-ladder":6641,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fblackbody-radiation-and-specific-intensity":6645,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fradiative-transfer-and-the-transfer-equation":6650,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fspectral-line-formation-and-broadening":6654,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fopacity-and-the-rosseland-mean":6658,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fhydrostatic-equilibrium-and-the-virial-theorem":6662,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equations-of-stellar-structure":6667,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equation-of-state-and-polytropes":6671,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-standard-solar-model":6675,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fthermonuclear-reaction-rates-and-the-gamow-peak":6679,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhydrogen-burning-pp-chains-and-cno":6684,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhelium-burning-and-the-triple-alpha-process":6688,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fadvanced-burning-and-neutron-capture-nucleosynthesis":6692,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fphases-of-the-interstellar-medium":6696,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fmolecular-clouds-and-gravitational-collapse":6701,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fprotostars-and-the-pre-main-sequence":6705,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-main-sequence-and-its-structure":6709,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fpost-main-sequence-low-mass-evolution":6714,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-evolution-of-massive-stars":6718,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fstellar-pulsation-and-the-instability-strip":6722,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":6726,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fcore-collapse-supernovae":6730,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fthermonuclear-supernovae-type-ia":6734,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fneutron-stars-and-pulsars":6738,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fblack-holes-schwarzschild-and-kerr":6742,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fbinary-systems-and-mass-transfer":6746,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Faccreting-compact-objects":6751,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fgravitational-waves-from-inspiraling-binaries":6755,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fmultimessenger-astronomy-and-gamma-ray-bursts":6759,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fthe-milky-way":6763,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-morphology-and-classification":6768,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-rotation-curves-and-dark-matter":6772,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Factive-galactic-nuclei-and-supermassive-black-holes":6776,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-clusters-and-large-scale-structure":6780,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-expanding-universe-and-hubbles-law":6784,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-frw-metric-and-cosmological-redshift":6789,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-friedmann-equations-and-cosmic-dynamics":6793,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fcosmological-models-and-distances":6796,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fdark-energy-and-the-accelerating-universe":6800,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fthe-thermal-history-of-the-universe":6804,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fbig-bang-nucleosynthesis":6809,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Frecombination-and-the-cosmic-microwave-background":6813,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcmb-anisotropies-and-cosmological-parameters":6817,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcosmic-inflation":6821,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fstructure-formation-and-the-growth-of-perturbations":6825,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fdark-matter-dark-energy-and-open-questions":6829,"\u002Fastrophysics-cosmology":6833,"\u002Fcolophon":6836,"\u002F":6839},{"path":2166,"title":2167,"module":1231,"summary":2168},"\u002Falgorithms\u002Ffoundations\u002Fwhat-is-an-algorithm","What Is an Algorithm?","An algorithm is a finite, mechanical recipe that transforms inputs into outputs. We define what counts as an algorithm, how we write one down, and the three things we always ask of it: is it correct, is it fast, and can we prove it.\n",{"path":2170,"title":2171,"module":1231,"summary":2172},"\u002Falgorithms\u002Ffoundations\u002Fproof-techniques","Proof Techniques","An algorithm without a proof is a conjecture. This lesson collects the handful\nof arguments that certify the algorithms in this course — direct proof,\ncontrapositive, contradiction, ordinary and strong induction, construction, and\ndisproof by counterexample — each with a small worked\nexample and a picture. Loop invariants are a form of induction,\nrecursive correctness falls to strong induction, and the classic broken proofs\n(all horses are the same color) show where inductions go wrong.\n",{"path":2174,"title":2175,"module":1231,"summary":2176},"\u002Falgorithms\u002Ffoundations\u002Fasymptotic-analysis","Asymptotic Analysis","We measure an algorithm's running time as a function of its input size, then strip away machine-specific constants and lower-order terms to compare algorithms cleanly. This lesson defines the RAM model and the $O$, $\\Omega$, $\\Theta$, $o$, and $\\omega$ notations, proves the polynomial theorem, and shows how to rank growth rates with the limit test, L'Hôpital, base substitution, and the logarithm identities the arguments lean on.\n",{"path":2178,"title":2179,"module":1231,"summary":2180},"\u002Falgorithms\u002Ffoundations\u002Fgrowth-rates-and-loop-analysis","Growth Rates and Loop Analysis","With the asymptotic notations in hand, we rank the functions that actually arise in running times — from constant to factorial — proving the orderings between rungs, then read the running time of a loop nest straight off the page. Sequential blocks add, nested loops multiply, index scaling gives logarithms; a worked trace and a tour of cache-aware and galactic algorithms close the lesson.\n",{"path":2182,"title":2183,"module":1231,"summary":2184},"\u002Falgorithms\u002Ffoundations\u002Frecurrences","Recurrences and the Master Theorem","Recursive and divide-and-conquer algorithms describe their own running time with a recurrence: $T(n)$ in terms of $T$ on smaller inputs. We solve recurrences three ways — drawing the recursion tree, guessing-and-verifying by induction, and applying the Master Theorem — using merge sort as the running example, then handle unequal splits with Akra–Bazzi.\n",{"path":2186,"title":2187,"module":1231,"summary":2188},"\u002Falgorithms\u002Ffoundations\u002Famortized-analysis","Amortized Analysis","Some operations are occasionally expensive but cheap on average across any\nsequence. Amortized analysis bounds the average cost per operation over a\nworst-case sequence — not an expectation — so a rare costly step is paid for by\nthe many cheap ones around it. This lesson develops the aggregate, accounting,\nand potential methods on dynamic-array doubling, the binary counter, and a\nstack with multipop.\n",{"path":2190,"title":2191,"module":2192,"summary":2193},"\u002Falgorithms\u002Fdivide-and-conquer\u002Fmergesort","Divide and Conquer & Mergesort","Divide & Conquer","Divide and conquer breaks a problem into smaller copies of itself, solves\nthem recursively, and stitches the answers together. We meet the paradigm\nthrough mergesort — its merge step, its loop-invariant proof, and the\nrecursion tree that pins its cost at $\\Theta(n\\log n)$ — then count inversions\nwith the same machinery and distill the whole pattern into the master theorem.\n",{"path":2195,"title":2196,"module":2192,"summary":2197},"\u002Falgorithms\u002Fdivide-and-conquer\u002Fquicksort","Quicksort","Quicksort sorts in place by partitioning around a pivot and recursing on\neach side. We give Lomuto and Hoare partitioning with a correctness\ninvariant, see why a bad pivot costs $\\Theta(n^2)$ while a balanced one gives\n$\\Theta(n\\log n)$, and prove that randomizing the pivot makes the expected\ncost $\\Theta(n\\log n)$ on every input.\n",{"path":2199,"title":2200,"module":2192,"summary":2201},"\u002Falgorithms\u002Fdivide-and-conquer\u002Fselection","Linear-Time Selection","Finding the $k$-th smallest element looks like it should require sorting, but\nit does not. Quickselect adapts quicksort's partition to recurse on just one\nside, achieving expected $O(n)$. The median-of-medians algorithm guarantees a\ngood pivot with the groups-of-five trick, pushing the worst case down to a\nprovable $O(n)$.\n",{"path":2203,"title":2204,"module":2192,"summary":2205},"\u002Falgorithms\u002Fdivide-and-conquer\u002Ffast-multiplication","Fast Multiplication","Grade-school multiplication is $\\Theta(n^2)$, yet divide and conquer beats it.\nKaratsuba multiplies $n$-bit integers with three half-size products instead of\nfour, giving $\\Theta(n^{\\log_2 3})$, and Strassen multiplies matrices with\nseven block products instead of eight, giving $\\Theta(n^{\\log_2 7})$. Both\nspend cheap additions to save an expensive multiplication, and the master\ntheorem quantifies the savings.\n",{"path":2207,"title":2208,"module":2209,"summary":2210},"\u002Falgorithms\u002Fsorting\u002Fheaps-and-heapsort","Heaps and Heapsort","Sorting & Order Statistics","A binary heap is a tree we store flat in an array, with index arithmetic\nstanding in for pointers. We build the max-heap property bottom-up in $O(n)$\ntime, sort in place in $\\Theta(n\\log n)$ by repeatedly extracting the maximum,\nand reuse the same structure to implement a priority queue.\n",{"path":2212,"title":2213,"module":2209,"summary":2214},"\u002Falgorithms\u002Fsorting\u002Fsorting-lower-bounds","Lower Bounds for Comparison Sorting","Every sort we have seen runs in $\\Omega(n\\log n)$, and that is no accident.\nModeling a sort as a decision tree of comparisons, we show any such tree must\nhave $n!$ leaves, forcing height $\\ge \\log_2(n!) = \\Omega(n\\log n)$ — a bound\nno comparison sort beats in the worst case, on average, or with randomness.\n",{"path":2216,"title":2217,"module":2209,"summary":2218},"\u002Falgorithms\u002Fsorting\u002Flinear-time-sorting","Sorting in Linear Time","The $\\Omega(n\\log n)$ barrier only binds algorithms that compare. By instead\nusing keys as array indices we slip past it: counting sort runs in\n$\\Theta(n+k)$ and is stable, radix sort layers it digit by digit, and bucket\nsort averages $\\Theta(n)$ on uniform data. We see exactly when each applies.\n",{"path":2220,"title":2221,"module":2209,"summary":2222},"\u002Falgorithms\u002Fsorting\u002Fexternal-sorting","External Sorting","When the data dwarfs main memory, the cost that matters is no longer\ncomparisons but block transfers to and from disk. External merge sort sorts\nmemory-sized runs, then folds them together with a heap-driven $k$-way merge in\n$\\Theta(\\log_k(N\u002FM))$ passes. Larger fan-out cuts passes; replacement selection\nbuilds longer runs to cut them further.\n",{"path":2224,"title":2225,"module":2226,"summary":2227},"\u002Falgorithms\u002Fdata-structures\u002Felementary-structures","Elementary Data Structures","Data Structures","Every container is built one of two ways: **contiguous** in an array, or\n**linked** through pointers. We trade cache-friendly random access against\n$O(1)$ splicing, derive the **amortized $O(1)$** append of a doubling dynamic\narray, and assemble the two ordered access disciplines — the LIFO **stack** and\nthe FIFO **queue** (with its generalization, the **deque**) — on top of both.\n",{"path":2229,"title":2230,"module":2226,"summary":2231},"\u002Falgorithms\u002Fdata-structures\u002Fhash-tables","Hash Tables","A hash table implements the dictionary — insert, search, delete — in expected\n$O(1)$ time by scattering keys across an array with a hash function. We build\nup from direct addressing, handle collisions by chaining and by open\naddressing, analyze the load factor $\\alpha$, and see how universal hashing\nachieves its expected-time guarantee against every input.\n",{"path":2233,"title":2234,"module":2226,"summary":2235},"\u002Falgorithms\u002Fdata-structures\u002Fbinary-search-trees","Binary Search Trees","A binary search tree keeps keys ordered so that every operation follows a\nsingle root-to-leaf path. We state the BST property, trace search, insert,\nsuccessor, and all three delete cases on concrete trees, prove the inorder\nwalk sorts, and note the drawback — every operation costs $O(h)$, and a\ncarelessly built tree degrades to height $h = \\Theta(n)$, motivating balance.\n",{"path":2237,"title":2238,"module":2226,"summary":2239},"\u002Falgorithms\u002Fdata-structures\u002Favl-trees","AVL Trees","An AVL tree is the first balanced BST: at every node the two subtrees' heights\ndiffer by at most $1$. A Fibonacci-style minimal-node argument forces height\n$h \\le 1.44\\log_2 n = O(\\log n)$, so search, insert, and delete are all\n$O(\\log n)$. Insertion rebalances with at most one of four rotation cases\n(LL, RR, LR, RL); deletion may rotate all the way to the root.\n",{"path":2241,"title":2242,"module":2226,"summary":2243},"\u002Falgorithms\u002Fdata-structures\u002Fbalanced-trees","Balanced Search Trees","An ordinary BST can degrade to height $\\Theta(n)$; balanced search trees\nguarantee $h = O(\\log n)$ by maintaining invariants and repairing them after\nevery update. We meet rotations, the local restructuring primitive, then\nred-black trees, whose color invariants force logarithmic height, and finally\nB-trees, which trade tall-and-thin for short-and-wide to win on disk.\n",{"path":2245,"title":2246,"module":2226,"summary":2247},"\u002Falgorithms\u002Fdata-structures\u002Funion-find","Disjoint Sets (Union-Find)","The disjoint-set data structure tracks a partition of elements into groups,\nanswering \"are these two in the same group?\" and merging groups on demand. A\nforest of parent pointers, sped up by union by rank and path compression,\ndrives every operation to near-constant $O(\\alpha(n))$ amortized time — the\nstructure behind connectivity queries and Kruskal's minimum spanning tree.\n",{"path":2249,"title":2250,"module":2226,"summary":2251},"\u002Falgorithms\u002Fdata-structures\u002Ffenwick-and-segment-trees","Fenwick & Segment Trees","A prefix-sum array answers a range sum in $O(1)$ but pays $O(n)$ per update;\na plain array updates in $O(1)$ but pays $O(n)$ per range sum. Fenwick and\nsegment trees give us _both_ in $O(\\log n)$. The Fenwick (binary indexed) tree\nis a tiny array keyed by the low bit; the segment tree is a general balanced\ntree over canonical ranges that handles any associative aggregate and, with\nlazy propagation, range updates too.\n",{"path":2253,"title":2254,"module":2226,"summary":2255},"\u002Falgorithms\u002Fdata-structures\u002Fspatial-data-structures","Spatial Data Structures","A balanced BST orders keys on a line, but points in the plane have no single\nnatural order. Quadtrees subdivide space recursively into quadrants; k-d trees\nsplit on alternating coordinates at the median. Both make range and\nnearest-neighbour queries fast by carving the plane into boxes a query can\nprune away. Range trees nest a y-tree in an x-tree for fast orthogonal range\nreporting; interval trees index intervals to answer stabbing queries.\n",{"path":2257,"title":2258,"module":2226,"summary":2259},"\u002Falgorithms\u002Fdata-structures\u002Fskip-lists-and-probabilistic-structures","Skip Lists & Probabilistic Structures","Balanced trees achieve $O(\\log n)$ with rotations and invariants; randomization\ngives the same bound far more simply. A skip list is a layered linked list whose\nexpress lanes are chosen by coin flips, giving expected $O(\\log n)$ search and\ninsert with no rebalancing. A Bloom filter trades exactness for space: a bit\narray and a few hashes answer set membership with no false negatives and a\ntunable false-positive rate, but cannot delete.\n",{"path":2261,"title":2262,"module":2226,"summary":2263},"\u002Falgorithms\u002Fdata-structures\u002Fb-trees","B-Trees","When data lives on disk, the cost that dominates is block transfers, not\ncomparisons — and a binary tree of a billion keys is thirty reads deep. A\nB-tree of minimum degree $t$ is short and wide: $t-1$ to $2t-1$ keys per node,\nall leaves at one depth, height $O(\\log_t n)$. Insertion splits a full node on\nthe way down and pushes its median up; deletion borrows or merges to keep nodes\nfull enough. High fan-out is what minimizes disk I\u002FO.\n",{"path":2265,"title":2266,"module":2226,"summary":2267},"\u002Falgorithms\u002Fdata-structures\u002Fdata-stream-algorithms","Data-Stream Algorithms","Most of this course assumes data sits in fast memory, addressable at will.\nExternal sorting relaxed that to a re-readable disk. The streaming model goes\nfurther: items arrive one at a time, are seen once, and must be discarded, with\nonly sublinear, often polylogarithmic, memory. In exchange, the answers are\napproximate and probabilistic. We set up the model, then meet reservoir\nsampling for a uniform sample of an unknown-length stream and Morris counting\nfor an approximate tally in doubly-logarithmic space.\n",{"path":2269,"title":2270,"module":2226,"summary":2271},"\u002Falgorithms\u002Fdata-structures\u002Fstreaming-sketches","Streaming Sketches","Sampling and counting kept a random subset or a single approximate tally.\nSketches go further: fixed, tiny summaries that answer questions about a\nstream's frequencies. We meet the Count–Min sketch for point frequency\nestimation, Misra–Gries for heavy hitters, and HyperLogLog for distinct\ncounts, each trading a controlled error for space that never grows with the\nstream.\n",{"path":2273,"title":2274,"module":2275,"summary":2276},"\u002Falgorithms\u002Fsequences\u002Ftwo-pointers-and-windows","Two Pointers & Sliding Windows","Sequences & Strings","A family of array idioms that collapse an obvious $O(n^2)$ scan into a single\n$O(n)$ pass by maintaining an invariant as indices move. We meet two pointers\n(converging on a sorted array, and a fast\u002Fslow pair for in-place rewriting)\nand the sliding window (fixed and variable size, amortized $O(n)$). The\ncompanion lesson on prefix sums picks up where the window's positivity\nassumption fails.\n",{"path":2278,"title":2279,"module":2275,"summary":2280},"\u002Falgorithms\u002Fsequences\u002Fprefix-sums","Prefix Sums & Difference Arrays","Prefix sums precompute the running total once so that any range-sum query is a\nsingle subtraction, $P[r{+}1]-P[l]$, in $O(1)$. A hash map of prefix\nfrequencies then counts subarrays summing to $k$ in $O(n)$ — even with negative\nentries, where the sliding window fails. The difference-array dual turns $m$\nrange-adds into $O(m+n)$, and the whole idea lifts to 2-D rectangle sums by\ninclusion–exclusion.\n",{"path":2282,"title":2283,"module":2275,"summary":2284},"\u002Falgorithms\u002Fsequences\u002Fmonotonic-stacks","Monotonic Stacks & Queues","A **monotonic stack** keeps its contents sorted by popping every element that\nwould break the order before each push — turning a family of \"previous\u002Fnext\ngreater (or smaller) element\" questions into a single $O(n)$ scan. We trace\nthe next-greater-element routine push by push and prove its amortized bound,\nfuse two such scans to measure the **largest rectangle in a histogram** in\nlinear time, extend the idea to a **monotonic deque** that streams the\n**sliding-window maximum** in $O(n)$, and use asymmetric tie-breaking to\ncount **subarray minimums** without double-counting duplicates.\n",{"path":2286,"title":2287,"module":2275,"summary":2288},"\u002Falgorithms\u002Fsequences\u002Fbinary-search-on-the-answer","Binary Search on the Answer","Binary search locates the boundary of a **monotone predicate** $p(x)$ in\n$O(\\log(\\text{range}))$ probes; sorted arrays are only one instance. We first\nestablish the half-open `while (lo \u003C hi)` template for $\\textsc{lower\\_bound}$\nand $\\textsc{upper\\_bound}$, then generalize to \"binary search on the answer\":\nwhenever feasibility is monotone in a numeric parameter, we binary search the\nparameter itself, calling a feasibility check at each step.\n",{"path":2290,"title":2291,"module":2275,"summary":2292},"\u002Falgorithms\u002Fsequences\u002Fstring-matching","String Matching: Naive & Rabin–Karp","Given a text $T$ of length $n$ and a pattern $P$ of length $m$, find every\noccurrence of $P$ in $T$. The naive scan costs $O(nm)$ and re-reads text it has\nalready seen. Rabin–Karp fixes the first inefficiency with a **rolling hash**:\neach length-$m$ window is summarized by one number, updated in $O(1)$ per slide,\nverified on a hash match to kill collisions, for expected $O(n+m)$. A companion\nlesson removes the re-reading entirely with KMP and the Z-function.\n",{"path":2294,"title":2295,"module":2275,"summary":2296},"\u002Falgorithms\u002Fsequences\u002Fkmp-and-z-function","String Matching: KMP & the Z-Function","Two linear-time matchers that beat Rabin–Karp's expected bound with a\nworst-case guarantee and no randomness. KMP precomputes a **failure function**\n$\\pi$ so a mismatch slides the pattern by $q-\\pi[q-1]$ and the text pointer\nnever backs up, for $O(n+m)$. The **Z-function** computes the longest\nprefix-match at every position via the Z-box, giving the same bound from a\ndifferent angle; the two encodings of a string's self-overlap convert freely.\n",{"path":2298,"title":2299,"module":2275,"summary":2300},"\u002Falgorithms\u002Fsequences\u002Ftries","Tries & Prefix Trees","A **trie** stores a set of strings in a tree keyed by _characters_, so that\ninsert, search, delete, and prefix-test all run in $O(L)$ time — the length\nof the key, _independent of how many keys are stored_. Shared prefixes are\nstored once, which makes tries the natural structure for autocomplete,\nwildcard dictionaries, board word-search, and — over the alphabet $\\{0,1\\}$\n— the maximum-XOR-pair problem. Radix (Patricia) trees compress the chains.\n",{"path":2302,"title":2303,"module":2275,"summary":2304},"\u002Falgorithms\u002Fsequences\u002Fsuffix-arrays-and-aho-corasick","Suffix Arrays, LCP & Aho–Corasick","A **suffix array** sorts all $n$ suffixes of a string, indexing every substring\nat once; built in $O(n\\log n)$, it locates a pattern by binary search in\n$O(m\\log n)$. Its companion **LCP array** (Kasai's $O(n)$ algorithm) counts\ndistinct substrings and finds the longest repeated substring. **Aho–Corasick**\ngeneralises KMP to a whole dictionary: a trie of patterns plus failure links\nscans the text once in $O(\\text{text} + \\text{matches})$ to report every\noccurrence of every pattern. Manacher's algorithm finds all palindromic\nsubstrings in $O(n)$.\n",{"path":2306,"title":2307,"module":2308,"summary":2309},"\u002Falgorithms\u002Fgraphs\u002Frepresentations-and-traversal","Graph Representations and Traversal","Graphs","A graph captures _relationships_ — who connects to whom. We fix the\nvocabulary, weigh the two standard representations (adjacency list versus\nmatrix), then meet the single search skeleton behind everything that follows:\nWhatever-First-Search, and its breadth-first reading, which finds shortest\npaths by number of edges in $O(V + E)$.\n",{"path":2311,"title":2312,"module":2308,"summary":2313},"\u002Falgorithms\u002Fgraphs\u002Fdepth-first-search","Depth-First Search","Swap BFS's queue for a stack and the search plunges instead of fanning out.\nDepth-first search stamps every vertex with discovery and finish times that\nnest like parentheses, classifies each edge as tree, back, forward, or cross,\nand — through the back edge — decides in one pass whether a graph has a cycle.\nThese timestamps underpin topological sort, strong\nconnectivity, and the rest of this module.\n",{"path":2315,"title":2316,"module":2308,"summary":2317},"\u002Falgorithms\u002Fgraphs\u002Ftopological-sort-and-scc","Topological Sort and Strong Connectivity","Directed acyclic graphs model dependencies: tasks that must precede other\ntasks. A _topological order_ lays such a graph out in a line so every edge\npoints forward, and depth-first finish times yield one almost for free.\nWe then ask the harder question for graphs _with_ cycles: which vertices can\nreach each other? The answer is the strongly connected components, found by a\ntwo-pass DFS.\n",{"path":2319,"title":2320,"module":2308,"summary":2321},"\u002Falgorithms\u002Fgraphs\u002Fminimum-spanning-trees","Minimum Spanning Trees","Given a weighted network, how do we connect everything as cheaply as possible?\nThe answer is a minimum spanning tree, and one lemma — the cut property —\njustifies _every_ correct MST algorithm. We prove the cut and cycle\nproperties by exchange arguments, use them to settle uniqueness, and meet the\noldest MST algorithm, Borůvka's, whose parallel component-merging rounds fall\nstraight out of the cut rule.\n",{"path":2323,"title":2324,"module":2308,"summary":2325},"\u002Falgorithms\u002Fgraphs\u002Fkruskal-and-prim","Kruskal and Prim","The two minimum-spanning-tree algorithms you will actually implement.\nKruskal grows a forest edge by edge, cheapest first, using a union-find\nstructure to reject cycle-closing edges; Prim grows one tree outward from a\nroot with a priority queue, exactly Dijkstra rekeyed by attachment cost. Both\ntraced in full on a nine-town graph, with the edge cases, the bottleneck\nproperty, and where each one wins.\n",{"path":2327,"title":2328,"module":2308,"summary":2329},"\u002Falgorithms\u002Fgraphs\u002Fshortest-paths","Shortest Paths","Finding the cheapest route through a weighted network is one of the most-used\nalgorithms in computing, and a single operation — _relaxation_ — underlies\nevery method. We build the primitive, prove the triangle inequality and\noptimal substructure that make it work, then meet Dijkstra's algorithm: the\ngreedy solution for non-negative weights, traced vertex by vertex, with the\ncut argument that proves each extraction is final.\n",{"path":2331,"title":2332,"module":2308,"summary":2333},"\u002Falgorithms\u002Fgraphs\u002Fall-pairs-and-negative-weights","All-Pairs and Negative Weights","Dijkstra's greedy schedule breaks the moment an edge goes negative. We give it\nup for dynamic programming: Bellman-Ford derived as a DP over edge budgets,\nwith its negative-cycle detector, and Floyd-Warshall computing the distance\nbetween _every_ pair of vertices via a DP over which vertices a path may pass\nthrough. We close with Johnson's algorithm and the arbitrage problems that\nnegative cycles encode.\n",{"path":2335,"title":2336,"module":2308,"summary":2337},"\u002Falgorithms\u002Fgraphs\u002Fnetwork-flow","Network Flow","How much can flow through a network from source to sink? We build flow\nnetworks with capacity and conservation constraints, increase a flow by\npushing along augmenting paths in the residual graph, and see how reverse\nedges let the algorithm undo earlier routing. Ford-Fulkerson and its BFS refinement\nEdmonds-Karp find a maximum flow, traced end to end on a worked network.\n",{"path":2339,"title":2340,"module":2308,"summary":2341},"\u002Falgorithms\u002Fgraphs\u002Fmax-flow-min-cut","Max-Flow Min-Cut and Applications","Why is the flow found when no augmenting path remains actually optimal? The\nanswer is a duality theorem: the maximum flow equals the minimum cut. We prove\nit, read the minimum cut off the final residual graph, then derive bipartite\nmatching and a catalog of modeling reductions from the flow\nabstraction — before touching the modern algorithms that supersede\nEdmonds-Karp.\n",{"path":2343,"title":2344,"module":2308,"summary":2345},"\u002Falgorithms\u002Fgraphs\u002Fbridges-and-articulation-points","Bridges & Articulation Points","A **bridge** is an edge whose removal disconnects the graph; an **articulation\npoint** is a vertex whose removal does. Both are single points of failure in a\nnetwork. A single depth-first search computes discovery times and **low-links**,\nand two local criteria — $low[v] > disc[u]$ for bridges, $low[v] \\ge disc[u]$\nfor cut vertices — find them all in $O(V+E)$.\n",{"path":2347,"title":2348,"module":2308,"summary":2349},"\u002Falgorithms\u002Fgraphs\u002Flowest-common-ancestor","Lowest Common Ancestor & Binary Lifting","Given a rooted tree, the lowest common ancestor of $u$ and $v$ is the deepest\nnode that is an ancestor of both. A naive walk answers one query in $O(h)$;\n**binary lifting** precomputes the $2^k$-th ancestor of every node in\n$O(n\\log n)$, then answers $k$-th-ancestor and LCA queries in $O(\\log n)$ each.\nWe derive both jumps, apply them to tree distance, and compare against the\nEuler-tour + RMQ and Tarjan offline alternatives.\n",{"path":2351,"title":2352,"module":2308,"summary":2353},"\u002Falgorithms\u002Fgraphs\u002Ftwo-sat","2-SAT via Implication Graphs","A boolean formula whose every clause has exactly two literals can be solved in\n_linear_ time — even though its three-literal cousin is NP-complete. The idea\nis to read each clause as a pair of implications, build a directed graph on the\n$2n$ literals, and ask a question we already know how to answer: which literals\nshare a strongly connected component? The formula is satisfiable iff no variable\nlands in the same SCC as its own negation, and the SCCs' topological order\nyields a satisfying assignment for free.\n",{"path":2355,"title":2356,"module":2308,"summary":2357},"\u002Falgorithms\u002Fgraphs\u002Feulerian-tours","Eulerian Tours","An **Eulerian tour** uses every _edge_ of a graph exactly once. We give the\nexact parity and balance conditions under which one exists (even degree\nfor undirected graphs, in-degree equal to out-degree for directed) and Hierholzer's\n$O(E)$ algorithm that constructs one by splicing closed sub-tours. We contrast\nthis sharply with the **Hamiltonian** problem (visit every _vertex_ once),\nwhich is NP-complete: visiting edges is easy, visiting vertices is hard.\n",{"path":2359,"title":2360,"module":2308,"summary":2361},"\u002Falgorithms\u002Fgraphs\u002Fbipartite-matching","Bipartite Matching","Pairing applicants to jobs, students to slots, files to disks: all are\n**maximum bipartite matching**. We solve it combinatorially with **augmenting\npaths** (Kuhn's algorithm, $O(VE)$), speed it up to $O(E\\sqrt V)$ with\n**Hopcroft–Karp**, and uncover the structure behind it — **König's theorem**\n(max matching equals min vertex cover) and **Hall's marriage theorem** (a\nperfect matching exists iff every set has enough neighbors).\n",{"path":2363,"title":2364,"module":2365,"summary":2366},"\u002Falgorithms\u002Fgreedy\u002Fthe-greedy-method","The Greedy Method","Greedy Algorithms","A greedy algorithm builds a solution one locally-best choice at a time and\nnever looks back. We isolate the two properties that make this work — the\ngreedy-choice property and optimal substructure — prove the canonical\nactivity-selection algorithm correct with an exchange argument, watch greedy\nfail on the 0\u002F1 knapsack, and glimpse matroids as the theory\nthat says exactly when the greedy method is optimal.\n",{"path":2368,"title":2369,"module":2365,"summary":2370},"\u002Falgorithms\u002Fgreedy\u002Fscheduling-and-intervals","Scheduling & Interval Partitioning","Three classic scheduling problems all yield to greedy algorithms — and all\nthree turn on a single design decision: which key to sort by. Interval\nscheduling sorts by **finish** time to pack the most compatible jobs;\ninterval partitioning sorts by **start** time and proves the rooms needed\nequal the maximum overlap **depth**; minimizing maximum lateness sorts by\n**deadline** and is justified by an adjacent-swap exchange argument.\n",{"path":2372,"title":2373,"module":2365,"summary":2374},"\u002Falgorithms\u002Fgreedy\u002Fhuffman-codes","Huffman Codes","Huffman coding builds a\nprovably optimal prefix-free binary code by repeatedly merging the two least\nfrequent symbols. We develop prefix-free codes as binary trees, give the\nalgorithm with a priority queue, build a Huffman tree from example\nfrequencies, prove optimality with the same greedy-choice-plus-substructure\nargument, and pin the running time at $O(n\\log n)$.\n",{"path":2376,"title":2377,"module":2365,"summary":2378},"\u002Falgorithms\u002Fgreedy\u002Fmatroids","Matroids & Exchange Arguments","The capstone of the greedy module: _why_ and _when_ a greedy algorithm is\nprovably optimal. We recap the two correctness templates — **greedy-stays-ahead**\nand the **exchange argument** — then meet the **matroid** $M=(S,\\mathcal{I})$, an\nabstraction whose **exchange property** is the structure greedy needs.\nThe matroid–greedy theorem says sorting by weight and taking what stays\nindependent yields a maximum-weight basis _if and only if_ the structure is a\nmatroid. Kruskal's MST is the canonical instance; 0\u002F1 knapsack and TSP are the\ncanonical failures.\n",{"path":2380,"title":2381,"module":2365,"summary":2382},"\u002Falgorithms\u002Fgreedy\u002Fstable-matching","Stable Matching (Gale–Shapley)","Two sides each rank the other; we want a matching with no **blocking pair** — no\ntwo participants who both prefer each other to their assigned partners. The\n**Gale–Shapley deferred-acceptance** algorithm has proposers propose in\npreference order while receivers tentatively hold the best offer so far. We prove\nit terminates in $\\O(n^2)$ proposals, returns a **perfect** matching, and that\nthe matching is **stable**. A sharper asymmetry follows: deferred acceptance is\n**proposer-optimal** and **receiver-pessimal**, the structural fact behind the\nresidency match and school-choice systems.\n",{"path":2384,"title":2385,"module":2386,"summary":2387},"\u002Falgorithms\u002Fdynamic-programming\u002Fprinciples","Principles of Dynamic Programming","Dynamic Programming","Dynamic programming is recursion with memory: when a recursive solution\nre-solves the same subproblems again and again, we solve each one once and\nstore the answer. We identify the two structural conditions that make this\nwork — overlapping subproblems and optimal substructure — contrast top-down\nmemoization with bottom-up tabulation, and distil the whole method into a\nfive-step recipe.\n",{"path":2389,"title":2390,"module":2386,"summary":2391},"\u002Falgorithms\u002Fdynamic-programming\u002Fsequence-dp","Sequence Alignment & LCS","Two strings can be compared by how much of one appears inside the\nother. The longest common subsequence (LCS) and edit distance are the two\nclassic measures, and they are the _same_ dynamic program with different\ncosts. We derive the LCS recurrence by examining the last characters, fill a\nworked DP table, reconstruct the subsequence, and then show edit distance as\nthe identical $\\Theta(mn)$ pattern.\n",{"path":2393,"title":2394,"module":2386,"summary":2395},"\u002Falgorithms\u002Fdynamic-programming\u002Flongest-increasing-subsequence","Longest Increasing Subsequence","Given a sequence of numbers, how long is its longest strictly increasing\nsubsequence? A first dynamic program indexes subproblems by the element each\nsubsequence _ends at_, giving an $O(n^2)$ solution with parent-pointer\nreconstruction. A sharper idea, the patience-sorting _tails_ array searched by\nbinary search, drops the time to $O(n\\log n)$. We then fold in the\nvariants: non-decreasing, counting, Russian-doll envelopes, and bitonic.\n",{"path":2397,"title":2398,"module":2386,"summary":2399},"\u002Falgorithms\u002Fdynamic-programming\u002Fknapsack","Knapsack & Subset Problems","We start from $\\textsc{Subset-sum}$ — does some sublist hit a target $t$? — and its\ninclude\u002Fexclude recurrence over a boolean table $A(i, u)$, then bolt on values\nto get 0\u002F1 knapsack as the same machine with $\\lor$ promoted to $\\max$. We fill\nboth tables, recover the chosen items, and confront the surprise that the\n$\\Theta(nt)$ running time is only _pseudo-polynomial_ — exponential in the bit\nlength $b$, and unimprovable unless $\\mathrm{P}=\\mathrm{NP}$ since subset-sum is\n$\\textsc{NP-complete}$. The fractional variant reveals the sharp line between greedy\nand dynamic programming.\n",{"path":2401,"title":2402,"module":2386,"summary":2403},"\u002Falgorithms\u002Fdynamic-programming\u002Fcoin-change-and-unbounded","Coin Change & Unbounded Knapsack","The previous lesson let each item be taken at most once. Drop that cap — items\nmay be reused _any number of times_ — and the 0\u002F1 knapsack collapses from a\ntwo-dimensional table to a one-dimensional one, because there is no longer a\nprefix of \"already-used\" items to track. We meet **unbounded knapsack**, then\nits most famous instance, **coin change**: the minimum-coins recurrence\n$C[a] = 1 + \\min_c C[a-c]$, and the counting variant where the _order of the\nloops_ decides whether you count unordered combinations or ordered sequences —\nthe classic bug. Greed fails in general but works for canonical coin systems.\n",{"path":2405,"title":2406,"module":2386,"summary":2407},"\u002Falgorithms\u002Fdynamic-programming\u002Finterval-dp","Interval DP","Many problems ask for the best way to combine a contiguous range of items, and\nthe answer is a dynamic program over subintervals $[i,j]$ that chooses a split\npoint $k$. We derive the pattern from matrix-chain multiplication —\nparenthesising a product to minimize scalar multiplications in $O(n^3)$ — distil\nit into a reusable template filled by increasing interval length, and then meet\nits sharpest variant: the \"last operation\" trick behind Burst Balloons and\ncutting a stick, where fixing the _last_ move (not the first) makes the two\nsides independent.\n",{"path":2409,"title":2410,"module":2386,"summary":2411},"\u002Falgorithms\u002Fdynamic-programming\u002Ftree-dp","Dynamic Programming on Trees","When the subproblems of a dynamic program are _rooted subtrees_, a single\npost-order DFS solves the whole thing in $O(n)$: each node combines the\nalready-computed answers of its children. We meet the archetype — maximum-weight\nindependent set on a tree — then the \"path through a node\" pattern behind tree\ndiameter and maximum path sum, and finally **rerooting**, which computes a\nper-node answer for _every_ node as root in $O(n)$ with two passes.\n",{"path":2413,"title":2414,"module":2386,"summary":2415},"\u002Falgorithms\u002Fdynamic-programming\u002Fbitmask-dp","Bitmask DP","When a subproblem depends not on an index or a prefix but on _which subset_ of\na small ground set has been used, we can encode that subset as the bits of an\ninteger and index a DP table by it. With $n \\le \\sim 20$ the $2^n$ subsets fit\nin a table, turning $\\Theta(n!)$ brute force into $O(2^n \\cdot \\text{poly}(n))$.\nWe meet the bit tricks, the Held–Karp TSP archetype, assignment by mask,\nsubset-sum partitioning, and submask enumeration with its $3^n$ bound.\n",{"path":2417,"title":2418,"module":2386,"summary":2419},"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-optimizations","DP Optimizations","A correct DP recurrence is only half the battle; its naive evaluation is often\na factor of $n$ slower than necessary. This capstone surveys five techniques,\nmonotonic-queue, the convex hull trick, divide-and-conquer optimization,\nKnuth's optimization, and SOS DP, that each exploit _structure in the\ntransition_ (a sliding window, linear costs, monotone optimal splits, the\nquadrangle inequality, or subset lattices) to shave an $O(n)$, $O(\\log n)$, or\nworse factor off the running time.\n",{"path":2421,"title":2422,"module":2386,"summary":2423},"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-on-graphs","Dynamic Programming on Graphs","Many graph algorithms are dynamic programs: the subproblem is the\n_best value reachable under a restricted resource_ — intermediate vertices\nallowed, edges allowed, or a topological prefix — and edge _relaxation_ is the\nDP transition. We frame Floyd–Warshall as the archetype ($O(V^3)$ all-pairs\nshortest paths), Bellman–Ford as a DP over path length (the at-most-$K$-stops\nvariant), DAG-DP in topological order ($O(V+E)$), and Warshall's transitive\nclosure as the boolean analog.\n",{"path":2425,"title":2426,"module":2386,"summary":2427},"\u002Falgorithms\u002Fdynamic-programming\u002Fdigit-and-probability-dp","Digit & Probability DP","Two DP patterns with unusual state. _Digit DP_ counts the\nintegers in a range $[L, R]$ that satisfy a digit constraint by walking the\ndecimal places of the bound, carrying a _tight_ flag that marks when the prefix\nstill equals the bound's. _Probability\u002FExpectation DP_ replaces \"best value\" with\n\"expected value,\" using linearity of expectation to make each state an\naverage over its weighted transitions — the natural tool for expected step\ncounts and absorbing Markov chains.\n",{"path":2429,"title":2430,"module":2431,"summary":2432},"\u002Falgorithms\u002Fbacktracking\u002Fbacktracking-fundamentals","Backtracking: Subsets, Permutations & Combinations","Backtracking & Search","Backtracking builds a solution one choice at a time and abandons a partial\nsolution the moment it cannot be completed, exploring a state-space tree by\ndepth-first search. We meet the universal choose\u002Fexplore\u002Fun-choose template,\nderive the canonical enumerations — subsets ($2^n$), permutations ($n!$), and\ncombinations ($\\binom{n}{k}$) — handle duplicate elements by skipping equal\nsiblings, and see how pruning turns an exponential search into a tractable one.\n",{"path":2434,"title":2435,"module":2431,"summary":2436},"\u002Falgorithms\u002Fbacktracking\u002Fconstraint-search","Constraint Search: N-Queens & Sudoku","Many hard puzzles are **constraint satisfaction problems**: assign each\nvariable a value from its domain so that every constraint holds. Backtracking\nsolves them by assigning variables one at a time and rejecting a partial\nassignment the instant a constraint breaks. We make the rejection cheap — $O(1)$\nconflict checks for N-Queens via column and diagonal sets — and prune harder\nwith **forward checking**, **MRV** ordering, and **constraint propagation**,\nwhich is what lets an exponential search actually finish.\n",{"path":2438,"title":2439,"module":2431,"summary":2440},"\u002Falgorithms\u002Fbacktracking\u002Fbranch-and-bound","Branch & Bound and Meet in the Middle","Plain backtracking prunes a search tree by _feasibility_; for _optimization_\nproblems we can prune far more aggressively by _value_. **Branch and bound**\nkeeps the best complete solution found so far and discards any partial solution\nwhose optimistic bound cannot beat it. **Meet in the middle** splits the\ninstance in two, enumerates each half, and recombines by binary search — turning\n$2^n$ into $O(2^{n\u002F2}\\,n)$ and pushing exact search out to $n \\approx 40$.\n",{"path":2442,"title":2443,"module":2431,"summary":2444},"\u002Falgorithms\u002Fbacktracking\u002Fgraph-backtracking","Graph Backtracking: m-Coloring & Hamiltonian Paths","Two famous graph problems have no known efficient algorithm, yet yield cleanly\nto backtracking with the right pruning. **Graph $m$-coloring** assigns one of\n$m$ colors to each vertex so no edge is monochromatic; we color vertices in turn\nand reject a color the instant a neighbor already has it. **Hamiltonian\npath\u002Fcycle** asks for a walk visiting every vertex exactly once; we extend a path\ngreedily and backtrack on dead ends. Both are NP-complete, so the worst case is\nexponential — but feasibility pruning and good vertex ordering make real\ninstances tractable, and the contrast with the easy Eulerian condition shows why.\n",{"path":2446,"title":2447,"module":2448,"summary":2449},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fnumber-theory-basics","Number Theory: GCD & Modular Arithmetic","Mathematical Algorithms","This lesson opens the mathematical-algorithms module with the bedrock of\ncomputational number theory. We prove Euclid's recurrence\n$\\gcd(a,b)=\\gcd(b,\\,a\\bmod b)$ and its $O(\\log\\min(a,b))$ running time, extend\nit to recover Bézout coefficients $x,y$ with $ax+by=\\gcd(a,b)$, and build\nmodular arithmetic on residue classes — including when a modular inverse\n$a^{-1}\\bmod m$ exists and how to compute it.\n",{"path":2451,"title":2452,"module":2448,"summary":2453},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmodular-exponentiation-and-primality","Modular Exponentiation & Primality","Computing $a^n \\bmod m$ naively costs $n$ multiplications; **repeated squaring**\ndoes it in $O(\\log n)$ by reading the bits of the exponent. We use this routine\nto state **Fermat's little theorem** (and the modular inverse it gives), then to\ntest primality — trial division, the probabilistic **Fermat** and **Miller–Rabin**\ntests, and the deterministic witness set that settles primality for every 64-bit\nnumber.\n",{"path":2455,"title":2456,"module":2448,"summary":2457},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fsieve-and-factorization","Sieves & Factorization","The previous lesson tested one number for primality; here we ask for _all_\nprimes up to $n$ at once. The **sieve of Eratosthenes** cross-cuts composites\nin $O(n\\log\\log n)$, and a **linear sieve** does it in $O(n)$ while recording\neach number's **smallest prime factor**, which then factors any $x \\le n$ in\n$O(\\log x)$. From a factorization $x = \\prod p_i^{e_i}$ the multiplicative\nfunctions $\\tau$, $\\sigma$, and Euler's totient $\\varphi$ fall out immediately.\n",{"path":2459,"title":2460,"module":2448,"summary":2461},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fcombinatorics","Combinatorics & Counting","Counting is the arithmetic of finite sets. We build up from permutations\n$n!$ and combinations $\\binom{n}{k}$, prove Pascal's rule by a bijection,\nand count multisets with stars and bars. The practical core is computing\n$\\binom{n}{k}\\bmod p$ in $O(1)$ from precomputed factorials and inverse\nfactorials. We close with inclusion–exclusion and the Chinese Remainder\nTheorem, both of which lean on the modular inverse from the previous lesson.\n",{"path":2463,"title":2464,"module":2448,"summary":2465},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmatrix-exponentiation","Matrix Exponentiation","A linear recurrence advances by a fixed linear rule, so one step is a\n**matrix–vector** product and $n$ steps are a **matrix power**. Packaging\nFibonacci, and any $k$-term recurrence, into a transition matrix lets us jump\nto the $n$-th term in $O(k^3 \\log n)$ by **exponentiation by squaring** — the\nsame doubling trick from modular exponentiation, now over matrices.\n",{"path":2467,"title":2468,"module":2448,"summary":2469},"\u002Falgorithms\u002Fmathematical-algorithms\u002Ffast-fourier-transform","Fast Fourier Transform","Multiplying two degree-$n$ polynomials by the schoolbook method costs\n$\\Theta(n^2)$. Evaluating them at the **$n$-th roots of unity** turns\nmultiplication into pointwise products, and the **Cooley–Tukey FFT** computes\nall those evaluations in $\\Theta(n\\log n)$ by splitting even and odd\ncoefficients. The inverse FFT interpolates back, giving $\\Theta(n\\log n)$\npolynomial and big-integer multiplication.\n",{"path":2471,"title":2472,"module":2448,"summary":2473},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fgradient-descent","Numerical Optimization and Gradient Descent","Most of this course chases **discrete** optima over finite structures; here the\nsearch space is **continuous** and the objective $f$ is differentiable. The\n**gradient** points uphill, so stepping against it —\n$x_{t+1} = x_t - \\eta\\,\\nabla f(x_t)$ — walks downhill. **Convexity** makes every\nlocal minimum global; for convex $L$-smooth $f$ gradient descent converges at\n$O(1\u002Ft)$, and **geometrically** under strong convexity. **Newton's method** uses\nthe Hessian for local quadratic convergence, and **bisection** is the robust\nbracketing fallback for roots.\n",{"path":2475,"title":2476,"module":2477,"summary":2478},"\u002Falgorithms\u002Fcomputational-geometry\u002Fgeometric-primitives","Geometric Primitives & Orientation","Computational Geometry","Computational geometry is built on a single reliable primitive — the\n**orientation test**, a sign of a cross product that tells whether three points\nturn left, right, or lie collinear. From points-as-vectors and the dot and\ncross products we derive orientation, segment intersection, the shoelace area\nformula, and point-in-polygon tests, keeping all arithmetic **exact and\ninteger** so that no floating-point rounding can corrupt a sign.\n",{"path":2480,"title":2481,"module":2477,"summary":2482},"\u002Falgorithms\u002Fcomputational-geometry\u002Fconvex-hull","Convex Hull","The convex hull is the smallest convex polygon enclosing a point set — the\nrubber band snapped around the nails. We build it with Andrew's monotone chain,\nsorting by $(x,y)$ and sweeping a lower and upper hull while popping any\nnon-left turn via the orientation primitive, in $O(n\\log n)$. A reduction from\nsorting shows that bound is optimal, and the hull yields diameter, smallest\nenclosing rectangle, and more through rotating calipers.\n",{"path":2484,"title":2485,"module":2477,"summary":2486},"\u002Falgorithms\u002Fcomputational-geometry\u002Fsweep-line","Sweep-Line Algorithms","The plane-sweep paradigm turns a static $2$-D geometry problem into a dynamic\n$1$-D ordered-set problem: a vertical line sweeps left to right, stopping at an\n$x$-sorted **event queue** while a balanced-BST **status structure** tracks the\nobjects it currently crosses, ordered by $y$. We derive Bentley–Ottmann segment\nintersection in $O((n+k)\\log n)$, recover closest-pair in $O(n\\log n)$, and\nreduce skyline, rectangle-area, and overlap problems to $\\pm1$ event sweeps.\n",{"path":2488,"title":2489,"module":2477,"summary":2490},"\u002Falgorithms\u002Fcomputational-geometry\u002Fpolygons-and-proximity","Polygons & Proximity","Four classics that live on top of the orientation primitive and the convex\nhull. **Closest pair** falls to divide-and-conquer in $\\Theta(n\\log n)$, where a\npacking argument caps the cross-boundary combine at seven neighbours per point.\n**Point-in-polygon** is the ray-casting parity test or the winding-number count\nthat also handles self-intersecting boundaries, both with their edge caveats. The **shoelace formula**\ngives signed area as a sum of cross products, and **rotating calipers** walk the\nhull to read off diameter and width in $O(n)$.\n",{"path":2492,"title":2493,"module":2494,"summary":2495},"\u002Falgorithms\u002Fintractability\u002Fp-np-reductions","P, NP, and Reductions","Intractability","Most problems we have met so far have fast algorithms. A vast and important\nfamily seemingly does not. This lesson builds the vocabulary for that\ndivide: decision problems, the class $\\mathsf{P}$ of problems we can solve\nquickly, the class $\\mathsf{NP}$ of problems whose solutions we can _check_\nquickly, and polynomial-time reductions, the tool that lets us compare the\ndifficulty of two problems without solving either.\n",{"path":2497,"title":2498,"module":2494,"summary":2499},"\u002Falgorithms\u002Fintractability\u002Fnp-completeness","NP-Completeness","Some problems in $\\mathsf{NP}$ are universally hardest: every other problem\nin $\\mathsf{NP}$ reduces to them. This lesson defines $\\mathsf{NP}$-hard and\n$\\mathsf{NP}$-complete, states the Cook–Levin theorem that anchors the\ntheory on **SAT**, walks the web of reductions that grows from it, and gives\nthe four-step recipe for proving a brand-new problem $\\mathsf{NP}$-complete.\n",{"path":2501,"title":2502,"module":2494,"summary":2503},"\u002Falgorithms\u002Fintractability\u002Fcoping-with-hardness","Coping with NP-Hardness","An $\\mathsf{NP}$-hardness proof rules out an exact polynomial-time algorithm,\nnot the need for answers. This lesson surveys four practical responses to\nhardness: approximation algorithms with a provable ratio (worked through a\n2-approximation for vertex cover), heuristics and local search, exact\nexponential methods like branch and bound, and exploiting special structure\nin the instances you actually face.\n",{"path":2505,"title":2506,"module":2494,"summary":2507},"\u002Falgorithms\u002Fintractability\u002Fapproximation-algorithms","Approximation Algorithms","When a problem is $\\mathsf{NP}$-hard we can still ask for a solution\nprovably close to optimal. This lesson makes the approximation ratio\n$\\rho$ precise, separates absolute from relative guarantees, and proves the\nratios of four classic algorithms: greedy set cover ($H_n \\approx \\ln n$),\nthe MST-doubling $2$-approximation for metric TSP, load balancing, and the\nknapsack FPTAS. It closes with the hierarchy PTAS \u002F FPTAS and the limits of\ninapproximability.\n",{"path":2509,"title":2510,"module":6,"summary":6},"\u002Falgorithms","Algorithms",{"path":2512,"title":2513,"module":2514,"summary":2515},"\u002Fcalculus\u002Flimits-and-continuity\u002Ffunctions-and-models","Functions and Mathematical Models","Limits and Continuity","A function assigns exactly one output to each input and can be presented four ways: verbally, numerically, graphically, or by a formula. The elementary families — linear, polynomial, power, rational, trigonometric, exponential — model most elementary phenomena, and transformation, combination, and composition build every other function from them.\n",{"path":2517,"title":2518,"module":2514,"summary":2519},"\u002Fcalculus\u002Flimits-and-continuity\u002Fthe-limit-of-a-function","The Limit of a Function","The tangent and velocity problems both ask for a value a ratio approaches but never reaches — the limit. Its intuitive two-sided form splits into one-sided limits that must agree; a limit fails to exist when they disagree or when the function grows without bound, the latter producing a vertical asymptote.\n",{"path":2521,"title":2522,"module":2514,"summary":2523},"\u002Fcalculus\u002Flimits-and-continuity\u002Flimit-laws-and-the-precise-definition","Limit Laws and the ε–δ Definition","The Limit Laws reduce a limit to arithmetic on simpler limits, and direct substitution settles polynomials and rational functions outright. The 0\u002F0 forms that resist substitution yield to algebra or the Squeeze Theorem, and the ε–δ definition makes \"arbitrarily close\" precise as a pair of quantified inequalities.\n",{"path":2525,"title":2526,"module":2514,"summary":2527},"\u002Fcalculus\u002Flimits-and-continuity\u002Fcontinuity","Continuity","A function is continuous at a point when its limit there equals its value, so the graph has no break. Continuity fails in three geometric ways; it is closed under arithmetic and composition, so the elementary families and their combinations are continuous; and on a closed interval it forces the Intermediate Value Theorem, which locates roots.\n",{"path":2529,"title":2530,"module":2531,"summary":2532},"\u002Fcalculus\u002Fderivatives\u002Fthe-derivative-and-rates-of-change","The Derivative and Rates of Change","Derivatives","A single limit with three readings: the slope of the tangent line, the instantaneous velocity of a moving object, and the rate of change of one quantity with respect to another. Built from the difference quotient, extended from a value at one point to a function of x, and undefined exactly where a corner, jump, or vertical tangent appears.\n",{"path":2534,"title":2535,"module":2531,"summary":2536},"\u002Fcalculus\u002Fderivatives\u002Fdifferentiation-rules-and-the-chain-rule","Differentiation Rules and the Chain Rule","Computing every derivative from the limit definition is tedious. A short list of rules — power, constant multiple, sum, product, quotient — differentiates any polynomial or rational function by inspection. The trigonometric derivatives follow from one limit, and the chain rule extends everything to composite functions by multiplying rates along the composition.\n",{"path":2538,"title":2539,"module":2531,"summary":2540},"\u002Fcalculus\u002Fderivatives\u002Fimplicit-differentiation-and-related-rates","Implicit Differentiation and Related Rates","Not every curve is the graph of y = f(x). Implicit differentiation finds a slope from an equation in x and y directly, treating y as an unknown function and differentiating both sides. The same chain-rule idea drives related rates, where one measured rate of change forces another through a geometric constraint, and interprets the derivative as a rate across the sciences.\n",{"path":2542,"title":2543,"module":2531,"summary":2544},"\u002Fcalculus\u002Fderivatives\u002Flinear-approximations-and-differentials","Linear Approximations and Differentials","A differentiable curve looks like its tangent line under enough magnification, so the tangent is a usable stand-in for the function near the point of contact. The linear approximation and its linearization, written in the language of differentials dy and dx, estimate both function values and the measurement error propagated into a computed quantity.\n",{"path":2546,"title":2547,"module":2548,"summary":2549},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fextrema-and-the-mean-value-theorem","Extrema and the Mean Value Theorem","Applications of Derivatives","Absolute and local extrema, the Extreme Value Theorem that guarantees them, and Fermat's Theorem pinning candidates to critical numbers. The Closed Interval Method turns the search for extrema into a finite checklist. Rolle's Theorem and the Mean Value Theorem then connect a function's values to its derivative, giving the tool that most of differential calculus rests on.\n",{"path":2551,"title":2552,"module":2548,"summary":2553},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fhow-derivatives-shape-a-graph","How Derivatives Shape a Graph","The sign of the first derivative fixes where a function rises and falls, and a sign change identifies each local extremum through the First Derivative Test. The second derivative sets concavity and inflection points and gives a faster Second Derivative Test. Limits at infinity describe end behavior and the horizontal asymptotes a curve settles toward.\n",{"path":2555,"title":2556,"module":2548,"summary":2557},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fcurve-sketching-and-optimization","Curve Sketching and Optimization","A checklist that synthesizes domain, symmetry, asymptotes, monotonicity, extrema, and concavity into a hand sketch of any function, plus the slant asymptote for rational functions whose degree exceeds the denominator's. The same extremum machinery, applied to a word problem, becomes the optimization template: model one quantity, reduce it to a function of a single variable, and find its absolute extremum.\n",{"path":2559,"title":2560,"module":2548,"summary":2561},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fnewtons-method-and-antiderivatives","Newton's Method and Antiderivatives","Newton's method solves $f(x) = 0$ by repeatedly replacing the curve with its tangent line and jumping to the tangent's root, converging fast when it works and diverging when the derivative is small. Antiderivatives reverse differentiation: every antiderivative of a function differs from another by a constant, so the general antiderivative is a family of parallel curves, pinned to one by an initial condition.\n",{"path":2563,"title":2564,"module":2565,"summary":2566},"\u002Fcalculus\u002Fintegrals\u002Farea-and-the-definite-integral","Area and the Definite Integral","Integrals","The area under a curve is defined as a limit of sums of rectangle areas. The same limit — a Riemann sum taken as the mesh shrinks to zero — defines the definite integral, a single number measuring signed area, total distance, and every accumulated quantity built the same way. Its properties, comparison bounds, and reading as net area follow directly from the limit.\n",{"path":2568,"title":2569,"module":2565,"summary":2570},"\u002Fcalculus\u002Fintegrals\u002Fthe-fundamental-theorem-of-calculus","The Fundamental Theorem of Calculus","Differentiation and integration are inverse operations. Part 1 says the derivative of an area-accumulation function is the integrand; Part 2 says a definite integral equals the change in any antiderivative across the interval. Together they replace limits of Riemann sums with antiderivative lookups, define the indefinite integral, and give the Net Change Theorem for rates.\n",{"path":2572,"title":2573,"module":2565,"summary":2574},"\u002Fcalculus\u002Fintegrals\u002Fthe-substitution-rule","The Substitution Rule","Substitution runs the Chain Rule backward: spotting an inner function whose derivative also appears in the integrand lets the variable change to $u$ and collapse a composite integral to a simple one. The rule applies to indefinite and definite integrals, with two ways to handle the limits, and it yields the symmetry shortcuts that double even integrands and vanish odd ones.\n",{"path":2576,"title":2577,"module":2578,"summary":2579},"\u002Fcalculus\u002Fapplications-of-integration\u002Fareas-and-volumes","Areas Between Curves and Volumes","Applications of Integration","A definite integral computes any quantity that a limit of Riemann sums approximates. Applied to geometry it gives the area between two curves and the volume of a solid: by cross-sections, by disks and washers when the region is revolved, and by cylindrical shells when inverting the boundary is awkward.\n",{"path":2581,"title":2582,"module":2578,"summary":2583},"\u002Fcalculus\u002Fapplications-of-integration\u002Fwork-average-value-and-arc-length","Work, Average Value, Arc Length, and Surface Area","The work done by a force that varies with position, the average value of a function and the Mean Value Theorem it satisfies, the length of a curve, and the area of a surface swept out by revolving that curve. Each is a limit of Riemann sums, hence a definite integral.\n",{"path":2585,"title":2586,"module":2578,"summary":2587},"\u002Fcalculus\u002Fapplications-of-integration\u002Fphysics-economics-and-probability","Applications to Physics, Economics, and Probability","Definite integrals in physics, economics, and statistics: the force a fluid exerts on a submerged plate, the balance point of a plane region, the money consumers save at a market price, and the probability that a continuous random variable lands in an interval, together with its mean.\n",{"path":2589,"title":2590,"module":2591,"summary":2592},"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Finverse-functions-logarithms-and-exponentials","Inverse Functions, Logarithms, and Exponentials","Exponential, Logarithmic, and Inverse Functions","A one-to-one function has an inverse that reverses it, with a graph mirrored across y = x and a derivative given by the reciprocal-slope rule. The exponential e^x is its own derivative and the natural logarithm has derivative 1\u002Fx; logarithmic differentiation turns products, quotients, and variable powers into sums.\n",{"path":2594,"title":2595,"module":2591,"summary":2596},"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Fgrowth-decay-inverse-trig-and-hyperbolic-functions","Growth, Decay, Inverse Trigonometric, and Hyperbolic Functions","Any quantity whose rate of change is proportional to its size grows or decays exponentially, the single equation y' = ky behind populations, radioactive decay, cooling, and continuously compounded interest. The inverse trigonometric functions have algebraic derivatives, and the hyperbolic functions, built from e^x and e^{-x}, describe the hanging cable.\n",{"path":2598,"title":2599,"module":2591,"summary":2600},"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Flhospitals-rule","Indeterminate Forms and l'Hospital's Rule","When a limit produces 0\u002F0 or infinity over infinity, the value is undetermined by the forms alone. l'Hospital's Rule resolves both by replacing the ratio of functions with the ratio of their derivatives. Products, differences, and powers reduce to a quotient the rule can handle, and repeated use ranks the growth of logarithms, powers, and exponentials.\n",{"path":2602,"title":2603,"module":2604,"summary":2605},"\u002Fcalculus\u002Ftechniques-of-integration\u002Fintegration-by-parts","Integration by Parts","Techniques of Integration","The product rule for derivatives reverses into integration by parts, trading the integral of $u\\,\\d v$ for the integral of $v\\,\\d u$ whenever the second is easier. The LIATE ordering fixes which factor to differentiate. Standard cases: a polynomial against a transcendental factor, repeated parts, cyclic integrals that solve for themselves, and reduction formulas that peel an exponent down by recursion.\n",{"path":2607,"title":2608,"module":2604,"summary":2609},"\u002Fcalculus\u002Ftechniques-of-integration\u002Ftrigonometric-integrals-and-substitution","Trigonometric Integrals and Substitution","Two related techniques. Trigonometric integrals evaluate powers and products of sine, cosine, tangent, and secant by splitting off one factor and converting the rest with a Pythagorean identity, or by dropping even powers with half-angle formulas. Trigonometric substitution runs the idea in reverse: replace x by a sine, tangent, or secant to clear a radical, integrate, then read the answer back off a reference triangle.\n",{"path":2611,"title":2612,"module":2604,"summary":2613},"\u002Fcalculus\u002Ftechniques-of-integration\u002Fpartial-fractions-and-integration-strategy","Partial Fractions and Integration Strategy","Any rational function integrates in closed form: factor the denominator, split the fraction into simple pieces by partial fractions, and integrate each piece as a logarithm or an arctangent. Four denominator cases exhaust the possibilities. A four-step strategy then sorts an arbitrary integrand by its shape to the technique that fits it, and a short catalog records elementary functions whose antiderivatives are not elementary.\n",{"path":2615,"title":2616,"module":2604,"summary":2617},"\u002Fcalculus\u002Ftechniques-of-integration\u002Fapproximate-and-improper-integrals","Approximate and Improper Integrals","Two definite integrals the Fundamental Theorem cannot reach. With no antiderivative available, the Midpoint, Trapezoidal, and Simpson rules approximate the integral from sample values, each carrying a provable error bound. With an infinite interval or an integrand that blows up, the improper integral is defined as a limit that either converges or diverges; the Comparison Test settles which without evaluating it.\n",{"path":2619,"title":2620,"module":2621,"summary":2622},"\u002Fcalculus\u002Fparametric-and-polar\u002Fparametric-curves-and-their-calculus","Parametric Curves and Their Calculus","Parametric Equations and Polar Coordinates","A parametric curve gives x and y separately as functions of a third variable, recording not only a path but the direction and timing with which it is traced. Eliminating the parameter recovers a Cartesian equation; the slope, area, arc-length, and surface-area formulas run directly on the parameter, with the cycloid and astroid as worked examples.\n",{"path":2624,"title":2625,"module":2621,"summary":2626},"\u002Fcalculus\u002Fparametric-and-polar\u002Fpolar-coordinates","Polar Coordinates","Polar coordinates locate a point by a distance from the pole and an angle from the polar axis, giving circles, spirals, and flower-shaped curves short equations. Conversion between the two systems is right-triangle trigonometry, and treating a polar curve as a parametric curve in the angle yields the tangent, area, and arc-length formulas.\n",{"path":2628,"title":2629,"module":2621,"summary":2630},"\u002Fcalculus\u002Fparametric-and-polar\u002Fconic-sections","Conic Sections","Parabolas, ellipses, and hyperbolas are the plane curves cut from a double cone. Each has a focus-based geometric definition and a standard Cartesian equation. A single number, the eccentricity, ties the three together, and placing a focus at the pole gives all of them one polar equation that describes planetary orbits.\n",{"path":2632,"title":2633,"module":2634,"summary":2635},"\u002Fcalculus\u002Fsequences-and-series\u002Fsequences","Sequences","Infinite Sequences and Series","A sequence is a function on the positive integers, and its limit is defined almost exactly like a limit at infinity. The Limit Laws and Squeeze Theorem carry over from functions, monotonic and bounded sequences give a convergence criterion, and the Monotonic Sequence Theorem guarantees a limit exists without naming it.\n",{"path":2637,"title":2638,"module":2634,"summary":2639},"\u002Fcalculus\u002Fsequences-and-series\u002Fseries-and-the-integral-test","Series and the Integral Test","Adding infinitely many terms is made precise as the limit of partial sums. The two series with closed-form partial sums are geometric and telescoping; the harmonic series diverges even as its terms shrink to zero. The Integral Test compares a positive series to an improper integral, settling the p-series and supplying a remainder bound for estimating sums.\n",{"path":2641,"title":2642,"module":2634,"summary":2643},"\u002Fcalculus\u002Fsequences-and-series\u002Fthe-convergence-tests","The Convergence Tests","The comparison, alternating-series, ratio, and root tests decide convergence without a closed-form partial sum. Absolute convergence is stronger than conditional convergence and is preserved under rearrangement; an alternating series errs by less than its first omitted term. A test is chosen from the shape of the general term.\n",{"path":2645,"title":2646,"module":2634,"summary":2647},"\u002Fcalculus\u002Fsequences-and-series\u002Fpower-series","Power Series","A power series is a polynomial of infinite degree whose convergence set is an interval centered at $a$, with a radius the Ratio Test finds and endpoints that must be tested by hand. Inside that interval the series represents a function that can be differentiated and integrated term by term, generating new representations from the geometric series.\n",{"path":2649,"title":2650,"module":2634,"summary":2651},"\u002Fcalculus\u002Fsequences-and-series\u002Ftaylor-and-maclaurin-series","Taylor and Maclaurin Series","If a function equals a power series, its coefficients are forced: the nth is the nth derivative at the center over n factorial. We derive that formula, use Taylor's Inequality to prove the standard series for the exponential, sine, and cosine, record the binomial series and a reference table, and bound the error when a Taylor polynomial replaces a function.\n",{"path":2653,"title":2654,"module":2655,"summary":2656},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvectors-and-the-dot-product","Three-Dimensional Coordinates, Vectors, and the Dot Product","Vectors and the Geometry of Space","Space needs three coordinates, so we set up the rectangular system, the distance formula, and the equation of a sphere. Vectors then package magnitude and direction into a single algebraic object with its own arithmetic. The dot product turns two vectors into a number that measures the angle between them, gives a clean test for orthogonality, and produces the projection of one vector onto another.\n",{"path":2658,"title":2659,"module":2655,"summary":2660},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fthe-cross-product-lines-and-planes","The Cross Product, Lines, and Planes","The cross product multiplies two vectors into a third perpendicular to both, with length equal to the area of the parallelogram they span. That one construction supplies the direction of a line, the normal of a plane, and, through the scalar triple product, the volume of a parallelepiped. Lines carry a point and a direction vector; planes carry a point and a normal, which fixes the angle between planes and the distance from a point to a plane.\n",{"path":2662,"title":2663,"module":2655,"summary":2664},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fcylinders-and-quadric-surfaces","Cylinders and Quadric Surfaces","A surface whose equation omits one variable is a cylinder: the graph of a plane curve swept along the missing axis. A second-degree equation in three variables is a quadric, and translation and rotation reduce every one to a short standard list. Traces — the curves cut by planes parallel to the coordinate planes — sort the six quadrics into ellipsoid, the two paraboloids, the cone, and the two hyperboloids.\n",{"path":2666,"title":2667,"module":2655,"summary":2668},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvector-functions-and-space-curves","Vector Functions and Space Curves","A vector function assigns a vector to each value of a parameter, and as the parameter runs its tip traces a space curve. Taking limits, derivatives, and integrals component by component carries all of single-variable calculus into three dimensions. The derivative of a vector function is the tangent vector to its curve, and normalizing it gives the unit tangent that points the way along the path.\n",{"path":2670,"title":2671,"module":2655,"summary":2672},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Farc-length-curvature-and-motion","Arc Length, Curvature, and Motion in Space","Integrating the speed of a vector function gives the length of its curve and a natural parameter, arc length, that depends only on the curve's shape. Curvature measures how fast the unit tangent turns, and together with the normal and binormal it builds the moving TNB frame. Reading the same vector function as a trajectory, its first two derivatives are velocity and acceleration, and acceleration splits cleanly into tangential and normal parts.\n",{"path":2674,"title":2675,"module":2676,"summary":2677},"\u002Fcalculus\u002Fpartial-derivatives\u002Ffunctions-of-several-variables","Functions of Several Variables, Limits, and Continuity","Partial Derivatives","A function of several variables assigns one number to each point of a region in the plane or in space. Domain, graph, level curve, and level surface describe it; limits and continuity extend to two variables, where a limit must agree along every path of approach, not just from the left and the right.\n",{"path":2679,"title":2676,"module":2676,"summary":2680},"\u002Fcalculus\u002Fpartial-derivatives\u002Fpartial-derivatives","A partial derivative holds every variable but one fixed and differentiates in the ordinary sense. Geometrically it is the slope of a trace curve cut from the surface by a coordinate plane. The freeze-and-differentiate rule computes the two first partials; the four second partials follow, and the two mixed ones agree under Clairaut's Theorem when they are continuous.\n",{"path":2682,"title":2683,"module":2676,"summary":2684},"\u002Fcalculus\u002Fpartial-derivatives\u002Ftangent-planes-and-the-chain-rule","Tangent Planes, Linear Approximation, and the Chain Rule","Near a point, a smooth surface looks like its tangent plane, and the plane's equation is built from the two partial derivatives. That linearization defines the total differential and the meaning of differentiability in two variables. The chain rule then propagates derivatives through composed functions, tracked by a tree diagram, and yields clean formulas for implicit differentiation.\n",{"path":2686,"title":2687,"module":2676,"summary":2688},"\u002Fcalculus\u002Fpartial-derivatives\u002Fdirectional-derivatives-and-the-gradient","Directional Derivatives and the Gradient","The partial derivatives measure slope along the two axes; the directional derivative measures slope along any chosen direction, and equals the gradient dotted with a unit vector. The gradient points in the direction of steepest increase, its length is the greatest rate, and it stands perpendicular to level curves and surfaces, which fixes the tangent plane to a level surface.\n",{"path":2690,"title":2691,"module":2676,"summary":2692},"\u002Fcalculus\u002Fpartial-derivatives\u002Foptimization-and-lagrange-multipliers","Optimization and Lagrange Multipliers","Extrema of a two-variable function sit at critical points where the gradient vanishes; the Second Derivatives Test sorts them into peaks, valleys, and saddles by the sign of a discriminant. Absolute extrema on a closed region also need the boundary. When the domain is itself a constraint curve, Lagrange multipliers set the two gradients parallel and solve the constrained problem.\n",{"path":2694,"title":2695,"module":2696,"summary":2697},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fdouble-integrals","Double Integrals","Multiple Integrals and Vector Calculus","The double integral extends the definite integral to functions of two variables: a limit of Riemann sums that measures signed volume under a surface. Fubini's Theorem turns it into two ordinary integrations done one after the other, general regions of type I and type II fix the inner limits, polar coordinates absorb circular symmetry through the factor r, and the same machine computes mass, center of mass, and moments of a lamina.\n",{"path":2699,"title":2700,"module":2696,"summary":2701},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Ftriple-integrals-and-coordinate-systems","Triple Integrals and Coordinate Systems","The triple integral integrates a function of three variables over a solid, as a limit of Riemann sums evaluated by three nested single integrations. Cylindrical coordinates add the factor r to handle axial symmetry, spherical coordinates add rho-squared sine-phi for radial symmetry, and the general change of variables shows both volume elements are Jacobian determinants of the coordinate map. Surface area for a graph completes the measurement toolkit.\n",{"path":2703,"title":2704,"module":2696,"summary":2705},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fvector-fields-and-line-integrals","Vector Fields and Line Integrals","A vector field assigns a vector to every point of space; the line integral of a field along a curve accumulates its tangential component, measuring work. Conservative fields are gradients of a potential, and for them the Fundamental Theorem for Line Integrals makes the integral depend only on the endpoints. Path independence, closed-loop integrals of zero, and the component test for a potential are three faces of the same property.\n",{"path":2707,"title":2708,"module":2696,"summary":2709},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fgreens-theorem-curl-and-divergence","Green's Theorem, Curl, and Divergence","Green's Theorem equates the line integral of a field around a positively oriented closed curve with a double integral over the enclosed region, turning a boundary computation into an area computation and vice versa. Curl measures local circulation and divergence measures local outflow; the two vector forms of Green's Theorem express the boundary integral as the integrated curl or divergence, the planar case of Stokes' and the Divergence Theorem.\n",{"path":2711,"title":2712,"module":2696,"summary":2713},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fsurface-integrals","Parametric Surfaces and Surface Integrals","A parametric surface is the image of a two-variable vector function; its area element is the magnitude of the cross product of the two tangent vectors. The surface integral of a scalar function sums it over that area, and the flux integral of a vector field sums the field's normal component, measuring flow through the surface. Orientation by a choice of unit normal makes flux well-defined, the integral Stokes' and the Divergence Theorem operate on.\n",{"path":2715,"title":2716,"module":2696,"summary":2717},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fstokes-and-the-divergence-theorem","Stokes' Theorem and the Divergence Theorem","Stokes' Theorem lifts Green's Theorem into space: the line integral of a field around the boundary of a surface equals the flux of its curl through the surface. The Divergence Theorem relates the outward flux across a closed surface to the triple integral of divergence over the solid it encloses. Together with the Fundamental Theorem of Calculus and its line-integral and Green counterparts, they are one theorem: the integral of a derivative over a region equals the integral of the field over its oriented boundary.\n",{"path":2719,"title":2720,"module":6,"summary":6},"\u002Fcalculus","Calculus",{"path":2722,"title":2723,"module":1231,"summary":2724},"\u002Fmechanics\u002Ffoundations\u002Fmeasurement-and-dimensions","Measurement and Dimensions","Every physical quantity is a number attached to a unit, and that pairing is what lets you check an equation before computing anything, since terms that add together must carry the same dimensions. We build the SI base units and the notion of dimension, then use dimensional analysis to test a proposed relation and form scaling groups — a method that fixes a formula's shape but never its numerical constants. The lesson also sets how precisely a result may be stated, through significant figures, propagated uncertainty, and order-of-magnitude checks that catch errors a raw calculator answer hides.\n",{"path":2726,"title":2727,"module":1231,"summary":2728},"\u002Fmechanics\u002Ffoundations\u002Fvector-algebra","Vector Algebra","Force, velocity, and displacement all carry a direction, so mechanics needs an arithmetic that respects it; adding magnitudes alone gives the wrong answer the moment two arrows point different ways. We set up vectors and their components in a chosen basis, then build the two products that carry most of the physics — the dot product, which extracts the part of one vector along another and yields work and power, and the cross product, which measures oriented area and yields torque and angular momentum. Rotating the axes changes the components while leaving the vector itself untouched, and the same component method resolves a force along whatever directions a constraint picks out.\n",{"path":2730,"title":2731,"module":2732,"summary":2733},"\u002Fmechanics\u002Fkinematics\u002Fone-dimensional-motion","One-Dimensional Motion","Kinematics","Motion along a line already forces the two questions the whole of kinematics repeats: how fast is the object moving now, and where will it be next? Velocity and acceleration answer the first as derivatives of position; integrating them back — the signed area under a graph — answers the second. We derive the constant-acceleration equations, mark exactly where the \"constant\" assumption is load-bearing, and see why sign, not magnitude, is what carries direction.\n",{"path":2735,"title":2736,"module":2732,"summary":2737},"\u002Fmechanics\u002Fkinematics\u002Fmotion-graphs","Motion Graphs","Draw a motion as a graph and its two most useful facts turn geometric: the slope of the position curve is the velocity, and the area under the velocity curve is the displacement. We read motion in both directions — differentiating a graph for the next rate, integrating it back to recover position — and handle the curved, piecewise, and noisy graphs that real measurements produce. Along the way we see why a velocity estimated from two positions belongs to the midpoint of their interval, not its end.\n",{"path":2739,"title":2740,"module":2732,"summary":2741},"\u002Fmechanics\u002Fkinematics\u002Fprojectile-motion","Projectile Motion","Throw an object and it seems to trace one curved path, but the motion is really two independent one-dimensional motions running at once: constant velocity across the ground and free fall in the vertical. Splitting it that way turns every projectile question — how long it stays up, how far it lands, how high it climbs, whether it clears an obstacle — into a pair of equations you already know. We derive the parabolic trajectory, work both the forward and the inverse problems, and show why the familiar $45^\\circ$ range-maximizing angle holds only when launch and landing heights match.\n",{"path":2743,"title":2744,"module":2732,"summary":2745},"\u002Fmechanics\u002Fkinematics\u002Frelative-motion","Relative Motion","A velocity is only ever measured relative to some observer, so a boat's speed through the water, over the ground, and as seen from another boat are three different vectors. Choosing the right frame — and subtracting one motion from another — collapses river crossings, crosswind headings, pursuit, and closest-approach problems into a single vector equation. We build the relative-velocity and relative-position relations for uniformly moving frames, show why acceleration is the one quantity all such observers agree on, and note where rotating frames break the simple subtraction.\n",{"path":2747,"title":2748,"module":2732,"summary":2749},"\u002Fmechanics\u002Fkinematics\u002Fcircular-motion","Circular Motion","An object going around a circle at a steady speed is still accelerating, because its velocity is forever changing direction — the fact that governs everything from a car on a curve to a satellite in orbit. We tie the angular description (angle, angular velocity, angular acceleration) to the linear one through $v=r\\omega$, split the acceleration into an inward part that turns the velocity and a tangential part that changes its speed, and extend the inward $v^2\u002Fr$ result to any curved path through its local radius of curvature. Constant angular acceleration then mirrors straight-line motion equation for equation.\n",{"path":2751,"title":2752,"module":2753,"summary":2754},"\u002Fmechanics\u002Fdynamics\u002Fnewtons-laws","Newton's Laws","Dynamics","What makes a body change its motion, and in which frames does the answer take its simplest form? Newton's three laws settle both: inertial frames are the ones where a force-free body coasts, force is whatever changes momentum, and every interaction pushes back on its source. We write the second law as $\\sum\\vec F=\\d\\vec p\u002F\\d t$, reduce it to $m\\vec a$ at constant mass, and separate what a scale actually reads — the support force — from the weight $m\\vec g$ it is so often mistaken for.\n",{"path":2756,"title":2757,"module":2753,"summary":2758},"\u002Fmechanics\u002Fdynamics\u002Ffree-body-diagrams","Free-Body Diagrams","Once several forces act on a body at once, the reliable way to predict its motion is to isolate that one body and draw every external push and pull on it — nothing more, nothing less. The free-body diagram is that discipline. We fix a system boundary, resolve $\\sum\\vec F=m\\vec a$ into components along axes chosen to fit the geometry, and solve for the unknowns a problem hands us — normal forces, tensions, friction, and the acceleration a constraint permits — seeing why internal forces drop out only when the boundary encloses both bodies that share them.\n",{"path":2760,"title":2761,"module":2753,"summary":2762},"\u002Fmechanics\u002Fdynamics\u002Ffriction-and-curved-motion","Friction and Curved Motion","Real surfaces grip before they slip, fluids push back harder the faster you move through them, and anything rounding a bend must be pulled toward the inside of the curve by something. This lesson supplies the force laws for those three cases. We bound static friction by $|f_s|\\leq\\mu_sN$ and switch to kinetic friction $\\mu_kN$ once sliding starts, model drag as a speed-dependent resistance that levels off at a terminal speed, and show that circular motion demands an inward net force $mv^2\u002Fr$ furnished by real interactions — friction, a banked normal force, tension — never by an invented outward one.\n",{"path":2764,"title":2765,"module":2753,"summary":2766},"\u002Fmechanics\u002Fdynamics\u002Fnumerical-dynamics","Numerical Dynamics","Most force laws — quadratic drag, coupled oscillators, anything nonlinear — admit no closed-form trajectory, so we advance the motion one small time step at a time and let arithmetic do what algebra cannot. This lesson turns $\\d\\vec y\u002F\\d t=f(t,\\vec y)$ into a marching rule. We derive the Euler, Euler--Cromer, midpoint, and Verlet updates, weigh their accuracy and stability, watch a drifting energy expose a bad scheme, and use step-halving and conserved quantities to separate the error of the method from the error of the model.\n",{"path":2768,"title":2769,"module":2753,"summary":2770},"\u002Fmechanics\u002Fdynamics\u002Fcenter-of-mass-systems","Center-of-Mass Systems","A firework bursts into a dozen fragments, yet one point keeps gliding along the original parabola as though nothing had happened. That point is the centre of mass, and following it collapses a many-body tangle into a single equation of motion. We define $\\vec R=\\frac1M\\sum_i m_i\\vec r_i$ and its continuous form, show that internal forces cancel so that only external ones move it, $M\\vec A_{\\rm cm}=\\sum\\vec F_{\\rm ext}$, and put the result to work on recoil, collisions viewed from the centre-of-mass frame, and rocket propulsion, where mass leaving the boundary carries momentum with it.\n",{"path":2772,"title":2773,"module":2774,"summary":2775},"\u002Fmechanics\u002Fenergy\u002Fwork-and-kinetic-energy","Work and Kinetic Energy","Energy","A constant push along a straight path is trivial to score, but real forces vary and bend along curved trajectories, and only the component along the motion transfers any energy. Work captures exactly that transfer as the line integral $W=\\int\\vec F\\cdot\\d\\vec r$, and the work-kinetic-energy theorem turns it into a statement about speed: the net work on a particle equals the change in its $\\tfrac12 mv^2$. We build work up from the dot product to the signed area under a force curve, derive the theorem from Newton's second law, and read power as its instantaneous rate $P=\\vec F\\cdot\\vec v$.\n",{"path":2777,"title":2778,"module":2774,"summary":2779},"\u002Fmechanics\u002Fenergy\u002Fpotential-energy","Potential Energy","When a force does the same work no matter which path a particle takes, that work can be stored as a function of position alone, and solving for the motion becomes bookkeeping instead of integration. We single out the forces that qualify — the conservative ones, for which $\\oint\\vec F\\cdot\\d\\vec r=0$ — define their potential energy through $\\vec F=-\\nabla U$, and use conservation of mechanical energy to read speeds, turning points, and equilibria straight off a potential curve. Friction breaks the shortcut, so we also track where mechanical energy leaks away as heat.\n",{"path":2781,"title":2782,"module":2774,"summary":2783},"\u002Fmechanics\u002Fenergy\u002Fmultiparticle-work","Multiparticle Work","A single particle has one velocity and one kinetic energy; a system of many can spin, deform, explode, and warm up while its centre of mass glides along as if nothing happened. Splitting the motion into a centre-of-mass part and an internal part separates the energy that momentum already fixes from the energy left free for relative motion, $K=\\tfrac12MV_{\\rm cm}^2+K'$. We derive the centre-of-mass work theorem, see why an explosion or a released spring can raise total kinetic energy with no external work at all, and use the reduced-mass and centre-of-mass frames to make collisions and internal transfers clean.\n",{"path":2785,"title":2786,"module":2774,"summary":2787},"\u002Fmechanics\u002Fenergy\u002Fmass-energy-and-binding","Mass-Energy and Binding","Relativity puts rest itself on the energy ledger: a mass $m$ carries energy $mc^2$ even when it sits still, so weighing a system's separated pieces and weighing the assembled whole give different answers, and the gap is binding energy. We convert freely between mass units and MeV, compute the energy that holds a nucleus together, and read the binding-energy-per-nucleon curve that explains why fusing light nuclei and splitting heavy ones both release energy. Reaction $Q$ values, thresholds, and recoil then follow from the same mass-difference accounting, once the frame and mass convention are fixed.\n",{"path":2789,"title":2790,"module":2774,"summary":2791},"\u002Fmechanics\u002Fenergy\u002Fphotons-and-quantization","Photons and Quantization","Light delivers its energy in indivisible lumps: a photon of frequency $f$ carries exactly $hf$, and this one fact explains why a dim blue lamp ejects electrons that an intense red one cannot. We fix a photon's energy and momentum from its wavelength, follow the quanta through emission, absorption, and the photoelectric threshold $K_{\\rm max}=hf-\\phi$, and watch energy and momentum conservation together produce the Compton wavelength shift when a photon scatters from an electron. The recurring discipline is unit and frame care, where a stray factor of $10^9$ or a forgotten rest energy quietly ruins an answer.\n",{"path":2793,"title":2794,"module":2795,"summary":2796},"\u002Fmechanics\u002Fmomentum\u002Fmomentum-and-collisions","Momentum and Collisions","Momentum","When two objects collide, the forces between them are too brief and too tangled to integrate directly, yet the result is fixed by one conserved quantity. Linear momentum $\\vec p=m\\vec v$ turns Newton's second law into the impulse-momentum theorem $\\vec J=\\Delta\\vec p$, and for an isolated system into a conservation law that holds through any internal collision, however dissipative. We use it to separate elastic from inelastic collisions, follow the centre of mass, and read impulse as the signed area under a force-time curve — always tracking which external impulses the chosen system and interval let us drop.\n",{"path":2798,"title":2799,"module":2795,"summary":2800},"\u002Fmechanics\u002Fmomentum\u002Fcenter-of-mass-collisions","Center-of-Mass Collisions","A two-body collision that looks asymmetric in the laboratory becomes almost trivial in the frame that rides along with the centre of mass, where the total momentum is zero and the two momenta stay equal and opposite. We build that frame, reduce the pair to a single relative coordinate carrying the reduced mass $\\mu$, and show that an elastic collision there only rotates one momentum vector while its length holds fixed. Transforming back to the laboratory then handles elastic and inelastic collisions, scattering angles, and reaction thresholds with the same construction — and shows why relative speed, not laboratory kinetic energy, measures what a collision can convert.\n",{"path":2802,"title":2803,"module":2795,"summary":2804},"\u002Fmechanics\u002Fmomentum\u002Frocket-propulsion","Rocket Propulsion","A rocket speeds up by throwing mass backward, so its own mass drops as it flies and $\\vec F=m\\vec a$ no longer applies to a fixed body. Tracking the momentum the exhaust carries across the vehicle boundary gives thrust $T=Ru_e$ and, for a force-free burn, the rocket equation $\\Delta v=u_e\\ln(m_i\u002Fm_f)$ — a logarithm that makes large velocity changes expensive in propellant and forces staging. We then add the forces a real ascent cannot ignore, gravity, drag, and steering, and show how thrust and mass-flow records are cross-checked to infer the exhaust speed.\n",{"path":2806,"title":2807,"module":2808,"summary":2809},"\u002Fmechanics\u002Frotation\u002Frotational-inertia","Rotational Inertia","Rotation","Push a wheel and a merry-go-round with the same force and they speed up at wildly different rates: the same mass resists rotation differently depending on where it sits relative to the axis. That single fact is the moment of inertia, $I=\\int r_\\perp^2\\,\\d m$, and this lesson builds it from the ground up. We tie angular motion to linear through $s=r\\theta$, $v=r\\omega$, and $a_t=r\\alpha$, derive $I$ for rods, disks, and spheres, and use the parallel- and perpendicular-axis theorems to move between axes — always naming the axis, because the same body has as many moments of inertia as it has lines to spin about.\n",{"path":2811,"title":2812,"module":2808,"summary":2813},"\u002Fmechanics\u002Frotation\u002Frotational-dynamics","Rotational Dynamics","A force applied to a wheel does nothing unless it acts off the axis: what turns a rigid body is torque, force times lever arm. This lesson makes that precise and turns it into the rotational Newton's second law, $\\sum\\tau=I\\alpha$ about a fixed axis, the exact analogue of $\\sum F=ma$. From there we get rotational work $W=\\int\\tau\\,\\d\\theta$ and power $P=\\tau\\omega$, size a motor to a load, and solve pulleys and Atwood machines where the pulley's own inertia can no longer be ignored — always insisting that every torque be measured about the same axis.\n",{"path":2815,"title":2816,"module":2808,"summary":2817},"\u002Fmechanics\u002Frotation\u002Frolling-motion","Rolling Motion","A rolling wheel is doing two things at once — translating and spinning — but the no-slip condition $v_{cm}=R\\omega$ locks them together, and that single constraint is what makes rolling tractable. We use it to split the kinetic energy into $\\tfrac12Mv_{cm}^2+\\tfrac12I\\omega^2$, find how fast a cylinder reaches the bottom of an incline, and show why the contact point is instantaneously at rest. The static friction that enforces rolling does no work; we track its direction from the tendency to slip, and mark exactly where the model breaks once the required friction exceeds $\\mu_sN$.\n",{"path":2819,"title":2820,"module":2808,"summary":2821},"\u002Fmechanics\u002Frotation\u002Fangular-momentum","Angular Momentum","A skater pulls in her arms and spins faster, with no torque acting: that is angular momentum conservation, and it lets us answer questions that would be hopeless force by force. We build $\\vec L=\\vec r\\times\\vec p$, show it obeys $\\vec\\tau_{ext}=\\d\\vec L\u002F\\d t$, and use its conservation under zero external torque to link before and after in collisions, reconfigurations, and coupled rotors without ever resolving the internal forces. The catch is bookkeeping: the origin, the system boundary, and the frame must be fixed first, and a change in total $\\vec L$ always points to an external impulse someone forgot.\n",{"path":2823,"title":2824,"module":2808,"summary":2825},"\u002Fmechanics\u002Frotation\u002Frolling-resistance","Rolling Resistance","Ideal rolling should coast forever, yet every real wheel slows down. The reason is that a deformable tire and road do not press through a single point: the contact patch spreads, the normal-force resultant shifts ahead of the axle, and that offset is a resisting moment even with no gross sliding. We package it as an equivalent force $F_{rr}=C_{rr}N$, tie the coefficient to load, surface, speed, and temperature, and use coast-down, towing, and traction tests to separate this contact loss from aerodynamic drag, bearing friction, and the adhesion limit where rolling gives way to skidding.\n",{"path":2827,"title":2828,"module":2808,"summary":2829},"\u002Fmechanics\u002Frotation\u002Fgyroscopic-precession","Gyroscopic Precession","A spinning top leans over but does not fall — it swings its axis in a slow horizontal circle instead. The paradox dissolves once torque is read as the rate of change of a vector: gravity's torque is perpendicular to the spin angular momentum, so it turns $\\vec L$ rather than toppling it. We derive the steady precession rate $\\Omega\\simeq Mgr\u002F(I_s\\omega_s)$ in the fast-top limit, state the assumptions it leans on — dominant spin, slow tilt, negligible bearing torque — and read nutation, support motion, and a decaying spin as the ways real gyroscopes depart from it.\n",{"path":2831,"title":2832,"module":2833,"summary":2834},"\u002Fmechanics\u002Fgravity-and-matter\u002Fkeplerian-orbits","Keplerian Orbits","Gravitation and Matter","Why do the planets trace ellipses rather than any other curve? Newton's inverse-square law collapses the two-body problem onto a single conic section, and the answer falls out of two conserved quantities: a central force can exert no torque, so angular momentum is fixed, and gravity is conservative, so energy is fixed. We read an orbit's size and shape straight off those invariants, recover all three of Kepler's laws, and derive escape speed, the vis-viva relation, and the timing of a pass. We also mark where the ideal ellipse breaks down — drag, oblateness, and a third body slowly move a real orbit.\n",{"path":2836,"title":2837,"module":2833,"summary":2838},"\u002Fmechanics\u002Fgravity-and-matter\u002Fgravitational-fields","Gravitational Fields","Instead of tracking the force between every pair of masses, we attach a field to the source and ask a test mass to read it off locally. That move pays off because gravity is conservative: the field is the gradient of a single scalar potential, and potentials from many sources simply add. We build the field-potential picture, use spherical symmetry and the shell theorem to get the point-mass exterior field and the zero interior field of a shell, and read tides straight out of the field's gradient. Along the way we mark exactly when the constant-$g$ and point-mass shortcuts hold and when a shape correction is needed.\n",{"path":2840,"title":2841,"module":2833,"summary":2842},"\u002Fmechanics\u002Fgravity-and-matter\u002Fstatic-equilibrium","Static Equilibrium","What does it take for a loaded structure to stay put? A body at rest needs its forces to cancel and its turning effects to cancel — $\\sum\\vec F=0$ and $\\sum\\vec\\tau=0$ about any point — and almost all of statics is the craft of turning a physical setup into those equations. We build free-body diagrams, replace supports, cables, friction, couples, and distributed loads with their idealized reactions, and locate the centre of gravity that decides whether a body tips. We also count equations against unknowns to separate a determinate problem from one that needs the material's deformation to resolve, and read every negative or inconsistent reaction as a sign that a contact or a boundary was chosen wrong.\n",{"path":2844,"title":2845,"module":2833,"summary":2846},"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-statics","Fluid Statics","A fluid at rest cannot support a shear, so the only stress it carries is a pressure that must grow with depth to hold up the fluid above it. That single balance, $\\d p\u002F\\d z=-\\rho g$, runs the whole subject: it sets manometer readings, the force on a dam, and — integrated over a submerged boundary — Archimedes' buoyant force $F_B=\\rho g V_{\\rm disp}$. We derive these, use them to decide when a body floats and whether it floats upright, and mark where acceleration, rotation, compressibility, or capillarity forces a richer pressure model.\n",{"path":2848,"title":2849,"module":2833,"summary":2850},"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-flow","Fluid Flow","Two accounting rules carry most of steady flow: mass cannot pile up, so the same volume crosses every section each second, and mechanical energy is conserved along a streamline when the fluid is ideal. From those we get continuity, Bernoulli's relation between pressure, speed, and height, and the results that follow — Torricelli's efflux speed, the Venturi meter, the Pitot tube. We then let go of the ideal assumptions one at a time: viscosity adds wall shear and head loss, Reynolds number decides laminar versus turbulent, and Mach number marks where a gas stops behaving as incompressible.\n",{"path":2852,"title":2853,"module":2833,"summary":2854},"\u002Fmechanics\u002Fgravity-and-matter\u002Forbital-motion","Orbital Motion","A circular orbit is nothing but free fall with enough sideways speed to keep missing the ground, and setting gravity equal to the centripetal requirement fixes that speed and the period once and for all. From the same energy bookkeeping we read off escape speed, sort orbits into bound, parabolic, and hyperbolic by the sign of their specific energy, and see why a tangential burn is the efficient way to change an orbit. We build the Hohmann transfer and its launch window, work the numbers for a geostationary orbit and an escape burn, and mark where finite thrust, perturbations, and an uncertain initial state pull a real trajectory off the ideal.\n",{"path":2856,"title":2857,"module":2833,"summary":2858},"\u002Fmechanics\u002Fgravity-and-matter\u002Fstress-and-elasticity","Stress and Elasticity","Rigid bodies are a fiction; every real material stretches, shears, or squeezes under load, and the useful question is how much. We define stress as force per area and strain as fractional deformation, then find that for small deformations the two are simply proportional — Hooke's law — with Young's, shear, and bulk moduli as the constants for stretch, twist, and volume change. From these we compute extensions, torsional twist, and stored elastic energy, and read a tensile curve for the yield, ultimate, and fracture points where linear elasticity ends. We also mark the practical limits: stress concentrations, fatigue, and the multiaxial states a single uniaxial modulus cannot capture.\n",{"path":2860,"title":2861,"module":2862,"summary":2863},"\u002Fmechanics\u002Foscillations-waves\u002Fdamped-oscillators","Damped Oscillators","Oscillations and Waves","Every real oscillator eventually stops: friction, drag, and internal loss drain its energy, so free motion is a decay rather than a permanent swing. Adding a velocity-proportional resistance to the spring-mass equation produces one dimensionless number, $b\u002F(2\\sqrt{mk})$, that decides whether the mass rings down through many cycles, returns once without overshoot, or crawls back slowly. We solve the three regimes, tie the observed decay to the power balance $b\\dot x^2$, and turn a measured ring-down into the decay rate and quality factor of the apparatus — reading damping off the data instead of assuming it.\n",{"path":2865,"title":2866,"module":2862,"summary":2867},"\u002Fmechanics\u002Foscillations-waves\u002Ftravelling-waves","Travelling Waves","A wave carries a shape, not the material: each element of a rope or air column oscillates in place while the disturbance travels through it. Writing that shape as $f(x\\mp vt)$ turns \"the pattern moves\" into a statement about the cosine's argument, and a local force balance on one string segment fixes the speed at $v=\\sqrt{T\u002F\\mu}$ — restoring stiffness over inertia, with amplitude nowhere in it. We build the sinusoidal wave and its phase, derive the wave equation from Newton's second law, and follow the energy a travelling wave transports, then check speed and power against those predictions.\n",{"path":2869,"title":2870,"module":2862,"summary":2871},"\u002Fmechanics\u002Foscillations-waves\u002Fwave-superposition","Wave Superposition","When two waves cross the same point, what does a probe read? In a linear medium the answer is arithmetic: the displacements add, $y=y_1+y_2$, and the pulses pass through each other unchanged. That one rule produces interference — reinforcement where the signs agree, cancellation where they oppose — and it guards against a common mistake, since displacement can vanish at an instant while the energy sits in transverse motion instead. We work out the signed sum, the phase bookkeeping for equal-frequency components, and why a null in the record is not a null in the wave.\n",{"path":2873,"title":2874,"module":2862,"summary":2875},"\u002Fmechanics\u002Foscillations-waves\u002Fstanding-waves","Standing Waves","Clamp a string at both ends and only certain frequencies survive: the ends must be nodes, and that single geometric demand quantizes the wave into a discrete set of modes $f_n=nv\u002F(2L)$. The travelling wave becomes a fixed pattern of nodes and antinodes — standing, not moving — because equal waves running in opposite directions superpose. We build the standing wave from its counter-propagating pieces, read the harmonic sequence off the boundary conditions (half-wavelengths for a fixed-fixed string, odd quarter-wavelengths for a closed pipe), and test the ideal model against node scans and resonance peaks.\n",{"path":2877,"title":2878,"module":2862,"summary":2879},"\u002Fmechanics\u002Foscillations-waves\u002Fsound-waves","Sound Waves","Sound is a pressure wave so small that a loud tone displaces air molecules by less than the width of an atom, yet a microphone reads it easily — because pressure, not displacement, is what the ear and the instrument sense. The acoustic impedance $Z=\\rho c$ ties pressure, density, and particle velocity together, fixes the intensity a wave carries, and sets the reference for the decibel, a logarithm that tames a $10^{12}$ range in power. We derive the sound speed from the gas's stiffness, convert between pressure and intensity levels, and treat the measurement itself — calibration, geometry, background, averaging — as part of the physics.\n",{"path":2881,"title":2882,"module":2862,"summary":2883},"\u002Fmechanics\u002Foscillations-waves\u002Fdoppler-effect","Doppler Effect","A passing siren drops in pitch not because the source changes but because motion repacks the wavefronts: an approaching source crowds its crests, a receding one stretches them, and a moving listener samples them at a different rate. For mechanical waves every velocity is measured against the medium, and one signed ratio $f_r=f_s(v-u_r)\u002F(v-u_s)$ captures both effects at once. We separate source motion, which sets crest spacing, from receiver motion, which sets arrival rate, invert the shift to recover radial velocity, and mark where the model breaks — supersonic sources, moving air, and reflected paths that carry two shifts, not one.\n",{"path":2885,"title":2886,"module":2862,"summary":2887},"\u002Fmechanics\u002Foscillations-waves\u002Fwave-packets","Wave Packets","No real signal is a single frequency: a disturbance that starts and stops is built from a band of wave numbers, and the width of that band is what makes it local. We ask how such a packet moves — carrier crests at the phase velocity $v_\\mathrm p=\\omega\u002Fk$, the envelope at the group velocity $v_\\mathrm g=\\d\\omega\u002F\\d k$ — and why the two differ once a medium is dispersive. Curvature $\\d^2\\omega\u002F\\d k^2$ spreads and chirps the packet as it travels, and the Fourier reciprocity that ties bandwidth to duration explains why a finite record, aliasing, or a coarse probe can imitate that spreading unless the sampling limits are respected.\n",{"path":2889,"title":2890,"module":2862,"summary":2891},"\u002Fmechanics\u002Foscillations-waves\u002Fbeats-and-coupling","Beats and Coupling","Add two tones a few hertz apart and the sum swells and fades at their difference frequency — a beat — though neither source is changing. We work out that envelope, then ask the mechanical version of the same question: join two oscillators and a single resonance splits into normal modes, with energy sloshing between the coordinates at their frequency difference. The lesson identifies when a slow amplitude envelope signals genuine coupling rather than two independent sources, drift, or deliberate modulation, reading it from envelope timing, spectral sidebands, and the mode shapes.\n",{"path":2893,"title":2894,"module":2862,"summary":2895},"\u002Fmechanics\u002Foscillations-waves\u002Fsimple-harmonic-motion","Simple Harmonic Motion","Any system pushed back toward equilibrium by a force proportional to its displacement obeys one equation, $\\ddot x+\\omega_0^2x=0$, and so moves sinusoidally at $\\omega_0=\\sqrt{k\u002Fm}$ whatever the amplitude. We derive that motion, follow its energy $E=mv^2\u002F2+kx^2\u002F2$ trading between kinetic and potential form at constant total, and read the elliptical phase-space orbit Hooke's law implies. Period, amplitude, velocity, and acceleration then supply redundant checks: an amplitude-dependent period or a curved force residual is the signature that the linear model has failed, and mass-loading and offset tests separate a calibration error from a real frequency shift.\n",{"path":2897,"title":2898,"module":2862,"summary":2899},"\u002Fmechanics\u002Foscillations-waves\u002Fpendulum-motion","Pendulum Motion","A pendulum keeps time only because, for small swings, gravity supplies a restoring torque proportional to the angle — and $T=2\\pi\\sqrt{L\u002Fg}$ then follows without the mass appearing at all. We derive that result, mark exactly which assumptions carry it (small angle, negligible pivot loss, a rigid support), then relax them: finite amplitude lengthens the period through an elliptic integral, and an extended body replaces $L$ with the ratio of its moment of inertia to its center-of-mass distance. How the period drifts with amplitude or pivot position is what diagnoses the geometric, damping, and distributed-mass corrections.\n",{"path":2901,"title":2902,"module":2862,"summary":2903},"\u002Fmechanics\u002Foscillations-waves\u002Fdriven-oscillators","Driven Oscillators","Drive a damped oscillator at a frequency you control and it eventually forgets its own: $m\\ddot x+b\\dot x+kx=F_0\\cos\\omega t$ settles into a steady response whose amplitude and phase depend sharply on how close the drive sits to resonance. We solve for that response, show how damping alone fixes the resonance width, the peak power, and the settling time, and treat base excitation as the same problem with a different input. The steady-state formulas hold only for constant $m$, $b$, and $k$; level-dependent peaks or hysteresis between up- and down-sweeps are how nonlinearity or an extra mode announces itself.\n",{"path":2905,"title":2906,"module":2862,"summary":2907},"\u002Fmechanics\u002Foscillations-waves\u002Fwave-boundaries","Wave Boundaries","A pulse traveling along a string does something abrupt where the string's properties change: part reflects, part transmits, and which is which is set by the impedance mismatch alone. We impose continuity of displacement and transverse force at the join to get the reflection and transmission coefficients in terms of $Z=\\sqrt{T\\mu}$, fix their signs and the polarity flip, and balance the energy. The clean result assumes linear, nondispersive segments meeting at a localized join; pulse polarity, return timing, and energy ratios are the measurements that expose a real connector's mass, loss, or distributed transition.\n",{"path":2909,"title":2910,"module":2911,"summary":2912},"\u002Fmechanics\u002Fthermodynamics\u002Fkinetic-theory-of-ideal-gases","Kinetic Theory of Ideal Gases","Thermodynamics","A gas has no springs and no gears, yet it pushes on its container with a definite pressure and stores energy in a lawful way. Kinetic theory explains both from the motion of the molecules alone: pressure is the accumulated recoil of countless elastic impacts, and temperature is the average translational kinetic energy each molecule carries. We derive $pV=\\tfrac13Nm\\overline{v^2}$ from momentum transfer, read off $\\overline{K}_{\\rm tr}=\\tfrac32kT$, and use the Maxwell–Boltzmann distribution to separate the most probable, mean, and rms speeds — each the right average for a different question — while marking where the dilute, classical assumptions stop holding.\n",{"path":2914,"title":2915,"module":2911,"summary":2916},"\u002Fmechanics\u002Fthermodynamics\u002Ffirst-law-of-thermodynamics","First Law of Thermodynamics","Heat a gas and it may warm, expand, or both; compress it and the same energy can reappear as a temperature rise. The first law settles the bookkeeping: internal energy is a state property whose change equals the heat added plus the work done on the system, $\\Delta E_{\\rm int}=Q_{\\rm in}+W_{\\rm on}$. We fix a system boundary and one sign convention, compute boundary work as $\\int p\\,\\d V$ along a path, and use calorimetry to measure heat and heat capacities. The recurring point is that heat and work are path-dependent transfers while their sum is not, so an energy ledger closes only once every boundary crossing is named.\n",{"path":2918,"title":2919,"module":2911,"summary":2920},"\u002Fmechanics\u002Fthermodynamics\u002Fentropy-and-the-second-law","Entropy and the Second Law","The first law lets energy flow either way; it never says which way heat actually goes. The second law supplies the missing arrow. Entropy, defined through the reversible transfer $\\d S=\\delta Q_{\\rm rev}\u002FT$, can only increase in an isolated system, and that single inequality fixes the direction of heat flow and caps every engine, refrigerator, and heat pump at its Carnot value. We build entropy ledgers for reservoirs and working substances, separate the entropy carried by heat from the entropy generated by irreversibility, and read the sign of the total as a hard check on any proposed thermal machine.\n",{"path":2922,"title":2923,"module":2911,"summary":2924},"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-processes","Thermal Processes","Heat rarely sits still: it stretches solids, pushes real gases off their ideal isotherms, and leaks across walls by conduction, convection, and radiation. Each behavior becomes a number a designer can use. Thermal expansion sets the gaps in a bridge and the stress in a clamped rod; the van der Waals equation and a phase diagram fix when $pV=nRT$ or a latent-heat term applies; Fourier's law, Newton cooling, and Stefan–Boltzmann radiation give the rate of heat flow. We assemble these into thermal-resistance networks and transient time constants, then mark where contact resistance, phase change, or a hidden thermal bridge breaks the simple model.\n",{"path":2926,"title":2927,"module":2911,"summary":2928},"\u002Fmechanics\u002Fthermodynamics\u002Fphase-changes","Phase Changes","Add heat to ice and its temperature climbs — until it reaches $0\\ ^\\circ\\mathrm C$, where the thermometer stalls while the ice melts. That plateau is the whole subject: at a phase boundary the energy rearranges molecules, $Q=mL$, instead of raising temperature, which resumes only once one phase is gone. We stage a heating path into sensible-heat legs ($Q=mc\\Delta T$) and latent plateaus, use the Clausius–Clapeyron relation to track how a boiling point moves with pressure, and solve calorimetry by testing each coexistence endpoint — so a melt fraction that lands outside $[0,1]$ flags a wrong final-state guess rather than a real state.\n",{"path":2930,"title":2931,"module":2911,"summary":2932},"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-machines","Thermal Machines","An engine, a refrigerator, and a heat pump are one machine read three ways: each shuttles heat between a hot and a cold reservoir while trading work at the boundary, and only the flow you call useful separates them. A heat engine turns part of $Q_h$ into work, $W=Q_h-Q_c$; a refrigerator spends work to pull $Q_c$ from the cold side; a heat pump counts the warm-side delivery instead. We measure each with its own ratio — efficiency or coefficient of performance — bound them all by the Carnot limit that reservoir temperatures alone set, and track how finite temperature differences, throttling, and friction generate entropy and pull real machines below that bound.\n",{"path":2934,"title":2935,"module":6,"summary":6},"\u002Fmechanics","Mechanics & Dynamics",{"path":2937,"title":2938,"module":2939,"summary":2940},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcharge-and-conductors","Charge and Conductors","Electric Fields","Rub two objects together and one pulls electrons from the other; nothing is created, only moved. We define what electric charge is — conserved, additive, and quantized in units of $e$ — and why a conductor's mobile carriers rearrange until its interior field vanishes and its surface sits at one potential. We follow charge through contact, induction, and grounding, treat the field-free cavity that turns a conductor into a shield, and mark where finite conductivity and leakage set the limits of the electrostatic picture.\n",{"path":2942,"title":2943,"module":2939,"summary":2944},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcoulombs-law","Coulomb's Law","Two charges at rest push or pull along the line joining them, and the whole of electrostatics is assembled by adding up such pairs. We measure that force — its inverse-square falloff, its linear dependence on each charge, the sign that says attract or repel — and write it as a vector so direction survives superposition. We work the magnitude and component forms on real numbers, check them against limiting cases and dimensions, and fix the point-charge approximation to source sizes small against every separation.\n",{"path":2946,"title":2947,"module":2939,"summary":2948},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-and-force","Electric Field and Force","Rather than ask how one charge reaches across empty space to another, we credit the source with a field that fills the space and let a second charge respond to whatever field sits at its own location. Electric field is force per unit positive test charge, $\\vec E=kq\\hat r\u002Fr^2$ for a point source, and source fields add before any receiving charge is placed. We compute those fields and the force $\\vec F=q\\vec E$ they exert, then follow a charge along its parabolic path through a uniform field and into nonuniform fields where the dynamics turn position-dependent.\n",{"path":2950,"title":2951,"module":2939,"summary":2952},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-maps","Electric Field Maps","A field is a vector at every point of space, and the quickest way to grasp one is to draw it. We build the two standard pictures — continuous field lines tangent to $\\vec E$, and scaled vector arrows — and read direction, magnitude, and the location of nulls straight off them. We fix what a line drawing can and cannot say: density encodes magnitude only under a stated seeding rule, and integral curves never cross at a regular point. From there we work the topology near sources, sinks, and conductor surfaces, and state the step-size and interpolation checks a numerical map must pass.\n",{"path":2954,"title":2955,"module":2939,"summary":2956},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-dipoles","Electric Dipoles","Most neutral matter carries no net charge yet still responds to an electric field, because its positive and negative charge sit slightly apart. That separation is a dipole, moment $\\vec p=q\\vec d$ pointing from the negative to the positive charge, and it is the leading term in how any neutral distribution looks from far away. We derive the torque $\\vec p\\times\\vec E$ and energy $-\\vec p\\cdot\\vec E$ a uniform field imposes, the net force a field gradient adds, and the axial and equatorial $1\u002Fr^3$ fields the pair produces, then measure how far out the point-dipole approximation still holds.\n",{"path":2958,"title":2959,"module":2960,"summary":2961},"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fcontinuous-charge-fields","Continuous Charge Fields","Continuous Charge Distributions","A charged rod, ring, or disk is not a point, yet its field is still nothing but Coulomb's law added up over the charge it carries. We replace the discrete sum by an integral, with $\\d q=\\lambda\\d\\ell$, $\\sigma\\d A$, or $\\rho\\d V$, so the real work becomes geometry: writing the vector from each source element to the field point, and letting symmetry cancel the components that must cancel before any integral is attempted. We carry the line, ring, and disk fields through in full, then check each result against its near field, its far field, and its dimensions.\n",{"path":2963,"title":2964,"module":2960,"summary":2965},"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fgauss-law-and-conductors","Gauss's Law and Conductors","Adding up Coulomb's law over a whole distribution is laborious; Gauss's law trades that sum for a single statement, that the flux of $\\vec E$ out of any closed surface counts the charge inside, $\\oint\\vec E\\cdot\\d\\vec A=Q_{\\rm enc}\u002F\\varepsilon_0$. The law is always true, but it hands over the field only when the source is symmetric enough to pull $E$ outside the integral. We apply it to spheres, lines, and sheets, then turn it on conductors, where the zero interior field drives every excess charge to the surface and fixes the normal-field jump $\\sigma\u002F\\varepsilon_0$, the charge induced on a cavity wall, and electrostatic shielding.\n",{"path":2967,"title":2968,"module":2969,"summary":2970},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpoint-charge-potential","Point-Charge Potential","Electric Potential","The electrostatic force is conservative, so the work it does between two points\ndepends only on the endpoints. That lets us trade the vector field for a single\nscalar attached to each point, the electric potential, the potential energy a unit\ncharge would have there. We build potential from the work integral, fix the usual\nreference at infinity, and add point sources as scalars, $V=k\\sum_i q_i\u002Fr_i$,\navoiding the vector bookkeeping the field demands. Signed charges, the reference\nchoice, equipotential motion, and far-field expansions each give an independent\ncheck on a result.\n",{"path":2972,"title":2973,"module":2969,"summary":2974},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpotential-gradients-and-equipotentials","Potential Gradients and Equipotentials","Given the potential everywhere, how do we recover the field? The field is the\nnegative gradient, $\\vec E=-\\nabla V$: it points down the steepest local drop in\npotential, and its magnitude is set by how fast $V$ changes, not by the shape of a\ncontour. We read off components with directional derivatives, reconstruct fields\nfrom measured potential grids using centered differences, and use closed-loop\nintegrals and grid refinement to test whether a reconstructed field is physically\nconsistent.\n",{"path":2976,"title":2977,"module":2969,"summary":2978},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Felectrostatic-energy-and-pressure","Electrostatic Energy and Pressure","Assembling a charge configuration takes work, and that work is stored, but where\nis it kept and how much is there? We total it two ways: as a sum over the charges,\n$U=\\tfrac12\\sum_i q_iV_i$, and as an integral over the field itself,\n$u_E=\\tfrac12\\varepsilon_0E^2$, energy the field carries in every region it fills.\nDifferentiating the stored energy at fixed charge or at fixed voltage recovers the\nmechanical force on a conductor, and at a charged surface the same field scale\nappears as an outward electrostatic pressure. We work the parallel-plate case in\nfull and mark where curvature and fringing make the pressure nonuniform.\n",{"path":2980,"title":2981,"module":2969,"summary":2982},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Flaplace-boundary-problems","Laplace Boundary Problems","Often the charges are not given, only the conductors and the voltages held on\nthem, and the potential in the empty space between has to be found. There $V$ obeys\nLaplace's equation $\\nabla^2V=0$, and the boundary data alone determine a unique solution.\nWe solve it two ways: separation of variables into boundary-matched modes, whose\nhigher spatial frequencies die away with depth into the domain, and finite-difference\nrelaxation for boundaries no analytic mode fits. Residual norms, boundary error, and\nflux balance tell us when the computed potential and its field can be trusted.\n",{"path":2984,"title":2985,"module":2969,"summary":2986},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fcontinuous-charge-potentials","Continuous Charge Potentials","When charge is spread over a line, a surface, or a volume, the sum over point\nsources becomes an integral, $V(\\vec r)=k\\int \\d q\u002F|\\vec r-\\vec r'|$. Because\npotential is a scalar, this integral sidesteps the component algebra the field\nwould force, until the field is actually wanted through $\\vec E=-\\nabla V$. We set\nup the right density element for each geometry, choose a workable reference, handle\nthe integrable singularities that arise when the observation point sits on the\ncharge, and check every result against symmetry, dimensions, and the far-field\nmultipole limit.\n",{"path":2988,"title":2989,"module":2990,"summary":2991},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitance-fundamentals","Capacitance Fundamentals","Capacitance","How much charge must you separate onto two conductors to hold a given voltage between\nthem? That ratio, $C=Q\u002F\\Delta V$, is fixed by the conductor geometry and the medium,\nnot by how much charge is presently stored. We compute it from the field for the\nparallel-plate, isolated-sphere, concentric-sphere, and coaxial geometries, trace how\nsurface charge and boundary conditions set each result, and see where fringing,\nguarding, and stray coupling separate the ideal formula from what a bridge measures.\n",{"path":2993,"title":2994,"module":2990,"summary":2995},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-networks","Capacitor Networks","Wire several capacitors together and the source sees one equivalent capacitance — but\nwhich? The answer comes not from how the symbols are drawn but from which conductors\nshare a node: parallel branches hold a common voltage and add, $C_{\\rm eq}=\\sum_iC_i$,\nwhile series branches share a common charge and add reciprocally. We derive both rules\nfrom charge conservation on the floating internal node, then extend the node-charge\nmethod to unequal, precharged, and stray-coupled branches and carry a worked reduction\nthrough to the charge and voltage on every element.\n",{"path":2997,"title":2998,"module":2990,"summary":2999},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-energy-and-force","Capacitor Energy and Force","Charging a capacitor takes work, because every increment of charge is pushed through\nthe voltage the earlier charge already established. We total that work three\nequivalent ways, $U=Q^2\u002F(2C)=Q\\Delta V\u002F2=C(\\Delta V)^2\u002F2$, locate it in the field as\na density $u=\\tfrac12\\epsilon_0E^2$, then let the plates move. Differentiating the\nstored energy at fixed charge, or the coenergy at fixed voltage, gives the mechanical\nforce; the two boundaries differ only by the work the source supplies. We work the\nparallel-plate attraction and its electrostatic pressure in full, and follow the same\ngradient into pull-in, tilt, comb drives, and traceable force calibration.\n",{"path":3001,"title":3002,"module":2990,"summary":3003},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fdielectric-polarization-and-breakdown","Dielectric Polarization and Breakdown","Slide a dielectric between the plates and the capacitance rises — but why, and how\nhard can you drive it before the insulator fails? Bound charge answers the first:\npolarization $\\vec P$ sets up surface and volume charge that partly cancels the\napplied field, so $\\vec D=\\varepsilon_0\\vec E+\\vec P$ separates what the circuit\ncontrols from what the material contributes. We follow the field across layered\ndielectrics and interfaces, tie permittivity and loss to their frequency dependence,\nand treat dielectric strength as a measured, geometry-dependent limit rather than one\nmaterial number.\n",{"path":3005,"title":3006,"module":3007,"summary":3008},"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fcurrent-and-resistance","Current and Resistance","Direct-Current Circuits","What does it mean, physically, for charge to flow, and what sets how hard a wire resists that flow? Current counts charge crossing a surface, $I=\\int\\vec J\\cdot\\d\\vec A$, and traces back to a slow drift of many carriers, $\\vec J=nq\\vec v_d$. We establish when the linear law $V=IR$ actually holds, how resistivity and geometry combine into bulk resistance, why real sources sag under load through their internal resistance, and how the three power forms $P=IV=I^2R=V^2\u002FR$ tie electrical work to heating and component ratings.\n",{"path":3010,"title":3011,"module":3007,"summary":3012},"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fkirchhoff-network-analysis","Kirchhoff Network Analysis","Once a circuit has more than one loop, no amount of series-parallel folding will reduce it — you need the two conservation laws written as equations. Kirchhoff's junction law is charge conservation at a node; his loop law is energy conservation around a closed path. We turn a labelled network into a linear system in node voltages or mesh currents, fix the sign conventions so a negative answer just means a reversed arrow, and use power balance as an independent check that the algebra describes the circuit that was actually built.\n",{"path":3014,"title":3015,"module":3007,"summary":3016},"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Frc-transients","RC Transients","How does a circuit get from one steady state to the next when a capacitor refuses to change its voltage all at once? Because a jump would demand infinite current, an RC circuit slides between states exponentially, with a single time constant $\\tau=RC$ that sets the whole schedule: charging fills as $1-e^{-t\u002F\\tau}$, discharge empties as $e^{-t\u002F\\tau}$. We solve the first-order loop equation, read the response off three numbers — the switch-instant voltage, the final dc voltage, and the Thevenin resistance the capacitor sees — and mark where source and probe resistance shift $\\tau$ or where a second storage element hides a mode a one-$\\tau$ fit misses.\n",{"path":3018,"title":3019,"module":3020,"summary":3021},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-trajectories","Magnetic Trajectories","Magnetic Field","A charged particle in a magnetic field never speeds up or slows down, yet its path curves relentlessly. We work out why: the magnetic force is always perpendicular to velocity, so it does no work and bends the transverse motion into a circle of radius $r=mv_\\perp\u002F(|q|B)$ while leaving the parallel motion untouched, producing a helix. We derive the cyclotron frequency, show why it is independent of speed until relativity intervenes, and turn the geometry around: a measured curvature reads back a particle's momentum, which is how tracking detectors weigh what they cannot see.\n",{"path":3023,"title":3024,"module":3020,"summary":3025},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fhall-effect","Hall Effect","Current tells you charge is moving, but not whether the movers are positive or negative, nor how many there are. A magnetic field settles both questions. Push current through a strip in a transverse field and the carriers pile up on one edge until a transverse electric field just balances the magnetic deflection; the sign of the resulting Hall voltage names the carrier's charge and its size counts the carriers per volume. We derive the balance $q\\vec E+q\\vec v_d\\times\\vec B=0$, read off $V_H=IB\u002F(nqt)$, and see why field-and-current reversal is what separates the real Hall signal from the offsets that mimic it.\n",{"path":3027,"title":3028,"module":3020,"summary":3029},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-force-on-conductors","Magnetic Force on Conductors","A magnet pushes on a current-carrying wire even though the wire is electrically neutral. The reason is that each moving carrier feels the Lorentz force, and those microscopic pushes add up to a force the wire's supports must hold. We sum them into $\\d\\vec F=I\\,\\d\\vec\\ell\\times\\vec B$, collapse it to $\\vec F=I\\vec L\\times\\vec B$ for a straight segment in a uniform field, and see exactly when that shortcut fails and the full path integral is needed. The same law runs backward as a measurement: a force-versus-current slope weighs a magnetic field against a known length.\n",{"path":3031,"title":3032,"module":3020,"summary":3033},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-dipoles","Magnetic Dipoles","A compass needle turns to point north; a current loop in a field does the same thing, and for the same reason. Both are magnetic dipoles, and a uniform field cannot push a dipole anywhere, only twist it. We package a loop's response into one vector, the magnetic moment $\\vec\\mu=IA\\hat n$, from which torque $\\vec\\tau=\\vec\\mu\\times\\vec B$ and orientation energy $U=-\\vec\\mu\\cdot\\vec B$ both follow. Stable alignment sits at the energy minimum, a field gradient is what it takes to produce a net force $\\vec F=\\nabla(\\vec\\mu\\cdot\\vec B)$, and the same moment reappears whenever anything from an electron to a planet acts magnetic.\n",{"path":3035,"title":3036,"module":3020,"summary":3037},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmass-spectrometry","Mass Spectrometry","To weigh a single atom you cannot use a scale, so you use a magnetic field instead. A charged ion of unknown mass bends in a field by an amount that depends on its momentum and charge, so if every ion enters with the same velocity, its landing position reads off its mass-to-charge ratio directly. We build the instrument in two stages: crossed electric and magnetic fields that pass only ions with $v=E\u002FB$, and a magnetic sector that bends the survivors along $r=mv\u002F(|q|B)$. Then we ask what blurs a spectral line and how reference ions turn a position into a calibrated mass.\n",{"path":3039,"title":3040,"module":3041,"summary":3042},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmoving-charge-fields","Moving-Charge Fields","Magnetic Sources","Every magnetic field comes from charge in motion, and the simplest source is a single point charge drifting past. We work out the field it produces — normal to both the velocity and the line of sight, falling off as the inverse square — and read off why it vanishes straight ahead of the charge and peaks broadside. Summing many such charges is the bridge to steady currents, valid while speeds stay far below $c$ and the motion changes little during the time its field takes to propagate outward.\n",{"path":3044,"title":3045,"module":3041,"summary":3046},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fbiot-savart-law","Biot–Savart Law","A steady current is a continuous stream of current elements, and the Biot–Savart law hands each one a magnetic contribution — a right-hand cross product that falls off as the inverse square of distance. Summing the contributions along a conductor is a vector line integral, which we carry out for the straight wire to get the endpoint-angle formula. The infinite-wire field $B=\\mu_0 I\u002F2\\pi s$ falls out as the limit where both ends recede, and we mark how fast a finite wire departs from it and when a thin-filament model is safe.\n",{"path":3048,"title":3049,"module":3041,"summary":3050},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fcircular-current-loops","Circular Current Loops","A ring of current is the simplest source with a well-defined magnetic axis, and it is the building block of every coil and electromagnet. Symmetry kills the transverse Biot–Savart contributions along that axis and leaves a single clean integral; we evaluate it to get $B_z=\\mu_0 I R^2\u002F[2(R^2+z^2)^{3\u002F2}]$, read off the centre field $\\mu_0 I\u002F2R$, and watch it fall into the $1\u002Fz^3$ tail of a magnetic dipole far away. Stacking turns just adds their axial contributions, which is what makes a solenoid out of a pile of loops.\n",{"path":3052,"title":3053,"module":3041,"summary":3054},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Famperes-law","Ampère’s Law","When a current arrangement is symmetric enough, the Biot–Savart integral is overkill: Ampère's law, $\\oint_C\\vec B\\cdot\\d\\vec\\ell=\\mu_0 I_{\\rm enc}$, gets the field from a single line of reasoning about how much current a loop encloses. We see why the law holds for any steady current, then use cylindrical, planar, and toroidal symmetry to turn the circulation into simple algebra — the field inside and outside a wire, an infinite sheet, a solenoid, and a toroid. We also mark the catch: without symmetry the law still holds but no longer hands you the field pointwise.\n",{"path":3056,"title":3057,"module":3041,"summary":3058},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fgauss-law-for-magnetism","Gauss’s Law for Magnetism","Electric field lines start and end on charges; magnetic field lines do neither, because no one has ever found an isolated magnetic pole. That single experimental fact is Gauss's law for magnetism: the flux of $\\vec B$ through any closed surface is zero, $\\oint\\vec B\\cdot\\d\\vec A=0$, or in differential form $\\nabla\\cdot\\vec B=0$. We work through what it says — every field line that enters a closed surface must leave it, so field lines close on themselves — and, just as important, what it does not say, since flux through an open surface is generally nonzero.\n",{"path":3060,"title":3061,"module":3041,"summary":3062},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmagnetic-materials","Magnetic Materials","Put matter in a magnetic field and its atoms respond, each acting as a tiny current loop; the aligned moments per unit volume are the magnetization $\\vec M$, whose bound currents add to the field. Separating what we control (the free current) from what the material supplies leads to $\\vec H$ and the relation $\\vec B=\\mu_0(\\vec H+\\vec M)$. We sort materials into diamagnets, paramagnets, and ferromagnets by how $\\vec M$ answers, follow a ferromagnet around its hysteresis loop, and see why the loop's area is the energy dissipated per cycle and why a sample's shape changes the field it actually feels.\n",{"path":3064,"title":3065,"module":3066,"summary":3067},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-flux","Magnetic Flux","Electromagnetic Induction","A magnetic field threading a loop collapses to one signed number, the flux, and every induced voltage in this module turns out to be a rate of change of that number — so defining the flux and its sign comes first. We define it as the surface integral of $\\vec B$ over an oriented surface, reduce it to $BA\\cos\\theta$ for a uniform field on a flat loop, and carry the flux linkage $N\\Phi_B$ of a coil. The chosen normal fixes the sign; reversing it flips the sign without touching the field. Nonuniform fields and curved surfaces force the integral, so we also build the numerical estimate and the checks that separate a reliable value from a nominal field-times-area product.\n",{"path":3069,"title":3070,"module":3066,"summary":3071},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Ffaradays-law","Faraday's Law","Move a magnet toward a coil, or ramp the current in a nearby circuit, and a voltage appears with no battery in sight. Faraday's law names the cause: the emf around a loop equals minus the rate of change of the magnetic flux through it, so any change of field, area, orientation, or position that alters the flux drives an emf. We separate the emf, which lives around the boundary whether or not current can flow, from the current that follows only when the path is closed; fix the single sign convention that ties flux to loop orientation; and read the emf off rotating coils and off flux sampled at discrete times.\n",{"path":3073,"title":3074,"module":3066,"summary":3075},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Flenzs-law","Lenz's Law","The minus sign in Faraday's law is not decoration: it decides which way the induced current flows, and it always chooses the direction that fights the change that produced it. Lenz's law reads that sign off energy conservation — a current that aided the change would be free energy — and turns it into a repeatable procedure. We fix a surface normal and a positive loop direction so the sign is calculable, then work through approaching magnets, expanding loops, coupled coils, and rotating generators, using mechanical work and Joule heating as an independent check on every direction we draw.\n",{"path":3077,"title":3078,"module":3066,"summary":3079},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmotional-emf","Motional EMF","Push a wire through a magnetic field and its free charges feel a sideways magnetic force that piles them up at the ends — a battery made of motion. Motional emf is that effect: the work per unit charge a moving conductor supplies is the line integral of $\\vec v\\times\\vec B$ along it, which for a rod moving perpendicular to both its length and the field collapses to $B\\ell v$. We chase where the energy comes from — the hand or motor fighting the magnetic drag, never the magnetic force itself — solve the sliding-rail circuit from both flux and carrier forces, and carry the idea into rotating rods, homopolar disks, generators, and the back emf of a motor.\n",{"path":3081,"title":3082,"module":3066,"summary":3083},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Feddy-currents","Eddy Currents","A wire carries current along one path; a solid block of metal offers a continuum of them, and any changing flux threading that block sets charge circulating in closed loops it chooses for itself. We ask what those eddy currents do — where they heat, where they drag, and how Lenz's law fixes their direction — and why the same circulation is a feature in an induction furnace and a loss to be suppressed in a transformer core. From a representative-loop estimate we get the scaling (heating grows with the square of frequency and flux rate) and the two design levers, lamination and resistivity, that break the paths a solid conductor would otherwise hand the current.\n",{"path":3085,"title":3086,"module":3066,"summary":3087},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fself-inductance","Self-Inductance","A coil resists changes to its own current. Drive current through it and the flux it produces threads its own turns; change that current and Faraday's law turns the coil against the source with a back emf $\\mathcal E_L=-L\\,\\d I\u002F\\d t$. We define self-inductance as the flux linkage per ampere fixed by winding and core geometry, derive the long-solenoid value $L=\\mu_0 N^2A\u002F\\ell$, and follow the consequence that dominates circuits: because a finite voltage can only sustain a finite $\\d I\u002F\\d t$, an inductor's current cannot jump — which is why opening a switch on a live coil throws a spark.\n",{"path":3089,"title":3090,"module":3066,"summary":3091},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-energy","Magnetic Energy","Building current in a coil means working against its back emf, and that work does not vanish — it sits in the magnetic field as recoverable energy $U_B=\\tfrac12LI^2$, spread through space at density $u_B=B^2\u002F(2\\mu_0)$. We derive both forms, show they agree for a solenoid, and read a force out of the same energy: an armature is pulled toward higher inductance, and $B^2\u002F(2\\mu_0)$ doubles as a magnetic pressure. The lesson closes on the accounting a real switching event demands, where recoverable energy, copper heating, core loss, and clamp dissipation must balance a single ledger.\n",{"path":3093,"title":3094,"module":3066,"summary":3095},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Frl-circuits","RL Circuits","Put a resistor and an inductor in series and the current cannot switch on or off at will: it climbs to $V_0\u002FR$ and falls away exponentially on a single time scale $\\tau=L\u002FR$ set by how much flux the coil hoards against how fast the resistor bleeds it. We solve the turn-on and turn-off, then confront the practical sting — because the coil's current refuses to stop instantly, breaking its path throws up a large voltage, which is why real inductive circuits carry freewheel diodes and clamps that trade voltage stress against how quickly the current dies.\n",{"path":3097,"title":3098,"module":3099,"summary":3100},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-fundamentals","AC Fundamentals","Alternating Current","A wall socket delivers a voltage that averages to zero over each cycle, yet it still heats a filament and runs a motor. The resolution is that dissipation follows the mean of the square, not the mean, so we define the root-mean-square value that makes an alternating source the equal of a DC one for resistive heating. We show a sinusoid's RMS is its peak divided by $\\sqrt2$, work out the average power an ideal resistor draws when its current stays in phase with the applied voltage, and separate the peak, average, and RMS descriptions that a single number cannot combine.\n",{"path":3102,"title":3103,"module":3099,"summary":3104},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Freactance","Reactance","A resistor obeys Ohm's law instant by instant, but a capacitor responds to how fast its voltage changes and an inductor to how fast its current changes. Under a steady sinusoid that rate-dependence collapses to a fixed quarter-cycle phase shift and a frequency-dependent amplitude ratio, the reactance. We derive $X_C=1\u002F(\\omega C)$ and $X_L=\\omega L$, adopt phasors to turn the defining derivatives into multiplication by $j\\omega$ so a single complex impedance carries amplitude and phase together, and track the energy an ideal reactance stores and returns without dissipating it. Real windings and dielectrics add loss, leakage, and self-resonance that bound where the ideal formulas hold.\n",{"path":3106,"title":3107,"module":3099,"summary":3108},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Frlc-resonance","RLC Resonance","Put a resistor, inductor, and capacitor in one loop and their reactances work against each other: inductive reactance grows with frequency while capacitive reactance shrinks, and at one frequency they cancel exactly. There the branch looks purely resistive, the current peaks, and the inductor and capacitor voltages can swing far above the source. We locate that resonance at $\\omega_0=1\u002F\\sqrt{LC}$, measure how sharp the peak is with the quality factor $Q=\\omega_0L\u002FR$, tie its half-power bandwidth $R\u002FL$ to the ringdown of the unforced circuit, and read the same poles off as bandpass and peaked filters at the R, L, or C terminals.\n",{"path":3110,"title":3111,"module":3099,"summary":3112},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-power","AC Power","Multiply an AC load's RMS voltage by its RMS current and you get an answer in volt-amperes that the wiring must carry, but not in general the watts the load consumes. The phase between voltage and current splits that product into a part that does net work and a part that merely sloshes energy back and forth. We derive the average power $P=V_{\\rm rms}I_{\\rm rms}\\cos\\phi$, package amplitude and phase into complex power $S=P+jQ$ so that real, reactive, and apparent power form one right triangle, and see why a harmonic-rich current forces the time-domain definition $P=\\langle vi\\rangle$ in place of a single phase angle.\n",{"path":3114,"title":3115,"module":3099,"summary":3116},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Ftransformers","Transformers","Two coils sharing an iron core exchange no charge, yet a changing current in one drives a voltage in the other, and the ratio of their turns sets how voltage and current trade off between the windings. That lets a transformer step a voltage up or down, isolate two circuits, and make a load look larger or smaller to the source by the square of the turns ratio. We build the ideal ratio element from Faraday's law and the dot convention, derive the reflected-impedance rule, then add the winding resistance, leakage, magnetizing current, and core loss that turn the ideal ratios into real regulation, efficiency, and a bounded voltage-frequency range.\n",{"path":3118,"title":3119,"module":3120,"summary":3121},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdisplacement-current","Displacement Current","Maxwell’s Equations and Electromagnetic Waves","Ampère's law asks for the current through a surface bounded by a loop, but a charging capacitor breaks it: slide the surface off the wire and into the gap and the enclosed conduction current drops to zero, while the magnetic field around the loop plainly does not. Maxwell's repair is to count a changing electric flux as itself a source of magnetic circulation. We derive the displacement-current term $\\varepsilon_0\\,\\d\\Phi_E\u002F\\d t$, show that charge continuity demands it, compute the magnetic field it produces inside a charging capacitor, and see how it closes the Ampère–Maxwell law so that electric and magnetic fields can sustain one another as a wave.\n",{"path":3123,"title":3124,"module":3120,"summary":3125},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-waves","Electromagnetic Waves","Once a changing electric flux can drive a magnetic field, the two curl laws feed each other: a disturbance in one regenerates the other, and the pair walks off through empty space with no medium holding it up. We take the curl of Faraday's law, land on a wave equation whose speed is fixed entirely by $\\mu_0$ and $\\varepsilon_0$, and find that $c=1\u002F\\sqrt{\\mu_0\\varepsilon_0}$ falls out of purely electric and magnetic constants. The plane-wave solution then fixes the geometry — $\\vec E$, $\\vec B$, and the propagation direction mutually perpendicular, oscillating in phase, with amplitudes locked at $E=cB$ — a set of independent predictions any real measurement must meet at once.\n",{"path":3127,"title":3128,"module":3120,"summary":3129},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-momentum","Electromagnetic Momentum","A light beam carries no mass, yet it pushes: shine it on a surface and the surface feels a force. We trace that force back to the fields, which store energy with density $\\varepsilon_0E^2$ and carry it along the Poynting vector $\\vec S=\\vec E\\times\\vec B\u002F\\mu_0$. Because that energy also carries momentum $U\u002Fc$, an absorbed beam presses with $I\u002Fc$ and a mirror with $2I\u002Fc$. We derive the Poynting theorem as local energy conservation, tie intensity to field amplitude, and work the momentum balance carefully enough that oblique incidence, partial reflection, and finite beams all drop out of one accounting.\n",{"path":3131,"title":3132,"module":3120,"summary":3133},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdipole-radiation","Dipole Radiation","Only accelerating charge radiates, and the simplest accelerator is a charge sloshing back and forth: an oscillating electric dipole. We work out the field it throws off, keeping the part that survives to large distance — the $1\u002Fr$ radiation field whose intensity goes as $\\sin^2\\theta\u002Fr^2$, zero along the dipole axis and strongest broadside. From it follow the $\\omega^4$ scaling of total radiated power, radiation resistance as the feed's view of that escaping power, and, through reciprocity, the fact that a good transmitter receives well in the same directions. The near-zone terms that fall off faster carry no net power, and we mark carefully where each description is allowed to be used.\n",{"path":3135,"title":3136,"module":3120,"summary":3137},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fpolarization","Polarization","A plane wave still leaves one thing free: which way its electric field points as it oscillates. That freedom is polarization, set entirely by the relative amplitude and phase of the two transverse field components — in phase gives a line, equal amplitudes a quarter cycle apart give a circle, everything else an ellipse. We work out how a linear analyzer reads a state through Malus's law $I=I_0\\cos^2\\theta$, why that scan alone cannot tell circular light from unpolarized, and how a quarter-wave plate plus a few analyzer settings recover the full Stokes vector and the degree of polarization.\n",{"path":3139,"title":3140,"module":3141,"summary":3142},"\u002Felectricity-and-magnetism\u002Foptics\u002Freflection-and-refraction","Reflection and Refraction","Geometrical Optics","Light meeting a boundary between two transparent media splits into a reflected ray and a bent transmitted one, and predicting where those rays go is the whole starting point of geometrical optics. Fixing one convention — every angle measured from the surface normal — we get reflection's equal angles and derive Snell's law $n_1\\sin\\theta_1=n_2\\sin\\theta_2$ from wavefront timing. That single relation, applied once or twice, yields the critical angle and total internal reflection, prism deviation, the lateral shift through a window, apparent depth, and a fiber's acceptance cone; a wavelength-dependent index then adds dispersion. We mark throughout where the ray picture is trustworthy: feature sizes large against the wavelength and clean interface geometry.\n",{"path":3144,"title":3145,"module":3141,"summary":3146},"\u002Felectricity-and-magnetism\u002Foptics\u002Fthin-lenses","Thin Lenses","A lens gathers the light spreading from one point back onto another, and a single paraxial relation $1\u002Fs+1\u002Fs'=1\u002Ff$ predicts where that image lands and how large it is. We collapse two refractions into one bending plane, read image position and orientation off the three principal rays, and trace focal length back to glass and curvature through the lensmaker equation. Sign conventions carry the physics here — they separate real from virtual images and upright from inverted — so we drill them before chaining lenses in sequence and in contact. The lesson ends on how focal length is actually measured on a bench, and where finite thickness, aperture, and dispersion break the thin-lens picture.\n",{"path":3148,"title":3149,"module":3141,"summary":3150},"\u002Felectricity-and-magnetism\u002Foptics\u002Fspherical-mirrors","Spherical Mirrors","Curve a mirror and it stops merely reflecting an image and starts forming one: the same $1\u002Fs+1\u002Fs'=1\u002Ff$ that governs lenses reappears, now with $f=R\u002F2$ and reflected rays and object sharing one side of the glass. We derive the mirror equation from the reflection geometry of a single paraxial ray, then let signed distances do the sorting — real inverted images on the near branch, virtual upright ones behind the surface — and check the concave, convex, and plane-mirror limits against each other. The second half turns to how focal length is actually measured on a bench, by finite conjugates, distant targets, return imaging, and sagitta, and to the aperture and off-axis aberrations the single paraxial focus cannot capture.\n",{"path":3152,"title":3153,"module":6,"summary":6},"\u002Felectricity-and-magnetism","Electricity & Magnetism",{"path":3155,"title":3156,"module":3157,"summary":3158},"\u002Flinear-algebra\u002Flinear-systems\u002Fsystems-and-echelon-forms","Systems of Linear Equations and Row Reduction","Linear Equations in Linear Algebra","A linear system is a finite set of linear equations in shared variables. Elementary row operations rewrite it without changing its solution set, and reducing the augmented matrix to echelon form decides both existence and uniqueness. Pivot positions say whether the solution set is empty, a single point, or infinite.\n",{"path":3160,"title":3161,"module":3157,"summary":3162},"\u002Flinear-algebra\u002Flinear-systems\u002Fvector-and-matrix-equations","Vector Equations and the Matrix Equation Ax = b","The same linear system reads three equivalent ways: a system of equations, a vector equation asking whether b is a linear combination of fixed vectors, and a matrix equation Ax = b. Ax is the linear combination of A's columns weighted by x, so consistency for a given b means b lies in the span of the columns, and consistency for every b means the columns span all of R^m.\n",{"path":3164,"title":3165,"module":3157,"summary":3166},"\u002Flinear-algebra\u002Flinear-systems\u002Fsolution-sets-and-applications","Solution Sets and Applied Linear Systems","A homogeneous system Ax = 0 has a solution set that is a span through the origin; a consistent Ax = b has that same span translated by any one particular solution. Parametric vector form writes both explicitly. The structure shows up in applied systems with many solutions: equilibrium prices, balanced chemical reactions, network flows, weight-loss diets, and migration models.\n",{"path":3168,"title":3169,"module":3157,"summary":3170},"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-independence","Linear Independence","A set of vectors is linearly independent when the only linear combination equal to zero is the trivial one; otherwise a dependence relation writes one vector in terms of the others. For the columns of A the question becomes whether Ax = 0 has only the trivial solution — a pivot in every column. Counting pivots settles independence, and any set with more vectors than entries is automatically dependent.\n",{"path":3172,"title":3173,"module":3157,"summary":3174},"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-transformations","Linear Transformations and Their Matrices","Reading A as an action rather than an array, x maps to Ax is a transformation from R^n to R^m. The ones that preserve addition and scalar multiplication are the linear transformations, and every one is x maps to Ax for a unique standard matrix whose columns are the images of the standard basis vectors. Onto and one-to-one translate into the span and independence of those columns.\n",{"path":3176,"title":3177,"module":3178,"summary":3179},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-operations","Matrix Operations","Matrix Algebra","Matrices add and scale entrywise, but their product is defined so that multiplication corresponds to composition of linear maps: the columns of AB are A applied to the columns of B. From that requirement follow the row-column rule, the algebra of products (associative and distributive but not commutative), powers, and the transpose.\n",{"path":3181,"title":3182,"module":3178,"summary":3183},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-inverse-and-invertibility","The Inverse and the Invertible Matrix Theorem","The inverse of a square matrix is the matrix analogue of a reciprocal, defined by AA⁻¹ = I. A closed form settles the 2×2 case; the Gauss–Jordan algorithm row reduces [A | I] to [I | A⁻¹] in general; and elementary matrices record single row operations. The Invertible Matrix Theorem collects a dozen equivalent conditions for invertibility into one statement.\n",{"path":3185,"title":3186,"module":3178,"summary":3187},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fpartitioned-matrices-and-lu","Block Matrices and the LU Factorization","Partitioning a matrix into blocks lets sums, products, and inverses be computed block by block, as if the submatrices were scalars. Block structure also underlies the LU factorization A = LU, which splits solving Ax = b into two fast triangular solves and repays the cost whenever many systems share one coefficient matrix.\n",{"path":3189,"title":3190,"module":3178,"summary":3191},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fsubspaces-dimension-rank","Subspaces of Rⁿ, Dimension, and Rank","A subspace is a set closed under addition and scalar multiplication. Every matrix carries two: the column space of all attainable outputs Ax, and the null space of all solutions of Ax = 0. A basis measures each with a minimal spanning set, dimension counts it, and the Rank Theorem ties pivots and free variables together as rank + nullity = n.\n",{"path":3193,"title":3194,"module":3178,"summary":3195},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fapplications-leontief-and-graphics","Applications: Leontief Economics and Computer Graphics","The Leontief input–output model balances an economy through (I − C)x = d and expands the inverse as a geometric series in the consumption matrix. Computer graphics moves figures with matrix products, using homogeneous coordinates so that translation and perspective projection become matrix multiplications too.\n",{"path":3197,"title":3198,"module":3199,"summary":3200},"\u002Flinear-algebra\u002Fdeterminants\u002Fdeterminants-and-cofactors","Introduction to Determinants","Determinants","The determinant of a square matrix is defined recursively by cofactor expansion: an n-by-n determinant is a signed sum of (n-1)-by-(n-1) determinants built from the first row. The expansion can equally run along any row or down any column, and a triangular matrix has determinant equal to the product of its diagonal.\n",{"path":3202,"title":3203,"module":3199,"summary":3204},"\u002Flinear-algebra\u002Fdeterminants\u002Fproperties-of-determinants","Properties of Determinants","Row operations act on the determinant in three predictable ways, and this turns row reduction into a fast algorithm: the determinant is the product of the pivots times a sign for the interchanges. The same properties yield the invertibility test det A is nonzero, the transpose identity, and the multiplicative law det(AB) equals det A times det B.\n",{"path":3206,"title":3207,"module":3199,"summary":3208},"\u002Flinear-algebra\u002Fdeterminants\u002Fcramer-volume-and-area","Cramer's Rule, Volume, and Linear Transformations","Cramer's rule writes each unknown of an invertible system as a ratio of determinants, and the same idea gives a closed formula for the inverse through the adjugate. Geometrically the absolute determinant is the area of the parallelogram or the volume of the parallelepiped spanned by the columns, so a linear map scales every region's measure by that factor.\n",{"path":3210,"title":3211,"module":3212,"summary":3213},"\u002Flinear-algebra\u002Fvector-spaces\u002Fvector-spaces-and-subspaces","Vector Spaces and Subspaces","Vector Spaces","A vector space is any set closed under addition and scalar multiplication that obeys ten algebraic axioms. The same axioms that govern arrows in the plane govern polynomials, functions, matrices, and infinite signals, so one theory covers them all. A subspace is a subset that is a vector space in its own right, tested by three conditions, and the span of any set of vectors is the smallest subspace containing them.\n",{"path":3215,"title":3216,"module":3212,"summary":3217},"\u002Flinear-algebra\u002Fvector-spaces\u002Fnull-and-column-spaces","Null Spaces, Column Spaces, and Linear Transformations","Two subspaces sit inside every matrix. The null space collects all solutions of $Ax = 0$ and lives in the domain; the column space collects every attainable $Ax$ and lives in the codomain. One is defined implicitly by a condition, the other explicitly by a spanning set, and the same pair appears for an abstract linear transformation as its kernel and range.\n",{"path":3219,"title":3220,"module":3212,"summary":3221},"\u002Flinear-algebra\u002Fvector-spaces\u002Fbases-and-independent-sets","Linearly Independent Sets and Bases","A basis is a spanning set with no redundancy: linearly independent and still large enough to reach every vector. The spanning-set theorem shows any spanning set can be trimmed to a basis by discarding dependent vectors, and the pivot columns of a matrix give a basis for its column space. Independence and spanning are defined for abstract spaces exactly as in $\\mathbb{R}^n$.\n",{"path":3223,"title":3224,"module":3212,"summary":3225},"\u002Flinear-algebra\u002Fvector-spaces\u002Fcoordinate-systems","Coordinate Systems","Fixing a basis assigns every vector a unique list of coordinates, turning an abstract space into $\\mathbb{R}^n$. The coordinate mapping is a one-to-one linear transformation onto $\\mathbb{R}^n$ — an isomorphism — so any $n$-dimensional space is indistinguishable from $\\mathbb{R}^n$ as far as vector-space computations go. In $\\mathbb{R}^n$ the change-of-coordinates matrix $P_B$ and its inverse convert between basis coordinates and standard coordinates.\n",{"path":3227,"title":3228,"module":3212,"summary":3229},"\u002Flinear-algebra\u002Fvector-spaces\u002Fdimension-and-rank","The Dimension of a Vector Space and Rank","Every basis of a space has the same number of vectors, and that number is the dimension. Rank is the dimension of the column space, equal to the dimension of the row space and to the number of pivots. The Rank Theorem, rank plus nullity equals the number of columns, ties the four fundamental subspaces of a matrix together and adds six lines to the Invertible Matrix Theorem.\n",{"path":3231,"title":3232,"module":3212,"summary":3233},"\u002Flinear-algebra\u002Fvector-spaces\u002Fchange-of-basis","Change of Basis","Two bases give the same vector two different coordinate vectors, and a single invertible matrix converts between them. Its columns are the coordinate vectors of the old basis expressed in the new one, and its inverse reverses the conversion. In $\\mathbb{R}^n$ the change-of-coordinates matrix between two bases is found by one row reduction.\n",{"path":3235,"title":3236,"module":3212,"summary":3237},"\u002Flinear-algebra\u002Fvector-spaces\u002Fdifference-equations-and-markov","Applications: Difference Equations and Markov Chains","The solutions of an nth-order linear difference equation form an $n$-dimensional vector space, so finding $n$ independent solutions gives them all. A Markov chain evolves a probability distribution by repeated multiplication by a stochastic matrix, and a regular chain converges to a unique steady-state vector fixed by that matrix. Both applications turn a dynamic process into a subspace or a fixed-point question.\n",{"path":3239,"title":3240,"module":3241,"summary":3242},"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-eigenvalues","Eigenvectors and Eigenvalues","Eigenvalues and Eigenvectors","An eigenvector of a square matrix is a nonzero vector the matrix only stretches; its eigenvalue is the stretch factor. The eigenspace of an eigenvalue is the null space of A minus lambda times the identity, the eigenvalues of a triangular matrix are its diagonal entries, and eigenvectors for distinct eigenvalues are linearly independent.\n",{"path":3244,"title":3245,"module":3241,"summary":3246},"\u002Flinear-algebra\u002Feigenvalues\u002Fthe-characteristic-equation","The Characteristic Equation","The eigenvalues of a matrix are the roots of its characteristic polynomial det(A minus lambda I). This degree-n polynomial carries an algebraic multiplicity at each repeated root, a nonzero determinant is equivalent to zero not being an eigenvalue, and similar matrices share a characteristic polynomial and hence the same eigenvalues.\n",{"path":3248,"title":3249,"module":3241,"summary":3250},"\u002Flinear-algebra\u002Feigenvalues\u002Fdiagonalization","Diagonalization","A matrix is diagonalizable when it factors as A equals P D P inverse with D diagonal, which happens exactly when it has n linearly independent eigenvectors. The factorization computes matrix powers cheaply, distinct eigenvalues guarantee it, and a repeated eigenvalue permits it only when its eigenspace dimension equals its multiplicity.\n",{"path":3252,"title":3253,"module":3241,"summary":3254},"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-linear-transformations","Eigenvectors and Linear Transformations","Every linear transformation between finite-dimensional spaces has a matrix relative to chosen bases, built from the coordinate vectors of the images of the basis vectors. For a map from a space to itself, an eigenvector basis makes that matrix diagonal, and that change of basis is diagonalization; the matrices similar to A are the representations of the map in every basis.\n",{"path":3256,"title":3257,"module":3241,"summary":3258},"\u002Flinear-algebra\u002Feigenvalues\u002Fcomplex-eigenvalues","Complex Eigenvalues","A real matrix with no real eigenvalues still has complex ones, occurring in conjugate pairs. A real 2-by-2 matrix with eigenvalue a plus b i is similar to a rotation-scaling matrix, whose rotation angle is the argument of the eigenvalue and whose scale factor is its modulus; the modulus decides whether the trajectories close up, spiral in, or spiral out.\n",{"path":3260,"title":3261,"module":3241,"summary":3262},"\u002Flinear-algebra\u002Feigenvalues\u002Fdynamical-systems","Discrete and Continuous Dynamical Systems","Eigenvalues govern the long-term behavior of a system that evolves by x becomes A x or by x prime equals A x. An eigenvector basis decouples both kinds of system into independent scalar equations; the eigenvalues then classify the origin as attractor, repeller, saddle, or spiral, and the dominant eigenpair fixes the growth rate and limiting direction.\n",{"path":3264,"title":3265,"module":3241,"summary":3266},"\u002Flinear-algebra\u002Feigenvalues\u002Fpower-method","Iterative Estimates for Eigenvalues","When only a numerical eigenvalue is needed, iteration is preferred over the characteristic polynomial. The power method repeatedly multiplies by A to converge on the dominant eigenvalue and its eigenvector; the Rayleigh quotient sharpens the estimate for symmetric matrices; and the inverse power method targets any eigenvalue near a known guess.\n",{"path":3268,"title":3269,"module":3270,"summary":3271},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-length-orthogonality","Inner Product, Length, and Orthogonality","Orthogonality and Least Squares","The dot product turns the algebra of vectors in R^n into geometry: length, distance, and perpendicularity. The inner product yields the norm, the Pythagorean theorem, and the orthogonal complement, and the null space of a matrix is the orthogonal complement of its row space.\n",{"path":3273,"title":3274,"module":3270,"summary":3275},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Forthogonal-sets-and-projections","Orthogonal Sets and Orthogonal Projections","An orthogonal basis makes coordinates trivial: each weight is a single dot product, no linear system required. Orthogonal and orthonormal bases give a direct projection formula onto a line and onto a subspace, the orthogonal decomposition and best-approximation theorems, and the matrix form U U-transpose of a projection.\n",{"path":3277,"title":3278,"module":3270,"summary":3279},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fgram-schmidt-and-qr","The Gram-Schmidt Process and QR Factorization","Gram-Schmidt turns any basis into an orthogonal one by repeatedly subtracting off projections onto the span already built. Normalizing the result and recording the coefficients factors the matrix as A = QR, with Q orthonormal and R upper triangular, the factorization behind stable least-squares and eigenvalue algorithms.\n",{"path":3281,"title":3282,"module":3270,"summary":3283},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-problems","Least-Squares Problems","When Ax = b has no solution, the least-squares solution makes Ax as close to b as possible. The closest Ax is the projection of b onto the column space, and the vector that produces it solves the normal equations A-transpose A x = A-transpose b. Uniqueness, the residual error, and the stabler QR route follow.\n",{"path":3285,"title":3286,"module":3270,"summary":3287},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-applications","Applications to Linear Models","Curve fitting is a least-squares problem in statistical notation. The least-squares line, polynomial fits, and multiple regression all reduce to X beta = y with a design matrix X built from the data, solved by the same normal equations.\n",{"path":3289,"title":3290,"module":3270,"summary":3291},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-spaces","Inner Product Spaces","Promoting the four properties of the dot product to axioms defines an inner product on any vector space, including spaces of functions. Length, distance, orthogonality, Gram-Schmidt, and best approximation all carry over, along with the Cauchy-Schwarz and triangle inequalities and the integral inner product behind Fourier approximation.\n",{"path":3293,"title":3294,"module":3295,"summary":3296},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fdiagonalizing-symmetric-matrices","Diagonalization of Symmetric Matrices","Symmetric Matrices, Quadratic Forms, and the SVD","A symmetric matrix is one that equals its own transpose. Every such matrix can be diagonalized by an orthogonal change of basis, A = PDPᵀ, with real eigenvalues and perpendicular eigenvectors. This is the Spectral Theorem, and it rewrites A as a weighted sum of rank-one projections onto its eigenvectors.\n",{"path":3298,"title":3299,"module":3295,"summary":3300},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fquadratic-forms","Quadratic Forms","A quadratic form xᵀAx is the second-degree analogue of a linear map, attached to a symmetric matrix A. Orthogonal diagonalization changes variables to the eigenbasis, removing all cross-terms and rotating the form into standard position. The signs of the eigenvalues then classify it as definite or indefinite.\n",{"path":3302,"title":3303,"module":3295,"summary":3304},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fconstrained-optimization","Constrained Optimization","Maximizing a quadratic form xᵀAx over the unit sphere has an exact answer: the maximum is the largest eigenvalue of A, attained at its eigenvector, and the minimum is the smallest eigenvalue. Adding orthogonality constraints peels off the eigenvalues in order, characterizing the whole spectrum by optimization.\n",{"path":3306,"title":3307,"module":3295,"summary":3308},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsingular-value-decomposition","The Singular Value Decomposition","The singular value decomposition factors any m×n matrix as A = UΣVᵀ, with orthogonal U and V and a nonnegative diagonal Σ of singular values. The singular values are the square roots of the eigenvalues of AᵀA, and they describe the matrix geometrically as a rotation, an axiswise stretch, and another rotation, exposing rank, the four fundamental subspaces, and a best low-rank approximation.\n",{"path":3310,"title":3311,"module":3295,"summary":3312},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsvd-applications-pca-imaging","Applications: Image Processing and Statistics","Principal component analysis diagonalizes the covariance matrix of a data set, producing uncorrelated variables ordered by variance. The leading components capture most of the variation, which reduces dimension, compresses images through low-rank SVD approximation, and connects directly to the singular values of the data matrix.\n",{"path":3314,"title":3315,"module":3316,"summary":3317},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-thinking-and-matrix-computation","Numerical Thinking and Matrix Computation","Numerical Linear Algebra","Numerical analysis builds efficient discrete algorithms for continuous problems, and its cost is dominated as much by memory traffic as by arithmetic. Block matrix calculus, flop counts, and the BLAS efficiency ratio fix the cost model; triangular and unitary matrices are the two computational building blocks every factorization rests on.\n",{"path":3319,"title":3320,"module":3316,"summary":3321},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Flu-and-cholesky","LU and Cholesky Factorization in Practice","Gaussian elimination, read as a factorization A = LU, turns a linear system into two triangular solves. A single near-zero pivot wrecks it, so partial pivoting reorders rows to pick the largest available pivot and makes the method work for every invertible matrix. For symmetric positive-definite systems, Cholesky halves the cost and needs no pivoting.\n",{"path":3323,"title":3324,"module":3316,"summary":3325},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fconditioning-and-floating-point","Conditioning and Floating-Point Arithmetic","A problem's condition number measures how much its answer moves when its data is perturbed, independent of any algorithm. Subtraction is ill-conditioned under cancellation, and for a linear system the amplifier is the matrix condition number κ(A). Floating-point arithmetic supplies the perturbation: every real number is rounded to within a relative machine precision, so even perfect computation inherits an error of order κ times the unit roundoff.\n",{"path":3327,"title":3328,"module":3316,"summary":3329},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fstability-and-error-analysis","Numerical Stability and Backward Error Analysis","An algorithm is backward stable when its computed answer is the exact answer to a slightly perturbed problem. Combined with the condition number this gives the governing rule of thumb: forward error is at most condition times stability. Three cancellation case studies make the point, then the residual-based backward error applies it to Ax = b and shows why partial pivoting keeps Gaussian elimination stable.\n",{"path":3331,"title":3332,"module":3316,"summary":3333},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fqr-and-numerical-least-squares","QR, Householder, and Numerical Least Squares","The least-squares problem reduces to the normal equations, but forming AᵀA squares the condition number and can wreck accuracy. The stable route computes a QR factorization directly on A and solves Rx = Qᵀb. Householder reflectors build that QR one column at a time using length-preserving reflections, the unconditionally backward-stable building block behind every serious least-squares solver.\n",{"path":3335,"title":3336,"module":3316,"summary":3337},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-eigenvalues-and-svd","Numerical Eigenvalue Problems and the SVD","Eigenvalues cannot be found by a formula for large matrices, so they are found by iteration. Power and inverse iteration converge to one eigenvector at a rate set by the eigenvalue gap; the QR algorithm sweeps a matrix to Schur form and, with a good shift and a Hessenberg reduction, computes the whole spectrum in cubic time. Singular values follow from the same machinery applied without ever forming AᵀA.\n",{"path":3339,"title":3340,"module":3341,"summary":3342},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-combinations","Affine Combinations","Geometry of Vector Spaces","An affine combination is a linear combination whose weights sum to one. The affine hull of a set is the smallest flat containing it: a point, a line, a plane, or a translated subspace. Homogeneous coordinates turn every affine combination into an ordinary linear combination one dimension up.\n",{"path":3344,"title":3345,"module":3341,"summary":3346},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-independence-and-barycentric-coordinates","Affine Independence and Barycentric Coordinates","Affine independence is linear independence for the translated or lifted points, and it guarantees each point of an affine hull a unique weight vector. Those weights are barycentric coordinates: centers of mass, ratios of triangle areas, and the interpolation rule behind smooth shading in computer graphics.\n",{"path":3348,"title":3349,"module":3341,"summary":3350},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fconvex-combinations-and-convex-sets","Convex Combinations and Convex Sets","A convex combination is an affine combination with nonnegative weights, and the convex hull of a set is the smallest convex set containing it. Convex sets are closed under intersection, and Carathéodory's theorem bounds how many points a convex combination in $\\mathbb{R}^n$ ever needs: at most $n+1$.\n",{"path":3352,"title":3353,"module":3341,"summary":3354},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fhyperplanes-and-polytopes","Hyperplanes and Polytopes","A hyperplane is a level set of a linear functional, the set where an inner product equals a constant. Hyperplanes separate disjoint convex sets and support them at their boundaries. Polytopes are convex hulls of finite point sets; their vertices are the extreme points, and a linear functional attains its extremes there.\n",{"path":3356,"title":3357,"module":3341,"summary":3358},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fcurves-and-surfaces","Curves and Surfaces","Bézier curves are affine combinations of control points with polynomial weights, so they lie in the convex hull of those points and bend toward them. The de Casteljau algorithm evaluates them by repeated interpolation, a matrix form factors them for computation, and matching endpoints and tangents joins segments into smooth curves and surfaces.\n",{"path":3360,"title":3361,"module":6,"summary":6},"\u002Flinear-algebra","Linear Algebra",{"path":3363,"title":3364,"module":6,"summary":6},"\u002Ftheory-of-computation","Theory of Computation",{"path":3366,"title":3367,"module":1231,"summary":3368},"\u002Fcomputer-architecture\u002Ffoundations\u002Fbits-bytes-and-words","Bits, Bytes, and Words","Everything a machine stores is a string of bits grouped into bytes. We set out binary and hexadecimal, the byte as the unit of addressing, the word as the machine's natural integer size, and byte ordering — why the same four bytes read as 0x01234567 on one machine and 0x67452301 on another.\n",{"path":3370,"title":3371,"module":1231,"summary":3372},"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-representation","Integer Representation","A fixed-width byte string is just a pattern; what makes it a number is the rule we read it by. We define unsigned encoding and two's complement — where the top bit carries a negative weight — derive the ranges UMax, TMin, and TMax, and show how the same bits reinterpret between signed and unsigned, how widening sign-extends, and what truncation throws away.\n",{"path":3374,"title":3375,"module":1231,"summary":3376},"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-arithmetic","Integer Arithmetic","Fixed-width integer arithmetic is arithmetic modulo a power of two: add past the top and the result wraps. We work out unsigned and two's-complement addition and the rules that detect their overflow, why negation is a complement-plus-one, how multiplication truncates to the low-order bits and how compilers turn constant multiplies into shifts and adds, why C declares signed overflow undefined, and the bias fix that keeps shift-based signed division rounding toward zero.\n",{"path":3378,"title":3379,"module":1231,"summary":3380},"\u002Fcomputer-architecture\u002Ffoundations\u002Ffloating-point","Floating Point","IEEE-754 trades the exactness of integers for enormous range by storing numbers as sign, exponent, and fraction — scientific notation in binary. We lay out the single and double formats, the bias that encodes the exponent, the three regimes (normalized, denormalized, special), a worked encode\u002Fdecode, the four rounding modes and round-to-even at the bit level, why addition is not associative, the pitfalls of float-int conversion, and why 0.1 has no exact binary representation.\n",{"path":3382,"title":3383,"module":1231,"summary":3384},"\u002Fcomputer-architecture\u002Ffoundations\u002Fboolean-algebra-and-bit-manipulation","Boolean Algebra and Bit Manipulation","Treat a word as a vector of independent bits and the bitwise operators become an algebra. We define AND, OR, NOT, and XOR as bit vectors, build the masking idioms that set, clear, toggle, and test individual bits, extract fields with zero- and sign-extension, count set bits three ways, derive the classic x & (x - 1) family of tricks, and distinguish bitwise operators from C's short-circuiting logical operators.\n",{"path":3386,"title":3387,"module":3388,"summary":3389},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fthe-machines-view","The Machine's View","Machine-Level Programming","The instruction set architecture is the contract a compiler writes against: the program counter, sixteen integer registers with their sub-register widths, and the condition codes. We follow one C function down through gcc to assembly, learn to read an instruction as operation plus operands, and fix the vocabulary the rest of the module uses.\n",{"path":3391,"title":3392,"module":3388,"summary":3393},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fdata-movement","Data Movement","Most instructions a program runs simply move data. We cover the mov family and its size suffixes, the three operand forms, the full memory addressing mode D(Rb,Ri,S) and its special cases, lea for address arithmetic, and how push and pop manipulate the stack pointer %rsp on a stack that grows toward lower addresses.\n",{"path":3395,"title":3396,"module":3388,"summary":3397},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farithmetic-and-logic","Arithmetic and Logic","The ALU instructions that compute on register and memory values: add, sub, and imul; the unary inc\u002Fdec\u002Fneg\u002Fnot; the shifts sal\u002Fshr\u002Fsar; the bitwise and\u002For\u002Fxor; and lea reused as a fast arithmetic trick. Each binary operation also sets the condition-code flags CF, ZF, SF, and OF, which cmp and test compute without keeping a result.\n",{"path":3399,"title":3400,"module":3388,"summary":3401},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fcontrol-flow","Control Flow","How a flat instruction stream realizes branches and loops. The conditional jumps read the condition-code flags; set instructions turn flags into a 0\u002F1 byte. We translate if\u002Felse into the standard compare-and-branch pattern, while\u002Ffor loops into the guarded-do form, and dense switches into jump tables that index a target directly.\n",{"path":3403,"title":3404,"module":3388,"summary":3405},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fprocedures","Procedures","How a function call works at the machine level: the run-time stack, call and ret passing control through a saved return address, the System V convention that routes the first six arguments through %rdi..%r9 and the result through %rax, the caller-saved versus callee-saved split, the stack frame, and a recursive factorial traced through its frames.\n",{"path":3407,"title":3408,"module":3388,"summary":3409},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farrays-structs-and-alignment","Arrays, Structs, and Alignment","How aggregate data lays out in memory. Arrays as base-plus-scaled-index, the row-major ordering of multidimensional arrays, pointer arithmetic in units of the pointed-to type, struct fields at fixed byte offsets, the overlapping storage of unions, and the alignment rules that force padding into a struct.\n",{"path":3411,"title":3412,"module":3388,"summary":3413},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fmemory-layout-and-buffer-overflows","Memory Layout and Buffer Overflows","The process address space — text, data, heap, and stack — and the classic vulnerability it enables. A stack buffer that is written past its end can overwrite the saved return address and redirect ret, so we sketch the mechanism defensively and then the three standard protections: stack canaries, a non-executable stack, and address-space layout randomization.\n",{"path":3415,"title":3416,"module":3417,"summary":3418},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fwhat-an-isa-is","What an ISA Is","Instruction Set Architecture","The instruction set architecture is the contract that lets a compiler and a chip be written by people who never meet: the stable interface software targets and hardware implements. We separate architecture from microarchitecture, read RISC and CISC as opposite answers to where complexity should live, price out what each choice costs in decode hardware, code density, and pipeline friendliness, and see how x86-64 endures by translating its instructions into RISC-like operations on the fly.\n",{"path":3420,"title":3421,"module":3417,"summary":3422},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Finstruction-formats-and-operands","Instruction Formats and Operands","An instruction is an opcode plus a way to name its operands. We count operands — 3-address, 2-address, 1-address accumulator, and 0-address stack machines — by writing the same C = A + B four ways, weigh register operands against memory operands, then lay out the same add byte by byte in x86-64 (REX prefix, opcode, ModRM) and in Y86-64, and what fixed versus variable length costs at fetch time.\n",{"path":3424,"title":3425,"module":3417,"summary":3426},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Faddressing-modes","Addressing Modes","Once an operand field exists, it needs a rule for turning its bits into the data it names. That rule is the addressing mode. We walk the standard set — immediate, register, direct, register-indirect, displacement, scaled-indexed, and PC-relative — fixing the effective-address computation for each, run every mode against one concrete machine state, and price out what Y86-64 loses by keeping only base plus displacement.\n",{"path":3428,"title":3429,"module":3417,"summary":3430},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fthe-y86-64-instruction-set","The Y86-64 Instruction Set","Y86-64 is a teaching ISA — a stripped-down x86-64 simple enough to implement by hand yet real enough to compile to. We fix its programmer-visible state (fifteen registers, three condition codes, the PC, memory, and a status code), give the instruction set with exact byte encodings, spell out how the condition codes decide every jXX and cmovXX, and run the encoding both directions: assembly to bytes and raw bytes back to meaning.\n",{"path":3432,"title":3433,"module":3417,"summary":3434},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fy86-64-programming","Y86-64 Programming","With the encodings fixed, we write real Y86-64 assembly: the .pos, .align, and .quad directives, the calling convention borrowed from x86-64, a stack set up by hand, and complete programs — an array sum and a branch-free max. We watch the assembler turn the listing into the exact byte image the processor will execute, and trace the stack across the call.\n",{"path":3436,"title":3437,"module":3438,"summary":3439},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Ftransistors-gates-and-boolean-functions","Transistors, Gates, and Boolean Functions","Digital Logic","A processor is built from millions of transistor switches. We start at the MOS transistor as a voltage-controlled switch, build the CMOS inverter and NAND transistor by transistor, meet the seven standard gates with their truth tables, show that NAND alone is functionally complete, price each gate in transistors and in time, and turn any truth table into a sum-of-products circuit.\n",{"path":3441,"title":3442,"module":3438,"summary":3443},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fcombinational-logic-and-hcl","Combinational Logic and HCL","A combinational circuit is a pure Boolean function of its current inputs — no memory, no clock. We draw the line between combinational and sequential logic, do the gate-delay accounting that finds a circuit's critical path and bounds the clock, meet don't-cares, then introduce CS:APP's Hardware Control Language: bit-level operators, word-level signals, equality nets, and the case expression that compiles to a multiplexer tree.\n",{"path":3445,"title":3446,"module":3438,"summary":3447},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmultiplexers-decoders-and-the-alu","Multiplexers, Decoders, and the ALU","The combinational building blocks that make a datapath. We build the 2:1 and 4:1 multiplexer and tie it back to HCL's case expression, the n-to-2^n decoder, a one-bit full adder (sum is XOR, carry is majority), the ripple-carry adder that chains them, and finally the ALU — a function unit that selects among add, sub, and, and xor under a control input and exposes condition flags.\n",{"path":3449,"title":3450,"module":3438,"summary":3451},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmemory-elements-latches-flip-flops-and-clocking","Memory Elements: Latches, Flip-Flops, and Clocking","A combinational circuit holds no state; feeding a circuit's output back to its input creates memory. We build the SR latch from cross-coupled gates, the level-sensitive D latch, and the master\u002Fslave edge-triggered D flip-flop, then introduce the clock and the synchronous design discipline, the setup\u002Fhold timing window, clock skew, metastability, and the register as n flip-flops sharing one clock.\n",{"path":3453,"title":3454,"module":3438,"summary":3455},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fregister-files-and-random-access-memory","Register Files and Random-Access Memory","Storage organized for access by address. We build the register file (a small bank of registers with addressed read ports and clocked write ports, the exact structure Y86-64's decode and write-back stages use), then descend to the SRAM and DRAM cells of main memory, why one is fast and dear and the other dense and slow, and how a row decoder picks a word out of a memory array.\n",{"path":3457,"title":3458,"module":3459,"summary":3460},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-fetch-decode-execute-cycle","The Fetch-Decode-Execute Cycle","Processor Design","A processor is a machine that repeats one loop forever: read the next instruction from memory, figure out what it asks for, do it, and advance. We fix the stored-program idea, lay out the datapath at a high level — PC, instruction memory, register file, ALU, data memory — and the control unit that sequences them, break the work into the six stages the rest of the module builds in hardware, and work out exactly how fetch parses variable-length instructions and computes the next PC.\n",{"path":3462,"title":3463,"module":3459,"summary":3464},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-seq-stages","The SEQ Stages","The six SEQ stages, made exact. For every Y86-64 instruction — halt, nop, the moves, OPq, the jumps, call and ret, pushq and popq — we write down what Fetch, Decode, Execute, Memory, Write-back, and PC update each compute, as per-instruction stage tables with every row justified. Once the tables are filled in, the processor is fully specified; the remaining lessons turn them into wires.\n",{"path":3466,"title":3467,"module":3459,"summary":3468},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fcontrol-logic-and-sequencing","Control Logic and Sequencing","The stage tables say what each instruction needs; the control logic computes it from icode. We write the HCL for the register-port selections (srcA, srcB, dstE, dstM), the ALU function and input selection, the memory read\u002Fwrite and address, the branch condition, and the next-PC mux — each a case expression on icode that compiles to a mux — and see how one blob of combinational logic serves every instruction at once. We close by contrasting hardwired control with the microprogrammed alternative.\n",{"path":3470,"title":3471,"module":3459,"summary":3472},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fassembling-seq","Assembling SEQ","We wire the whole thing together. The functional units from digital logic and the control signals from the last lesson assemble into the complete SEQ datapath, laid out the way CS:APP draws it — six stages stacked bottom to top, Fetch at the floor and PC update at the ceiling, signals flowing up the margins. Then the timing analysis: why everything must settle in one cycle, the no-reading-back principle that makes single-cycle execution consistent, and the critical path that sets the clock. We close by walking an OPq and a ret through the assembled machine.\n",{"path":3474,"title":3475,"module":3459,"summary":3476},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Ftracing-a-program","Tracing a Program","To close the module, we take a complete Y86-64 program — a loop that sums 1 through 3 — and run it through SEQ one cycle at a time, recording the PC, the fetched instruction, every stage computation, and the registers, condition codes, and memory after each cycle. Then we examine single cycles in detail: every named signal of an OPq in concrete hex, and a second program whose call and ret we trace through the stack. The traces confirm that the assembled datapath and control logic behave as a processor.\n",{"path":3478,"title":3479,"module":3480,"summary":3481},"\u002Fcomputer-architecture\u002Fpipelining\u002Fpipelining-principles","Pipelining Principles","Pipelining","A processor that runs one instruction to completion before starting the next wastes most of its hardware most of the time. Pipelining splits the work into stages separated by registers so several instructions are in flight at once. We separate throughput from latency, work the 300 ps example through one, two, and three stages, and derive the three ceilings on the gain: uneven stages, register overhead, and the dependencies between instructions.\n",{"path":3483,"title":3484,"module":3480,"summary":3485},"\u002Fcomputer-architecture\u002Fpipelining\u002Ffrom-seq-to-pipe","From SEQ to PIPE","We turn the sequential Y86-64 processor into a pipelined one by inserting pipeline registers between its stages so each cycle holds one instruction per stage. Doing it correctly forces a rearrangement: the next-PC computation must move into Fetch as a prediction, because the later stages that used to compute it are now busy with other instructions. We walk SEQ to SEQ+ to PIPE, spell out exactly what each pipeline register carries, and fix the naming discipline (D_stat versus d_stat) that keeps five in-flight instructions straight.\n",{"path":3487,"title":3488,"module":3480,"summary":3489},"\u002Fcomputer-architecture\u002Fpipelining\u002Fdata-hazards-stalling-and-forwarding","Data Hazards: Stalling and Forwarding","Overlapping instructions collide when a later one needs a value an earlier one has not finished computing: a read-after-write data hazard. We map exactly which instruction distances are dangerous, fix hazards the slow way by stalling (three bubbles), then the fast way by forwarding from five distinct sources into Decode, in a priority order that sequential semantics forces. Forwarding handles almost everything; the load-use hazard still needs exactly one stall.\n",{"path":3491,"title":3492,"module":3480,"summary":3493},"\u002Fcomputer-architecture\u002Fpipelining\u002Fcontrol-hazards-and-branch-prediction","Control Hazards and Branch Prediction","A pipeline must fetch an instruction every cycle, but after a conditional jump or a ret the next address is not yet known: a control hazard. We measure the branch penalty, weigh predict-taken against its alternatives with real loop arithmetic, watch PIPE detect a misprediction in Execute and squash the two wrong-path instructions, and meet the ret hazard, which has nothing to predict and stalls three cycles. A 2-bit counter gives a taste of dynamic prediction.\n",{"path":3495,"title":3496,"module":3480,"summary":3497},"\u002Fcomputer-architecture\u002Fpipelining\u002Fthe-complete-pipe-processor","The Complete PIPE Processor","We assemble the full pipelined Y86-64: five stages, five pipeline registers, forwarding paths, and a small control unit that decides, each cycle, whether to stall or bubble each register. The subtle part is when hazards combine: one pairing hides a genuine bug. A fourth control case reads stat and keeps exceptions precise. Performance reduces to CPI = 1 + lp + mp + rp, worked out to 1.27 with realistic frequencies, and PIPE beats SEQ by several times despite every penalty.\n",{"path":3499,"title":3500,"module":3501,"summary":3502},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fstorage-technologies-and-the-latency-gap","Storage Technologies and the Latency Gap","The Memory Hierarchy","No single memory is both fast and large and cheap. We survey the technologies a machine can store bits in — SRAM, DRAM, flash, and rotating disk — open up a DRAM chip to find the row buffer, work a disk access down to the millisecond, and rank everything by speed, density, and cost per bit. Then we watch the processor outrun memory decade after decade. That widening gap is the whole reason a machine stacks fast small storage on top of slow large storage into a hierarchy.\n",{"path":3504,"title":3505,"module":3501,"summary":3506},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Flocality","Locality","A hierarchy only pays off because programs do not touch memory at random. They reuse recently-used data (temporal locality) and touch nearby data soon after (spatial locality). We make both precise and then quantitative: miss rates for stride-1 and stride-k traversals against a concrete block size, and the loop-order pair on a 2-D array where the same sum misses 16 times one way and 64 times the other — why row-major versus column-major order can change a program's speed by an order of magnitude.\n",{"path":3508,"title":3509,"module":3501,"summary":3510},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-memories-direct-mapped","Cache Memories and Direct Mapping","A cache is fast SRAM that holds copies of recently-used blocks of main memory. We fix its organization — S sets, E lines per set, B bytes per block — and the way it dissects an address into tag, set index, and block offset, worked bit by bit on a concrete 16-byte cache. Then we run the direct-mapped (E=1) access algorithm end to end on a seven-access trace: index to a set, compare the tag, hit or miss, evict. Cold and conflict misses fall out of the structure, and a two-array ping-pong shows conflict thrashing and its padding fix.\n",{"path":3512,"title":3513,"module":3501,"summary":3514},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fset-associative-and-write-policies","Set-Associative Caches and Write Policies","Give each set several lines and a block has a choice of homes — fewer conflict misses, at the cost of comparing E tags in parallel and choosing a victim to evict. We re-run the direct-mapped ping-pong trace on a 2-way cache and watch the conflicts vanish, weigh LRU against random replacement, then turn to writes: write-through versus write-back with a dirty bit on a hit, write-allocate versus no-write-allocate on a miss, and a worked traffic count showing when each pairing wins.\n",{"path":3516,"title":3517,"module":3501,"summary":3518},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-performance-and-cache-friendly-code","Cache Performance and Cache-Friendly Code","Turn the cache mechanism into a number. Hit time, miss rate, and miss penalty combine into the average memory access time; we compute AMAT for a two-level hierarchy with real numbers, weigh the design knobs against each other, and read the memory mountain. Then we write cache-friendly code — the matrix-multiply loop-order case study (ijk versus kij, misses counted per iteration) and loop blocking, where cache-sized tiles turn evicted reuse back into hits.\n",{"path":3520,"title":3521,"module":3522,"summary":3523},"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Faddress-spaces-and-translation","Address Spaces and Translation","Virtual Memory","Every process runs as if it owns a private, contiguous span of memory — its virtual address space — while the hardware maps those addresses onto a single shared physical memory. We fix virtual memory's three jobs (a cache for disk, a memory manager, a protection boundary), the page as the unit of mapping, and the MMU replacing the virtual page number while the offset passes through untouched — then run one translation end to end at the bit level and trace the control flow of a page hit against a page fault.\n",{"path":3525,"title":3526,"module":3522,"summary":3527},"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fpage-tables-and-page-faults","Page Tables and Page Faults","The page table is an array of page-table entries indexed by virtual page number; each entry's valid bit says whether the page is in DRAM, on disk, or unallocated, and its permission, reference, and dirty bits drive protection and replacement. We walk translation as a table lookup, the page fault and demand paging, the clock algorithm the OS uses to approximate LRU, memory mapping and copy-on-write (why fork is cheap), the taxonomy of bad references, and thrashing.\n",{"path":3529,"title":3530,"module":3522,"summary":3531},"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fthe-tlb-and-multi-level-page-tables","The TLB and Multi-Level Page Tables","A page-table read on every access would double memory traffic; a flat table for a 48-bit space would occupy 512 GB per process. The TLB fixes the first: a small set-associative cache of PTEs inside the MMU whose tag and index come from the VPN. Multi-level page tables fix the second, allocating only the sub-tables a process uses; x86-64 walks four levels with a 9+9+9+9+12 split. We trace one reference end to end through TLB, walk, and cache, and close with the overlap trick that lets the L1 cache start before translation ends.\n",{"path":3533,"title":3534,"module":3535,"summary":3536},"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Fexceptional-control-flow","Exceptional Control Flow","Exceptions & I\u002FO","Beyond the sequential, branch, and call flow a program controls itself, the hardware can divert the processor in response to events. We sort these into four classes — interrupts (asynchronous, from devices), traps (intentional syscalls), faults (recoverable, like a page fault), and aborts (unrecoverable) — then take the mechanism apart: exception numbers and the table dispatch, what the hardware pushes and why it differs from a procedure call, the divide-error \u002F page-fault \u002F general-protection trio on x86-64, the full syscall round trip with a worked write in assembly, and processes and signals as the abstractions ECF makes possible.\n",{"path":3538,"title":3539,"module":3535,"summary":3540},"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Finterrupts-and-the-kernel","Interrupts and the Kernel","An I\u002FO device signals completion by raising an interrupt, crossing the privilege boundary from user mode into the kernel. We fix that boundary, follow an interrupt from device through the interrupt controller to its vectored handler, and use the timer interrupt to drive preemptive scheduling and the context switch. Then the I\u002FO mechanics: polling versus interrupt-driven I\u002FO with a cycle count, device registers and memory-mapped I\u002FO versus port I\u002FO, DMA's full transfer walkthrough and its cache hazard, and a disk read traced end to end, from the read syscall to the completion interrupt.\n",{"path":3542,"title":3543,"module":3544,"summary":3545},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fprocesses-threads-and-parallelism","Processes, Threads, and Parallelism","Multithreading & Multicore","Around 2004 the single core stopped getting faster, and the industry's answer was to hand programmers more cores instead. This lesson builds the vocabulary that shift demands: process versus thread and exactly which hardware state each one owns, concurrency versus parallelism, the three kinds of parallelism a machine can exploit, why Dennard scaling ended and forced the multicore turn, and Amdahl's law — the arithmetic that bounds the speedup those cores can deliver.\n",{"path":3547,"title":3548,"module":3544,"summary":3549},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fhardware-multithreading","Hardware Multithreading","A pipeline spends much of its life waiting — on cache misses, on dependences, on branches. Hardware multithreading fills the dead cycles with instructions from another thread. We compare coarse-grained switching (change threads on a long stall), fine-grained interleaving (change every cycle), and simultaneous multithreading (mix threads inside a single cycle), work out exactly which hardware a second thread context duplicates and which it shares, and weigh when SMT pays off and when two threads just fight over one cache.\n",{"path":3551,"title":3552,"module":3544,"summary":3553},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fcache-coherence","Cache Coherence","Give each core its own cache and the same address can live in two places at once, with copies that disagree. We reproduce the stale-copy bug with a two-core trace, then fix it the way hardware does: snooping caches that watch a shared bus and keep every line in a protocol state. We build MSI in full, upgrade it to MESI, contrast invalidation with updating, add coherence misses as the fourth C, and end with false sharing: the performance bug where cores fight over a line while never touching the same byte.\n",{"path":3555,"title":3556,"module":3544,"summary":3557},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmemory-consistency-and-synchronization","Memory Consistency and Synchronization","Coherence keeps cores agreeing about one location; consistency is the contract about many. We define sequential consistency, then watch real hardware break it: the store buffer lets a load slip ahead of an older store, and the classic two-thread litmus test ends with both sides reading zero. We state x86-TSO precisely, restore order with mfence, build atomic read-modify-write from the lock prefix, xchg, and cmpxchg, and write a spinlock twice — once naively, once bus-friendly — closing with what lock-free progress actually guarantees.\n",{"path":3559,"title":3560,"module":3544,"summary":3561},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmulticore-organization","Multicore Organization","Where everything sits on the die. A modern die gives each core private L1 and L2 caches, spreads a shared last-level cache across slices, and wires it all together with a ring or mesh; multi-socket servers add NUMA, where memory is local to one socket and every remote access pays a latency penalty. We walk the floorplan, put numbers on local versus remote latency, meet thread affinity, and account for the two shared resources — coherence traffic and LLC capacity — that decide how far a parallel program scales.\n",{"path":3563,"title":3564,"module":3565,"summary":3566},"\u002Fcomputer-architecture\u002Fcapstone\u002Fthe-whole-machine","The Whole Machine","Capstone","We take one line of C down the whole tower the course built — compiler to assembly, assembly to machine-code bytes, the bytes into the fetch–decode–execute datapath — then trace one load and one add through the pipelined, cached, translated, interruptible machine, each step cross-linked to the lesson that built it. We close with the map of the course as a stack of layers and an accounting of what we simplified: out-of-order execution, superscalar issue, and speculation past the branch predictor.\n",{"path":3568,"title":3569,"module":3565,"summary":3570},"\u002Fcomputer-architecture\u002Fcapstone\u002Fassembling-a-complete-cpu","Assembling a Complete CPU","We bolt the parts the course built — PC, instruction memory and its fetch logic, register file, ALU, condition codes, data memory, and the control unit — into one complete CPU, name the lesson that built each, wire them in a deliberate order, and power the machine on from reset. Then we assemble a real test program (sum a four-element array through a call\u002Fret procedure), give its exact bytes and memory layout, and trace it cycle by cycle to the answer 0xabcdabcdabcd. We close with how to validate such a machine, and what it takes to put two of them on one die.\n",{"path":3572,"title":3573,"module":6,"summary":6},"\u002Fcomputer-architecture","Computer Architecture",{"path":3575,"title":3576,"module":1231,"summary":3577},"\u002Fdifferential-equations\u002Ffoundations\u002Fmodels-and-direction-fields","Models, Direction Fields, and Solution Curves","A differential equation relates an unknown function to its own rates of change. Three first-order models — a falling body, a cooling object, a population under predation — share the form dy\u002Fdt = ay - b; the slope field fixes their equilibria and long-run behavior before any formula is found. Solving the linear case gives the general solution, its integral curves, and the particular solution selected by an initial condition.\n",{"path":3579,"title":3580,"module":1231,"summary":3581},"\u002Fdifferential-equations\u002Ffoundations\u002Fclassification-and-terminology","Classifying Equations: Order, Linearity, ODE vs. PDE","Every solution method targets a specific class of equation, so the first question about any differential equation is which classes it belongs to. Four independent axes sort them: ordinary versus partial, order, linear versus nonlinear, and homogeneous versus nonhomogeneous. Systems, verification of a solution by substitution, and the split between initial and boundary value problems complete the vocabulary.\n",{"path":3583,"title":3584,"module":3585,"summary":3586},"\u002Fdifferential-equations\u002Ffirst-order\u002Flinear-first-order-integrating-factors","Linear Equations and Integrating Factors","First-Order Equations","A first-order linear equation has the unknown and its derivative to the first power only. Multiplying by an integrating factor collapses the left side into a single derivative, and one integration gives the general solution in closed form. The solution exists wherever the coefficients are continuous, and for a constant coefficient it splits into a decaying transient and a steady state set by the forcing.\n",{"path":3588,"title":3589,"module":3585,"summary":3590},"\u002Fdifferential-equations\u002Ffirst-order\u002Fseparable-and-exact","Separable and Exact Equations","Two nonlinear first-order classes solve by direct integration. A separable equation splits so that each variable can be integrated on its own side, giving an implicit relation. An exact equation is the total differential of a hidden potential function, recognized by a symmetry test on its coefficients; when the test fails, an integrating factor can sometimes restore exactness. A change of variable brings homogeneous equations into the separable class.\n",{"path":3592,"title":3593,"module":3585,"summary":3594},"\u002Fdifferential-equations\u002Ffirst-order\u002Fmodeling-first-order","Modeling with First-Order Equations","A rate law is a differential equation. Each first-order model starts from one governing principle: conservation of mass for a mixing tank, proportional change for interest and radioactive decay, Newton's law of cooling, a force balance for a body falling against drag, and Kirchhoff's law for a series circuit. Setting the derivative to zero recovers the steady state, and the transient records how the initial condition relaxes toward it.\n",{"path":3596,"title":3597,"module":3585,"summary":3598},"\u002Fdifferential-equations\u002Ffirst-order\u002Fautonomous-and-population-dynamics","Autonomous Equations, Phase Lines, and Population Dynamics","An autonomous equation y' = f(y) can be analyzed qualitatively without being solved. Its constant solutions are the zeros of f, and the sign of f between them fixes whether nearby solutions rise or fall, which the phase line records as a column of arrows. The logistic and threshold models, constant- and effort-proportional harvesting, and the properties nonlinear equations lose all follow from this reading.\n",{"path":3600,"title":3601,"module":3585,"summary":3602},"\u002Fdifferential-equations\u002Ffirst-order\u002Fexistence-uniqueness-euler","Existence, Uniqueness, and Euler's Method","Existence and uniqueness can be settled before any attempt to solve. The existence-uniqueness theorem gives sufficient conditions on f, and a standard example shows what fails when they do not hold. Picard's successive approximations build the solution as the limit of an iteration, and Euler's method turns the same tangent-line idea into a numerical procedure for the equations no formula reaches.\n",{"path":3604,"title":3605,"module":3585,"summary":3606},"\u002Fdifferential-equations\u002Ffirst-order\u002Ffirst-order-difference-equations","First-Order Difference Equations","A difference equation advances a sequence one index at a time by a rule y_{n+1} = f(y_n). The linear case y_{n+1} = rho*y_n + b solves in closed form and converges to its equilibrium exactly when the ratio has magnitude below one, which underlies compound-interest and loan calculations. The logistic difference equation shows the nonlinear counterpart: an exchange of stability, a cascade of period doublings, and the onset of chaos.\n",{"path":3608,"title":3609,"module":3610,"summary":3611},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhomogeneous-constant-coefficients","Homogeneous Equations, the Wronskian, and Real Roots","Second-Order Linear Equations","A second-order linear homogeneous equation with constant coefficients is solved by guessing an exponential and reducing to the quadratic characteristic equation. Two solutions span every solution exactly when their Wronskian is nonzero; that condition, superposition, and Abel's formula give the full structure of the general solution for the case of two distinct real roots.\n",{"path":3613,"title":3614,"module":3610,"summary":3615},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fcomplex-and-repeated-roots","Complex Roots, Repeated Roots, and Reduction of Order","When the characteristic equation has complex conjugate roots, Euler's formula converts the complex exponentials into a real fundamental set of decaying or growing oscillations. When it has a repeated root, one exponential is lost and reduction of order recovers the missing second solution as $t\\,e^{rt}$. The same substitution $y = v(t)y_1(t)$ finds a second solution from any known one.\n",{"path":3617,"title":3618,"module":3610,"summary":3619},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fnonhomogeneous-undetermined-coefficients","Nonhomogeneous Equations: Undetermined Coefficients","The general solution of a nonhomogeneous linear equation is a complementary solution plus any one particular solution. When the forcing term is a polynomial, exponential, sine, or cosine, a particular solution can be found by assuming a trial form of the same shape with unknown coefficients and solving for them. The one complication is resonance, handled by multiplying the trial by a power of $t$.\n",{"path":3621,"title":3622,"module":3610,"summary":3623},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fvariation-of-parameters","Variation of Parameters","Variation of parameters finds a particular solution of any nonhomogeneous linear equation from a fundamental set of the homogeneous one. Replacing the constants in the complementary solution by functions and imposing one convenient constraint reduces the problem to a two-by-two linear system whose solution is expressed through the Wronskian, giving an integral formula that works for forcing terms undetermined coefficients cannot touch.\n",{"path":3625,"title":3626,"module":3610,"summary":3627},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fmechanical-electrical-vibrations","Mechanical and Electrical Vibrations","A spring-mass-damper obeys a second-order linear equation, and so does a series RLC circuit, with the same mathematics governing both. Free undamped motion is a pure sinusoid; damping adds a decaying envelope with three regimes; periodic forcing produces a transient that dies out and a steady-state oscillation whose amplitude peaks sharply near the natural frequency, the phenomenon of resonance.\n",{"path":3629,"title":3630,"module":3610,"summary":3631},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhigher-order-linear","Higher-Order Linear Equations","The second-order theory extends directly to order $n$: the solution space is $n$-dimensional, spanned by any $n$ solutions with nonzero Wronskian. For constant coefficients the characteristic polynomial has degree $n$, and its roots (counted with multiplicity, real and complex) build the basis by the same rules as before. Coupled oscillators are the natural application that raises the order.\n",{"path":3633,"title":3634,"module":3635,"summary":3636},"\u002Fdifferential-equations\u002Fseries-solutions\u002Fpower-series-ordinary-points","Power Series Solutions Near Ordinary Points","Series Solutions and Special Functions","A linear equation with variable coefficients has no characteristic equation. A power series substituted into the equation matches coefficients to a recurrence relation, which near an ordinary point yields two independent analytic solutions. The radius of convergence is at least the distance from the expansion point to the nearest singular point in the complex plane.\n",{"path":3638,"title":3639,"module":3635,"summary":3640},"\u002Fdifferential-equations\u002Fseries-solutions\u002Fregular-singular-frobenius","Euler Equations, Regular Singular Points, and Frobenius","The Euler equation x^2 y'' + a x y' + b y = 0 is solved outright by y = x^r, and its three root cases fix the behavior at any regular singular point. The Frobenius method multiplies x^r by a power series; the indicial equation chooses the exponents, and equal or integer-separated roots force a logarithm in the second solution. Gauss's hypergeometric equation is the archetype containing most classical functions as special cases.\n",{"path":3642,"title":3643,"module":3635,"summary":3644},"\u002Fdifferential-equations\u002Fseries-solutions\u002Fbessel-and-special-functions","Bessel's Equation, Legendre Polynomials, and Special Functions","Bessel's equation puts the Frobenius machinery through all three of its cases and produces the functions J and Y that govern anything vibrating or diffusing with circular symmetry. The gamma function extends the factorial so that Bessel functions of every order make sense; Legendre's equation, run through the hypergeometric form, yields the polynomials that play the same role in spherical geometry. Orthogonality ties both families to the eigenfunction expansions of Sturm–Liouville theory.\n",{"path":3646,"title":3647,"module":3648,"summary":3649},"\u002Fdifferential-equations\u002Flaplace\u002Flaplace-definition-ivps","The Laplace Transform: Definition, Properties, and Solving IVPs","The Laplace Transform","The Laplace transform sends a function of time to a function of a complex frequency by integrating it against the kernel e^{-st}. Differentiation in t becomes multiplication by s, so a linear constant-coefficient initial value problem turns into an algebraic equation. Existence rests on piecewise continuity and exponential order; the derivative rule folds in the initial data; and inversion runs through a transform table and partial fractions.\n",{"path":3651,"title":3652,"module":3648,"summary":3653},"\u002Fdifferential-equations\u002Flaplace\u002Fstep-impulse-convolution","Step Functions, Discontinuous Forcing, Impulses, and Convolution","The Heaviside step function and the second shifting theorem transform switches and discontinuous forcing into exponential factors on the transform. The Dirac delta idealizes an instantaneous impulse and transforms to a pure exponential. The convolution theorem inverts a product of transforms, writes the forced response as the impulse response convolved with the input, and solves Abel's tautochrone by transform.\n",{"path":3655,"title":3656,"module":3657,"summary":3658},"\u002Fdifferential-equations\u002Fsystems\u002Fmatrices-eigenvalues-review","Matrices, Linear Systems, and the Eigenvalue Toolkit","Systems of First-Order Linear Equations","Any nth-order linear equation, and any coupled collection of them, rewrites as a single first-order system x' = P(t)x + g(t). The matrix and vector algebra behind that form, the eigenvalue problem det(A - λI) = 0 that drives every solution method, and the fundamental theory — superposition, the Wronskian, Abel's theorem — together establish that n independent solutions span all solutions.\n",{"path":3660,"title":3661,"module":3657,"summary":3662},"\u002Fdifferential-equations\u002Fsystems\u002Fconstant-coefficient-systems-phase-portraits","Homogeneous Constant-Coefficient Systems and Phase Portraits","For x' = Ax with A constant, the trial x = ξe^{rt} turns the differential equation into the eigenvalue problem Aξ = rξ. The eigenvalues fix the geometry of the phase plane: real opposite signs give a saddle, real same sign a node, complex a spiral, purely imaginary a center. Worked in the plane, these cases form the eigenvalue-type classification of equilibria.\n",{"path":3664,"title":3665,"module":3657,"summary":3666},"\u002Fdifferential-equations\u002Fsystems\u002Frepeated-eigenvalues-fundamental-matrices","Repeated Eigenvalues, Fundamental Matrices, and Nonhomogeneous Systems","When a repeated eigenvalue supplies too few eigenvectors, a generalized eigenvector supplies the missing solution as ξte^{ρt} + ηe^{ρt}, giving an improper node. A fundamental set packaged as a matrix Φ(t) yields the matrix exponential e^{At}, the propagator mapping initial states to later ones. Variation of parameters solves the nonhomogeneous system x' = Ax + g(t).\n",{"path":3668,"title":3669,"module":3670,"summary":3671},"\u002Fdifferential-equations\u002Fnumerical\u002Feuler-and-runge-kutta","Euler, Improved Euler, and Runge–Kutta","Numerical Methods","Most initial value problems have no closed-form solution, so the solution is approximated on a grid. Euler's method steps along the tangent line, the improved Euler method averages two slopes, and the classical Runge–Kutta method averages four. Each added stage raises the order of accuracy at the cost of more evaluations per step, measured by how the local and global truncation errors scale with the step size.\n",{"path":3673,"title":3674,"module":3670,"summary":3675},"\u002Fdifferential-equations\u002Fnumerical\u002Fmultistep-systems-stability","Multistep Methods, Systems, and Stability","One-step methods discard everything but the last point. Multistep methods fit a polynomial to several past values and integrate it forward: the explicit Adams–Bashforth formulas, the implicit and more accurate Adams–Moulton formulas, and predictor–corrector pairs that combine them. The same rules extend verbatim to systems in vector form. A separate concern is stability: round-off can dominate truncation, and stiff equations force a tiny step for stability even when accuracy would allow a large one.\n",{"path":3677,"title":3678,"module":3679,"summary":3680},"\u002Fdifferential-equations\u002Fnonlinear\u002Fphase-plane-autonomous-stability","The Phase Plane, Critical Points, and Stability","Nonlinear Systems and Stability","Most nonlinear systems cannot be solved in closed form, so they are studied geometrically. The phase plane turns an autonomous planar system into a family of trajectories; the five archetypes of critical point follow from the eigenvalues of the coefficient matrix; the trace-determinant plane reads off type and stability directly; and epsilon-delta definitions make stability, asymptotic stability, and instability precise.\n",{"path":3682,"title":3683,"module":3679,"summary":3684},"\u002Fdifferential-equations\u002Fnonlinear\u002Flocally-linear-and-liapunov","Locally Linear Systems and Liapunov's Method","Near a critical point a nonlinear system looks linear, and the linear part is the Jacobian. The linearization fixes the type and stability of the nonlinear critical point in every case except a center or a repeated eigenvalue. Liapunov's direct method settles those cases and bounds the basin of attraction by constructing an energy-like function, without solving the system.\n",{"path":3686,"title":3687,"module":3679,"summary":3688},"\u002Fdifferential-equations\u002Fnonlinear\u002Fcompeting-species-predator-prey-limit-cycles","Population Models, Limit Cycles, and Chaos","The phase-plane methods apply directly to interacting-population models. Competing species either coexist or drive one another to extinction, decided by a single inequality among the interaction constants; the Lotka-Volterra predator-prey system produces closed population cycles. Limit cycles and the Poincaré-Bendixson theorem, the van der Pol oscillator, and the Lorenz equations with their strange attractor carry the theory into chaos.\n",{"path":3690,"title":3691,"module":3692,"summary":3693},"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Ffourier-series","Fourier Series and Convergence","PDEs, Fourier Series, and Boundary Value Problems","A two-point boundary value problem has nontrivial solutions only at a discrete set of eigenvalues, the same trichotomy that governs a singular linear system. For y'' + lambda y = 0 with zero endpoints the eigenfunctions are sines and cosines, and their orthogonality gives the Euler-Fourier coefficient formulas. The convergence theorem fixes when the series returns the function, the Gibbs phenomenon measures the overshoot at a jump, and even\u002Fodd symmetry produces half-range sine and cosine series.\n",{"path":3695,"title":3696,"module":3692,"summary":3697},"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fheat-wave-laplace-equations","Separation of Variables: Heat, Wave, and Laplace Equations","Separation of variables replaces a partial differential equation by a pair of ordinary ones joined through a shared separation constant. Applied to the heat equation it produces the eigenvalue problem X'' + lambda X = 0, and the solution assembles as a Fourier series in the eigenfunctions. The same steps solve the wave equation, whose modes are standing waves, and Laplace's equation, the steady-state limit posed on a region rather than an interval.\n",{"path":3699,"title":3700,"module":3692,"summary":3701},"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fsturm-liouville","Sturm-Liouville Theory","The eigenvalue problem behind separation of variables generalizes to the self-adjoint Sturm-Liouville form. Lagrange's identity makes the operator symmetric, and from that one fact follow real eigenvalues, orthogonal eigenfunctions, and eigenfunction expansions that behave like Fourier series. Singular problems admit Bessel and Legendre functions, and Sturm's separation and comparison theorems describe how the eigenfunctions oscillate.\n",{"path":3703,"title":3704,"module":3705,"summary":3706},"\u002Fdifferential-equations\u002Fhistory-variations\u002Fcalculus-of-variations","The Calculus of Variations","Historical Notes and the Calculus of Variations","Ordinary calculus finds the point where a function is stationary; the calculus of variations finds the whole curve where an integral is stationary. Euler's differential equation is the necessary condition for an extremal, and it becomes integrable in three cases, solving the shortest-path, minimal-surface, and brachistochrone problems. Lagrange multipliers extend the method to isoperimetric constraints, and Hamilton's principle recovers Newton's law from a single stationary integral.\n",{"path":3708,"title":3709,"module":3705,"summary":3710},"\u002Fdifferential-equations\u002Fhistory-variations\u002Fhistorical-notes","Great Problems and the People Who Solved Them","Differential equations grew out of specific problems, not a plan: the invention of calculus by Newton and Leibniz, the Bernoulli brachistochrone challenge, Euler's flood of methods, Lagrange's analytical mechanics, Gauss and Riemann's rigor, Laplace's celestial mechanics, and Poincaré's qualitative theory. Each method descends from a named problem, and reading the subject forward from those problems explains why its parts fit together.\n",{"path":3712,"title":3713,"module":6,"summary":6},"\u002Fdifferential-equations","Differential Equations",{"path":3715,"title":3716,"module":3717,"summary":3718},"\u002Frelativity\u002Ffoundations\u002Fspecial-relativity-postulates","The Postulates of Special Relativity","Foundations of Relativity","Newton's laws are the same in every inertial frame, but Maxwell's are not: the equations of electromagnetism single out one speed, c, and the nineteenth century read that as the speed of light relative to a medium, the ether. The Michelson-Morley experiment looked for Earth's motion through that medium and found nothing. Einstein's two postulates replace the ether, and their first consequence is that simultaneity is frame-dependent.\n",{"path":3720,"title":3721,"module":3717,"summary":3722},"\u002Frelativity\u002Ffoundations\u002Florentz-transformation-spacetime","The Lorentz Transformation and Spacetime","Requiring that a light sphere stay a light sphere in every inertial frame fixes the coordinate change between frames uniquely: the Lorentz transformation, with its factor gamma. Differentiating it gives relativistic velocity addition, which caps composed speeds at c. Plotting the same events on skewed spacetime axes turns the algebra into geometry, with calibration hyperbolae, an invariant interval, and a light cone that sorts events into past, future, and elsewhere.\n",{"path":3724,"title":3725,"module":3717,"summary":3726},"\u002Frelativity\u002Ffoundations\u002Ftime-dilation-length-contraction","Time Dilation, Length Contraction, and Paradoxes","A light clock and the constancy of c give the two headline effects directly: a moving clock runs slow by gamma, and a moving rod is short by the same factor. Cosmic-ray muons reaching sea level are the standing experimental proof. The relativistic Doppler effect adds the time-dilation factor to the classical shift, and the twin and pole-barn paradoxes dissolve once the relativity of simultaneity is taken seriously.\n",{"path":3728,"title":3729,"module":3717,"summary":3730},"\u002Frelativity\u002Ffoundations\u002Frelativistic-momentum-energy","Relativistic Momentum and Energy","Conserving momentum in every inertial frame forces the redefinition p = gamma m u, which diverges as the speed approaches c. Integrating the corresponding force gives the total energy E = gamma m c-squared, whose rest term m c-squared is Einstein's mass-energy equivalence. Energy and momentum join into a four-vector whose invariant length is the rest energy, giving E-squared = (pc)-squared + (m c-squared)-squared, massless particles, and nuclear binding energy.\n",{"path":3732,"title":3733,"module":3717,"summary":3734},"\u002Frelativity\u002Ffoundations\u002Fgeneral-relativity","A Taste of General Relativity","Einstein's happiest thought was that a freely falling observer feels no gravity: a uniform gravitational field is locally indistinguishable from an accelerating frame. That equivalence principle predicts that light bends near a mass, that clocks run slow deep in a gravitational well, that Mercury's orbit precesses, and that radar echoes are delayed. Every prediction has been confirmed, and pushing the redshift to its limit gives the black hole.\n",{"path":3736,"title":3737,"module":3738,"summary":3739},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fminkowski-spacetime-and-the-interval","Minkowski Spacetime and the Interval","Spacetime and the Lorentz Group","The Lorentz transformation of the foundations module is repackaged as the geometry of a four-dimensional space whose invariant is not a distance but the spacetime interval. Events, worldlines, and the metric signature define a causal structure that every observer shares. Proper time is the length of a timelike worldline, and the twin paradox becomes the statement that a straight worldline accumulates the most proper time.\n",{"path":3741,"title":3742,"module":3738,"summary":3743},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Ffour-vectors-and-index-notation","Four-Vectors and Index Notation","The index calculus that the rest of the course runs on. Contravariant and covariant components, the Minkowski metric as the machine that raises and lowers indices, and the Einstein summation convention are assembled into scalar products that are the same in every frame. The four-velocity and four-acceleration follow, together with the identity that the four-velocity has constant invariant length.\n",{"path":3745,"title":3746,"module":3738,"summary":3747},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fthe-lorentz-group-and-rapidity","The Lorentz Group and Rapidity","The Lorentz transformations are the linear maps that preserve the Minkowski metric, and they form the group O(1,3). Boosts are hyperbolic rotations parametrized by rapidity, which adds along a line where velocity does not. The boost and rotation generators fix the group's local structure; its four disconnected components are set by two signs; and two non-collinear boosts compose into a boost plus a rotation, the Wigner rotation behind Thomas precession.\n",{"path":3749,"title":3750,"module":3738,"summary":3751},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fdoppler-aberration-and-appearance","Doppler, Aberration, and Appearance","Light carries a null four-momentum, and boosting it produces every optical effect of relativity at once. The covariant Doppler formula follows from the transformation of frequency, aberration from the transformation of direction, and the headlight effect from the resulting concentration of light forward. The Terrell-Penrose result shows that a fast object photographs as rotated, not contracted.\n",{"path":3753,"title":3754,"module":3755,"summary":3756},"\u002Frelativity\u002Frelativistic-dynamics\u002Ffour-momentum-force-and-accelerated-motion","Four-Momentum, Four-Force, and Accelerated Motion","Relativistic Dynamics","The four-momentum packages energy and momentum into a single vector whose invariant length is the rest mass. Its proper-time derivative is the four-force, always orthogonal to the four-velocity, and a constant orthogonal four-force produces hyperbolic motion. Constant proper acceleration gives rapidity linear in proper time, the relativistic rocket equation, and the Rindler horizon behind an eternally accelerating observer.\n",{"path":3758,"title":3759,"module":3755,"summary":3760},"\u002Frelativity\u002Frelativistic-dynamics\u002Fparticle-decays-and-two-body-kinematics","Particle Decays and Two-Body Kinematics","Conservation of four-momentum fixes the kinematics of a decay from the masses alone. In the center-of-momentum frame a parent breaks into two daughters with equal and opposite momenta and energies set by the Kallen triangle function. Boosting to the lab opens the decay into a cone, and the invariant mass built from the daughters reconstructs the parent as a peak. Worked cases: the two-photon decay of the neutral pion and a heavy two-body hadronic decay.\n",{"path":3762,"title":3763,"module":3755,"summary":3764},"\u002Frelativity\u002Frelativistic-dynamics\u002Fcollisions-thresholds-and-the-cm-frame","Relativistic Collisions and Threshold Energies","Two-body collisions run on the same conserved four-momentum as decays. The invariant s sets the total energy available in the center-of-momentum frame and therefore the threshold for producing new particles. Fixed-target energy grows only as the square root of beam energy while a collider grows linearly, which is why colliders reach high energy. Compton scattering follows as a worked photon-electron collision giving the wavelength shift.\n",{"path":3766,"title":3767,"module":3755,"summary":3768},"\u002Frelativity\u002Frelativistic-dynamics\u002Fmandelstam-variables-and-invariants","Mandelstam Variables and Lorentz Invariants","For a two-to-two process the three Mandelstam invariants s, t, and u encode all the kinematics in frame-independent form. They obey a single linear constraint, the sum of the four squared masses, so only two are independent. s is the center-of-momentum energy squared, t and u are momentum transfers tied to the scattering angle, and crossing symmetry relates one amplitude across three channels through these variables.\n",{"path":3770,"title":3771,"module":3772,"summary":3773},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ffour-current-and-the-four-potential","The Four-Current and Four-Potential","Covariant Electromagnetism","Charge density and current combine into a single four-vector whose divergence is charge conservation. The scalar and vector potentials combine likewise into the four-potential, whose gauge freedom fixes to the Lorenz condition, reducing Maxwell's equations for the potentials to a single wave equation sourced by the four-current.\n",{"path":3775,"title":3776,"module":3772,"summary":3777},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fthe-electromagnetic-field-tensor","The Electromagnetic Field Tensor","The antisymmetric derivative of the four-potential is the field-strength tensor F, gauge invariant by construction, with the electric and magnetic fields as its components. Its dual exchanges E and B, and its two contractions form the Lorentz invariants that classify a field as electric, magnetic, or radiative in every frame.\n",{"path":3779,"title":3780,"module":3772,"summary":3781},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ftransformation-of-electric-and-magnetic-fields","How E and B Transform","Transforming the field tensor under a boost gives explicit rules for the electric and magnetic fields: components along the motion are unchanged, transverse components mix and pick up a gamma. The field of a uniformly moving charge compresses transversely, and the force between a current and a moving charge shows that magnetism is the relativistic shadow of electrostatics.\n",{"path":3783,"title":3784,"module":3772,"summary":3785},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fcovariant-maxwell-and-the-stress-energy-tensor","Covariant Maxwell and the Stress–Energy Tensor","Maxwell's four equations collapse into two tensor equations, one sourced by the four-current and one an identity on the field strength, with charge conservation automatic. The Lorentz force becomes a four-vector law, and the field's energy, momentum, and stress assemble into a symmetric, conserved stress–energy tensor — the object that will source gravity.\n",{"path":3787,"title":3788,"module":3789,"summary":3790},"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-equivalence-principle-formalized","The Equivalence Principle","Curved Spacetime","The equality of gravitational and inertial mass promotes to a physical principle in three graded strengths — weak, Einstein, and strong. A freely falling laboratory is locally indistinguishable from an inertial frame, but the qualifier \"locally\" is essential: the size of the patch over which gravity vanishes is set by the tidal field, which no change of frame can remove. Tidal forces are the true, coordinate-independent signature of gravity, and they are what curvature will measure.\n",{"path":3792,"title":3793,"module":3789,"summary":3794},"\u002Frelativity\u002Fcurved-spacetime\u002Fmanifolds-vectors-and-the-metric","Manifolds, Vectors, and the Metric","A manifold is a space that looks locally like flat space, described by overlapping coordinate charts. Tangent vectors are directional derivatives with the coordinate basis vectors as partial-derivative operators; one-forms live in the dual space; and the metric tensor turns a coordinate line element into an invariant length. The 2-sphere and Rindler metrics serve as worked examples, including the coordinate singularities that are artefacts of the chart, not of the geometry.\n",{"path":3796,"title":3797,"module":3789,"summary":3798},"\u002Frelativity\u002Fcurved-spacetime\u002Fcovariant-derivative-and-christoffel-symbols","Parallel Transport and the Covariant Derivative","The ordinary derivative of a vector field is not a tensor, because it subtracts vectors living in different tangent spaces. A connection supplies the missing comparison: the covariant derivative adds Christoffel-symbol correction terms that cancel the coordinate artefacts. Requiring the connection to be torsion-free and to preserve the metric fixes the Christoffel symbols uniquely in terms of derivatives of the metric, giving the Levi-Civita connection that general relativity uses.\n",{"path":3800,"title":3801,"module":3789,"summary":3802},"\u002Frelativity\u002Fcurved-spacetime\u002Fgeodesics-and-the-geodesic-equation","Geodesics and the Newtonian Limit","Free fall is geodesic motion: a freely falling particle follows the straightest possible worldline, obtained either by parallel-transporting its own tangent vector or by extremizing proper time. Both routes give the geodesic equation. Affine parameters, and conserved quantities from symmetries via Killing vectors, make it solvable. In the weak-field slow-motion limit the geodesic equation reproduces Newton's law of gravity, fixing the time-time metric component as the Newtonian potential.\n",{"path":3804,"title":3805,"module":3789,"summary":3806},"\u002Frelativity\u002Fcurved-spacetime\u002Fcurvature-riemann-and-geodesic-deviation","Curvature and the Riemann Tensor","Curvature is the failure of parallel transport to commute: carrying a vector around an infinitesimal loop returns it rotated, and the rotation per unit area is the Riemann tensor. Its symmetries cut the components to twenty in four dimensions. Geodesic deviation makes it the equation of tidal forces, and its contractions — the Ricci tensor, the Ricci scalar, and the divergence-free Einstein tensor — assemble the objects the field equation is built from.\n",{"path":3808,"title":3809,"module":3789,"summary":3810},"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-einstein-field-equations","The Einstein Field Equations","The field equation is assembled from a short list of requirements: a symmetric, divergence-free, second-order geometric tensor set proportional to the stress–energy tensor, with the coefficient fixed by the Newtonian limit. The cosmological constant is the one extra term the requirements allow. The Einstein–Hilbert action gives the same equation from a variational principle, and the coupled system closes the logic of the module: matter curves spacetime, and spacetime tells matter how to move.\n",{"path":3812,"title":3813,"module":3814,"summary":3815},"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fthe-schwarzschild-metric","The Schwarzschild Metric","The Schwarzschild Solution","The first exact solution of Einstein's equation follows from two assumptions, staticity and spherical symmetry, imposed on the vacuum outside a mass. Solving the vacuum field equations fixes two metric functions and produces the Schwarzschild geometry, whose one length scale is the Schwarzschild radius $r_s = 2GM\u002Fc^2$. Birkhoff's theorem shows this is the only spherical vacuum, and the far field reduces to Newtonian gravity.\n",{"path":3817,"title":3818,"module":3814,"summary":3819},"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fgeodesics-and-orbits-in-schwarzschild","Orbits in the Schwarzschild Geometry","The two Killing symmetries of the Schwarzschild metric give a conserved energy and angular momentum per unit mass, reducing geodesic motion to a one-dimensional problem in an effective potential. The potential carries an extra attractive $1\u002Fr^3$ term absent from Newton's, which caps the centrifugal barrier, produces an innermost stable circular orbit at $6GM\u002Fc^2$, and makes bound orbits precess instead of closing.\n",{"path":3821,"title":3822,"module":3814,"summary":3823},"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Flight-bending-and-null-geodesics","Null Geodesics and the Photon Sphere","Light follows null geodesics, governed by a photon effective potential with a single unstable maximum at $3GM\u002Fc^2$, the photon sphere. The impact parameter sorts rays into those that escape with a deflection and those captured, with the critical value $b_c = 3\\sqrt{3}\\,GM\u002Fc^2$ dividing them. A grazing ray bends by $4GM\u002F(c^2 b)$, twice the naive Newtonian value, and the critical impact parameter sets the edge of a black hole's shadow.\n",{"path":3825,"title":3826,"module":3827,"summary":3828},"\u002Frelativity\u002Ftests-of-general-relativity\u002Fperihelion-precession-of-mercury","The Perihelion Precession of Mercury","Tests of General Relativity","A single extra term in the Schwarzschild orbit equation, cubic in the inverse radius, keeps a bound orbit from closing. The perturbation advances the perihelion by 6πGM\u002F(c²a(1−e²)) per revolution, which for Mercury is 43 arcseconds per century — exactly the anomaly left after Newtonian planetary perturbations are subtracted. A note on frame dragging closes the lesson.\n",{"path":3830,"title":3831,"module":3827,"summary":3832},"\u002Frelativity\u002Ftests-of-general-relativity\u002Fdeflection-of-light-and-gravitational-lensing","Light Deflection and Gravitational Lensing","A light ray grazing the Sun bends by 4GM\u002F(c²b), exactly twice the value a Newtonian corpuscle would give; the extra factor is the curvature of space. The 1919 eclipse confirmed it. The same bending focuses light from distant sources into Einstein rings, multiple images, and microlensing brightenings, making lensing a direct probe of mass, including mass that emits no light.\n",{"path":3834,"title":3835,"module":3827,"summary":3836},"\u002Frelativity\u002Ftests-of-general-relativity\u002Fgravitational-redshift-and-shapiro-delay","Gravitational Redshift and the Shapiro Delay","A clock deeper in a gravitational well ticks slower, and a photon climbing out loses frequency by the ratio of the metric's time-time components. Pound and Rebka measured the 2.5×10⁻¹⁵ shift over a 22.5-metre tower. Radar signals grazing the Sun return late by about 250 microseconds, the Shapiro delay. Both probe the time part of the metric directly.\n",{"path":3838,"title":3839,"module":3827,"summary":3840},"\u002Frelativity\u002Ftests-of-general-relativity\u002Frelativity-in-technology-gps","Relativity and the Global Positioning System","A GPS satellite clock runs slow by 7 microseconds a day from its orbital speed and fast by 46 from its higher gravitational potential, a net gain of about 38 microseconds a day. Left uncorrected, the timing error would grow into kilometres of position error within a day and exceed navigation tolerance within minutes. The satellites carry a pre-launch frequency offset to cancel it.\n",{"path":3842,"title":3843,"module":3844,"summary":3845},"\u002Frelativity\u002Fblack-holes\u002Fhorizons-and-coordinate-singularities","Horizons and Coordinate Singularities","Black Holes","The Schwarzschild radius is a coordinate singularity, not a curvature singularity: the metric blows up there only because the static coordinates fail, while the geometry stays finite. Eddington–Finkelstein and Kruskal– Szekeres coordinates cross the horizon smoothly and show the light cones tipping toward the center. A freely falling observer reaches the true singularity at r=0 in finite proper time, while a distant observer sees the infall freeze and redden at the horizon.\n",{"path":3847,"title":3848,"module":3844,"summary":3849},"\u002Frelativity\u002Fblack-holes\u002Frotating-and-charged-black-holes","Rotating and Charged Black Holes","A stationary black hole is fixed by three numbers: mass, angular momentum, and charge. The Reissner–Nordström metric adds charge and splits the horizon in two; the Kerr metric adds rotation, drags inertial frames, and wraps the horizon in an ergosphere where nothing can stay still. Inside the ergosphere the Penrose process extracts rotational energy, and the no-hair theorem states that no other detail of the collapsed matter survives.\n",{"path":3851,"title":3852,"module":3844,"summary":3853},"\u002Frelativity\u002Fblack-holes\u002Fblack-hole-thermodynamics","Black-Hole Thermodynamics","The four laws of black-hole mechanics mirror the four laws of thermodynamics term for term, with horizon area playing the role of entropy and surface gravity the role of temperature. Hawking's calculation makes the analogy literal: a black hole radiates at a temperature set by its surface gravity, carries a real entropy proportional to its horizon area, and slowly evaporates. The thermal spectrum raises the information paradox.\n",{"path":3855,"title":3856,"module":3857,"summary":3858},"\u002Frelativity\u002Fgravitational-waves\u002Flinearized-gravity-and-wave-solutions","Linearized Gravity and Wave Solutions","Gravitational Waves","Weak gravity is a small perturbation of flat spacetime, and the linearized Einstein equation in the Lorenz gauge is an ordinary wave equation propagating at the speed of light. The trace-reversed perturbation carries the dynamics, residual gauge freedom fixes the transverse-traceless form, and the two physical polarizations deform a ring of freely falling masses into oscillating ellipses whose fractional size change is the strain.\n",{"path":3860,"title":3861,"module":3857,"summary":3862},"\u002Frelativity\u002Fgravitational-waves\u002Fgeneration-and-the-quadrupole-formula","The Quadrupole Formula","The retarded solution of the linearized field equation gives the field of a moving source, and conservation of mass and momentum forbids monopole and dipole radiation, leaving the mass quadrupole as the leading emitter. The quadrupole formula fixes the strain and the radiated luminosity, and applied to a compact binary it predicts the inspiral chirp of rising frequency and amplitude. The Hulse-Taylor pulsar's orbital decay confirmed it to a fraction of a percent.\n",{"path":3864,"title":3865,"module":3857,"summary":3866},"\u002Frelativity\u002Fgravitational-waves\u002Fdetection-ligo-and-the-first-events","LIGO and the First Detections","A gravitational wave is measured as a differential length change of the two arms of a kilometre-scale Michelson interferometer, a strain of order ten to the minus twenty-one that moves the mirrors by a fraction of a proton radius. GW150914 recorded the inspiral, merger, and ringdown of two black holes, fixing their masses and the energy radiated, and GW170817 with its coincident gamma-ray burst and kilonova opened multimessenger astronomy.\n",{"path":3868,"title":3869,"module":3870,"summary":3871},"\u002Frelativity\u002Fcosmological-bridge\u002Fthe-cosmological-principle-and-flrw-metric","The Cosmological Principle and the FLRW Metric","A Bridge to Cosmology","Homogeneity and isotropy restrict the spacetime of the universe to a single family of metrics: a flat cosmic-time slicing of spatial sections of constant curvature, scaled by a time-dependent factor a(t). This lesson builds the Friedmann–Lemaître–Robertson–Walker metric from those symmetries, separates comoving from proper distance, and derives cosmological redshift as the stretching of wavelengths with the scale factor.\n",{"path":3873,"title":3874,"module":3870,"summary":3875},"\u002Frelativity\u002Fcosmological-bridge\u002Ffriedmann-equations-and-cosmic-dynamics","The Friedmann Equations and Cosmic Dynamics","The Einstein equation applied to the FLRW metric with a perfect-fluid source yields the two Friedmann equations and the conservation law that ties them together. This lesson derives them, defines the critical density and the density parameters that fix the spatial geometry, works out how matter, radiation, and a cosmological constant dilute and drive the expansion, and hands off to a dedicated cosmology subject.\n",{"path":3877,"title":3878,"module":6,"summary":6},"\u002Frelativity","Relativity",{"path":3880,"title":3881,"module":6,"summary":6},"\u002Fphysical-computing","Physical Computing",{"path":3883,"title":3884,"module":3885,"summary":3886},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fblackbody-radiation-and-the-planck-quantum","Blackbody Radiation and the Planck Quantum","Origins of the Quantum","Millikan's oil-drop experiment fixed the electron charge as an indivisible unit, and the spectrum of thermal radiation forced a second, deeper quantum. Classical physics predicts an infinite energy density at short wavelengths; Planck removed the divergence by allowing a cavity oscillator to hold only energies that are integer multiples of hf, the first appearance of the quantum of action.\n",{"path":3888,"title":3889,"module":3885,"summary":3890},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-photoelectric-effect-and-the-photon","The Photoelectric Effect and the Photon","Light shone on a clean metal ejects electrons, but the details defied the wave theory: the electrons' maximum energy depends on the light's frequency, not its brightness, and there is a sharp threshold frequency below which nothing happens. Einstein resolved every anomaly by treating light as a stream of energy quanta hf, each absorbed whole by one electron, and Millikan's measurement of the stopping-potential slope confirmed h to a decade before anyone expected.\n",{"path":3892,"title":3893,"module":3885,"summary":3894},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fx-rays-and-the-compton-effect","X-Rays and the Compton Effect","X-rays are short-wavelength electromagnetic waves produced when fast electrons are braked in a target, and their diffraction by crystals lets Bragg's law measure atomic spacings. Compton then scattered X-rays off electrons and found the wavelength shifted by an amount that only a photon carrying momentum hf\u002Fc could explain, closing the case for the particle nature of light.\n",{"path":3896,"title":3897,"module":3885,"summary":3898},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-old-quantum-theory-bohr-and-sommerfeld","The Old Quantum Theory: Bohr, Sommerfeld, and Correspondence","Between Bohr's 1913 atom and Schrödinger's 1926 equation, physics ran on a provisional recipe: keep classical orbits, but admit only those whose action integral is a whole multiple of Planck's constant. This lesson develops the Wilson-Sommerfeld phase-integral rule, applies it to the oscillator and to the elliptical Kepler orbits of hydrogen, derives Sommerfeld's relativistic fine structure and the quantization of orbit orientation, and shows how the correspondence principle fixed intensities and selection rules. The systematic failures — helium, line intensities, the anomalous Zeeman effect — mark exactly where a theory of orbits had to give way to a theory of waves.\n",{"path":3900,"title":3901,"module":3902,"summary":3903},"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fde-broglie-waves-and-electron-diffraction","De Broglie Waves and Electron Diffraction","The Wave Nature of Matter","In 1924 de Broglie proposed that every particle carries a wave of wavelength h\u002Fp. The hypothesis explains Bohr's quantized orbits as standing waves, and Davisson and Germer, then G. P. Thomson, confirmed it by diffracting electrons from crystals exactly as X-rays diffract. We derive the electron wavelength, work the Bragg analysis of the data, and give the relativistic form.\n",{"path":3905,"title":3906,"module":3902,"summary":3907},"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fwave-packets-and-the-probability-interpretation","Wave Packets and the Probabilistic Wave Function","A single de Broglie wave fills all space, but a particle is localized. Adding many waves of nearby wavelength builds a wave packet that is confined and moves at the group velocity, which equals the particle velocity. Born's rule reads the squared amplitude of the wave function as a probability density, the meaning confirmed by electron interference building up one detection at a time.\n",{"path":3909,"title":3910,"module":3902,"summary":3911},"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fthe-uncertainty-principle","The Uncertainty Principle and Wave-Particle Duality","The packet relations delta-k delta-x about 1 become Heisenberg's principle once momentum is hbar times wave number: position and momentum cannot both be sharp, nor energy and time. The gamma-ray microscope shows the limit is physical, not technical. It fixes the zero-point energy of a confined particle, the size of the hydrogen atom, and the natural width of spectral lines, and it frames the wave-particle duality of all matter and radiation.\n",{"path":3913,"title":3914,"module":3915,"summary":3916},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-schrodinger-equation-in-one-dimension","The Schrödinger Equation in One Dimension","Wave Mechanics in One Dimension","The wave equation for matter cannot be derived; it is postulated and judged by experiment. We build the time-dependent Schrödinger equation from the de Broglie relations, read Born's probability rule off the complex wave function, and separate the time and space dependence to get the time-independent equation whose bound-state solutions are the stationary states. The five acceptability conditions on the wave function are what force energy to be quantized.\n",{"path":3918,"title":3919,"module":3915,"summary":3920},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-free-particle-and-wave-packet-dynamics","The Free Particle and Wave-Packet Dynamics","The free particle has no bound states: its stationary solutions are non-normalizable plane waves forming a continuum. Physical states are wave packets built by superposing them, and the superposition is a Fourier transform. We delta-normalize the plane waves, assemble a Gaussian packet, solve for its exact time evolution, and read off the two facts that reconcile the wave picture with mechanics: the packet moves at the group velocity ħk\u002Fm, the classical velocity, and it spreads because its component momenta travel at different speeds.\n",{"path":3922,"title":3923,"module":3915,"summary":3924},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fparticle-in-infinite-and-finite-square-wells","Particle in Infinite and Finite Square Wells","The infinite square well is the simplest bound-state problem: two boundary conditions quantize the energy into a ladder E_n = n² E_1, and the eigenfunctions are the standing waves of a string fixed at both ends. Relaxing the walls to a finite depth lets the wave function leak into the classically forbidden region, keeps the number of bound states finite, and turns the eigenvalue condition into a transcendental equation solved graphically.\n",{"path":3926,"title":3927,"module":3915,"summary":3928},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Foperators-expectation-values-and-the-harmonic-oscillator","Operators, Expectation Values, and the Harmonic Oscillator","Measurable quantities are extracted from the wave function as expectation values, and each observable is represented by an operator that acts between Ψ* and Ψ — position by multiplication, momentum by a derivative, energy by the Hamiltonian. Applied to the harmonic oscillator, the machinery yields evenly spaced levels E_n = (n+½)ℏω, Gaussian- times-Hermite eigenfunctions of definite parity, and the selection rule Δn = ±1.\n",{"path":3930,"title":3931,"module":3915,"summary":3932},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-dirac-delta-potential","The Dirac-Delta Potential: A Single Bound State and Scattering","A potential concentrated at a single point is solvable in closed form and isolates the physics of matching a wave function across a discontinuity. Integrating the Schrödinger equation across the spike gives a jump condition on the derivative; the attractive delta well then supports exactly one bound state, of energy set by the strength alone, while the same spike scatters an incoming beam with a transmission that rises from zero to one. The attractive well and the repulsive barrier scatter identically yet only the well binds.\n",{"path":3934,"title":3935,"module":3915,"summary":3936},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fbarrier-penetration-and-quantum-tunneling","Barrier Penetration and Quantum Tunneling","Unbound states scatter rather than bind. A particle meeting a step is partly reflected even when it has more than enough energy to pass, and a particle meeting a barrier taller than its energy has a nonzero chance of appearing on the far side. Matching the wave function across the boundaries gives the reflection and transmission coefficients and the exponential tunneling probability that explains alpha decay, the scanning tunneling microscope, and the ammonia clock.\n",{"path":3938,"title":3939,"module":3940,"summary":3941},"\u002Fquantum-mechanics\u002Fformalism\u002Fhilbert-space-and-dirac-notation","Hilbert Space and Dirac Bra–Ket Notation","The Formalism of Quantum Mechanics","Wave mechanics is one representation of a deeper structure: quantum states are vectors in a complex inner-product space, and observables act on them as linear operators. We build that space from the axioms, introduce Dirac's kets and bras as vectors and the linear functionals that measure them, and identify the wavefunction as the components of an abstract state in the position basis. The resolution of the identity is the single algebraic tool that ties every basis, expansion, and matrix element together.\n",{"path":3943,"title":3944,"module":3940,"summary":3945},"\u002Fquantum-mechanics\u002Fformalism\u002Fobservables-hermitian-operators-and-eigenvalues","Observables, Hermitian Operators, and the Spectral Theorem","Every measurable quantity is represented by a Hermitian operator, and the reason is forced: a measurement needs real eigenvalues, orthogonal eigenvectors, and a complete eigenbasis, and Hermiticity delivers precisely those. We derive those properties from self-adjointness, state the spectral theorem, handle degeneracy, and show that two observables share an eigenbasis precisely when they commute — the algebraic condition behind compatible and incompatible measurements.\n",{"path":3947,"title":3948,"module":3940,"summary":3949},"\u002Fquantum-mechanics\u002Fformalism\u002Fthe-postulates-and-quantum-measurement","The Postulates and Quantum Measurement","With states as vectors and observables as Hermitian operators, the physical content of quantum mechanics reduces to a short list of postulates. We state them precisely, derive the Born probability rule for discrete and continuous spectra, work out projective collapse and its idempotence, compute expectation values and their variance, and state the measurement problem cleanly — the one place the postulates split unitary evolution from measurement without explaining the seam.\n",{"path":3951,"title":3952,"module":3940,"summary":3953},"\u002Fquantum-mechanics\u002Fformalism\u002Fposition-momentum-and-continuous-spectra","Position, Momentum, and Continuous Spectra","Position and momentum are the observables with no normalizable eigenstates: their spectra are continuous, their eigenkets are delta-normalized, and the two are Fourier conjugates. We derive the canonical commutator from the momentum operator, build the continuous-basis machinery (Dirac deltas replacing Kronecker deltas), show the position and momentum wavefunctions are a Fourier-transform pair, and compute expectation values in either representation.\n",{"path":3955,"title":3956,"module":3940,"summary":3957},"\u002Fquantum-mechanics\u002Fformalism\u002Fcommutators-and-the-generalized-uncertainty-principle","Commutators and the Generalized Uncertainty Principle","The commutator of two observables measures the obstruction to sharing an eigenbasis, and it bounds how sharply both can be known at once. We derive the generalized uncertainty relation from the Schwarz inequality, recover the position–momentum bound as a special case, characterize the minimum-uncertainty states that saturate it as Gaussians, and give the energy–time relation its correct reading as a lifetime bound rather than a commutator relation.\n",{"path":3959,"title":3960,"module":3940,"summary":3961},"\u002Fquantum-mechanics\u002Fformalism\u002Ftime-evolution-schrodinger-and-heisenberg-pictures","Time Evolution, Propagators, and the Heisenberg Picture","Time evolution is generated by the Hamiltonian and implemented by a unitary operator that preserves probability. We build that operator, expand a state in stationary states to see why probability densities freeze while phases wind, introduce the propagator, transfer the time dependence onto operators in the Heisenberg picture, and derive Ehrenfest's theorem — which recovers classical equations of motion for expectation values and identifies conserved quantities as observables commuting with the Hamiltonian.\n",{"path":3963,"title":3964,"module":3965,"summary":3966},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fladder-operators-and-the-number-states","Ladder Operators and the Number States","The Oscillator Algebraically, and Symmetry","The harmonic oscillator can be solved without touching a differential equation. Factoring the Hamiltonian into a lowering operator and its adjoint turns the spectrum into pure algebra: the commutator relation fixes the ladder, the vacuum condition fixes the ground state, and the energies fall out as equally spaced rungs. The same operators give the matrix elements of position and momentum for free.\n",{"path":3968,"title":3969,"module":3965,"summary":3970},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fcoherent-and-squeezed-states","Coherent and Squeezed States","A single number state never moves — its position expectation is pinned at the origin. The superposition that oscillates like a classical particle is the eigenstate of the annihilation operator: the coherent state. It is a displaced vacuum, carries Poissonian photon statistics, saturates the uncertainty bound, and traces a rigid Gaussian orbit in phase space. Squeezing deforms that circle, trading precision in one quadrature for noise in the other.\n",{"path":3972,"title":3973,"module":3965,"summary":3974},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fsymmetries-generators-and-conservation-laws","Symmetries, Generators, and Conservation Laws","Every continuous symmetry of a quantum system is a unitary operator built by exponentiating a Hermitian generator: momentum generates translations, angular momentum generates rotations, the Hamiltonian generates time evolution. When a generator commutes with the Hamiltonian, the transformation leaves the dynamics unchanged and the generator is conserved — the quantum form of Noether's theorem — and any symmetry that mixes states within a level forces degeneracy.\n",{"path":3976,"title":3977,"module":3965,"summary":3978},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fparity-time-reversal-and-discrete-symmetries","Parity, Time Reversal, and Discrete Symmetries","Parity and time reversal are symmetries no continuous generator can reach. Parity is a unitary involution whose eigenvalues label states even or odd, fixing the dipole selection rules. Time reversal is antiunitary: it conjugates i, flips momenta and spins, and for half-integer spin squares to minus one, which by Kramers' theorem makes every level of a time-reversal-invariant Hamiltonian at least doubly degenerate.\n",{"path":3980,"title":3981,"module":2820,"summary":3982},"\u002Fquantum-mechanics\u002Fangular-momentum\u002Forbital-angular-momentum-and-spherical-harmonics","Orbital Angular Momentum and Spherical Harmonics","Orbital angular momentum is the operator triple built from position and momentum. Its components fail to commute, so no state carries sharp values of more than one of them, but each commutes with the total square. Solving the common eigenvalue problem in spherical coordinates quantizes both the magnitude and the projection and produces the spherical harmonics, the angular part of every central-force wavefunction.\n",{"path":3984,"title":3985,"module":2820,"summary":3986},"\u002Fquantum-mechanics\u002Fangular-momentum\u002Fthe-angular-momentum-algebra","The Angular-Momentum Algebra and Ladder Operators","The eigenvalues of angular momentum follow from the commutation relations alone, with no reference to coordinates or wavefunctions. Raising and lowering operators built from the components generate finite multiplets, force the total quantum number to be a non-negative integer or half-integer, and fix the matrix elements of every component. The half-integer values excluded by orbital motion appear here, and they are what spin realizes.\n",{"path":3988,"title":3989,"module":2820,"summary":3990},"\u002Fquantum-mechanics\u002Fangular-momentum\u002Faddition-of-angular-momenta-and-clebsch-gordan","Addition of Angular Momenta and Clebsch–Gordan Coefficients","Two angular momenta combine into a total whose allowed magnitudes run from the difference to the sum of the parts in integer steps. The change from the uncoupled product basis to the coupled total-angular-momentum basis is carried out with the lowering operator and orthogonality, and its matrix of overlaps is the table of Clebsch–Gordan coefficients. Two spin-halves split into a triplet and a singlet, the prototype for every composite spin.\n",{"path":3992,"title":3993,"module":3994,"summary":3995},"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-schrodinger-equation-in-three-dimensions","The Schrödinger Equation in Three Dimensions","Central Potentials","A central potential depends only on the distance from a force center, so the three-dimensional Schrödinger equation separates in spherical coordinates. The angular factor is a spherical harmonic; the radial factor obeys a one-dimensional equation with an effective potential whose centrifugal barrier depends on the angular-momentum quantum number. The free particle and the spherical box fix the two limiting cases through the spherical Bessel functions.\n",{"path":3997,"title":3998,"module":3994,"summary":3999},"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-hydrogen-atom","The Hydrogen Atom","The Coulomb potential turns the radial equation into one whose bound states exist only for a discrete set of energies. A power-series solution truncated to keep the wavefunction normalizable forces the principal quantum number, and the energy comes out proportional to minus one over its square, recovering the Rydberg spectrum. The bound states are the associated Laguerre functions times spherical harmonics, and their energy depends on the principal number alone, giving an n-squared degeneracy larger than rotational symmetry can explain.\n",{"path":4001,"title":4002,"module":3994,"summary":4003},"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-isotropic-oscillator-and-hidden-symmetry","The Isotropic Oscillator and Hidden Symmetry","The three-dimensional isotropic harmonic oscillator solves in both Cartesian and spherical bases, and the two solutions must agree on the degeneracy of every level. That agreement, and the accidental degeneracy of hydrogen, both come from a symmetry larger than rotation: the oscillator carries an SU(3) invariance built from a conserved quadrupole tensor, and the Coulomb problem carries an SO(4) invariance built from the conserved Runge–Lenz vector. These hidden symmetries pin the degeneracies that rotational invariance alone leaves unexplained.\n",{"path":4005,"title":4006,"module":4007,"summary":4008},"\u002Fquantum-mechanics\u002Fspin\u002Fspin-half-pauli-matrices-and-stern-gerlach","Spin-½, the Pauli Matrices, and Stern–Gerlach","Spin","A silver atom passing through an inhomogeneous magnetic field splits into two beams, not a smear. That single fact fixes the internal angular momentum of the electron to a two-valued quantity with no spatial wavefunction. We build the two-dimensional spin space, the Pauli matrices and their algebra, the spinor for measurement along an arbitrary axis, and the sequential Stern–Gerlach filters that expose measurement disturbance.\n",{"path":4010,"title":4011,"module":4007,"summary":4012},"\u002Fquantum-mechanics\u002Fspin\u002Fspin-in-a-magnetic-field-precession-and-resonance","Spin in a Magnetic Field: Precession and Resonance","A spin coupled to a magnetic field is the simplest nontrivial quantum dynamics. A static field makes the spin expectation precess on a cone at the Larmor frequency while the energy levels split linearly. Adding a weak oscillating field and passing to the rotating frame produces Rabi oscillations and a resonance lineshape — the physics of NMR and ESR, and the driven qubit.\n",{"path":4014,"title":4015,"module":4007,"summary":4016},"\u002Fquantum-mechanics\u002Fspin\u002Ftwo-level-systems-and-the-bloch-sphere","Two-Level Systems and the Bloch Sphere","Every two-state quantum system is a spin-½ in disguise. Its Hamiltonian is an effective magnetic field, its pure states are points on the Bloch sphere, and its unitary evolution is a rigid rotation of that sphere. The same structure produces avoided level crossings, the ammonia inversion doublet and its maser, and the qubit.\n",{"path":4018,"title":4019,"module":4020,"summary":4021},"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fidentical-particles-and-exchange-symmetry","Identical Particles and Exchange Symmetry","Identical Particles","Two electrons carry no label that distinguishes one from the other, and that bare fact reshapes the state space. The exchange operator that swaps particle labels commutes with any Hamiltonian built from identical particles, so its eigenvalue is conserved, and nature admits only its two extremes: totally symmetric states for bosons and totally antisymmetric states for fermions. The antisymmetry forces a statistical correlation, the exchange \"force,\" that keeps fermions apart and draws bosons together even with no interaction between them.\n",{"path":4023,"title":4024,"module":4020,"summary":4025},"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fthe-pauli-principle-atoms-and-the-periodic-table","The Pauli Principle, Atoms, and the Periodic Table","Antisymmetry packaged as a Slater determinant turns the exclusion principle into an operating rule for building atoms. Helium shows the machinery in full: the electron-electron repulsion splits into a direct Coulomb integral and an exchange integral, and the exchange term alone pushes the spin-triplet (orthohelium) below the spin-singlet (parahelium) with no magnetic interaction in sight. Screening, the aufbau order, and Hund's rules then assemble the whole periodic table from the same antisymmetry.\n",{"path":4027,"title":4028,"module":4029,"summary":4030},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ftime-independent-perturbation-theory","Time-Independent Perturbation Theory","Approximation Methods for Bound States","Almost no realistic Hamiltonian can be solved exactly. Perturbation theory treats a hard Hamiltonian as a solvable one plus a small correction and expands the eigenvalues and eigenstates in powers of that correction. We derive the first- and second-order energy shifts and the first-order state correction for a nondegenerate level, expose the small-denominator failure that degeneracy forces, and fix it by diagonalizing the perturbation inside the degenerate subspace to find the \"good\" zeroth-order states.\n",{"path":4032,"title":4033,"module":4029,"summary":4034},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ffine-structure-and-the-real-hydrogen-atom","Fine Structure and the Real Hydrogen Atom","The Bohr spectrum is only the leading term. Two relativistic corrections of order alpha-squared — the relativistic kinetic-energy correction and spin–orbit coupling, joined by the Darwin term for s states — split the hydrogen levels into fine structure that depends on the total angular momentum j. We derive each shift as a first-order perturbation, combine them into a formula depending only on n and j, and continue down the energy ladder to the Lamb shift and the hyperfine 21 cm line.\n",{"path":4036,"title":4037,"module":4029,"summary":4038},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-zeeman-and-stark-effects","The Zeeman and Stark Effects","An atom in an external field is a perturbation problem whose good basis depends on which interaction wins. A magnetic field competes with the internal spin–orbit coupling: the weak-field limit gives the anomalous Zeeman splitting set by the Landé g-factor, the strong-field limit gives the Paschen–Back pattern in the uncoupled basis, and the intermediate regime is a matrix diagonalization. An electric field gives a quadratic shift for the nondegenerate ground state and a linear splitting for the degenerate n = 2 level.\n",{"path":4040,"title":4041,"module":4029,"summary":4042},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-variational-method","The Variational Method","The expectation of the Hamiltonian in any trial state is an upper bound on the true ground-state energy. Minimizing that expectation over a parametrized family of trial functions turns the ground-state problem into ordinary calculus and needs no small parameter. We prove the bound, apply it to the helium atom with a screened effective charge, use a two-center trial to predict binding in the hydrogen molecular ion, and extend the method to excited states through orthogonality.\n",{"path":4044,"title":4045,"module":4029,"summary":4046},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-wkb-approximation","The WKB Approximation","When the potential varies slowly on the scale of the de Broglie wavelength, the wavefunction is locally a plane wave with a position-dependent wavelength. This semiclassical picture builds the wavefunction from the classical momentum, breaks down at the turning points where the momentum vanishes, and is repaired there by connection formulas. The result recovers the Bohr–Sommerfeld quantization rule with its half-integer correction and gives the exponential tunneling rate through a smooth barrier, the Gamow factor.\n",{"path":4048,"title":4049,"module":6,"summary":6},"\u002Fquantum-mechanics","Quantum Mechanics",{"path":4051,"title":4052,"module":4053,"summary":4054},"\u002Freal-analysis\u002Ffoundations\u002Fsets-logic-functions","Sets, Logic, and Functions","Foundations and the Real Number System","The working language of analysis: quantifiers and the proof patterns (contrapositive, contradiction, induction), sets and their operations, relations and equivalence classes, and functions with their images, injections, surjections, and bijections. Cardinality is measured by bijection, and Cantor's theorem that no set surjects onto its power set forces uncountable sets to exist.\n",{"path":4056,"title":4057,"module":4053,"summary":4058},"\u002Freal-analysis\u002Ffoundations\u002Fordered-fields-completeness","Ordered Fields and the Completeness Axiom","The real numbers are the unique ordered field with the least-upper-bound property. The field and order axioms, the exact failure of the rationals (no supremum for the set of rationals below √2), and completeness as the defining axiom of ℝ lead to the first consequences: the existence of √2, the Archimedean property, and the density of ℚ in ℝ.\n",{"path":4060,"title":4061,"module":4053,"summary":4062},"\u002Freal-analysis\u002Ffoundations\u002Fabsolute-value-bounds","Absolute Value, Bounded Sets, and Inequalities","The absolute value turns the order on ℝ into a notion of distance, with the triangle inequality as the estimate underlying most later proofs. Covered: its algebra, the triangle and reverse-triangle inequalities, and the extension of the sup\u002Finf vocabulary from sets to bounded functions.\n",{"path":4064,"title":4065,"module":4053,"summary":4066},"\u002Freal-analysis\u002Ffoundations\u002Fintervals-uncountability","Intervals, Uncountability, and Decimals","Intervals are classified, and ℝ is proved uncountable two ways: a nested-interval construction and the decimal diagonal argument. Decimal expansions are built as suprema of truncations, which pins the source of their non-uniqueness (the 0.4999… equals 0.5000… identity) and the identification of the rationals with the eventually-repeating expansions. The middle-thirds Cantor set is an uncountable set of measure zero.\n",{"path":4068,"title":4069,"module":4070,"summary":4071},"\u002Freal-analysis\u002Fsequences-series\u002Fsequences-limits","Sequences and Their Limits","Sequences and Series","A sequence is a function on the natural numbers; it converges to a limit when its terms eventually stay within any prescribed tolerance of that number. The epsilon-M definition fixes the order of the quantifiers, and from it the limit is unique, every convergent sequence is bounded, and only the tail matters. Divergence to plus or minus infinity records terms that outgrow every bound.\n",{"path":4073,"title":4074,"module":4070,"summary":4075},"\u002Freal-analysis\u002Fsequences-series\u002Flimit-laws-monotone","Limit Laws and Monotone Convergence","Limits commute with sums, products, quotients, roots, and absolute values and preserve non-strict inequalities, so a limit can be assembled from the limits of its parts without returning to epsilon and M. The squeeze lemma transfers a limit through two envelopes; the monotone convergence theorem produces a limit from boundedness alone; and the ratio test settles the geometric and factorial standard limits.\n",{"path":4077,"title":4078,"module":4070,"summary":4079},"\u002Freal-analysis\u002Fsequences-series\u002Flimsup-bolzano-weierstrass","Subsequences, Limit Superior, and Bolzano–Weierstrass","A bounded sequence need not converge, but it always has convergent subsequences, and its terms cluster between two extreme values. The limit superior and inferior are the limits of the tail suprema and infima; they always exist for a bounded sequence, coincide exactly when it converges, and are its largest and smallest subsequential limits. Bolzano–Weierstrass extracts a convergent subsequence from boundedness alone.\n",{"path":4081,"title":4082,"module":4070,"summary":4083},"\u002Freal-analysis\u002Fsequences-series\u002Fcauchy-completeness","Cauchy Sequences and the Completeness of the Reals","The Cauchy criterion tests convergence without knowing the limit: a sequence converges exactly when its terms eventually all lie within any tolerance of one another. Cauchy sequences are bounded, in the reals Cauchy and convergent are equivalent, and this completeness property is interchangeable with the least-upper-bound axiom — the single feature that separates the real line from the rationals.\n",{"path":4085,"title":4086,"module":4070,"summary":4087},"\u002Freal-analysis\u002Fsequences-series\u002Fseries-convergence","Series and Convergence Tests","A series converges when its sequence of partial sums does, so every fact about sequences transfers. Geometric and telescoping series sum in closed form; the n-th term test rejects series whose terms miss zero, though the harmonic series shows the converse fails; and the comparison test against the geometric and p-series benchmarks settles most nonnegative-term series.\n",{"path":4089,"title":4090,"module":4070,"summary":4091},"\u002Freal-analysis\u002Fsequences-series\u002Fabsolute-conditional-rearrangement","Absolute Convergence, the Ratio and Root Tests, and Rearrangements","Absolute convergence is the strong form of convergence that permits free manipulation; conditional convergence is fragile. Absolute convergence implies convergence, and the ratio and root tests detect it by comparison with the geometric series. The alternating series test supplies conditionally convergent series, Riemann's theorem rearranges any of them to any sum, and Mertens' theorem multiplies series when at least one converges absolutely.\n",{"path":4093,"title":4094,"module":4095,"summary":4096},"\u002Freal-analysis\u002Fmetric-spaces\u002Fmetric-spaces-norms","Metric Spaces, Norms, and Examples","Metric Spaces and Topology","A metric is a function $d(x,y)$ obeying four axioms: nonnegativity, identity of indiscernibles, symmetry, and the triangle inequality. The Euclidean, taxicab, sup, discrete, and great-circle metrics all qualify, as does the sup metric on $C[a,b]$. Every norm induces a metric, and strongly equivalent metrics share the same open sets.\n",{"path":4098,"title":4099,"module":4095,"summary":4100},"\u002Freal-analysis\u002Fmetric-spaces\u002Fopen-closed-sets","Open and Closed Sets, Interior, Closure","Open sets are those in which every point has room to move; closed sets are their complements. From the single ball construction come the topology axioms (arbitrary unions, finite intersections), the interior, closure, and boundary of a set, and the fact that openness is always relative to the ambient space.\n",{"path":4102,"title":4103,"module":4095,"summary":4104},"\u002Freal-analysis\u002Fmetric-spaces\u002Fconvergence-completeness","Convergence, Cauchy Sequences, and Completeness","The $\\varepsilon$-$N$ definition of a limit transfers verbatim to any metric space once $|x-y|$ is replaced by $d(x,y)$. Convergent sequences characterize closed sets and closures; Cauchy sequences and completeness capture spaces with no missing limits, with $\\mathbb{R}^n$ and $C[a,b]$ complete and $\\mathbb{Q}$ and $(0,1]$ not.\n",{"path":4106,"title":4107,"module":4095,"summary":4108},"\u002Freal-analysis\u002Fmetric-spaces\u002Fcompactness","Compactness","A set is compact if every open cover has a finite subcover. In a metric space this is equivalent to sequential compactness and to being complete and totally bounded. Compact sets are closed and bounded; the Heine–Borel theorem gives the converse in $\\mathbb{R}^n$ but nowhere else in general.\n",{"path":4110,"title":4111,"module":4095,"summary":4112},"\u002Freal-analysis\u002Fmetric-spaces\u002Fconnectedness","Connectedness","A space is connected when it cannot be split into two nonempty open pieces. The connected subsets of $\\mathbb{R}$ are precisely the intervals, path- connectedness gives a constructive sufficient condition, and connectedness is a topological invariant preserved by continuous maps, the fact behind the intermediate value theorem.\n",{"path":4114,"title":4115,"module":2514,"summary":4116},"\u002Freal-analysis\u002Fcontinuity\u002Flimits-of-functions","Limits of Functions","The limit of a function at a point is an epsilon–delta condition pinning one value L as the target of f(x) as x approaches c, mirroring the sequence definition with distance replacing index. It is stated only at cluster points of the domain, is unique when it exists, and reduces to sequential limits through the Heine criterion. The algebra of limits and one-sided limits follow from that reduction.\n",{"path":4118,"title":4119,"module":2514,"summary":4120},"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuous-functions","Continuous Functions","A function is continuous at c when its limit there equals its own value, lim f(x) = f(c). The epsilon–delta and sequential forms agree; sums, products, quotients, and compositions of continuous functions are continuous; and the failures split into jump, Dirichlet, popcorn, and removable types. The topological reading is that preimages of open sets are open.\n",{"path":4122,"title":4123,"module":2514,"summary":4124},"\u002Freal-analysis\u002Fcontinuity\u002Fevt-ivt","Extreme and Intermediate Value Theorems","On a closed bounded interval a continuous function attains an absolute maximum and minimum (the extreme value theorem, compactness preserved by continuity) and takes every value between its endpoint values (the intermediate value theorem, connectedness preserved). Both proofs run through Bolzano–Weierstrass and bisection, and yield root-finding, existence of k-th roots, and fixed-point theorems.\n",{"path":4126,"title":4127,"module":2514,"summary":4128},"\u002Freal-analysis\u002Fcontinuity\u002Funiform-continuity","Uniform Continuity","Uniform continuity strengthens continuity by demanding one delta that works at every point of the domain, not a delta re-chosen at each point. It separates x^2 on a compact interval from x^2 on the whole line and from 1\u002Fx near zero; continuity on a closed bounded interval is automatically uniform; uniformly continuous functions preserve Cauchy sequences and extend to endpoints; and Lipschitz continuity is the strongest of the three, through its secant-slope bound.\n",{"path":4130,"title":4131,"module":2514,"summary":4132},"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuity-metric-spaces","Continuity on Metric Spaces","The epsilon–delta definition used only distances, so continuity transfers to maps between metric spaces by replacing absolute values with the two metrics. In this generality continuity still admits a sequential form, preserves compactness and connectedness, is uniform on a compact domain, and reads topologically as preimages of open sets being open, the formulation that defines homeomorphisms.\n",{"path":4134,"title":4135,"module":2514,"summary":4136},"\u002Freal-analysis\u002Fcontinuity\u002Flimits-infinity-monotone","Limits at Infinity and Monotone Functions","Treating infinity as a cluster point extends the epsilon–delta limit to x approaching plus or minus infinity, giving horizontal asymptotes and infinite limits. For monotone functions the one-sided limits always exist as suprema and infima, the discontinuities are jumps and at most countably many, the continuity is equivalent to the image being an interval, and a strictly monotone function always has a continuous inverse.\n",{"path":4138,"title":4139,"module":4140,"summary":4141},"\u002Freal-analysis\u002Fdifferentiation\u002Fthe-derivative","The Derivative","Differentiation","The derivative is the limit of the difference quotient, the slope the secant lines approach as the second point slides into the first. Differentiability forces continuity; linearity and the product, quotient, and chain rules follow from the definition; and a continuous function can fail to be differentiable, as the absolute value does at the origin.\n",{"path":4143,"title":4144,"module":4140,"summary":4145},"\u002Freal-analysis\u002Fdifferentiation\u002Fmean-value-theorem","The Mean Value Theorem","A relative extremum in the interior forces the derivative to vanish; Rolle's theorem and the mean value theorem turn that local fact into global control. The sign of the derivative fixes monotonicity, a bounded derivative yields a Lipschitz bound, and Darboux's theorem shows derivatives have the intermediate value property even where they are discontinuous.\n",{"path":4147,"title":4148,"module":4140,"summary":4149},"\u002Freal-analysis\u002Fdifferentiation\u002Ftaylors-theorem","Taylor's Theorem","Taylor's theorem generalizes the mean value theorem: an n-times differentiable function is matched near a point by a degree-n polynomial, with a Lagrange remainder that names the error exactly through one higher derivative. Iterating the mean value theorem proves it; the second-derivative test is the order-one case; and a smooth non-analytic bump separates a Taylor series from the function it fails to represent.\n",{"path":4151,"title":4152,"module":4140,"summary":4153},"\u002Freal-analysis\u002Fdifferentiation\u002Finverse-function-1d","The Inverse Function Theorem in One Variable","A nonzero derivative certifies a local inverse and fixes its slope. A strictly monotone differentiable function has a differentiable inverse whose derivative is the reciprocal of the original; the inverse function theorem removes the monotonicity hypothesis, and the reciprocal formula constructs nth roots and the logarithm's derivative, failing exactly where the derivative vanishes.\n",{"path":4155,"title":4156,"module":4157,"summary":4158},"\u002Freal-analysis\u002Friemann-integration\u002Fdarboux-integral","Partitions, Darboux Sums, and Integrability","The Riemann Integral","The Riemann integral is defined by trapping the area under a bounded function between under- and over-estimates. Partitions cut the domain into strips; lower and upper Darboux sums bracket the area; refining a partition tightens the bracket. A function is integrable exactly when the bracket can be made arbitrarily thin, and the tagged Riemann-sum limit gives the same number.\n",{"path":4160,"title":4161,"module":4157,"summary":4162},"\u002Freal-analysis\u002Friemann-integration\u002Fintegrability-classes","Which Functions Are Integrable","The Cauchy criterion certifies whole classes of functions as integrable. Continuous functions are integrable because uniform continuity makes every oscillation cap small; monotone functions are integrable because their caps telescope to a single total jump; bounded functions with finitely many discontinuities are integrable by isolating the bad points. The Dirichlet function fails, and the Lebesgue criterion names the exact boundary.\n",{"path":4164,"title":4165,"module":4157,"summary":4166},"\u002Freal-analysis\u002Friemann-integration\u002Fproperties-of-the-integral","Properties of the Integral","The integral is a linear, order-preserving, additive operator on the integrable functions. It splits across subintervals, respects inequalities, bounds the size of a function by the integral of its absolute value, and preserves products. The mean value theorem for integrals identifies the integral with an attained average height on a fixed rectangle.\n",{"path":4168,"title":2569,"module":4157,"summary":4169},"\u002Freal-analysis\u002Friemann-integration\u002Ffundamental-theorem","The fundamental theorem ties the integral to the derivative in two forms. The evaluation form computes a definite integral from any antiderivative; the differentiation form shows the area function has derivative equal to the integrand at points of continuity. Together they make differentiation and integration inverse operations, and yield integration by parts and change of variables.\n",{"path":4171,"title":4172,"module":4157,"summary":4173},"\u002Freal-analysis\u002Friemann-integration\u002Flog-exp-improper","The Logarithm, Exponential, and Improper Integrals","The integral defines transcendental functions. The logarithm is the area under 1\u002Ft, the exponential is its inverse, and their calculus properties follow from the fundamental theorem. Improper integrals extend integration to unbounded intervals and unbounded integrands as limits of proper integrals, with a p-test, a comparison test, absolute versus conditional convergence, and the integral test linking integrals to series.\n",{"path":4175,"title":4176,"module":4177,"summary":4178},"\u002Freal-analysis\u002Ffunction-sequences\u002Fpointwise-uniform-convergence","Pointwise and Uniform Convergence","Sequences and Series of Functions","A sequence of functions has two natural notions of limit. Pointwise convergence fixes each input and takes the limit of numbers; uniform convergence demands one rate that works for every input at once. The uniform norm turns the second into a statement about a single sequence of numbers, and the uniform Cauchy criterion and the Weierstrass M-test let us certify it.\n",{"path":4180,"title":4181,"module":4177,"summary":4182},"\u002Freal-analysis\u002Ffunction-sequences\u002Finterchange-of-limits","Interchange of Limits: Continuity, Integration, Differentiation","Passing to a limit inside a continuity statement, an integral, or a derivative is an interchange of two limits, and the two limits do not always commute. Uniform convergence licenses the first two swaps: the uniform limit of continuous functions is continuous, and the limit of the integrals is the integral of the limit. Differentiation needs uniform convergence of the derivatives, and counterexamples show why each hypothesis is required.\n",{"path":4184,"title":4185,"module":4177,"summary":4186},"\u002Freal-analysis\u002Ffunction-sequences\u002Fpower-series-weierstrass","Power Series and the Weierstrass Approximation Theorem","A power series converges uniformly on every closed subinterval inside its radius of convergence, together with all of its derivatives. That makes it continuous, differentiable, and integrable term by term, so a power series defines an infinitely differentiable function. The Weierstrass approximation theorem then shows that polynomials come uniformly close to any continuous function on a closed bounded interval.\n",{"path":4188,"title":4189,"module":4177,"summary":4190},"\u002Freal-analysis\u002Ffunction-sequences\u002Fpicard-ode","Picard's Existence and Uniqueness Theorem","The Banach fixed-point theorem says a contraction of a complete metric space has exactly one fixed point, found by iterating from any start. Applied to the space of continuous functions with the uniform norm, it proves Picard's theorem: a first-order differential equation with a Lipschitz right-hand side has a unique local solution. Picard iteration constructs that solution explicitly, and worked examples show the Lipschitz condition is not optional.\n",{"path":4192,"title":4193,"module":4194,"summary":4195},"\u002Freal-analysis\u002Fseveral-variables\u002Fdifferentiability-rn","The Derivative of a Map ℝⁿ → ℝᵐ","Functions of Several Variables (Introduction)","The derivative of a map between Euclidean spaces is the linear transformation of vanishing relative error, unique when it exists and represented in coordinates by the Jacobian matrix of partial derivatives. Differentiability forces continuity through a local Lipschitz bound. Existence of the partial derivatives alone does not suffice; continuity of the partials does.\n",{"path":4197,"title":4198,"module":4194,"summary":4199},"\u002Freal-analysis\u002Fseveral-variables\u002Fgradient-chain-rule","Directional Derivatives, the Gradient, and the Chain Rule","The directional derivative measures the rate of change of a scalar field along a chosen heading and equals the derivative applied to that direction. The gradient collects these into a vector that points along steepest ascent and sits orthogonal to level sets. The chain rule composes derivatives by multiplying Jacobians, and a mean value theorem holds for scalar fields but fails for vector-valued maps.\n",{"path":4201,"title":4202,"module":4194,"summary":4203},"\u002Freal-analysis\u002Fseveral-variables\u002Fhigher-derivatives-taylor-extrema","Higher Derivatives, Taylor's Theorem, and Extrema","Iterating the derivative gives a symmetric second derivative, the Hessian, whose mixed partials agree when they are continuous. Taylor's theorem expands a smooth map to any order with a Lagrange-type remainder, and at a critical point the definiteness of the Hessian decides between a local minimum, a local maximum, and a saddle.\n",{"path":4205,"title":4206,"module":4194,"summary":4207},"\u002Freal-analysis\u002Fseveral-variables\u002Finverse-implicit-theorems","The Inverse and Implicit Function Theorems","A nonlinear map with a nonsingular Jacobian is locally invertible, with the inverse's derivative given by the inverse matrix. The contraction mapping principle supplies the local inverse; the implicit function theorem then solves a system for some variables in terms of the rest whenever the relevant Jacobian block is invertible. Worked coordinate changes show both theorems in use.\n",{"path":4209,"title":4210,"module":4194,"summary":4211},"\u002Freal-analysis\u002Fseveral-variables\u002Fmultiple-integrals","Multiple Integrals","The Riemann integral of a bounded function over a closed rectangle in Euclidean space is built from Darboux upper and lower sums on a grid of subrectangles, with the same squeeze criterion that governs the one-variable integral. Continuous integrands are integrable, and a set of content zero can be ignored. Fubini's theorem evaluates a multiple integral as an iterated one in either order, and the indicator trick extends the theory to regions bounded by curves.\n",{"path":4213,"title":4214,"module":6,"summary":6},"\u002Freal-analysis","Real Analysis",{"path":4216,"title":4217,"module":1231,"summary":4218},"\u002Fabstract-algebra\u002Ffoundations\u002Fsets-functions-relations","Sets, Functions, and Equivalence Relations","Algebra is built on three prior notions: the set, the map between sets, and the equivalence relation that reorganizes a set into disjoint classes. Sets, maps (injective, surjective, bijective), fibers and preimages, and the correspondence between equivalence relations and partitions — the one structural fact reused in every later quotient construction.\n",{"path":4220,"title":4221,"module":1231,"summary":4222},"\u002Fabstract-algebra\u002Ffoundations\u002Fintegers-and-modular-arithmetic","The Integers and Modular Arithmetic","The integers carry the template every ring later imitates: well-ordering drives induction, induction drives the division algorithm, and division drives the Euclidean algorithm, gcd, Bézout's identity, and unique factorization into primes. Quotienting by congruence mod n builds the first finite arithmetic, Z\u002FnZ, whose invertible elements form the group of units.\n",{"path":4224,"title":4225,"module":4226,"summary":4227},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fgroup-axioms-and-first-examples","Group Axioms and First Examples","Groups and Symmetry","A group is a set with one associative operation that has an identity and inverses. We state the axioms, prove that the identity, inverses, and cancellation behave as expected, define the order of a group and of an element, and catalogue the running examples: the integers, the additive group of residues mod n, and the multiplicative group of units mod n.\n",{"path":4229,"title":4230,"module":4226,"summary":4231},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fdihedral-and-symmetric-groups","Dihedral and Symmetric Groups","The dihedral group D_{2n} is the symmetries of a regular n-gon, generated by a rotation r and a reflection s subject to three relations. The symmetric group S_n is all permutations of n objects, written in cycle notation. Orders, generators and relations, cycle decomposition, the order of a permutation from its cycle type, and the parity that splits S_n in half.\n",{"path":4233,"title":4234,"module":4226,"summary":4235},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fmatrix-and-quaternion-groups","Matrix and Quaternion Groups","Invertible matrices over a field form the general linear group GL_n(F), with the determinant-one matrices as the subgroup SL_n(F). Over a finite field the order of GL_n(F) has a clean product formula. The quaternion group Q_8 is a second small nonabelian group, distinct from the dihedral group of the same order; its multiplication and subgroup structure sharpen the contrast between the two.\n",{"path":4237,"title":4238,"module":4226,"summary":4239},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fhomomorphisms-and-group-actions","Homomorphisms, Isomorphisms, and Actions","A homomorphism is a map between groups that respects the operation; an isomorphism is a bijective one, making two groups the same up to relabeling. The kernel and image measure how far a homomorphism is from injective and surjective. A group action realizes a group as permutations of a set, and actions correspond exactly to homomorphisms into a symmetric group, with orbits and stabilizers as the first tools for counting.\n",{"path":4241,"title":4242,"module":4243,"summary":4244},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fsubgroups-and-substructures","Subgroups and Their Substructures","Subgroups and Quotients","A subgroup is a subset that is a group under the inherited operation. One test decides it: nonempty and closed under the map $(x,y) \\mapsto xy^{-1}$. From an arbitrary subset $A$ we build the centralizer, normalizer, and center, and from an action the stabilizer and kernel, all of them subgroups nested in a fixed chain inside $G$.\n",{"path":4246,"title":4247,"module":4243,"summary":4248},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcyclic-groups","Cyclic Groups","A cyclic group is generated by one element. Two facts organize the whole theory: the order of an element equals the order of the subgroup it generates, and cyclic groups of equal order are isomorphic, so $\\mathbb{Z}$ and $\\mathbb{Z}\u002Fn\\mathbb{Z}$ are the only ones. From there the generators ($\\varphi(n)$ of them), the subgroups (one per divisor of $n$), and a fast exponentiation algorithm all follow.\n",{"path":4250,"title":4251,"module":4243,"summary":4252},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fgeneration-and-subgroup-lattices","Generation and the Lattice of Subgroups","The subgroup generated by a subset $A$ is the smallest subgroup containing it, described top-down as an intersection and bottom-up as the set of words in $A$ and its inverses. Collecting all subgroups and ordering them by containment produces the subgroup lattice, whose Hasse diagram shows the joins, meets, and containment relations among all subgroups.\n",{"path":4254,"title":4255,"module":4243,"summary":4256},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcosets-lagrange-and-normal-subgroups","Cosets, Lagrange, and Normal Subgroups","The left cosets of a subgroup partition a group into equal-sized blocks, so the order of a subgroup divides the order of the group: Lagrange's theorem. When the blocks can be multiplied consistently — exactly when the subgroup is normal — they form the quotient group $G\u002FN$. Fermat's and Euler's theorems fall out as index computations.\n",{"path":4258,"title":4259,"module":4243,"summary":4260},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fisomorphism-theorems","The Isomorphism Theorems","Four theorems relate homomorphisms, quotients, and subgroup lattices. The first identifies the image of a homomorphism with the quotient by its kernel; the second and third compute quotients built from two subgroups and quotients of quotients; the fourth matches the subgroups of $G\u002FN$ with the subgroups of $G$ lying above $N$. Together they make quotient groups computable.\n",{"path":4262,"title":4263,"module":4243,"summary":4264},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcomposition-series-and-the-alternating-group","Composition Series and the Alternating Group","A composition series breaks a finite group into simple quotient factors, and Jordan-Hölder says those factors are unique up to order. This turns classification into two problems: list the simple groups, and describe how to reassemble them. The sign homomorphism splits $S_n$ into even and odd permutations, defining the alternating group $A_n$, simple for $n \\ge 5$.\n",{"path":4266,"title":4267,"module":4268,"summary":4269},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Factions-and-cayleys-theorem","Actions, Orbits, and Cayley's Theorem","Group Actions and Sylow Theory","A group action turns abstract elements into permutations of a set. The action splits the set into orbits, and the orbit-stabilizer theorem ties each orbit's size to the index of a stabilizer. Applied to a group acting on itself by left multiplication, this gives Cayley's theorem: every group is a group of permutations.\n",{"path":4271,"title":4272,"module":4268,"summary":4273},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fconjugation-and-the-class-equation","Conjugation and the Class Equation","A group acts on itself by conjugation, and the orbits are the conjugacy classes. Orbit-stabilizer turns the resulting partition into the class equation, which forces every group of prime-power order to have a nontrivial center. Conjugacy in the symmetric group is cycle type, and Burnside's lemma counts orbits by averaging fixed points.\n",{"path":4275,"title":4276,"module":4268,"summary":4277},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fsylow-theorems","The Sylow Theorems","Lagrange's theorem forbids subgroups whose order fails to divide the group order; Sylow's theorems supply a partial converse for prime powers. A Sylow p-subgroup always exists, all of them are conjugate, and their count satisfies two congruence-and-divisibility constraints tight enough to prove many groups non-simple from their order alone.\n",{"path":4279,"title":4280,"module":4268,"summary":4281},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fautomorphisms-and-simple-groups","Automorphisms and Simplicity of Aₙ","Conjugation makes a group act on itself and on its normal subgroups by automorphisms, giving the inner automorphism group G\u002FZ(G) and the embedding of N(H)\u002FC(H) into Aut(H). Characteristic subgroups are those every automorphism fixes, and the automorphism group of a cyclic group is its unit group. The lesson closes by proving the alternating group Aₙ is simple for n ≥ 5.\n",{"path":4283,"title":4284,"module":4285,"summary":4286},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fdirect-products-and-finite-abelian-groups","Direct Products and Finite Abelian Groups","Products and Group Structure","The direct product assembles a larger group from componentwise copies of smaller ones, and a recognition theorem reverses the process when two normal subgroups meet trivially and span the group. The Fundamental Theorem of Finitely Generated Abelian Groups then classifies every such group by two equivalent invariants, invariant factors and elementary divisors.\n",{"path":4288,"title":4289,"module":4285,"summary":4290},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fsemidirect-products","Semidirect Products","The semidirect product relaxes the direct product by requiring only one factor to be normal, with the other acting on it through a homomorphism into its automorphism group. This single twisting map lets abelian pieces assemble into non-abelian groups, realizes the dihedral groups as $\\mathbb{Z}_n \\rtimes \\mathbb{Z}_2$, and, with a recognition theorem, classifies groups of several small orders.\n",{"path":4292,"title":4293,"module":4285,"summary":4294},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fnilpotent-and-solvable-groups","p-Groups, Nilpotent, and Solvable Groups","Finite p-groups have nontrivial center, and iterating the center upward builds the nilpotent groups, which decompose as the direct product of their Sylow subgroups. Iterating the commutator downward builds the solvable groups, whose factors are abelian. The chain cyclic, abelian, nilpotent, solvable orders these classes, and A_5 breaks the last link.\n",{"path":4296,"title":4297,"module":4285,"summary":4298},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fclassifying-small-groups","Classifying Groups of Small Order","With Sylow's theorem to force normal subgroups, direct and semidirect products to assemble them, and presentations to name the result, every group up to order fifteen can be listed explicitly. Free groups make presentations precise: generators with no relations, from which any group is a quotient by the normal closure of its relations.\n",{"path":4300,"title":4301,"module":4302,"summary":4303},"\u002Fabstract-algebra\u002Fring-theory\u002Frings-definitions-and-examples","Rings: Definitions and Examples","Ring Theory","A ring carries two operations: an abelian group under addition and an associative multiplication linked by the distributive laws. The named special cases — commutative rings, integral domains, division rings, and fields — differ only in how their multiplication behaves. Standard examples include quadratic integer rings, polynomial rings, matrix rings, and group rings.\n",{"path":4305,"title":4306,"module":4302,"summary":4307},"\u002Fabstract-algebra\u002Fring-theory\u002Fideals-quotients-and-homomorphisms","Ideals, Quotient Rings, and Homomorphisms","Ring homomorphisms have kernels that absorb multiplication; such subsets are ideals, and every ideal is the kernel of the projection onto a quotient ring. The quotient construction yields the ring isomorphism theorems and classifies ideals by their quotients: R\u002FI is a field exactly when I is maximal, an integral domain exactly when I is prime.\n",{"path":4309,"title":4310,"module":4302,"summary":4311},"\u002Fabstract-algebra\u002Fring-theory\u002Ffractions-and-the-chinese-remainder-theorem","Fields of Fractions and the CRT","Rings of fractions invert a multiplicatively closed set, enlarging an integral domain into its field of fractions the way Z becomes Q. The Chinese Remainder Theorem splits a quotient by comaximal ideals into a direct product, generalizing Z\u002FmnZ ≅ Z\u002FmZ × Z\u002FnZ and explaining why the Euler function is multiplicative.\n",{"path":4313,"title":4314,"module":4315,"summary":4316},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Feuclidean-domains-pids-ufds","Euclidean Domains, PIDs, and UFDs","Factorization and Polynomial Rings","Three classes of integral domain, ordered by how much of elementary arithmetic survives: Euclidean domains carry a division algorithm, principal ideal domains make every ideal a single multiple, and unique factorization domains factor every element into irreducibles in one way. We prove the chain ED implies PID implies UFD, the classes are separated by explicit counterexamples, and irreducible and prime coincide exactly in a UFD.\n",{"path":4318,"title":4319,"module":4315,"summary":4320},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fpolynomial-rings-over-fields","Polynomial Rings over Fields","When the coefficients form a field, polynomial long division works exactly as it does over the rationals, and it works with a unique quotient and remainder. That single fact makes F[x] a Euclidean domain, hence a PID and a UFD: every ideal is the multiples of one polynomial, roots correspond to linear factors, and F[x]\u002F(f) is a field precisely when f is irreducible.\n",{"path":4322,"title":4323,"module":4315,"summary":4324},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fgauss-lemma-and-unique-factorization","Gauss's Lemma and Unique Factorization","A UFD is not a field, so its polynomial ring is not a PID — yet unique factorization survives the passage from R to R[x]. Gauss's lemma supplies the passage: a polynomial that factors over the fraction field already factors over R, once content is factored out. This gives the theorem that R[x] is a UFD whenever R is, so Z[x] and Q[x,y] factor uniquely even though neither is a PID.\n",{"path":4326,"title":4327,"module":4315,"summary":4328},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Firreducibility-criteria-and-groebner","Irreducibility Criteria and Gröbner Bases","Deciding whether a given polynomial is irreducible, and computing in multivariate polynomial rings. In one variable: the rational root test, reduction modulo a prime, and Eisenstein's criterion. In several variables, where division fails, a monomial order gives leading terms, a Gröbner basis restores a well-defined remainder, and Buchberger's algorithm computes it.\n",{"path":4330,"title":4331,"module":4332,"summary":4333},"\u002Fabstract-algebra\u002Fmodule-theory\u002Fintroduction-to-modules","Introduction to Modules","Module Theory","A module is an abelian group on which a ring acts, generalizing both vector spaces (when the ring is a field) and abelian groups (when the ring is the integers). Submodules, homomorphisms, quotients, and the isomorphism theorems carry over from groups, and an F[x]-module is the same datum as a vector space with a chosen linear operator — the correspondence behind the canonical forms.\n",{"path":4335,"title":4336,"module":4332,"summary":4337},"\u002Fabstract-algebra\u002Fmodule-theory\u002Ffree-modules-and-direct-sums","Generation, Direct Sums, and Free Modules","A generating set spans a module by R-linear combinations; a direct sum decomposes it into independent pieces; a free module has a basis and the universal property that a homomorphism is determined by arbitrary values on that basis. Rank is well defined over a commutative ring, torsion blocks a basis, and every module is a quotient of a free one — a presentation by generators and relations.\n",{"path":4339,"title":4340,"module":4332,"summary":4341},"\u002Fabstract-algebra\u002Fmodule-theory\u002Ftensor-products-and-exact-sequences","Tensor Products and Exact Sequences","The tensor product builds a module in which elements of two modules can be multiplied, characterized by a universal property turning bilinear maps into linear ones; extension of scalars is its guiding case. Exact sequences track how a module is assembled from a submodule and a quotient, when that assembly splits, and which modules — projective, injective, flat — make the Hom and tensor functors preserve exactness.\n",{"path":4343,"title":4344,"module":4332,"summary":4345},"\u002Fabstract-algebra\u002Fmodule-theory\u002Fvector-spaces-and-linear-maps","Vector Spaces and Linear Maps","A vector space is a module over a field, and the field hypothesis removes every pathology a general module can have: every vector space is free, so it has a basis, a well-defined dimension, and a coordinate isomorphism with F^n. Linear maps become matrices, change of basis becomes similarity, every space pairs with a dual of the same dimension, and the determinant is the unique alternating multilinear normalized form.\n",{"path":4347,"title":4348,"module":4349,"summary":4350},"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fstructure-theorem-over-pids","The Structure Theorem for Modules over a PID","Modules over PIDs and Canonical Forms","Every finitely generated module over a principal ideal domain splits as a free part plus a direct sum of cyclic torsion pieces, in two canonical ways: invariant factors, tied together by a divisibility chain, and elementary divisors, one prime power at a time. Existence follows from the stacked-basis theorem, both lists are unique, and the case $R = \\mathbb{Z}$ is the classification of finitely generated abelian groups.\n",{"path":4352,"title":4353,"module":4349,"summary":4354},"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Frational-canonical-form","Rational Canonical Form","A linear operator turns its vector space into a module over the polynomial ring $F[x]$, with $x$ acting as the operator. The structure theorem's invariant factors then become polynomials, each cyclic summand becomes a companion matrix, and the block-diagonal assembly is the rational canonical form. It is unique, it is computed inside the base field, and two matrices are similar exactly when their rational canonical forms agree.\n",{"path":4356,"title":4357,"module":4349,"summary":4358},"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fjordan-canonical-form","Jordan Canonical Form","When the base field contains all the eigenvalues, the elementary divisors of an operator are powers of linear polynomials, and each cyclic summand becomes a Jordan block: an eigenvalue on the diagonal with ones just above it. Stacking the blocks gives the Jordan canonical form, unique up to reordering, as close to diagonal as the operator allows. Diagonalizability reads off the minimal polynomial, and the block sizes are counted by ranks of powers of the operator minus the eigenvalue.\n",{"path":4360,"title":4361,"module":4362,"summary":4363},"\u002Fabstract-algebra\u002Ffield-theory\u002Ffield-extensions-and-algebraic-elements","Field Extensions and Algebraic Elements","Field Theory","A field extension makes a larger field K into a vector space over a smaller field F, and its degree [K:F] is that dimension. Adjoining a root of an irreducible polynomial builds a simple extension F(α) isomorphic to F[x]\u002F(m), whose degree is the degree of the minimal polynomial. The tower law makes these degrees multiply, which turns algebra over fields into bookkeeping with integers.\n",{"path":4365,"title":4366,"module":4362,"summary":4367},"\u002Fabstract-algebra\u002Ffield-theory\u002Fstraightedge-and-compass-constructions","Straightedge-and-Compass Constructions","The lengths a straightedge and compass can build from a unit form a field closed under square roots, and every constructible number lies in a tower of quadratic extensions. So its degree over the rationals is a power of two. That single obstruction settles three problems the Greeks left open: doubling the cube, trisecting a general angle, and squaring the circle are all impossible.\n",{"path":4369,"title":4370,"module":4362,"summary":4371},"\u002Fabstract-algebra\u002Ffield-theory\u002Fsplitting-fields-and-algebraic-closure","Splitting Fields and Algebraic Closure","The splitting field of a polynomial is the smallest extension in which it factors into linear pieces, obtained by adjoining all its roots. Every polynomial has one, its degree is at most n factorial, and any two splitting fields are isomorphic. Pushing this to all polynomials at once gives the algebraic closure, a field in which every polynomial splits and which is unique up to isomorphism.\n",{"path":4373,"title":4374,"module":4362,"summary":4375},"\u002Fabstract-algebra\u002Ffield-theory\u002Fseparable-and-cyclotomic-extensions","Separable Extensions and Cyclotomic Fields","A polynomial is separable when its roots are distinct, detected by whether it shares a factor with its formal derivative. Over perfect fields — characteristic zero and finite fields — every irreducible is separable, and the existence and uniqueness of the finite fields follow. Cyclotomic polynomials package the roots of unity by order, are irreducible over the rationals, and give the cyclotomic field its degree phi(n).\n",{"path":4377,"title":4378,"module":4379,"summary":4380},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fthe-galois-correspondence","The Galois Correspondence","Galois Theory","Galois theory attaches to a field extension its group of symmetries and shows that, for the right extensions, the subgroups of that group are in exact order-reversing correspondence with the intermediate fields. The automorphism group, Artin's theorem, the characterization of Galois extensions, and the Fundamental Theorem together turn questions about fields into questions about finite groups.\n",{"path":4382,"title":4383,"module":4379,"summary":4384},"\u002Fabstract-algebra\u002Fgalois-theory\u002Ffinite-fields","Finite Fields","Every finite field has prime-power order, is the splitting field of $x^{p^n} - x$, and is unique up to isomorphism. Its extension over the prime field is Galois with cyclic group generated by the Frobenius map $x \\mapsto x^p$, so the Galois correspondence reduces the subfield lattice to the divisor lattice of $n$. Möbius inversion counts the irreducible polynomials of each degree, and cyclic error-correcting codes are one application.\n",{"path":4386,"title":4387,"module":4379,"summary":4388},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fcyclotomic-and-abelian-extensions","Cyclotomic and Abelian Extensions","The Galois group of the $n$th cyclotomic field over $\\mathbb{Q}$ is the unit group $(\\mathbb{Z}\u002Fn\\mathbb{Z})^\\times$, which makes cyclotomic fields the worked catalogue of abelian extensions of $\\mathbb{Q}$. The isomorphism identifies subfields with subgroups, realizes every finite abelian group as a Galois group over $\\mathbb{Q}$, and leads to Kronecker–Weber. Composites of Galois extensions and the primitive element theorem supply the machinery.\n",{"path":4390,"title":4391,"module":4379,"summary":4392},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fgalois-groups-of-polynomials","Galois Groups of Polynomials","Ordering the roots of a separable polynomial embeds its Galois group in the symmetric group $S_n$, and the group is transitive exactly when the polynomial is irreducible. The discriminant decides membership in $A_n$; for cubics and quartics the resolvent cubic pins the group down; and reduction modulo a prime produces elements of prescribed cycle type, the standard tool for computing Galois groups over $\\mathbb{Q}$.\n",{"path":4394,"title":4395,"module":4379,"summary":4396},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fsolvability-by-radicals-and-the-quintic","Solvability by Radicals and the Quintic","A polynomial is solvable by radicals exactly when its Galois group is solvable. Cyclic extensions are radical extensions once roots of unity are present, which turns a radical tower into a solvable subnormal series. Since $S_n$ is solvable only for $n \\le 4$, the general quintic has no radical formula, and an explicit quintic with Galois group $S_5$ has roots provably not expressible in radicals.\n",{"path":4398,"title":4399,"module":4400,"summary":4401},"\u002Fabstract-algebra\u002Fcapstone\u002Fcommutative-algebra-and-algebraic-geometry","A Glimpse of Commutative Algebra and Algebraic Geometry","Capstone: Where Algebra Goes Next","Commutative algebra reads geometry off the ring of polynomial functions. The dictionary runs through Noetherian rings and the ascending chain condition, Hilbert's Basis Theorem, affine algebraic sets and the two maps connecting ideals to zero sets, radicals, the Zariski topology, and Hilbert's Nullstellensatz, which over an algebraically closed field makes radical ideals and algebraic sets the same object.\n",{"path":4403,"title":4404,"module":4400,"summary":4405},"\u002Fabstract-algebra\u002Fcapstone\u002Frepresentation-and-character-theory","A Glimpse of Representation and Character Theory","Representation theory studies a group by the ways it can act linearly on a vector space. Representations are equivalent to modules over the group ring; Maschke's theorem gives complete reducibility, the Wedderburn consequences bound the irreducible degrees, and character theory reduces a representation to a trace invariant governed by the orthogonality relations and displayed in the character table of a small group.\n",{"path":4407,"title":4408,"module":6,"summary":6},"\u002Fabstract-algebra","Abstract Algebra",{"path":4410,"title":4411,"module":4412,"summary":4413},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fatomic-spectra-rutherford","Atomic Spectra and Rutherford's Nucleus","Early Atomic Models and the Old Quantum Theory","Atoms emit light only at sharp, reproducible wavelengths, and by 1890 those wavelengths were captured by the Rydberg-Ritz formula. Neither empirical regularity had a mechanical explanation. Rutherford's alpha-scattering experiment supplied the missing structure: the atom's positive charge and nearly all its mass sit in a tiny central nucleus, with the electrons far outside.\n",{"path":4415,"title":4416,"module":4412,"summary":4417},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-model-hydrogen","The Bohr Model of Hydrogen","Bohr grafted three quantum postulates onto Rutherford's nuclear atom: certain orbits do not radiate, radiation accompanies a jump between them, and quantization must match classical physics for large orbits. Quantizing the angular momentum fixes the orbit radii and energies, reproduces the Rydberg-Ritz formula, and predicts the Rydberg constant from fundamental constants alone.\n",{"path":4419,"title":4420,"module":4412,"summary":4421},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fx-ray-spectra-franck-hertz","X-Ray Spectra and the Franck-Hertz Experiment","Two 1913-14 experiments confirmed the Bohr-Rutherford atom independently of optical spectra. Moseley found that the square root of a characteristic X-ray frequency is linear in atomic number, fixing Z as nuclear charge and ordering the periodic table. Franck and Hertz measured discrete atomic energy levels directly by scattering electrons through a mercury vapor.\n",{"path":4423,"title":4424,"module":4412,"summary":4425},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-sommerfeld-old-quantum-theory","The Bohr-Sommerfeld Old Quantum Theory","Bohr fixed the hydrogen levels with a single quantum number by quantizing angular momentum. Sommerfeld replaced that ad hoc rule with a general prescription: quantize the action of each separable coordinate. The rule produces elliptical orbits, a second (azimuthal) quantum number, space quantization, and — once the relativistic mass variation is included — a fine-structure splitting that matches experiment to order alpha squared.\n",{"path":4427,"title":4428,"module":4412,"summary":4429},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fold-quantum-theory-limits-wkb","Limits of the Old Quantum Theory and the WKB Bridge","The old quantum theory works only where the classical motion is separable into independent periodic coordinates. It fails for helium, forbids the correct zero angular momentum of the hydrogen ground state, and misses the half-integer in the oscillator and in molecular spectra. The WKB quantization condition, derived from the Schrodinger equation, is the modern descendant of the Sommerfeld rule and repairs the half-integer through the Maslov correction.\n",{"path":4431,"title":4432,"module":4433,"summary":4434},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fschrodinger-3d-hydrogen","The Schrödinger Equation in Three Dimensions and Hydrogen","The Quantum Hydrogen Atom","Extending the Schrödinger equation to three dimensions and separating it in spherical coordinates produces three ordinary differential equations, one per coordinate. Their boundary conditions generate the quantum numbers n, ℓ, and mℓ, quantize the angular momentum to √(ℓ(ℓ+1))ℏ with projections mℏ, and fix the bound-state energies of hydrogen at −Z²(13.6 eV)\u002Fn².\n",{"path":4436,"title":4437,"module":4433,"summary":4438},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fhydrogen-wave-functions","Hydrogen Wave Functions and Orbitals","The hydrogen wave functions factor into a radial part Rₙℓ(r) and an angular spherical harmonic Yℓm(θ,φ). Squaring gives the probability cloud; the radial distribution P(r) = r²|ψ|² peaks at the Bohr radius for the ground state and at the Bohr orbits for excited states. The angular part fixes the s, p, and d orbital shapes that govern chemical bonding.\n",{"path":4440,"title":4441,"module":4433,"summary":4442},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fradial-equation-in-full","Solving the Radial Equation in Full","The hydrogen radial equation is solved from the differential equation up. The substitution u = rR turns it into a one-dimensional problem with a centrifugal barrier; matching the asymptotic behaviour at the origin and at infinity peels off the factors r^(ℓ+1) and e^(−r\u002Fna₀); a Frobenius series for the remainder must terminate, and that termination condition yields the quantization n ≥ ℓ+1 with E = −Z²Ry\u002Fn². The surviving polynomials are the associated Laguerre functions, whose degree n−ℓ−1 counts the radial nodes.\n",{"path":4444,"title":4445,"module":4433,"summary":4446},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fsymmetry-degeneracy-runge-lenz","Accidental Degeneracy and the Runge-Lenz Symmetry","Hydrogen energies depend only on n, so states of different ℓ at the same n are degenerate. This is not a coincidence but the mark of a hidden symmetry: the quantum Runge-Lenz vector is conserved for the 1\u002Fr potential alone, and together with angular momentum it generates the group SO(4). The Casimir invariant of that group reproduces E = −Z²Ry\u002Fn² and its representations count the n² states. Any departure from 1\u002Fr breaks the symmetry and lifts the ℓ-degeneracy.\n",{"path":4448,"title":4449,"module":4433,"summary":4450},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fexpectation-values-virial","Expectation Values, the Virial Theorem, and Scaling","The radial matrix elements ⟨r^k⟩ of hydrogenic states are the raw material of every later correction. This lesson derives ⟨1\u002Fr⟩ from the virial theorem, builds the full family ⟨r⟩, ⟨r²⟩, ⟨1\u002Fr²⟩, ⟨1\u002Fr³⟩ from Kramers' recursion and the Feynman-Hellmann theorem, and reads off their scaling with n, ℓ, and Z. The virial balance ⟨T⟩ = −½⟨V⟩ = −E fixes the energy budget of every bound state.\n",{"path":4452,"title":4453,"module":4433,"summary":4454},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fquantum-defects-alkali-spectra","Quantum Defects and Alkali Spectra","An alkali atom is one valence electron outside a closed-shell core, and to a good approximation it is hydrogen with a modified quantum number. Core penetration makes low-ℓ states more bound than the Coulomb formula predicts, and the shortfall is captured by a single number per ℓ, the quantum defect δℓ. The spectrum then follows the Rydberg formula with n replaced by the effective n − δℓ, and the sodium D-line doublet is the worked case.\n",{"path":4456,"title":4457,"module":4433,"summary":4458},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Frydberg-atoms","Rydberg Atoms","A Rydberg atom is an atom excited to a very high principal quantum number, and every hydrogenic property becomes exaggerated by a power of n. Size grows as n², binding falls as n⁻², radiative lifetime lengthens as n³, and the static polarizability explodes as n⁷. The levels crowd toward the ionization limit, and the enormous dipole interaction between two Rydberg atoms produces the blockade that underlies neutral-atom quantum computing.\n",{"path":4460,"title":4461,"module":4462,"summary":4463},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Frelativistic-kinetic-correction","The Relativistic Kinetic-Energy Correction","Fine Structure and the Dirac Atom","The Bohr energies treat the electron as slowly moving, but its speed is of order αc, so the kinetic energy needs a relativistic correction. Expanding √(p²c²+m²c⁴) to order (v\u002Fc)² produces the perturbation −p⁴\u002F8m³c², whose first-order shift on a hydrogenic state is evaluated with the trick p²=2m(E−V). The result depends on n and ℓ, is smaller than the gross structure by α²≈5×10⁻⁵, and is one of the three pieces that combine into the fine-structure formula.\n",{"path":4465,"title":4466,"module":4462,"summary":4467},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fspin-orbit-thomas-precession","Spin-Orbit Coupling and Thomas Precession","In the electron's rest frame the nucleus orbits it, and the resulting current produces a magnetic field that couples to the electron's spin moment. The interaction is ξ(r) L·S, with ξ built from the Coulomb potential and the radial expectation ⟨1\u002Fr³⟩. A relativistic subtlety, Thomas precession, halves the naive coefficient because the electron's rest frame is accelerating. The result splits each ℓ≥1 level into a j=ℓ±½ doublet and makes (n, ℓ, j, mⱼ) the good quantum numbers.\n",{"path":4469,"title":4470,"module":4462,"summary":4471},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdarwin-term-fine-structure-formula","The Darwin Term and the Fine-Structure Formula","The third fine-structure correction, the Darwin term, is a contact interaction proportional to ∇²V that acts only on s-states, physically a smearing of the electron over a Compton wavelength. Adding the relativistic, spin-orbit, and Darwin shifts, the ℓ-dependence cancels and the total collapses to a formula in n and j alone. The n=2 shell splits into 2S₁\u002F₂, 2P₁\u002F₂, 2P₃\u002F₂, with the two j=½ levels exactly degenerate, a coincidence the Dirac theory explains.\n",{"path":4473,"title":4474,"module":4462,"summary":4475},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdirac-equation-hydrogen","The Dirac Equation for Hydrogen","The fine-structure formula was assembled from three perturbations; the Dirac equation produces it in one stroke and exactly. A first-order relativistic wave equation forces a four-component spinor, from which spin s=½, the g-factor of 2, the spin-orbit term, and antiparticles all emerge automatically. Its exact Coulomb spectrum depends only on n and j, and expanding in Zα reproduces the perturbative result, including the 2S₁\u002F₂–2P₁\u002F₂ degeneracy that sets up the Lamb shift.\n",{"path":4477,"title":4478,"module":4479,"summary":4480},"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Flamb-shift-qed","The Lamb Shift and QED Radiative Corrections","QED Corrections and Hyperfine Structure","The Dirac equation makes the 2S₁\u002F₂ and 2P₁\u002F₂ levels of hydrogen exactly degenerate. Lamb and Retherford measured a splitting of about 1058 MHz that the Dirac theory cannot produce. The gap comes from the electron's coupling to the quantized electromagnetic field: self-energy, vacuum polarization, and the anomalous magnetic moment. Welton's vacuum-fluctuation estimate reproduces the size and shows why the effect lands almost entirely on s-states, and the same radiative corrections make hydrogen the most stringent test of QED.\n",{"path":4482,"title":4483,"module":4479,"summary":4484},"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fhyperfine-structure-21cm","Hyperfine Structure and the 21 cm Line","The proton carries a magnetic moment, and it interacts with the magnetic field the electron produces at the nucleus. For s-states that interaction is the Fermi contact term, proportional to the electron density at the origin and to the dot product of the nuclear and electronic spins. Coupling I and J into F = I + J splits each level by a Landé interval rule; in hydrogen's ground state it produces the F = 0\u002FF = 1 doublet whose 1420 MHz, 21 cm transition maps neutral hydrogen across the galaxy.\n",{"path":4486,"title":4487,"module":4479,"summary":4488},"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fnuclear-effects-isotope-shift","Nuclear Size, Moments, and Isotope Shifts","A real nucleus has a finite size, a mass that changes between isotopes, and, when its spin is at least one, an electric quadrupole moment. Each leaves a fingerprint in the atomic spectrum: the volume shift from s-electrons sampling the charge distribution, the mass and field isotope shifts that separate on a King plot, the quadrupole interaction that breaks the Landé interval rule, and the hyperfine anomaly from the magnetization distribution. Atomic spectroscopy reads nuclear properties out of these shifts.\n",{"path":4490,"title":4491,"module":4492,"summary":4493},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fperiodic-table-atomic-spectra","The Periodic Table and Atomic Spectra","Many-Electron Atoms","Identical electrons demand antisymmetric wave functions, which is the Pauli exclusion principle: no two electrons share all four quantum numbers. Filling shells in order of increasing energy — shifted by penetration and shielding — builds the periodic table and its recurring ionization pattern. Selection rules govern optical spectra, and an external field splits lines by the Zeeman effect.\n",{"path":4495,"title":4496,"module":4492,"summary":4497},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fcentral-field-self-consistent","The Central-Field Approximation and the Self-Consistent Field","The N-electron Hamiltonian does not separate because every pair of electrons repels. The central-field approximation replaces that pairwise repulsion with an averaged spherical potential each electron feels, restoring hydrogen-like orbitals labelled by n and ℓ. The Thomas-Fermi statistical model fixes the shape of the screened charge from Fermi-gas thermodynamics; the Hartree self-consistent field determines it exactly by iterating orbitals against the potential they generate until the two agree.\n",{"path":4499,"title":4500,"module":4492,"summary":4501},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fidentical-particles-hartree-fock","Exchange, Slater Determinants, and Hartree-Fock","A product wave function ignores that electrons are identical fermions. Enforcing antisymmetry writes the state as a Slater determinant, which vanishes whenever two electrons share a spin-orbital — the exclusion principle made algebraic. The energy of a determinant carries a new term with no classical analogue, the exchange integral, nonzero only for parallel spins; it lowers the energy of aligned electrons and carves a Fermi hole around each one. Adding the exchange operator to the mean field gives the Hartree-Fock equations, and what they still miss defines the correlation energy.\n",{"path":4503,"title":4504,"module":4492,"summary":4505},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhelium-two-electron-atom","Helium: the Prototype Two-Electron Atom","Helium is the smallest atom the Schrödinger equation cannot solve exactly, and the smallest that shows every many-electron effect. Ignoring the electron repulsion overbinds the ground state by 30 eV; first-order perturbation theory and a one-parameter variational calculation with an effective charge close most of the gap. The excited configurations split into para (singlet) and ortho (triplet) states separated by the exchange integral, with the triplet lower — and the absence of a 1s² triplet is the Pauli principle in its plainest form.\n",{"path":4507,"title":4508,"module":4492,"summary":4509},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fls-jj-coupling-term-symbols","LS and jj Coupling; Term Symbols","A configuration is not a single energy level. The residual electrostatic repulsion and the spin-orbit interaction split it, and which one dominates fixes the coupling scheme. In light atoms the electrostatic term wins: orbital and spin angular momenta couple separately into L and S, then into J, giving Russell- Saunders term symbols. In heavy atoms spin-orbit wins and each electron's j forms first. The Pauli principle prunes the allowed terms of equivalent electrons, the Landé interval rule spaces the fine-structure multiplet, and the scheme crosses over from LS to jj down a column.\n",{"path":4511,"title":4512,"module":4492,"summary":4513},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhund-rules-ground-terms","Hund's Rules and Ground-State Terms","A configuration allows several terms; Hund's three rules pick the ground one. Maximize the spin S first, then the orbital L, then set J to |L−S| for a less-than-half shell and L+S for a more-than-half shell. The first two rules come from exchange lowering the energy of apart-kept electrons; the third comes from the sign of the spin-orbit coupling, which flips as a shell passes half-filling and turns the multiplet from normal to inverted. Worked ground terms for carbon, nitrogen, oxygen, and iron show the rules in action.\n",{"path":4515,"title":4516,"module":4517,"summary":4518},"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fzeeman-effect","The Zeeman Effect","Atoms in External Fields","A magnetic field couples to the atom through its magnetic moment, splitting each level into equally spaced sublevels labelled by the projection of the total angular momentum. When spin is present the spacing is not the classical one: it carries the Landé g-factor, a projection of the spin and orbital moments onto the total angular momentum. We derive the weak-field Hamiltonian from minimal coupling, evaluate the shift with the projection theorem, and read off the polarization of the emitted components.\n",{"path":4520,"title":4521,"module":4517,"summary":4522},"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fpaschen-back-intermediate","The Paschen-Back and Intermediate-Field Regimes","When the magnetic interaction grows past the fine-structure coupling, spin and orbital angular momentum decouple and precess independently about the field. The anomalous Zeeman pattern reverts to a simple triplet, the Paschen-Back effect. Between the two limits neither coupling dominates and the level positions follow from diagonalizing the combined spin-orbit and Zeeman Hamiltonian. We build the two-by-two problem for a single valence electron, solve it in closed form, and show both limits emerge from one expression.\n",{"path":4524,"title":4525,"module":4517,"summary":4526},"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fstark-effect-polarizability","The Stark Effect and Field Ionization","An electric field shifts atomic levels by coupling to the electron's position. Parity forbids a first-order shift for a non-degenerate state, so most atoms respond only at second order through their polarizability, a quadratic Stark shift. Hydrogen is the exception: its accidental degeneracy admits a permanent dipole and a linear shift, cleanest in parabolic coordinates. At large fields the Coulomb well develops a saddle, and Rydberg states field-ionize at a threshold that falls as the fourth power of the principal quantum number.\n",{"path":4528,"title":4529,"module":4530,"summary":4531},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Ftime-dependent-perturbation-golden-rule","Time-Dependent Perturbation Theory and the Golden Rule","Radiative Transitions and Spectral Lines","An atom in a weak oscillating field makes transitions between its stationary states. First-order time-dependent perturbation theory gives the transition amplitude as a Fourier component of the perturbation at the Bohr frequency, and the resulting probability is a sinc-squared resonance that sharpens as the field acts longer. For a two-level system the same coupling produces Rabi oscillations; for a transition into a continuum the long-time limit collapses the sinc-squared into a delta function and yields Fermi's golden rule, a constant transition rate set by the coupling strength and the density of final states.\n",{"path":4533,"title":4534,"module":4530,"summary":4535},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fdipole-approximation-einstein-coefficients","The Dipole Approximation and Einstein Coefficients","The coupling between an atom and light is the interaction of the electron with the electromagnetic field. Because an optical wavelength dwarfs the atom, the spatial variation of the field across the atom can be dropped, leaving the electric-dipole interaction and its matrix element. That matrix element defines the oscillator strength, which obeys the Thomas-Reiche-Kuhn sum rule. Einstein's three rate coefficients (absorption, stimulated emission, spontaneous emission) follow from detailed balance with thermal radiation, fixing the ratio of spontaneous to stimulated rates and its steep growth with frequency.\n",{"path":4537,"title":4538,"module":4530,"summary":4539},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fselection-rules-forbidden-transitions","Selection Rules and Forbidden Transitions","The dipole matrix element vanishes for most pairs of states, and the pattern of which survive is the set of selection rules. Parity forces the orbital angular momentum to change by one; the angular integral of three spherical harmonics restricts the magnetic quantum number to change by zero or one; the photon's spin restricts the total angular momentum. When the dipole element vanishes, higher multipoles (magnetic dipole and electric quadrupole) can still drive the transition at rates smaller by powers of the fine-structure constant, and states with no allowed decay become metastable.\n",{"path":4541,"title":4542,"module":4530,"summary":4543},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Flifetimes-and-line-shapes","Lifetimes, Line Widths, and Line Shapes","A spectral line is never infinitely sharp. The finite lifetime of the excited state gives every line a natural Lorentzian width set by the total decay rate, the Fourier transform of an exponentially damped emission. Thermal motion adds a Gaussian Doppler width that usually dominates in a gas; collisions add a further Lorentzian pressure width; the observed profile is the Voigt convolution of the Gaussian and Lorentzian parts. Strong driving fields broaden the line further through saturation. Each mechanism has a distinct dependence on temperature, density, and intensity that lets it be identified and, where possible, removed.\n",{"path":4545,"title":4546,"module":4547,"summary":4548},"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Flaser-principles","Population Inversion, Gain, and the Laser","Lasers and Spectroscopy","A laser is an optical amplifier placed inside a resonant cavity. Amplification requires that stimulated emission outrun absorption, which requires more atoms in the upper level than the lower one — a population inversion that the Einstein relations forbid in thermal equilibrium and that no two-level pump can produce. Three- and four-level schemes reach it by routing atoms through auxiliary states. The gain coefficient sets how strongly a weak beam grows, the cavity fixes the threshold and selects a comb of longitudinal modes, and gain saturation clamps the steady-state inversion at its threshold value.\n",{"path":4550,"title":4551,"module":4547,"summary":4552},"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fspectroscopy-techniques","Spectroscopic Techniques and Frequency Combs","A tunable laser turns spectroscopy from photographing a spectrum into interrogating a single transition, but at room temperature the Doppler width buries the natural linewidth under a thousandfold-broader Gaussian. Saturated absorption and two-photon spectroscopy defeat the first-order Doppler shift by selecting the zero-velocity class or cancelling the shift between counter-propagating photons, recovering natural-width features. Laser-induced fluorescence pushes sensitivity to single atoms, and the optical frequency comb converts an optical frequency into a countable radio-frequency beat, giving absolute frequency measurement across the visible spectrum.\n",{"path":4554,"title":4555,"module":4547,"summary":4556},"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fline-catalog-nist-asd","Reading Real Spectra with the NIST Database","Every quantity computed in this course — energy levels, transition frequencies, oscillator strengths, lifetimes — is tabulated for real atoms in the NIST Atomic Spectra Database. This lesson reads that data as physics: how levels are labelled by term symbols and energies in wavenumbers, how a transition list encodes wavelength, Einstein coefficient, and line strength, how a Grotrian diagram is reconstructed from the tables, and how a measured spectrum is matched to catalog lines. The residual between computed and tabulated positions is the running score of atomic theory.\n",{"path":4558,"title":4559,"module":4560,"summary":4561},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Flaser-cooling-doppler","Laser Cooling and Optical Molasses","Modern Atomic Physics","A near-resonant laser beam pushes an atom because every absorbed photon delivers one unit of momentum and the subsequent spontaneous emission averages to zero. Two counter-propagating red-detuned beams turn that push into friction: the Doppler shift brings a moving atom closer to resonance with the beam it moves against, so the net force opposes the velocity. Six beams give optical molasses in three dimensions. The random recoil of spontaneous emission heats against the friction, and the balance sets the Doppler cooling limit. Adding a magnetic-field gradient makes the force position-dependent as well, giving the magneto-optical trap.\n",{"path":4563,"title":4564,"module":4560,"summary":4565},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fsub-doppler-trapping","Sub-Doppler Cooling and Atom Traps","Optical molasses cools multilevel atoms below the Doppler limit. A polarization gradient plus optical pumping makes an atom repeatedly climb a light-shift hill and be pumped to the valley, losing kinetic energy each cycle — Sisyphus cooling. The floor is the recoil limit, one photon momentum of residual motion. Below it, cooling must avoid scattering photons: conservative magnetic and optical-dipole traps hold the atoms while forced evaporation removes the hot tail, driving the phase-space density up toward quantum degeneracy.\n",{"path":4567,"title":4568,"module":4560,"summary":4569},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fbose-einstein-condensation","Bose-Einstein Condensation of Atomic Gases","Below a critical temperature a gas of identical bosons places a macroscopic fraction of its atoms in the single lowest-energy state. The transition occurs when the thermal de Broglie wavelength grows to the interparticle spacing, so the phase- space density reaches order unity. The critical temperature follows from the Bose-Einstein distribution and the density of states, the condensate fraction grows as one minus (T\u002FTc) to the three-halves, and the condensate reveals itself in time-of-flight as a sharp bimodal peak in the momentum distribution. The 1995 rubidium and sodium experiments realized it in dilute trapped gases.\n",{"path":4571,"title":4572,"module":4560,"summary":4573},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Foptical-clocks-precision","Optical Atomic Clocks and Precision Measurement","An atomic clock counts the oscillations of a field locked to an atomic transition. The cesium microwave standard defines the second through the 9.19 GHz ground-state hyperfine transition, interrogated by Ramsey's separated-oscillatory-field method whose fringe width is set by the free-precession time. Optical clocks replace the microwave transition with an optical one five orders of magnitude higher in frequency, raising the quality factor and the fractional stability in proportion. Lattice and single-ion clocks reach fractional uncertainties near ten-to-the-minus- eighteen by trapping the atoms at a magic wavelength that cancels the light shift, and at that level they measure the gravitational redshift over centimetres of height.\n",{"path":4575,"title":4576,"module":6,"summary":6},"\u002Fatomic-physics","Atomic Physics",{"path":4578,"title":4579,"module":6,"summary":6},"\u002Fdatabases","Databases",{"path":4581,"title":4582,"module":1231,"summary":4583},"\u002Fcategory-theory\u002Ffoundations\u002Fwhat-is-a-category","Categories, Objects, and Arrows","A category is objects, arrows between them, a rule for composing arrows, and an identity arrow on every object, subject to associativity and the unit laws. The axioms mention no elements: arrows need not be functions, and an object is known only through the arrows into and out of it. Isomorphism, commutative diagrams, duality, and the terminal object are the first consequences.\n",{"path":4585,"title":4586,"module":1231,"summary":4587},"\u002Fcategory-theory\u002Ffoundations\u002Fexamples-of-categories","A Zoo of Categories","The axioms admit two very different kinds of model: large categories of structured sets and their structure-preserving maps (Set, Mon, Grp, Top, Vect), and small categories that are themselves single algebraic objects — a monoid as a one-object category, a poset as a thin category. The awkward cases Rel and Pfn have sets as objects but relations and partial functions as arrows, and a typed programming language presents its types and programs as a category.\n",{"path":4589,"title":4590,"module":1231,"summary":4591},"\u002Fcategory-theory\u002Ffoundations\u002Fspecial-morphisms","Isomorphisms, Monos, and Epis","Injectivity and surjectivity mention elements, so a general category re-expresses them by cancellation: monomorphisms cancel on the left, epimorphisms on the right. Sections and retractions are the split versions with an explicit one-sided inverse. Mono plus epi does not force an isomorphism, and subobjects are equivalence classes of monos into a fixed object.\n",{"path":4593,"title":4594,"module":1231,"summary":4595},"\u002Fcategory-theory\u002Ffoundations\u002Ffunctors","Functors: Maps Between Categories","A functor sends objects to objects and arrows to arrows while preserving composition and identities. Covariant and contravariant functors, the standard stock (forgetful, free, hom, and powerset), and the classification by faithfulness, fullness, and essential surjectivity all follow. Functors compose, so categories and functors form a category themselves.\n",{"path":4597,"title":4598,"module":1231,"summary":4599},"\u002Fcategory-theory\u002Ffoundations\u002Fnatural-transformations","Natural Transformations and Functor Categories","A natural transformation is a map between two parallel functors: one component arrow per object, subject to a commuting square for every arrow of the source. Naturality is verified for the determinant, the double dual, and list operations; functors and natural transformations form the functor category [C, D]; and vertical and horizontal composition satisfy the Godement interchange law.\n",{"path":4601,"title":4602,"module":1231,"summary":4603},"\u002Fcategory-theory\u002Ffoundations\u002Fsize-and-set-theory","Size: Small, Large, Locally Small","The objects of Set do not form a set, and pretending otherwise reproduces the classical paradoxes. Classes make the small\u002Flarge distinction precise, with locally small and essentially small as the intermediate notions. Cantor's theorem shows Set and its algebraic relatives are large, and the function-based axiomatization of sets is the one category theory prefers to ZFC.\n",{"path":4605,"title":4606,"module":4607,"summary":4608},"\u002Fcategory-theory\u002Funiversal-properties\u002Funiversal-properties","Universal Properties, Initial and Terminal Objects","Universal Properties and Basic Constructions","A universal property characterizes an object by a for-all\u002Fexists-unique condition on the arrows into or out of it, and any two objects satisfying the same property are isomorphic by a unique isomorphism. Initial and terminal objects are the simplest cases; the free vector space, the discrete topology, and the ring of integers show the pattern at work.\n",{"path":4610,"title":4611,"module":4607,"summary":4612},"\u002Fcategory-theory\u002Funiversal-properties\u002Fproducts-and-coproducts","Products and Coproducts","The product of two objects is a wedge of projections through which every other wedge factors uniquely; the coproduct is the dual, built from injections. In Set these are the cartesian product and the disjoint union, in a poset the meet and join, and in abelian groups the two coincide. The mediating-arrow discipline established here is the template for all limits.\n",{"path":4614,"title":4615,"module":4607,"summary":4616},"\u002Fcategory-theory\u002Funiversal-properties\u002Fconstructions-on-categories","Opposite, Product, Slice, and Comma Categories","Categories are themselves mathematical structures, and the standard algebraic constructions apply: opposites, products, subcategories, slices, and the comma category that subsumes them. The opposite category yields the duality principle, halving the subject's proofs; slice and comma categories repackage every universal property as an initial or terminal object.\n",{"path":4618,"title":4619,"module":4620,"summary":4621},"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Frepresentable-functors","Hom-Functors and Representables","Representables and the Yoneda Lemma","Fixing an object A of a locally small category produces a set-valued functor, the hom-functor A(A,-), that records every map out of A. A functor is representable when it is naturally isomorphic to such a hom-functor. We define the covariant and contravariant hom-functors, collect the standard representables (identity, forgetful, powerset), and read maps as generalized elements of varying shape.\n",{"path":4623,"title":4624,"module":4620,"summary":4625},"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-lemma","The Yoneda Lemma","The Yoneda lemma computes the natural transformations out of a representable presheaf: they form a set in natural bijection with X(A). The proof fixes a single degree of freedom, the image of the identity arrow, and shows naturality forces everything else. We prove the bijection, verify naturality in both variables, and read off that a natural transformation out of a representable is just one element.\n",{"path":4627,"title":4628,"module":4620,"summary":4629},"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-consequences","The Yoneda Embedding and Its Uses","Three corollaries turn the Yoneda lemma into working machinery. A representation of a presheaf is the same thing as a universal element; the Yoneda embedding of a category into its presheaf category is full and faithful; and two objects are isomorphic exactly when their representables are. Together they justify constructing arrows by constructing natural transformations between hom-functors, and they contain Cayley's theorem as the one-object case.\n",{"path":4631,"title":4632,"module":4633,"summary":4634},"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits","Cones and Limits","Limits and Colimits","A diagram is a functor from a small shape category; a cone over it is an object with compatible legs to every node; and a limit is the terminal cone, the one every other cone factors through uniquely. Products and terminal objects reappear as limits over particular shapes, and the whole construction is unique up to a single isomorphism.\n",{"path":4636,"title":4637,"module":4633,"summary":4638},"\u002Fcategory-theory\u002Flimits-colimits\u002Fproducts-equalizers-pullbacks","Equalizers and Pullbacks","The equalizer of a parallel pair is the universal arrow that makes the two composites agree; the pullback of a cospan is the universal commutative square. In Set they are solution sets and fibered products, every equalizer is monic, monics are stable under pullback, and products plus equalizers together generate all limits.\n",{"path":4640,"title":4641,"module":4633,"summary":4642},"\u002Fcategory-theory\u002Flimits-colimits\u002Fcolimits","Colimits: Coproducts, Coequalizers, Pushouts","Colimits are limits in the opposite category: cocones replace cones, and the universal cocone is initial rather than terminal. Coproducts glue objects side by side, coequalizers impose relations and produce quotients, pushouts glue along a shared part, and in Set every colimit is a quotient of a disjoint union. Directed colimits admit a clean elementwise description.\n",{"path":4644,"title":4645,"module":4633,"summary":4646},"\u002Fcategory-theory\u002Flimits-colimits\u002Fcomputing-limits","Computing Limits in Concrete Categories","In Set the limit of any diagram is the set of threads: choice functions through the nodes that commute with every edge. In Pos, Mon, and Top the recipe is the same limit downstairs plus the unique structure that makes the projections structure-preserving — pointwise order, componentwise operations, the topology generated by the projections. The pattern is what \"the forgetful functor creates limits\" means concretely.\n",{"path":4648,"title":4649,"module":4633,"summary":4650},"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits-and-functors","Preservation, Reflection, and Creation of Limits","A functor preserves limits if it sends limit cones to limit cones, reflects them if it recognizes them, and creates them if limits downstairs lift uniquely upstairs. Representable functors preserve all limits, forgetful functors from algebra create them, and limits in functor categories are computed pointwise, one evaluation at a time.\n",{"path":4652,"title":4653,"module":4654,"summary":4655},"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions","Adjoint Functors via Hom-Set Bijections","Adjunctions","An adjunction is a natural bijection between two hom-sets: maps out of $F(A)$ in one category correspond to maps into $G(B)$ in the other. We give the definition, spell out the naturality axioms that make the correspondence compatible with composition, and work the flagship examples — free vector spaces, free groups, discrete and indiscrete topologies, and currying.\n",{"path":4657,"title":4658,"module":4654,"summary":4659},"\u002Fcategory-theory\u002Fadjunctions\u002Funits-and-counits","Units, Counits, and the Triangle Identities","The whole hom-set bijection of an adjunction is generated by two natural transformations: the unit, obtained by transposing identity maps on one side, and the counit, by transposing them on the other. Two triangle identities are all they must satisfy, and any pair satisfying them determines a unique adjunction. The same correspondence specializes to order-preserving maps between posets and to free constructions.\n",{"path":4661,"title":4662,"module":4654,"summary":4663},"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions-via-universal-arrows","Adjunctions from Universal Arrows","The unit component at a single object is an initial object of a comma category, and this universal property alone rebuilds the whole adjunction. A functor has a left adjoint exactly when every object admits such a universal arrow, and the left adjoint is assembled from them one object at a time. We prove the equivalence of all three formulations of adjointness.\n",{"path":4665,"title":4666,"module":4654,"summary":4667},"\u002Fcategory-theory\u002Fadjunctions\u002Ffree-forgetful-adjunctions","Free Constructions and Free–Forgetful Adjunctions","Free monoids, free groups, and free vector spaces are left adjoints to forgetful functors, and the universal mapping property is all one needs to prove it. Some forgetful functors also have right adjoints (co-free constructions like the indiscrete topology), producing three-functor chains. Contravariant adjunctions, symmetric in their two functors, close the lesson with the pattern behind duality and representation theorems.\n",{"path":4669,"title":4670,"module":4671,"summary":4672},"\u002Fcategory-theory\u002Fadjoints-limits\u002Flimits-via-adjoints","Limits as Adjoints and as Representables","Adjoints, Representables, and Limits Together","A cone on a diagram is a natural transformation from a constant diagram, so a limit is a representation of the cone functor and, equivalently, a value of the right adjoint to the diagonal functor. We prove both rephrasings, derive uniqueness and functoriality of limits from them, and record the dual statement that a colimit is the left adjoint to the diagonal.\n",{"path":4674,"title":4675,"module":4671,"summary":4676},"\u002Fcategory-theory\u002Fadjoints-limits\u002Fpresheaf-limits-colimits","Limits and Colimits of Presheaves","Representables preserve limits, and limits in a functor category are computed one object at a time, so a presheaf category is complete and cocomplete with all its structure inherited pointwise from Set. The Yoneda embedding then preserves limits but not colimits, and the density theorem repairs the colimit side: every presheaf is a canonical colimit of representables.\n",{"path":4678,"title":4679,"module":4671,"summary":4680},"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoints-preserve-limits","Right Adjoints Preserve Limits (RAPL)","A functor with a left adjoint preserves every limit that exists, and dually a functor with a right adjoint preserves colimits. The proof is a four-line chain of natural isomorphisms through the adjunction and the continuity of representables. The theorem yields product-and-exponential arithmetic in Set, another proof that limits commute with limits, and a standard test for proving that a functor has no adjoint.\n",{"path":4682,"title":4683,"module":4671,"summary":4684},"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoint-functor-theorem","The Adjoint Functor Theorem","RAPL makes limit preservation necessary for having a left adjoint; the adjoint functor theorems identify when it is sufficient. For ordered sets no extra hypothesis is needed. In general the candidate adjoint is a limit over a comma category that may be large, and the general adjoint functor theorem tames it with a weakly initial set. We prove GAFT in full and apply it to free groups and, through the special adjoint functor theorem, the Stone–Čech compactification.\n",{"path":4686,"title":4687,"module":4688,"summary":4689},"\u002Fcategory-theory\u002Fmonads-algebras\u002Fmonads","Monads from Adjunctions","Monads and Algebras","A monad on a category is an endofunctor equipped with a unit and a multiplication satisfying associativity and unit laws — the data of a monoid, written internally to the category of endofunctors. Every adjunction induces one, and the list, exception, and state constructions that model computational effects are all monads on Set.\n",{"path":4691,"title":4692,"module":4688,"summary":4693},"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-eilenberg-moore","Algebras for a Monad","An algebra for a monad is an object with a structure map that interacts correctly with the unit and multiplication. The algebras form the Eilenberg–Moore category, whose free–forgetful adjunction induces the monad back; a comparison functor relates any other inducing adjunction to it, and for the list monad the algebras are exactly monoids.\n",{"path":4695,"title":4696,"module":4688,"summary":4697},"\u002Fcategory-theory\u002Fmonads-algebras\u002Fkleisli-and-programming","The Kleisli Category and Monads in Programming","The Kleisli category of a monad has the same objects as the base but takes arrows A to TB, composed by mapping and flattening. These arrows are effectful programs, Kleisli composition is the bind of functional programming, and the Kleisli adjunction is the initial resolution of the monad, with Eilenberg–Moore at the terminal end.\n",{"path":4699,"title":4700,"module":4688,"summary":4701},"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-for-endofunctors","Algebras for an Endofunctor and Recursion","Dropping the monad laws leaves algebras for a bare endofunctor, whose initial objects are the least fixed points of the functor by Lambek's lemma. The natural numbers, lists, and trees are initial algebras; the unique map out of an initial algebra is the fold of functional programming; and the Smyth–Plotkin fixed-point technique builds Scott domains the same way.\n",{"path":4703,"title":4704,"module":4705,"summary":4706},"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Fcartesian-closed-categories","Cartesian Closed Categories","Cartesian Closed Categories and Typed Lambda Calculus","A cartesian closed category has a terminal object, binary products, and for every pair of objects an exponential object that internalizes the hom-set as an object of the category. The defining data is an evaluation arrow and a currying operation, packaged by the adjunction between product-with-A and exponential-by-A. Set, Boolean and Heyting algebras, functor categories, and Cat are all cartesian closed.\n",{"path":4708,"title":4709,"module":4705,"summary":4710},"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Flambda-calculus-correspondence","Typed Lambda Calculus and CCCs","The typed lambda calculus and the cartesian closed category are two presentations of the same theory. Types become objects, terms with one free variable become arrows, product types become products, and function types become exponentials, with abstraction matching currying and application matching evaluation. Building the category of a lambda theory and the internal language of a category are mutually inverse up to equivalence.\n",{"path":4712,"title":4713,"module":4705,"summary":4714},"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Ffixed-points-and-recursion","Fixed Points in Cartesian Closed Categories","The untyped lambda calculus has a fixed-point combinator; the typed calculus cannot, and Lawvere's fixed-point theorem explains why: any point-surjection onto an exponential forces every endomap to have a fixed point, which is the abstract form of Cantor's diagonal argument. Recursion is recovered instead by restricting to omega-complete partially ordered objects, where every continuous endomap has a least fixed point built by iterating from bottom. This gives While loops a semantics.\n",{"path":4716,"title":4717,"module":6,"summary":6},"\u002Fcategory-theory","Category Theory",{"path":4719,"title":3361,"module":4720,"summary":4721},"\u002Fdeep-learning\u002Fmathematical-background\u002Flinear-algebra-for-deep-learning","Mathematical Background","Every quantity a network touches is a tensor, and every layer is a matrix acting on one. This lesson compiles the linear algebra deep learning actually uses: products and norms, the system $Ax=b$ and when it is solvable, the two decompositions (eigen and SVD) that diagonalize a transformation, and the pseudoinverse that solves what cannot be solved exactly. It then derives PCA as the worked example that ties it all together.\n",{"path":4723,"title":4724,"module":4720,"summary":4725},"\u002Fdeep-learning\u002Fmathematical-background\u002Fprobability-and-information-theory","Probability & Information Theory","This lesson assembles the probabilistic vocabulary a network is trained in (random variables, densities, the chain rule, expectation and covariance, the handful of distributions that recur everywhere) and then the information theory that turns a probabilistic model into a loss: self-information, entropy, and the KL divergence whose asymmetry is the cross-entropy objective itself.\n",{"path":4727,"title":4728,"module":4720,"summary":4729},"\u002Fdeep-learning\u002Fmathematical-background\u002Fnumerical-computation","Numerical Computation","Machine learning runs on finite-precision arithmetic, where every number is approximated and every operation rounds. This lesson sets the numerical ground rules: overflow and underflow and the standard stabilizations, the condition number that measures how much a problem amplifies error, and the gradient-based optimization (first and second order, constrained and unconstrained) that every training loop runs.\n",{"path":4731,"title":2720,"module":4720,"summary":4732},"\u002Fdeep-learning\u002Fmathematical-background\u002Fcalculus","This lesson assembles the differential calculus used in training networks: the gradient and directional derivative, the Jacobian and Hessian, and the chain rule in scalar, vector, and matrix form. From the chain rule it derives back-propagation as a single sweep over the computational graph, tabulates the matrix-calculus identities that recur in layer gradients, reads optimization off a second-order Taylor expansion, and ends with why reverse-mode automatic differentiation is the algorithm every framework runs.\n",{"path":4734,"title":4735,"module":1231,"summary":4736},"\u002Fdeep-learning\u002Ffoundations\u002Fwhat-is-deep-learning","What Is Deep Learning?","Deep learning is representation learning by composition: stack simple differentiable layers, define a loss, and let gradient descent discover the features a human would otherwise have to engineer by hand. We set up the whole vocabulary (model, loss, optimizer, data), the training loop that ties them together, and the three reasons the approach became practical.\n",{"path":4738,"title":4739,"module":1231,"summary":4740},"\u002Fdeep-learning\u002Ffoundations\u002Fmachine-learning-refresher","A Machine-Learning Refresher","The statistical framework the networks live in: data drawn from an unknown distribution, a loss to minimize, and the central question of generalization: will it work on data we have not seen? We set up empirical risk, capacity, the bias–variance tradeoff, and maximum likelihood.\n",{"path":4742,"title":4743,"module":1231,"summary":4744},"\u002Fdeep-learning\u002Ffoundations\u002Flinear-models-and-the-perceptron","Linear Models & the Perceptron","The simplest learners (linear regression, logistic regression, the perceptron) already contain the whole template: a weighted sum, a loss, a gradient step. They also fail on the XOR problem, which no linear model can solve — the limitation that motivates deep learning.\n",{"path":4746,"title":4747,"module":4748,"summary":4749},"\u002Fdeep-learning\u002Fneural-networks\u002Fthe-multilayer-perceptron","The Multilayer Perceptron","Neural Networks","Stacking linear layers with a nonlinearity between them removes the limitation that stopped the perceptron. We build the multilayer perceptron in explicit matrix form (the forward pass, its dimensions, a worked XOR network with concrete weights) and prove why the nonlinearity is essential: without it the deepest stack collapses to a single hyperplane.\n",{"path":4751,"title":4752,"module":4748,"summary":4753},"\u002Fdeep-learning\u002Fneural-networks\u002Factivation-functions","Activation Functions","The activation is the only nonlinear part of a layer, and the reason depth adds expressive power. We catalog the standard hidden units (sigmoid, tanh, ReLU and its descendants, plus GELU, softplus, swish and maxout), derive each unit's derivative in full, make the vanishing-gradient problem quantitative with the chain-rule product, work numeric examples, and explain why the saturating units gave way to ReLU and why ReLU's own dead-unit failure gave way to Leaky\u002FPReLU\u002FELU\u002FGELU.\n",{"path":4755,"title":4756,"module":4748,"summary":4757},"\u002Fdeep-learning\u002Fneural-networks\u002Funiversal-approximation","Universal Approximation","One hidden layer with a non-polynomial activation can approximate any continuous function on a compact set to arbitrary accuracy: the universal approximation theorem. We prove it constructively (two sigmoids make a bump; sums of bumps make any curve), then show the limitation: existence is not efficiency. Depth-separation results exhibit functions a deep net represents with $O(n)$ units that a shallow net needs $\\exp(n)$ units to match.\n",{"path":4759,"title":4760,"module":4748,"summary":4761},"\u002Fdeep-learning\u002Fneural-networks\u002Fbackpropagation","Backpropagation","Backpropagation is the chain rule run backward over a computational graph. We formalize the graph, derive the four backprop equations for an MLP, present the forward and backward passes as algorithms, and work a tiny two-layer net by hand with explicit numbers. The result: one scalar loss, reverse-mode autodiff, and a gradient for every parameter at twice the cost of a forward pass.\n",{"path":4763,"title":4764,"module":4748,"summary":4765},"\u002Fdeep-learning\u002Fneural-networks\u002Floss-functions-and-output-units","Loss Functions & Output Units","The last layer is where a network's hidden representation meets the task. Choosing an output unit and a loss is not two independent choices; maximum likelihood fixes the pair. We derive the standard couplings (linear\u002FMSE, sigmoid\u002FBCE, softmax\u002Fcross-entropy), show why softmax and cross-entropy were built to cancel into the residual $\\hat y - y$, and prove why squared error is the wrong loss for a saturating classifier.\n",{"path":4767,"title":4768,"module":4769,"summary":4770},"\u002Fdeep-learning\u002Foptimization\u002Fgradient-descent-and-sgd","Gradient Descent & SGD","Optimization","Training is descent on the empirical risk: step the parameters against the gradient. We derive the minibatch gradient as an unbiased estimator whose variance falls as $1\u002FB$, derive the learning-rate ceiling from the smoothness-stability bound $\\eta \u003C 2\u002FL$, and lay out the schedules (step, exponential, cosine, warmup) that anneal it over training.\n",{"path":4772,"title":4773,"module":4769,"summary":4774},"\u002Fdeep-learning\u002Foptimization\u002Fmomentum-and-adaptive-methods","Momentum & Adaptive Methods","Plain gradient descent zig-zags across ravines and moves slowly along flat valleys, because one global learning rate cannot suit a surface with wildly different curvature in different directions. Two fixes address the two problems: momentum accumulates a velocity that damps the oscillation and accelerates the drift, and adaptive methods give every parameter its own learning rate scaled by the history of its gradients. Adam fuses both, and is the default optimizer of modern deep learning.\n",{"path":4776,"title":4777,"module":4769,"summary":4778},"\u002Fdeep-learning\u002Foptimization\u002Finitialization","Weight Initialization","The initial weights determine whether training can succeed before the first gradient step. Initialize every weight equal and all hidden units compute the same function forever; initialize too small or too large and the signal vanishes or explodes as it crosses depth. A single variance condition, $n_{\\text{in}}\\mathrm{Var}(W)=1$, fixes both, and reading it off the forward and backward passes yields Xavier and He initialization directly.\n",{"path":4780,"title":4781,"module":4769,"summary":4782},"\u002Fdeep-learning\u002Foptimization\u002Fthe-optimization-landscape","The Optimization Landscape","The loss of a deep network is a non-convex surface in millions of dimensions, so local search carries no global guarantee, yet it works. We classify critical points by the eigenvalues of the Hessian, show that in high dimension nearly all of them are saddle points rather than bad local minima, and read off the practical terrain — plateaus, cliffs, ill-conditioning, and the sharp-versus-flat distinction that ties the geometry of a minimum to how well it generalizes.\n",{"path":4784,"title":4785,"module":4769,"summary":4786},"\u002Fdeep-learning\u002Foptimization\u002Fsecond-order-and-approximate-methods","Second-Order & Approximate Methods","Newton's method reads the curvature of the loss off its Hessian and jumps to the minimum of the local quadratic in a single step, rescaling away the ill-conditioning that slows first-order descent. We derive it, then explain the three obstacles that keep it out of deep learning: a $d \\times d$ Hessian for $d$ in the billions, an attraction to saddle points, and minibatch noise. The alternative is approximation (conjugate gradients, BFGS and L-BFGS, the natural gradient and Hessian-free methods), each buying some of Newton's curvature information without ever forming or inverting $H$.\n",{"path":4788,"title":4789,"module":4790,"summary":4791},"\u002Fdeep-learning\u002Fregularization\u002Fregularization-overview","Regularization Overview","Regularization","Regularization is any modification to a learning algorithm meant to lower test error at the possible expense of training error. We derive the bias–variance decomposition that explains why it helps, set up the two parameter-norm penalties, $L^2$ weight decay and $L^1$, derive their update rules and eigenbasis shrinkage, show geometrically why $L^1$ alone produces sparse weights (soft-thresholding), distinguish weight decay from loss-added $L^2$ under AdamW, and read both penalties through the two lenses that recur across the chapter: a norm-ball constraint via KKT, and a prior via MAP estimation.\n",{"path":4793,"title":4794,"module":4790,"summary":4795},"\u002Fdeep-learning\u002Fregularization\u002Fdropout-and-data-augmentation","Dropout & Data Augmentation","Two of the most effective regularizers add no penalty term at all; they perturb the computation instead. Dropout multiplies hidden units by a random Bernoulli mask, training an exponential ensemble of thinned subnetworks that share weights; inverted scaling collapses that ensemble into one cheap forward pass at test time. Data augmentation enlarges the training set with label-preserving transforms, injecting the invariances the task demands, and noise injection (input, weight, label smoothing, Mixup) generalizes the same idea into a continuous family.\n",{"path":4797,"title":4798,"module":4790,"summary":4799},"\u002Fdeep-learning\u002Fregularization\u002Fearly-stopping-and-parameter-sharing","Early Stopping & Parameter Sharing","Two cheap regularizers that cost no extra term in the loss. Early stopping treats training time itself as a hyperparameter (watch the validation curve, halt at its minimum, keep the best checkpoint), and for a quadratic objective it is provably equivalent to $L^2$ weight decay. Parameter sharing goes the other way: it constrains many weights to be _equal_, the prior behind every convolution and every recurrent step, and the reason a CNN has orders of magnitude fewer parameters than the dense net it replaces.\n",{"path":4801,"title":4802,"module":4790,"summary":4803},"\u002Fdeep-learning\u002Fregularization\u002Fnormalization","Normalization","Normalization layers standardize activations to zero mean and unit variance inside the network, then hand the model a learnable scale and shift to undo the constraint when it pays to. Batch normalization does this across the batch and must keep separate train-time and test-time statistics; layer, instance, and group norm change only the axes they average over. The result is faster, better-conditioned optimization and a free dose of regularizing batch noise.\n",{"path":4805,"title":4806,"module":4807,"summary":4808},"\u002Fdeep-learning\u002Farchitectures\u002Fconvolutional-networks","Convolutional Networks","Architectures","A convolutional network replaces the dense layer's all-to-all weight matrix with a small kernel slid across the input. Three structural commitments (sparse connectivity, parameter sharing, and translation equivariance) collapse the parameter count by orders of magnitude and bake the right prior for images directly into the architecture. We derive the convolution arithmetic, the output geometry, pooling, and the receptive field, then assemble the canonical stack.\n",{"path":4810,"title":4811,"module":4807,"summary":4812},"\u002Fdeep-learning\u002Farchitectures\u002Fcnn-architectures","CNN Architectures","Six landmark networks, each contributing exactly one idea: LeNet's conv-pool stack, AlexNet's ReLU-and-dropout scale, VGG's $3\\times3$ uniformity, Inception's multi-scale module, ResNet's residual skip, and DenseNet's dense connectivity. The common thread is the degradation problem (why plain deeper nets train worse, not just overfit) and the residual block that solved it by keeping a $+1$ path open for the gradient.\n",{"path":4814,"title":4815,"module":4807,"summary":4816},"\u002Fdeep-learning\u002Farchitectures\u002Frecurrent-networks","Recurrent Networks","A recurrent network folds a sequence into a fixed-size hidden state, reusing one set of weights at every time step, the architectural prior that the same rule applies wherever it lands in time. Unrolling the recurrence exposes a deep feed-forward graph; backpropagation through it sums gradient contributions across all steps and chains a product of Jacobians, and that product is why long-range gradients vanish or explode. That failure motivates gated architectures.\n",{"path":4818,"title":4819,"module":4807,"summary":4820},"\u002Fdeep-learning\u002Farchitectures\u002Flstm-and-gru","LSTM & GRU","A plain recurrent network propagates its hidden state through a repeated weight-matrix multiply, and the Jacobian product that results vanishes or explodes long before a useful gradient can reach the early steps. Gated RNNs fix this with an additive memory path: a cell state that is carried forward almost unchanged, past which the gradient flows along a near-identity highway. We derive that highway, give the full LSTM and GRU equations, and compare the two.\n",{"path":4822,"title":4823,"module":4807,"summary":4824},"\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers","Attention & Transformers","Attention replaces fixed wiring with content-based routing: every position reads from every other through a soft, learned dot-product lookup. We derive scaled dot-product attention and its $\\sqrt{d_k}$ correction, build it into multi-head self-attention, inject order with positional encodings, and stack the whole thing into the Transformer block that displaced recurrence and convolution alike.\n",{"path":4826,"title":4827,"module":4807,"summary":4828},"\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture","The Transformer Architecture","The Transformer is the architecture built around the attention mechanism. This first part assembles the full encoder–decoder of \"Attention Is All You Need\" — embeddings and positional encoding, stacked self-attention and feed-forward sublayers wrapped in residual connections and LayerNorm, masked decoding and cross-attention — works through causal masking and the three modern families (encoder-only, decoder-only, encoder–decoder), and accounts for where the parameters and the $O(n^2)$ compute actually go.\n",{"path":4830,"title":4831,"module":4807,"summary":4832},"\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice","Transformers in Practice","The Transformer makes no assumption about what a token represents. This part follows the architecture out of language: image patches feed a plain encoder (the Vision Transformer), the decoder-only half scales into the GPT line of large language models, and one substrate covers translation, retrieval, and multimodal grounding. We work the ViT patch arithmetic and a GPT parameter count by hand, then close on the empirical scaling laws — power-law loss, the Chinchilla compute-optimal balance, and emergent behavior — that made scale the dominant lever.\n",{"path":4834,"title":4835,"module":4807,"summary":4836},"\u002Fdeep-learning\u002Farchitectures\u002Fgraph-neural-networks","Graph Neural Networks","A graph neural network learns on data with no grid and no canonical ordering: atoms in a molecule, users in a social network, road segments in a map. The unifying idea is message passing — each node repeatedly aggregates its neighbors' states and updates its own — built to respect the one symmetry graphs demand, permutation equivariance. We derive the message-passing framework, specialize it into GCN, GraphSAGE, GAT, and GIN, read off graph-level outputs, and bound what message passing can and cannot tell apart.\n",{"path":4838,"title":4839,"module":4807,"summary":4840},"\u002Fdeep-learning\u002Farchitectures\u002Fstate-space-models","State-Space Models and Mamba","A state-space model carries a continuous linear hidden state through a sequence, and that linearity buys two equivalent algorithms from one set of weights: a recurrence that runs in linear time with constant memory, and a global convolution that trains in parallel. Long-range memory comes from how the transition matrix is initialized (HiPPO) and parameterized (S4's diagonal-plus-low-rank form). Mamba breaks the convolution on purpose, making the parameters input-dependent so the model can select what to remember, recovered at speed by a hardware-aware parallel scan.\n",{"path":4842,"title":4843,"module":4844,"summary":4845},"\u002Fdeep-learning\u002Ftheory\u002Fgeneralization-theory","Generalization Theory","Theory & Frontiers","Classical learning theory bounds the gap between training and test error by a model's capacity (VC dimension, Rademacher complexity), and predicts that a model with more parameters than data should overfit catastrophically. Modern networks do the opposite: they interpolate, even fit pure noise, and still generalize. We derive the classical bounds, work the bias-variance decomposition, show why the bounds go vacuous, and survey what replaced them: double descent, the interpolation threshold, margin and norm-based bounds, and the implicit bias of the optimizer itself.\n",{"path":4847,"title":4848,"module":4844,"summary":4849},"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-robustness","Adversarial Robustness","A trained network can be fooled by a perturbation too small for a human to see: add a carefully aimed vector of magnitude $\\epsilon$ to a correctly classified image and the prediction flips. We derive the fast gradient sign method as the first-order-optimal step inside an $L_\\infty$ ball, explain the linearity hypothesis that makes high-dimensional models so easy to push around, build up to projected gradient descent, and frame adversarial training as a min-max robust-optimization problem with its own accuracy cost. Defenses beyond training continue in the next lesson.\n",{"path":4851,"title":4852,"module":4844,"summary":4853},"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-defenses","Adversarial Defenses","Defending a network against an adversary is far harder than attacking one. This lesson covers the defense side: certified guarantees via randomized smoothing, the transferability that makes black-box attacks possible, and the recurring failure of gradient masking, where a defense hides the attacker's gradient instead of moving the decision boundary. It ends with the adaptive-attack discipline (BPDA, EOT, transfer) that every robustness claim must be tested against.\n",{"path":4855,"title":4856,"module":4844,"summary":4857},"\u002Fdeep-learning\u002Ftheory\u002Fbayesian-and-ensemble-methods","Bayesian & Ensemble Methods","A trained network returns a single point prediction and, with the softmax, a confidence, but that confidence is usually miscalibrated, collapsing to near- certainty even on inputs the model has never seen. This lesson covers uncertainty estimation for networks: the two kinds of uncertainty, the Bayesian posterior over weights and its tractable stand-ins (MC dropout, deep ensembles), and how to check whether a model's reported confidences match observed frequencies.\n",{"path":4859,"title":4860,"module":4844,"summary":4861},"\u002Fdeep-learning\u002Ftheory\u002Fdeep-equilibrium-models","Deep Equilibrium Models","A deep network need not be a fixed stack of layers; it can be a single weight-tied layer iterated to convergence, its output defined implicitly as the fixed point $z^\\star = f_\\theta(z^\\star, x)$. The forward pass becomes root-finding and the backward pass becomes implicit differentiation, so training costs O(1) memory regardless of effective depth. We derive both passes from the implicit function theorem and close the course on defining a layer by a fixed-point condition rather than an explicit stack.\n",{"path":4863,"title":4864,"module":4865,"summary":4866},"\u002Fdeep-learning\u002Fgenerative-models\u002Flinear-factor-models","Linear Factor Models","Generative Models","The simplest generative models share one template: a latent variable drawn from a fixed prior, run through a linear decoder, plus noise. Probabilistic PCA, factor analysis, independent component analysis, and sparse coding are all this template with a different prior on the latents and a different noise model. We derive each marginal, see why ICA needs non-Gaussianity to identify its sources, and show how sparse coding learns Gabor-like dictionary atoms.\n",{"path":4868,"title":4869,"module":4865,"summary":4870},"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoencoders","Autoencoders","An autoencoder is a network trained to copy its input to its output through a narrow channel; the useful product is the bottleneck representation $h$, not the reconstruction. We derive the undercomplete autoencoder and prove its linear case recovers PCA, then trade the bottleneck for explicit regularization (sparse, denoising, contractive) and show how a denoising autoencoder learns the low-dimensional manifold the data lives on.\n",{"path":4872,"title":4873,"module":4865,"summary":4874},"\u002Fdeep-learning\u002Fgenerative-models\u002Fvariational-autoencoders","Variational Autoencoders","An autoencoder compresses, but its latent space has gaps: sample a point between two encodings and the decoder produces noise. The variational autoencoder fixes this by training a probabilistic encoder against a prior, so the latent space becomes a smooth, samplable density. We derive the evidence lower bound it maximizes, the reparameterization trick that lets gradients flow through a random sample, and the closed-form Gaussian regularizer that pulls the posterior toward the prior.\n",{"path":4876,"title":4877,"module":4865,"summary":4878},"\u002Fdeep-learning\u002Fgenerative-models\u002Fgenerative-adversarial-networks","Generative Adversarial Networks","A generative adversarial network trains two networks against each other: a generator that turns noise into samples, and a discriminator that tries to tell real data from forgeries. The game has a clean theory: the optimal discriminator is a likelihood ratio, and at equilibrium the generator minimizes the Jensen–Shannon divergence to the data, with a global optimum exactly when its distribution matches the data. We derive that result, fix the saturating loss that breaks training, and catalogue the failure modes (mode collapse, instability, vanishing gradients) and the architectural fixes.\n",{"path":4880,"title":4881,"module":4865,"summary":4882},"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoregressive-and-normalizing-flows","Autoregressive Models & Normalizing Flows","Two families that provide exact likelihoods, each at a cost. Autoregressive models factor the joint by the probability chain rule and learn each conditional with a masked network: exact $\\log p(x)$, but sampling proceeds one coordinate at a time. Normalizing flows push a simple base density through an invertible map and read $\\log p(x)$ off the change-of-variables formula, trading architectural freedom for a cheap Jacobian determinant via triangular coupling layers.\n",{"path":4884,"title":4885,"module":4865,"summary":4886},"\u002Fdeep-learning\u002Fgenerative-models\u002Fenergy-based-and-boltzmann-machines","Energy-Based & Boltzmann Machines","Energy-based models replace an explicit density with a scalar energy and a Boltzmann normalization, $p(x) = e^{-E(x)}\u002FZ$: simple to specify, but with an intractable partition function $Z$. The Boltzmann machine and its restricted variant make the energy bilinear so the hidden units factorize, and contrastive divergence sidesteps $Z$ by replacing the model expectation with a few Gibbs steps started at the data. We close on the undirected deep models (DBNs and DBMs) and how they differ from the directed VAE.\n",{"path":4888,"title":4889,"module":4865,"summary":4890},"\u002Fdeep-learning\u002Fgenerative-models\u002Fdiffusion-and-score-based-models","Diffusion and Score-Based Models","Corrupt a data point with Gaussian noise in small steps until only noise remains, then train a network to undo one step at a time. We derive the forward process and its closed-form marginal, reduce the variational bound to the single noise-prediction objective that makes diffusion trainable, and show the score-matching view that unifies it with Langevin sampling and the continuous SDE. The lesson closes with DDIM fast sampling, classifier-free guidance, and the latent diffusion that powers modern text-to-image systems.\n",{"path":4892,"title":4893,"module":4894,"summary":4895},"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fstructured-probabilistic-models","Structured Probabilistic Models","Probabilistic Methods","A joint distribution over $n$ variables is a table with exponentially many entries; nobody can store it, fit it, or sample from it directly. Structure fixes this: a graph whose missing edges encode conditional independencies that factor the joint into small local pieces. We build the two dialects, directed (Bayesian networks) and undirected (Markov random fields), read independence off the graph, and connect the machinery to the latent-variable and energy-based models that power deep generative learning.\n",{"path":4897,"title":4898,"module":4894,"summary":4899},"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fmonte-carlo-and-mcmc","Monte Carlo & MCMC","Most quantities of interest in a probabilistic model are integrals nobody can compute in closed form: expectations, marginals, partition functions. Monte Carlo replaces the integral with an average over samples; importance sampling reweights samples from a tractable proposal; and when even sampling the target is hard, Markov-chain Monte Carlo builds a chain whose stationary distribution _is_ the target. We derive Metropolis–Hastings and Gibbs, analyze mixing, and close on the partition-function gradient that powers energy-based learning.\n",{"path":4901,"title":4902,"module":4894,"summary":4903},"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fapproximate-inference","Approximate Inference","In a latent-variable model the quantity we need, the posterior $p(h\\mid v)$ over hidden causes, is almost never computable, because its normalizer is an intractable sum over configurations. Approximate inference reframes the problem as optimization: maximize the evidence lower bound, a tractable functional whose gap to the true log-evidence equals a KL divergence. From that single bound fall expectation–maximization, mean-field variational inference, MAP, and the learned encoders behind variational autoencoders.\n",{"path":4905,"title":4906,"module":4907,"summary":4908},"\u002Fdeep-learning\u002Fpractical\u002Fpractical-methodology","Practical Methodology","Practical Deep Learning","Knowing the algorithms is half the job; the other half is a disciplined loop. Fix a goal and a metric, stand up an end-to-end baseline, then read the train\u002Fvalidation gap to decide whether the next move is more data or a bigger model. We detail that loop: choosing metrics under class imbalance, default baselines by data type, extrapolating the data a target needs, and guarding the data pipeline against the leaks and label bugs that corrupt every gradient. Hyperparameter tuning, debugging, and deployment continue in the sequel.\n",{"path":4910,"title":4911,"module":4907,"summary":4912},"\u002Fdeep-learning\u002Fpractical\u002Fhyperparameters-and-debugging","Hyperparameters & Debugging","The tuning half of the methodology loop. The learning rate is the one hyperparameter that dominates, so we tune it first, on a log scale, coarse to fine, and prefer random search to grid when only a few dials matter. Then an ordered debugging playbook — overfit one batch, check the loss at initialization against ln C, watch the gradient norm, gradient-check against centered finite differences — and, after launch, monitoring for train-test skew and distribution drift with confidence-based abstention.\n",{"path":4914,"title":4915,"module":4907,"summary":4916},"\u002Fdeep-learning\u002Fpractical\u002Frepresentation-learning","Representation Learning","A good representation makes a hard task easy by changing coordinates: it disentangles the factors of variation, spends its bits as a distributed code, and respects the low-dimensional manifold the data lives on. We make those three properties precise, recover the manifold hypothesis, and close on the first method that turned them into training practice — greedy layer-wise unsupervised pretraining — before the sequel picks up how the field learned to reuse those features.\n",{"path":4918,"title":4919,"module":4907,"summary":4920},"\u002Fdeep-learning\u002Fpractical\u002Ftransfer-learning","Transfer Learning","A representation learned once can be reused everywhere. We cover the main mechanisms of reuse: feature extraction versus fine-tuning, the generic-to-specific gradient of features that sets the freeze boundary, the learning-rate discipline that keeps borrowed weights from being erased, domain adaptation when only the input distribution shifts, and the modern arc from supervised transfer to self-supervised foundation models.\n",{"path":4922,"title":4923,"module":4907,"summary":4924},"\u002Fdeep-learning\u002Fpractical\u002Fapplications","Applications","We survey large-scale training (the hardware, the two axes of parallelism, mixed precision, and the compression tricks that shrink a model after it is trained), then specialize the same gradient loop to vision, language, speech, and recommendation. Each domain is a different prior bolted onto one optimizer: convolutional invariance for pixels, distributed word vectors for tokens, sequence transduction for audio, low-rank factorization for the user–item matrix.\n",{"path":4926,"title":4927,"module":4907,"summary":4928},"\u002Fdeep-learning\u002Fpractical\u002Fmodel-compression-and-distillation","Model Compression and Distillation","A trained network and a deployable one are rarely the same object. This lesson is the toolkit for closing that gap: knowledge distillation transfers a large teacher's soft, information-rich logits into a small student; pruning deletes the weights that contribute least; quantization swaps 32-bit floats for 8- or 4-bit integers; and low-rank factorization replaces a fat matrix with two thin ones. We derive each method, show what it costs in accuracy, and lay out which combinations win on which hardware.\n",{"path":4930,"title":4931,"module":4907,"summary":4932},"\u002Fdeep-learning\u002Fpractical\u002Fmeta-learning-and-few-shot","Meta-Learning and Few-Shot Learning","A deep network trained on one example per class overfits. Meta-learning targets this few-shot regime by training across a distribution of tasks so that a new task is learnable from a handful of examples. We formalize the $N$-way $K$-shot episode, then derive the two dominant families: metric methods that learn an embedding where distance classifies (Prototypical Networks), and optimization methods that learn an initialization a few gradient steps can adapt (MAML). We close on the link to transfer learning and to the in-context few-shot behavior of large language models.\n",{"path":4934,"title":4935,"module":4936,"summary":4937},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Flarge-language-models","Large Language Models","Large Models & Agents","A large language model is a decoder-only Transformer trained on one objective, next-token prediction, then scaled until new behavior appears. This first part builds the object itself: the equivalence between next-token prediction and lossless compression, subword tokenization (BPE, WordPiece, Unigram, SentencePiece) worked on a real sentence, the four pretraining objectives and the attention masks that distinguish them, and the three model families (encoder-only, decoder-only, encoder--decoder) with their parameter budgets. Scaling, decoding, the KV cache, and alignment continue in part two.\n",{"path":4939,"title":4940,"module":4936,"summary":4941},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fscaling-inference-and-alignment","Scaling, Inference, and Alignment of Language Models","Once a language model is built, three questions remain: how does it improve as it grows, how is it decoded and served affordably, and how is a raw next-token predictor turned into an assistant. We derive the Kaplan power laws and the Chinchilla compute-optimal balance, trace emergent abilities and in-context learning, catalog the decoding strategies from greedy to nucleus sampling, work the KV cache that makes generation quadratic instead of cubic, cover parameter-efficient adaptation by low-rank updates (LoRA), and close on the alignment stack: instruction tuning, RLHF, and DPO.\n",{"path":4943,"title":4944,"module":4936,"summary":4945},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fseq2seq-pretraining-and-bart","Denoising Sequence-to-Sequence Pretraining: BART","BERT corrupts and reconstructs; GPT predicts the next token. Sequence-to-sequence pretraining unifies both by training a full encoder–decoder as a denoising autoencoder: corrupt the text with a noise function, then reconstruct the original through a bidirectional encoder and an autoregressive decoder. This first part derives the denoising objective, catalogs BART's five noise functions (with a worked Poisson-infilling budget), proves BART specializes to both BERT and GPT, and traces a dimension-annotated forward pass through its encoder--decoder. T5, PEGASUS, fine-tuning, and decoding continue in part two.\n",{"path":4947,"title":4948,"module":4936,"summary":4949},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ftext-to-text-transfer-and-conditional-generation","Text-to-Text Transfer and Conditional Generation","BART reconstructs a corrupted document; T5 pushes the same denoising idea into a single interface where every task is a string-to-string map. This second part covers T5's span corruption with sentinel tokens (with a worked token budget), PEGASUS's summarization-matched gap sentences and the MASS midpoint, supervised fine-tuning and beam-search decoding with a length penalty, the exposure-bias failure modes of autoregressive decoding, and a theorem showing why a bidirectional encoder--decoder strictly dominates a decoder-only model when the output is conditioned on a full input.\n",{"path":4951,"title":4952,"module":4936,"summary":4953},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fspeech-and-audio-models","Speech Recognition: Front-Ends and Alignment","Speech is a long, high-rate sequence whose label is short and unaligned, so the whole subject turns on bridging that mismatch. This first part builds the spectral front-ends that compress a waveform into frames (STFT, mel spectrogram, MFCC, with a worked frame-count), derives CTC's marginalization over alignments and its forward-backward recursion with a two-frame numeric example, and contrasts it with attention-based seq2seq (LAS) and the RNN transducer. Self-supervised and weakly-supervised models, and text-to-speech, continue in part two.\n",{"path":4955,"title":4956,"module":4936,"summary":4957},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fself-supervised-speech-and-synthesis","Self-Supervised Speech Models and Synthesis","The recognition front-ends and alignment losses of part one all need transcribed audio, which is scarce. This second part removes that dependence: wav2vec 2.0 learns speech representations from unlabeled audio by a masked contrastive objective, HuBERT swaps the contrast for masked prediction of clustered units, and Whisper trades curation for scale with weakly-supervised web audio and a multitask token interface. We close with text-to-speech (the same length mismatch run backwards) and a tour of speech foundation models, discrete audio codecs, and neural TTS.\n",{"path":4959,"title":4960,"module":4936,"summary":4961},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fai-agents","AI Agents: Tools and Reasoning","A language model that only emits text is a function from prompt to prompt; an agent closes the loop, letting that model act on an environment, read back the result, and decide again. This first part formalizes the agent as a policy over interaction histories, builds out tool calling and the executor trust boundary, the ReAct interleaving of reasoning and action (with concrete traces), and search over thoughts: chain-of-thought, self-consistency, least-to-most, and Tree of Thoughts. Memory, retrieval, reflection, and multi-agent orchestration continue in part two.\n",{"path":4963,"title":4964,"module":4936,"summary":4965},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fagent-memory-retrieval-and-orchestration","Agent Memory, Retrieval, and Orchestration","An agent's reasoning and tool use only matter if it can remember what it learned and coordinate work larger than one context window. This second part builds the systems around the loop: short-term scratchpad versus long-term vector store, retrieval-augmented generation with a worked softmax over passage scores, reflection (Reflexion, Self-Refine), and multi-agent orchestration. It closes on the failure modes that bound agents — invalid tool calls, horizon-error compounding, context overflow, non-terminating loops — and the benchmarks that score the full loop.\n",{"path":4967,"title":4968,"module":4936,"summary":4969},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmixture-of-experts","Mixture-of-Experts","A mixture-of-experts layer replaces one feed-forward network with many and a router that sends each token to only a few of them, so the parameter count and the per-token compute become separate dials. We derive the gated output, sparse top-$k$ routing softmax, the load-balancing loss that stops the router from collapsing onto a single expert, and expert\u002Ftoken capacity with dropping, then work the dimension-annotated tensor shapes and FLOP arithmetic. We trace the architectures from the sparsely-gated LSTM through GShard, Switch Transformer, and Mixtral, cover distributed expert parallelism, and close on the training dynamics, failure modes, and serving costs of a sparse model.\n",{"path":4971,"title":4972,"module":4936,"summary":4973},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmultimodal-models","Multimodal Contrastive Learning","A multimodal model places images, text, and audio in one representation space, so a picture and its caption land close together. This first part builds the contrastive route: the shared embedding space and its residual modality gap, the Vision Transformer image encoder (patch embedding, CLS token, position embeddings, with shapes), the symmetric InfoNCE loss that trains the CLIP dual encoder from a batch similarity matrix (with a worked numeric step), and zero-shot classification as a softmax over class-prompt embeddings. Fusion and vision-language models continue in part two.\n",{"path":4975,"title":4976,"module":4936,"summary":4977},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ffusion-and-vision-language-models","Fusion and Vision-Language Models","A contrastive model compares modalities but never lets one read another. This second part builds the fusion route: early, late, and cross-attention fusion, then the three designs that connect a frozen vision encoder to a frozen language model — Flamingo's zero-initialized gated cross-attention, BLIP-2's Q-Former, and LLaVA's linear projector. We work the token-budget arithmetic that separates them, name the object-hallucination and fine-detail failure modes, cover the contrastive-then- instruction-tune recipe and its retrieval\u002Fcaptioning\u002FVQA benchmarks, and close on natively multimodal models.\n",{"path":4979,"title":4980,"module":4981,"summary":4982},"\u002Fdeep-learning\u002Freinforcement-learning\u002Ffoundations-of-reinforcement-learning","Foundations of Reinforcement Learning","Reinforcement Learning","Reinforcement learning is the third paradigm: an agent learns to act by interacting with an environment that returns rewards, not labels. We formalize the interaction as a Markov decision process, define the value functions that rank states and actions, and derive the Bellman expectation and optimality equations that every method downstream solves. Dynamic programming gives the exact answer when the model is known, and its convergence rests on a single fact: the Bellman operator is a contraction.\n",{"path":4984,"title":4985,"module":4981,"summary":4986},"\u002Fdeep-learning\u002Freinforcement-learning\u002Fmodel-free-prediction-and-control","Model-Free Prediction and Control","When the dynamics are unknown, an agent cannot plan against a model; it must learn directly from sampled experience. We build prediction and control from two estimators of the same return: Monte Carlo averages whole episodes, while temporal-difference learning bootstraps from its own next estimate. We trace the bias-variance contrast between them, derive SARSA and Q-learning as the on-policy and off-policy forms of control, unify everything through n-step returns and eligibility traces, and close on the deadly triad that makes off-policy bootstrapping with function approximation diverge.\n",{"path":4988,"title":4989,"module":4981,"summary":4990},"\u002Fdeep-learning\u002Freinforcement-learning\u002Fdeep-q-networks","Deep Q-Networks","A Deep Q-Network replaces the tabular action-value function with a neural approximator $Q(s,a;\\theta)$ and trains it by regression toward a bootstrapped target. Naive online Q-learning with a network diverges, so DQN adds two stabilizers: an experience-replay buffer that decorrelates samples, and a periodically-frozen target network that holds the regression target still. We derive the loss, give the full algorithm and the Atari pipeline, and then layer on Double DQN, the dueling split, prioritized replay, and the Rainbow combination.\n",{"path":4992,"title":4993,"module":4981,"summary":4994},"\u002Fdeep-learning\u002Freinforcement-learning\u002Fpolicy-gradients-and-actor-critic","Policy Gradients and Actor-Critic Methods","Value-based reinforcement learning learns what each state is worth and acts greedily; policy-gradient methods skip the detour and optimize a parameterized policy directly by ascending the gradient of expected return. The policy gradient theorem makes this tractable through the log-derivative trick, turning an intractable gradient of an expectation into an expectation of a gradient. REINFORCE realizes the idea but suffers high variance; baselines, the advantage function, and actor-critic learning reduce it, and trust-region methods (TRPO, PPO) keep each update from destroying the policy it just learned.\n",{"path":4996,"title":4997,"module":4981,"summary":4998},"\u002Fdeep-learning\u002Freinforcement-learning\u002Frl-from-human-feedback","Reinforcement Learning from Human Feedback","Many objectives we want from a model, that it be helpful and harmless, are hard to write down but easy to judge by comparison. RLHF turns that asymmetry into a training signal: fit a reward model to pairwise human preferences under the Bradley-Terry likelihood, then fine-tune the policy to maximize that reward under a KL penalty toward a reference. We derive the reward loss, the KL-regularized RL objective and its closed-form optimum, then show how DPO inverts that optimum to collapse the whole pipeline into one supervised log-sigmoid loss, and survey IPO, KTO, RLAIF, and GRPO.\n",{"path":5000,"title":5001,"module":6,"summary":6},"\u002Fdeep-learning","Deep Learning",{"path":5003,"title":5004,"module":2911,"summary":5005},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fequilibrium-state-variables-zeroth-law","Equilibrium, State Variables, and the Zeroth Law","Thermodynamics describes a many-body system by a handful of macroscopic variables and the equilibrium relations among them. This lesson fixes the vocabulary: systems and the walls that separate them, state variables versus path-dependent process quantities, quasi-static and reversible idealizations, and the zeroth law, whose transitivity of thermal equilibrium is what lets temperature exist as a number. The ideal-gas thermometer turns that number into a scale, and an equation of state ties the variables into a surface.\n",{"path":5007,"title":5008,"module":2911,"summary":5009},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Ffirst-law-heat-and-work","The First Law: Internal Energy, Heat, and Work","The first law is energy conservation for a system that exchanges energy as both heat and work. Internal energy is a state function with an exact differential; heat and work are path-dependent process quantities. This lesson states $\\d U=\\delta Q+\\delta W$, computes compression work as an area on the $P$–$V$ plane, defines the heat capacities $C_V$ and $C_P$ and the enthalpy that makes $C_P$ natural, and works the isothermal and adiabatic processes of an ideal gas, including the adiabat $PV^\\gamma=\\text{const}$.\n",{"path":5011,"title":5012,"module":2911,"summary":5013},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fsecond-law-entropy-and-the-carnot-bound","The Second Law, Carnot Cycles, and Entropy","The second law forbids the free conversion of heat into work. This lesson states the Kelvin and Clausius forms, proves them equivalent, and analyzes the Carnot cycle to get the efficiency bound $1-T_c\u002FT_h$. Carnot's theorem makes that bound universal and defines the thermodynamic temperature scale. The Clausius inequality $\\oint \\delta Q\u002FT\\le 0$ then constructs entropy as a state function, $\\d S=\\delta Q_{\\rm rev}\u002FT$, whose non-decrease in isolated systems is the arrow of time.\n",{"path":5015,"title":5016,"module":2911,"summary":5017},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fthermodynamic-potentials-and-maxwell-relations","Thermodynamic Potentials and Maxwell Relations","The fundamental relation $\\d U=T\\,\\d S-P\\,\\d V+\\mu\\,\\d N$ packages the first and second laws into one exact differential. Legendre transforms swap each conjugate pair to produce the Helmholtz, enthalpy, Gibbs, and grand potentials, each minimized under its own natural variables. Equality of mixed second partials of these potentials gives the Maxwell relations, which convert unmeasurable entropy derivatives into measurable ones from the equation of state.\n",{"path":5019,"title":5020,"module":2911,"summary":5021},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fstability-response-functions-and-the-third-law","Response Functions, Stability, and the Third Law","Response functions — heat capacities, compressibilities, thermal expansion — are the second derivatives of the potentials and the quantities an experiment actually measures. This lesson derives the general relation $C_P-C_V=TV\\alpha^2\u002F\\kappa_T$, shows that convexity of the potentials forces the stability conditions $C_V>0$ and $\\kappa_T>0$, and states the third law: entropy approaches a constant as $T\\to0$, so heat capacities and expansion coefficients vanish there and absolute zero is unattainable.\n",{"path":5023,"title":5024,"module":5025,"summary":5026},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fclassical-statistics-and-equipartition","Classical Statistics and Equipartition","Microstates, Phase Space, and Statistical Entropy","A liter of gas holds on the order of a trillion trillion molecules, far too many to track by their equations of motion. Classical statistical mechanics replaces the trajectories with a single probability law, the Boltzmann distribution, and reads the measurable properties of matter off it: the Maxwell speed distribution, the average energy per degree of freedom, and the heat capacities of gases and solids — together with the low-temperature failures that forced the quantum revision.\n",{"path":5028,"title":5029,"module":5025,"summary":5030},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fphase-space-and-liouvilles-theorem","Phase Space, Trajectories, and Liouville's Theorem","A classical system of N particles is one point in a 6N-dimensional phase space, and its evolution is a single trajectory driven by Hamilton's equations. This lesson builds that geometric picture, introduces the phase-space density of an ensemble, and proves Liouville's theorem: the density is carried by the flow as an incompressible fluid, so phase-space volume is conserved. The stationary densities of equilibrium follow as functions of the conserved quantities alone.\n",{"path":5032,"title":5033,"module":5025,"summary":5034},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fensembles-and-the-equal-probability-postulate","Ensembles and the Postulate of Equal a Priori Probabilities","An ensemble is a probability distribution over the microstates of a system. This lesson states the single postulate on which equilibrium statistical mechanics rests — that an isolated system in equilibrium is equally likely to be in any of its accessible microstates — and works out its consequences: the accessible phase-space volume, the overwhelming dominance of the most probable macrostate as the particle number grows, and the ergodic hypothesis that lets a time average be replaced by an ensemble average.\n",{"path":5036,"title":5037,"module":5025,"summary":5038},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fstatistical-entropy-boltzmann-and-gibbs","Statistical Entropy: Boltzmann and Gibbs","Entropy is the logarithm of the number of accessible microstates. This lesson builds the two statistical entropies — Boltzmann's S = k ln Omega for an isolated system and Gibbs's S = -k sum p ln p for any ensemble — proves they agree for a uniform distribution, and connects both to Shannon's measure of missing information. The second law emerges as the drift toward maximum multiplicity, and maximizing the Gibbs entropy under constraints previews the canonical distribution.\n",{"path":5040,"title":5041,"module":5042,"summary":5043},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fmicrocanonical-ensemble-and-entropy","The Microcanonical Ensemble and Statistical Entropy","The Microcanonical Ensemble","An isolated system holds its energy, volume, and particle number fixed, and the fundamental postulate assigns equal probability to every microstate on its energy shell. This lesson builds the microcanonical distribution, defines the enclosed phase-space volume $\\Gamma(E)$, the surface density of states $\\omega(E)=\\d\\Gamma\u002F\\d E$, and the shell count $\\Omega(E)$, shows their logarithms agree to $O(\\ln N)$ for large $N$, and reads the Boltzmann entropy $S=k\\ln\\Omega$ off the count. The measure factors $h^{3N}$ and $N!$ enter here and make $S$ extensive.\n",{"path":5045,"title":5046,"module":5042,"summary":5047},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fequilibrium-conditions-temperature-pressure-chemical-potential","Thermal, Mechanical, and Diffusive Equilibrium","Two isolated subsystems that can exchange energy, volume, or particles reach equilibrium at the partition that maximizes their combined entropy. Setting the derivative of the total entropy to zero identifies the statistical definitions $1\u002FT=(\\partial S\u002F\\partial E)$, $P\u002FT=(\\partial S\u002F\\partial V)$, and $-\\mu\u002FT=(\\partial S\u002F\\partial N)$, shows heat flows from hot to cold as an entropy increase, and recovers the fundamental relation $\\d S=(\\d E+P\\,\\d V-\\mu\\,\\d N)\u002FT$ from pure counting.\n",{"path":5049,"title":5050,"module":5042,"summary":5051},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fideal-gas-phase-space-and-the-sackur-tetrode-entropy","The Ideal Gas, Phase-Space Volume, and the Sackur–Tetrode Entropy","The monatomic ideal gas is the first system whose microcanonical count can be done in closed form. The momentum integral is the volume of a $3N$-dimensional ball of radius $\\sqrt{2mE}$, the configuration integral is $V^N$, and together they give the Sackur–Tetrode entropy $S=Nk[\\ln(V\u002FN\\lambda^3)+5\u002F2]$ with the thermal wavelength $\\lambda=h\u002F\\sqrt{2\\pi mkT}$. The formula matches the measured entropy of helium, fixes the classical regime $n\\ll n_Q$, and shows why the $N!$ is needed for extensivity.\n",{"path":5053,"title":5054,"module":5042,"summary":5055},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Ftwo-state-systems-paramagnets-and-negative-temperature","Two-State Systems, Paramagnets, and Negative Temperature","The ideal two-state paramagnet has a multiplicity counted by the binomial coefficient, an entropy that is an inverted dome in the energy, and a temperature read from the slope $1\u002FT=\\partial S\u002F\\partial E$. Because the energy is bounded above, the slope changes sign past the entropy maximum: a population-inverted spin system has a negative absolute temperature, which is hotter than any positive temperature. Nuclear-spin experiments and lasers realize the inverted state.\n",{"path":5057,"title":5058,"module":5059,"summary":5060},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fcanonical-ensemble-and-the-boltzmann-distribution","The Canonical Ensemble and the Boltzmann Distribution","The Canonical Ensemble","A system held at fixed temperature by contact with a heat reservoir is described by the canonical ensemble. Expanding the reservoir entropy to first order in the system energy gives the Boltzmann distribution $p_i\\propto e^{-\\beta E_i}$, and the same law follows from maximizing the Gibbs entropy at fixed mean energy. Both routes identify $\\beta=1\u002Fk_BT$ and fix the probability of every microstate from the temperature alone.\n",{"path":5062,"title":5063,"module":5059,"summary":5064},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fpartition-function-and-the-helmholtz-free-energy","The Partition Function and the Helmholtz Free Energy","The normalizing sum of the Boltzmann distribution, the partition function $Z=\\sum_i e^{-\\beta E_i}$, is a generating function for the thermodynamics. The mean energy is $-\\partial\\ln Z\u002F\\partial\\beta$, and the Gibbs entropy of the canonical distribution collapses to the bridge relation $F=-k_BT\\ln Z$. From $F$ every thermodynamic quantity follows by differentiation, and $Z$ factorizes over independent degrees of freedom.\n",{"path":5066,"title":5067,"module":5059,"summary":5068},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fenergy-fluctuations-and-ensemble-equivalence","Energy Fluctuations and the Equivalence of Ensembles","In the canonical ensemble the energy fluctuates, and the second derivative of $\\ln Z$ gives its variance. The fluctuation–response identity $\\langle\\Delta E^2\\rangle = k_BT^2C_V$ ties the spread of the energy to the heat capacity, and the relative fluctuation falls as $1\u002F\\sqrt{N}$. In the thermodynamic limit the canonical energy distribution is a sharp spike, and the canonical and microcanonical ensembles predict the same thermodynamics.\n",{"path":5070,"title":5071,"module":5059,"summary":5072},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fthe-einstein-solid-and-harmonic-systems","Harmonic Systems: The Einstein Solid and Vibrational Heat Capacity","A quantum harmonic oscillator has a geometric partition function summed in closed form, giving a mean energy $\\hbar\\omega(\\tfrac12+\\langle n\\rangle)$ with the Bose occupation factor. Modeling a solid as $3N$ independent oscillators yields a heat capacity that rises from zero and saturates at the Dulong–Petit value $3Nk_B$. The Einstein temperature sets the crossover, and the model's exponential low-temperature falloff, too steep against the observed $T^3$, motivates the Debye theory.\n",{"path":5074,"title":5075,"module":5059,"summary":5076},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fparamagnetism-and-the-schottky-anomaly","Paramagnetism, Two-Level Systems, and the Schottky Anomaly","A magnetic moment in a field is a two-level system whose partition function is a hyperbolic cosine. The magnetization of a spin-$\\tfrac12$ paramagnet is $N\\mu\\tanh(\\mu B\u002Fk_BT)$, generalizing to the Brillouin function for spin $J$; it gives Curie's law $\\chi\\propto 1\u002FT$ at high temperature and saturates at low temperature. A finite level gap produces the Schottky heat-capacity peak, and the temperature dependence of the entropy on the field is the basis of adiabatic demagnetization cooling.\n",{"path":5078,"title":5079,"module":5080,"summary":5081},"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fideal-gas-partition-function-and-the-gibbs-paradox","The Ideal Gas Partition Function and the Gibbs Paradox","The Classical Ideal Gas","The classical monatomic ideal gas built from the partition function. The single-particle sum is $z_1=V\u002F\\lambda^3$ with the thermal de Broglie wavelength $\\lambda$; the $N$-particle partition function is $z_1^N\u002FN!$, and the $N!$ is forced by indistinguishability. From $Z$ the ideal-gas law, $U=\\tfrac32 Nk_BT$, and the Sackur–Tetrode entropy follow. The $N!$ makes the entropy extensive and resolves the Gibbs paradox: mixing identical gases produces no entropy change.\n",{"path":5083,"title":5084,"module":5080,"summary":5085},"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fequipartition-and-the-virial-theorem","Equipartition and the Virial Theorem","The equipartition theorem derived from the canonical ensemble: every phase-space coordinate that enters the Hamiltonian quadratically carries a mean energy $\\tfrac12 k_BT$. The generalized form $\\langle x_i\\,\\partial H\u002F\\partial x_j\\rangle = k_BT\\,\\delta_{ij}$ contains equipartition and the classical virial theorem as special cases. Equipartition fixes the classical heat capacities, fails by quantum freeze-out when a level gap exceeds $k_BT$, and shifts for a relativistic gas whose energy is linear rather than quadratic in momentum.\n",{"path":5087,"title":5088,"module":5080,"summary":5089},"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fmolecular-gases-rotation-and-vibration","Molecular Gases: Rotational and Vibrational Degrees of Freedom","The internal partition function of a diatomic gas factorizes into translational, rotational, vibrational, and electronic parts. The rigid rotor gives a rotational temperature $\\theta_{\\rm rot}$; the harmonic bond gives a vibrational temperature $\\theta_{\\rm vib}$. Each mode contributes to the heat capacity only above its characteristic temperature, producing the diatomic $C_V$ staircase from $\\tfrac32 R$ to $\\tfrac52 R$ to $\\tfrac72 R$. Homonuclear molecules carry a symmetry number, and hydrogen splits into ortho and para species.\n",{"path":5091,"title":5092,"module":5093,"summary":5094},"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fgrand-canonical-ensemble-and-the-grand-partition-function","The Grand Canonical Ensemble","Grand Canonical Ensemble","When a system exchanges both energy and particles with a reservoir, the reservoir fixes its temperature and its chemical potential. Expanding the reservoir entropy to first order in the exchanged energy and particle number gives the Gibbs factor $e^{-\\beta(E-\\mu N)}$, and summing it over every microstate of every particle number gives the grand partition function $\\Xi$. The grand potential $\\Phi = -k_BT\\ln\\Xi = -PV$ generates the mean particle number, energy, entropy, and pressure by differentiation.\n",{"path":5096,"title":5097,"module":5093,"summary":5098},"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fchemical-potential-fugacity-and-number-fluctuations","Chemical Potential, Fugacity, and Number Fluctuations","The chemical potential is the energy to add one particle at fixed entropy and volume, equal to the slope of the free energy in the particle number. For the classical ideal gas $\\mu=k_BT\\ln(n\\lambda^3)$ is large and negative, and the fugacity $z=n\\lambda^3$ is small. The grand ensemble makes the particle number fluctuate; its variance $\\langle\\Delta N^2\\rangle=k_BT(\\partial N\u002F\\partial\\mu)$ equals $k_BT\\,N^2\\kappa_T\u002FV$, tying density fluctuations to the isothermal compressibility. Equality of $\\mu$ is the condition for diffusive equilibrium and phase coexistence.\n",{"path":5100,"title":5101,"module":5093,"summary":5102},"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fensemble-summary-and-the-thermodynamic-web","The Three Ensembles and the Thermodynamic Web","The microcanonical, canonical, and grand canonical ensembles hold different variables fixed and generate different potentials — the entropy $S$, the Helmholtz free energy $F$, and the grand potential $\\Phi$ — linked by Legendre transforms that trade each fixed variable for its conjugate. Each successive ensemble lets one more quantity fluctuate. In the thermodynamic limit the three agree, the relative fluctuations vanishing as $1\u002F\\sqrt{N}$; the ideal gas gives the same equation of state in all three. The choice of ensemble is a matter of convenience, set by which sum is easiest.\n",{"path":5104,"title":5105,"module":5106,"summary":5107},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fquantum-statistics-bose-einstein-and-fermi-dirac","Quantum Statistics — Bose-Einstein and Fermi-Dirac","Quantum Statistics","Quantum particles of the same kind are genuinely indistinguishable: no label survives an overlap of their wave functions. Counting states with that constraint replaces the Boltzmann distribution with two quantum laws — the Bose-Einstein distribution for integer-spin particles, which clump into shared states, and the Fermi-Dirac distribution for half-integer-spin particles, which exclude one another. Both reduce to Boltzmann in the dilute, hot limit, and a de Broglie criterion says exactly when.\n",{"path":5109,"title":5110,"module":5106,"summary":5111},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fderiving-the-quantum-distributions","Deriving the Quantum Distributions from the Grand Ensemble","The Bose-Einstein and Fermi-Dirac distributions follow from one observation: in the occupation-number representation the single-particle modes are independent, so the grand partition function factorizes into one factor per mode. A boson mode sums a geometric series over all occupancies; a fermion mode sums two terms. Differentiating each factor gives the mean occupation $1\u002F(e^{\\beta(\\varepsilon-\\mu)}\\mp 1)$, the Maxwell-Boltzmann limit when occupancies are small, and the occupation fluctuations that distinguish bunching from anti-bunching.\n",{"path":5113,"title":5114,"module":5106,"summary":5115},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fthe-classical-limit-and-quantum-concentration","The Classical Limit and Quantum Concentration","When every single-particle level is nearly empty, both quantum distributions collapse to the Maxwell-Boltzmann form, and the fugacity equals the ratio of the number density to the quantum concentration $n_Q = 1\u002F\\lambda^3$. The gas is classical when $n \\ll n_Q$, degenerate when $n \\gtrsim n_Q$. The chemical potential is large and negative in the classical regime and rises through zero as the gas degenerates. The leading quantum correction to the ideal-gas law is a second virial term that lowers the pressure for bosons and raises it for fermions — a statistical attraction and repulsion with no interaction behind it.\n",{"path":5117,"title":5118,"module":5106,"summary":5119},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fideal-quantum-gases-general-framework","Ideal Quantum Gases: The General Framework","Every ideal quantum gas is handled by one calculation. The sum over single-particle modes becomes an energy integral weighted by a density of states $g(\\varepsilon)\\propto\\varepsilon^{1\u002F2}$, and the number and pressure reduce to the Bose and Fermi functions $g_\\nu(z)$ and $f_\\nu(z)$ of the fugacity. An integration by parts fixes $PV=\\tfrac23 U$ for a nonrelativistic gas and $PV=\\tfrac13 U$ for an ultrarelativistic one, independent of statistics. Specializing the density of states and the chemical potential then produces the photon gas, phonons, the Bose gas, and the Fermi gas as four branches of the same framework.\n",{"path":5121,"title":5122,"module":5123,"summary":5124},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-and-the-fermion-gas","Bose-Einstein Condensation and the Fermion Gas","Bosonic Systems","Below a critical temperature a boson gas drops a macroscopic fraction of its particles into the single ground state — Bose-Einstein condensation, the mechanism behind superfluid helium and the dilute-atom condensates cooled to nanokelvin. The same statistics applied to a photon gas reproduces Planck's blackbody spectrum. Fermions do the opposite: forbidden from sharing states, they fill every level up to the Fermi energy, and that filled sea governs the electrons in metals and the pressure that holds up a white dwarf.\n",{"path":5126,"title":5127,"module":5123,"summary":5128},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthe-photon-gas-and-plancks-radiation-law","The Photon Gas and Planck's Radiation Law","Electromagnetic radiation in equilibrium with cavity walls is a gas of non-conserved bosons, and non-conservation forces the chemical potential to zero. Counting standing-wave modes with two polarizations and weighting each by the Bose occupation gives the Planck spectral energy density. Its low-frequency tail reproduces the classical Rayleigh-Jeans law and the ultraviolet catastrophe; the Bose factor cuts the divergence off at high frequency and the peak obeys Wien's displacement law.\n",{"path":5130,"title":5131,"module":5123,"summary":5132},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fblackbody-thermodynamics-and-radiation-pressure","Blackbody Thermodynamics and Radiation Pressure","Integrating the Planck spectrum over all frequencies gives the total energy density proportional to the fourth power of temperature — the Stefan-Boltzmann law — and the isotropy of a relativistic gas fixes the radiation pressure at one third of the energy density. From the free energy follow the entropy and heat capacity, both proportional to T cubed, and the adiabatic law for radiation. The results govern the pressure inside stars and the cooling of the cosmic microwave background as the universe expands.\n",{"path":5134,"title":5135,"module":5123,"summary":5136},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fphonons-and-the-debye-model","Phonons and the Debye Model","The vibrations of a crystal lattice are quantized into phonons — bosons of zero chemical potential, counted exactly like cavity photons but with three polarizations, a finite sound speed, and a total of 3N modes. The Debye model replaces the true dispersion by a linear one cut off at a frequency that enforces that count. It gives the correct low-temperature T-cubed heat capacity the Einstein model missed and recovers the Dulong-Petit value at high temperature.\n",{"path":5138,"title":5139,"module":5123,"summary":5140},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-derived","Bose-Einstein Condensation Derived","For a gas of conserved bosons the excited states can hold only a finite number of particles at fixed temperature, set by the Bose function at unit fugacity. When the total exceeds that ceiling the surplus collapses into the single ground state, which the continuum density-of-states integral misses and which must be restored by hand. This fixes the critical temperature, the condensate fraction, and the fact that a uniform gas condenses only in three or more dimensions.\n",{"path":5142,"title":5143,"module":5123,"summary":5144},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthermodynamics-of-the-bose-gas-and-superfluidity","Thermodynamics of the Bose Gas and Superfluidity","The energy and pressure of the ideal Bose gas follow from the Bose function at the order above the density, and below the critical temperature the pressure depends on temperature alone because the condensate carries none. The heat capacity rises to a cusp at the transition. Real superfluid helium departs from the ideal gas because interactions matter: the Landau criterion ties frictionless flow to the phonon-roton excitation spectrum, and the two-fluid model carries a second sound.\n",{"path":5146,"title":5147,"module":5148,"summary":5149},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fthe-ideal-fermi-gas-at-zero-temperature","The Ideal Fermi Gas at Zero Temperature","Degenerate Fermi Gas","At absolute zero a gas of non-interacting fermions fills every single-particle state up to the Fermi energy and leaves the rest empty, a filled Fermi sphere in momentum space. This lesson computes the Fermi momentum, energy, and temperature from the density, the density of states, the total ground-state energy, and the degeneracy pressure that grows as $n^{5\u002F3}$. Numerical Fermi energies for metals set the scale: they are electron-volts, so room temperature is deep in the degenerate regime.\n",{"path":5151,"title":5152,"module":5148,"summary":5153},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fsommerfeld-expansion-and-electrons-in-metals","The Sommerfeld Expansion and Electrons in Metals","Turning on a small temperature blurs the Fermi step over a shell of width $k_BT$ around $\\epsilon_F$. The Sommerfeld expansion turns integrals over the Fermi function into a power series in $(k_BT\u002F\\epsilon_F)^2$, giving the shift of the chemical potential and a heat capacity linear in $T$. This resolves the old puzzle of the missing electronic heat capacity, predicts the combined $C=\\gamma T+AT^3$ of a metal, and gives the temperature-independent Pauli paramagnetism of the electron gas.\n",{"path":5155,"title":5156,"module":5148,"summary":5157},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fwhite-dwarfs-and-the-chandrasekhar-limit","White Dwarfs and the Chandrasekhar Limit","A white dwarf is held up against its own gravity by the degeneracy pressure of its electrons. Balancing that pressure against gravity gives a mass-radius relation $R\\propto M^{-1\u002F3}$: heavier white dwarfs are smaller and denser. As the density rises the electrons turn relativistic, the pressure softens from $n^{5\u002F3}$ to $n^{4\u002F3}$, and the star can no longer support itself above a critical mass. This lesson derives that Chandrasekhar mass, about $1.4\\,M_\\odot$, and what lies beyond it.\n",{"path":5159,"title":5160,"module":5148,"summary":5161},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fneutron-stars-and-nuclear-matter","Neutron Stars and Dense Matter","When a collapsing core passes nuclear density, electron capture converts the matter to neutrons and their degeneracy pressure takes over. The same balance that fixes a white dwarf, rescaled by the neutron mass, gives a neutron star of a few solar masses in a ten-kilometre radius. General relativity is no longer a correction: the Tolman-Oppenheimer-Volkoff equation replaces the Newtonian balance and sets a maximum mass around two solar masses. This lesson rescales the Fermi-gas argument, states where it breaks, and places the compact objects in one stability sequence.\n",{"path":5163,"title":5164,"module":5165,"summary":5166},"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-cluster-expansion-and-virial-coefficients","The Cluster Expansion and Virial Coefficients","Interacting Gases","A real gas departs from $PV=Nk_BT$ because its molecules interact. The configuration integral factors through the Mayer function $f_{ij}=e^{-\\beta u_{ij}}-1$, and expanding it in powers of density produces the virial expansion $PV\u002FNk_BT = 1 + B_2(T)n + B_3(T)n^2 + \\cdots$. The second virial coefficient $B_2(T)=-\\tfrac12\\int f\\,\\d^3r$ is a single integral over the pair potential; it is positive for a hard core, negative for an attractive well, and vanishes at the Boyle temperature where the two balance.\n",{"path":5168,"title":5169,"module":5165,"summary":5170},"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-van-der-waals-gas-and-liquid-gas-coexistence","The van der Waals Gas and Liquid-Gas Coexistence","Resumming the second virial coefficient $B_2=b-a\u002Fk_BT$ into an equation of state gives the van der Waals model $(P+a\u002Fv^2)(v-b)=k_BT$, the simplest theory of a fluid that condenses. Below the critical temperature its isotherms develop a mechanically unstable loop; the Maxwell equal-area construction replaces the loop with a coexistence tie line. The critical point sits at $v_c=3b$, $k_BT_c=8a\u002F27b$, $P_c=a\u002F27b^2$, and the model predicts universal but incorrect critical exponents because it ignores fluctuations.\n",{"path":5172,"title":5173,"module":5165,"summary":5174},"\u002Fstatistical-mechanics\u002Finteractions\u002Fquantum-gases-with-interactions-and-exchange","Quantum Gases with Interactions and Statistical Exchange","A quantum gas has a nonzero second virial coefficient even with no forces between the particles: symmetrization alone produces an effective statistical interaction, attractive for bosons and repulsive for fermions, with range the thermal wavelength $\\lambda$. This lesson derives that exchange contribution $B_2=\\mp\\lambda^3\u002F2^{5\u002F2}g$, writes it as a statistical potential $v_s(r)=-k_BT\\ln(1\\pm e^{-2\\pi r^2\u002F\\lambda^2})$, and shows how real interactions add on top through the Beth-Uhlenbeck phase-shift formula, reducing at low temperature to a single scattering length.\n",{"path":5176,"title":5177,"module":5178,"summary":5179},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fphases-coexistence-and-classification","Phases, Coexistence, and the Classification of Transitions","Phase Transitions","A phase transition is a point where the free energy of a substance loses analyticity, so a small change in temperature or pressure produces a qualitative change of state. This lesson maps the coexistence curves of a pure substance, derives the Clausius-Clapeyron relation between the slope of a coexistence line and its latent heat, and separates first-order transitions (discontinuous entropy and density) from continuous ones (a vanishing order parameter and divergent response). The Ehrenfest scheme, the order parameter, and the triple and critical points fix the vocabulary the rest of the module builds on.\n",{"path":5181,"title":5182,"module":5178,"summary":5183},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-ising-model-and-exact-solutions","The Ising Model and Exact Results","The Ising model reduces cooperative ordering to spins on a lattice coupled to their neighbors, and the same Hamiltonian describes uniaxial magnets, the liquid-gas critical point through the lattice gas, and binary alloys. This lesson solves the one-dimensional chain exactly with the transfer matrix, shows by a domain-wall argument why one dimension has no ordered phase at any positive temperature, contrasts the survival of order in two dimensions, and quotes Onsager's exact two-dimensional results: the critical temperature, the logarithmically divergent heat capacity, and the magnetization exponent one eighth.\n",{"path":5185,"title":5186,"module":5178,"summary":5187},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fmean-field-theory-and-the-weiss-model","Mean-Field Theory and Spontaneous Symmetry Breaking","Mean-field theory replaces the neighbors of each spin by their average, turning the interacting Ising model into a single spin in a self-consistent field. The resulting equation m = tanh(beta J z m + beta h) has only the zero solution above a critical temperature and gains a nonzero root below it, giving spontaneous magnetization and a mean-field critical temperature k T_c = J z. The Bragg-Williams free energy turns single-welled above T_c and double-welled below, the picture of spontaneous symmetry breaking. The approximation is exact in high dimension and fails below the upper critical dimension four, quantified by the Ginzburg criterion.\n",{"path":5189,"title":5190,"module":5178,"summary":5191},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fcritical-exponents-and-landau-theory","Critical Exponents, Scaling, and Landau Theory","Near a continuous transition every singular quantity follows a power law in the reduced temperature, and the exponents alpha, beta, gamma, delta, nu, and eta encode the transition more sharply than T_c itself. Landau theory expands the free energy in the order parameter and delivers the mean-field exponents in a few lines. They disagree with experiment and with the exact two-dimensional Ising values, but the exponents are not independent: the scaling relations of Rushbrooke, Widom, Fisher, and Josephson tie them together, and the correlation length sets the length scale that organizes universality classes.\n",{"path":5193,"title":5194,"module":5178,"summary":5195},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-renormalization-group-idea","Scaling and the Renormalization-Group Idea","At a critical point fluctuations exist on every length scale, so the system looks the same after coarse-graining. The renormalization group makes this self-similarity a computation: group spins into blocks, integrate out the short scales, and track how the couplings change. The transformation has fixed points, and the flow near a critical fixed point separates relevant couplings that grow from irrelevant ones that shrink, which is why only dimension and symmetry survive to set the exponents. The one-dimensional Ising decimation carries the whole scheme through in closed form and reproduces the absence of a finite-temperature transition.\n",{"path":5197,"title":5198,"module":5199,"summary":5200},"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fthermodynamic-fluctuations-and-response","Thermodynamic Fluctuations and Response Functions","Fluctuations and Response","Thermodynamic variables are sharp only on average; a macroscopic system in equilibrium fluctuates about its mean values. Einstein inverted Boltzmann's $S=k_B\\ln\\Omega$ into a Gaussian probability for a fluctuation, $w\\propto e^{\\Delta S\u002Fk_B}$, and the second moments it predicts reproduce the response functions: $\\langle\\Delta E^2\\rangle=k_BT^2C_V$, $\\langle\\Delta V^2\\rangle=k_BTV\\kappa_T$, $\\langle\\Delta M^2\\rangle=k_BT\\chi_T$. The variances diverge where the responses diverge, at a critical point, producing critical opalescence and the breakdown of the thermodynamic description.\n",{"path":5202,"title":5203,"module":5199,"summary":5204},"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fbrownian-motion-and-the-langevin-equation","Brownian Motion and the Langevin Equation","A pollen grain in water executes a random walk driven by molecular collisions. Einstein tied its diffusion constant to its mobility, $D=\\mu_{\\mathrm{mob}}k_BT$, turning a visible motion into a measurement of Avogadro's number. The Langevin equation splits the collisions into a systematic drag and a random force whose strength is fixed by the drag through $\\langle\\xi(t)\\xi(t')\\rangle=2\\gamma k_BT\\,\\delta(t-t')$ — the first fluctuation–dissipation relation. The mean-square displacement grows ballistically at short times and linearly, $\\langle r^2\\rangle=2dDt$, at long times, and the Stokes–Einstein relation $D=k_BT\u002F6\\pi\\eta a$ closes the loop to Perrin's experiments.\n",{"path":5206,"title":5207,"module":5199,"summary":5208},"\u002Fstatistical-mechanics\u002Ffluctuations\u002Flinear-response-and-the-fluctuation-dissipation-theorem","Linear Response and the Fluctuation-Dissipation Theorem","A system driven by a weak external field responds through a generalized susceptibility $\\chi(\\omega)$ whose imaginary part measures dissipation. The Wiener–Khinchin theorem makes the power spectrum of equilibrium fluctuations the Fourier transform of their correlation function, and the fluctuation–dissipation theorem ties the two together: $S_x(\\omega)=(2k_BT\u002F\\omega)\\,\\chi''(\\omega)$, so the spectrum of spontaneous fluctuations is fixed by the dissipative response. The Johnson–Nyquist noise of a resistor, $\\langle V^2\\rangle=4k_BTR\\,\\Delta f$, is the canonical example, and Onsager reciprocity closes the subject.\n",{"path":5210,"title":5211,"module":6,"summary":6},"\u002Fstatistical-mechanics","Statistical Mechanics",{"path":5213,"title":5214,"module":5215,"summary":5216},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fbonding-mechanisms","Bonding Mechanisms","Molecules and Chemical Bonding","A molecule forms when the total energy of two atoms drops below the energy of the separated pair. This lesson works through the four mechanisms that produce that minimum: the ionic bond from charge transfer, the covalent bond from shared electron wave functions, the metallic bond, and the weak dipole-dipole and hydrogen bonds, computing bond lengths and dissociation energies for NaCl, H₂, and H₂⁺.\n",{"path":5218,"title":5219,"module":5215,"summary":5220},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fmolecular-orbitals-and-h2-plus","The Molecular-Orbital Method and H₂⁺","The hydrogen molecule ion is the two-center problem that fixes the language of chemical bonding. This lesson builds the molecular orbital as a linear combination of atomic orbitals, minimizes the energy through the variational secular equation, and reduces the result to three two-center integrals: the overlap, the Coulomb term, and the exchange (resonance) integral. The bonding and antibonding levels, their potential-energy curves, and the charge piled between the nuclei follow from those integrals.\n",{"path":5222,"title":5223,"module":5215,"summary":5224},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fhydrogen-molecule-and-exchange","The Hydrogen Molecule, Exchange, and Hybridization","Adding the second electron turns the one-electron ion into the two-electron hydrogen molecule, where electron-electron repulsion and the Pauli principle govern the bond. This lesson contrasts the Heitler-London valence-bond and molecular-orbital wave functions, derives the singlet-triplet splitting as an exchange energy, shows why naive molecular orbitals fail at dissociation, and builds the sp, sp², and sp³ hybrids that fix the directed geometry of covalent bonds.\n",{"path":5226,"title":5227,"module":5215,"summary":5228},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fvan-der-waals-forces","Van der Waals Forces","The bond of last resort acts between all atoms, even closed-shell noble gases with no permanent moment. This lesson separates the three van der Waals contributions — Keesom orientation, Debye induction, and London dispersion — derives the London 1\u002Fr⁶ attraction from the coupled-oscillator and second-order perturbation pictures, and assembles the Lennard-Jones potential to compute the equilibrium spacing and cohesive energy of the noble-gas crystals, argon in particular.\n",{"path":5230,"title":5231,"module":5232,"summary":5233},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Frotational-vibrational-spectra","Rotational and Vibrational Spectra of Molecules","Molecular Spectra","A diatomic molecule stores energy in three well-separated ledgers: electronic, vibrational, and rotational. Quantizing the rigid rotor gives levels spaced as ℓ(ℓ+1); quantizing the bond as a harmonic oscillator gives equally spaced vibrational levels. Their combination produces the P and R branches of an infrared absorption band, from which the bond length and force constant are read directly.\n",{"path":5235,"title":5236,"module":5232,"summary":5237},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Fanharmonicity-and-rovibrational-structure","Anharmonicity and Rovibrational Structure","The rigid rotor and harmonic oscillator are first approximations. A real bond follows the Morse potential, whose levels converge toward dissociation; a real rotor stretches centrifugally; and vibration couples to rotation, so the rotational constant depends on the vibrational level. This lesson works out the anharmonic and centrifugal corrections, the Birge-Sponer route to the dissociation energy, the isotope shift, and the thermal band envelope.\n",{"path":5239,"title":5240,"module":5232,"summary":5241},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Framan-and-electronic-bands","Raman Scattering and Electronic Bands","Not every vibration absorbs in the infrared. Raman scattering reaches modes that modulate the polarizability, giving Stokes and anti-Stokes lines whose intensity ratio measures temperature, and the mutual-exclusion rule pairs it with infrared absorption. Electronic transitions add the vibronic structure of band spectra, governed by the Franck-Condon principle, and the radiative fates of an excited state are sorted by the Jablonski diagram into fluorescence and phosphorescence.\n",{"path":5243,"title":5244,"module":5232,"summary":5245},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Flasers-and-masers","Lasers, Masers, and Stimulated Emission","Einstein's three radiative processes — absorption, spontaneous emission, and stimulated emission — and the coefficients that relate them. Stimulated emission produces coherent photons, and inverting the level populations turns it into net amplification. We build the ruby three-level laser and the helium-neon four-level laser, and show why the fourth level makes inversion easy.\n",{"path":5247,"title":5248,"module":5249,"summary":5250},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fstructure-of-solids","The Structure of Solids","Crystal Structure","A crystal is a unit cell repeated in three dimensions. We classify the common cubic lattices, compute the Coulomb energy of an ionic crystal through the Madelung constant, and show how the divergent naive lattice sum is tamed by cubic shells. The cohesive energy that results predicts melting points and connects the diatomic bond of an earlier lesson to the bulk solid.\n",{"path":5252,"title":5253,"module":5249,"summary":5254},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fbravais-lattices-and-crystal-systems","Bravais Lattices, Bases, and Crystal Structures","A crystal is a Bravais lattice decorated by a basis. This lesson separates the two, builds primitive and Wigner-Seitz cells, enumerates the seven crystal systems and fourteen Bravais lattices, and fixes the language of point and space groups. Miller indices label planes and directions, and the packing fractions of the close-packed, cubic, and diamond structures follow from the geometry.\n",{"path":5256,"title":5257,"module":5249,"summary":5258},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Freciprocal-lattice-and-brillouin-zones","The Reciprocal Lattice and Brillouin Zones","Every periodic crystal has a dual lattice in wavevector space. This lesson defines the reciprocal lattice through the condition b_i dot a_j equals two pi delta, derives its properties, shows the reciprocal of fcc is bcc, links reciprocal vectors to families of lattice planes, and builds the first Brillouin zone as the Wigner-Seitz cell of the reciprocal lattice, including the higher zones.\n",{"path":5260,"title":5261,"module":5249,"summary":5262},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fdiffraction-and-structure-factors","X-ray and Neutron Diffraction","A crystal diffracts radiation whose wavelength matches its atomic spacing. This lesson derives the Bragg condition, the equivalent Laue condition 2k dot G equals G squared, and the Ewald-sphere construction, then computes the geometric structure factor that produces systematic absences for bcc and fcc, the atomic form factor, and the powder method. It closes on why neutrons and electrons complement X-rays.\n",{"path":5264,"title":5265,"module":5266,"summary":5267},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonon-dispersion","The Harmonic Crystal and Phonon Dispersion","Lattice Dynamics","Atoms in a crystal vibrate about their equilibrium sites, and expanding the potential to second order turns the whole lattice into a set of coupled harmonic oscillators. This lesson sets up the harmonic approximation and the dynamical matrix, solves the monatomic linear chain for its dispersion omega(k) = 2 sqrt(K\u002FM) times the absolute sine of ka over two, explains why wavevectors outside the first Brillouin zone are redundant, and extends the chain to two atoms per cell to produce acoustic and optical branches with a frequency gap.\n",{"path":5269,"title":5270,"module":5266,"summary":5271},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonons-quantization-and-dos","Phonons, Density of States, and Crystal Momentum","Quantizing the normal modes of a harmonic crystal turns each vibrational mode into a quantum oscillator whose excitations are phonons. This lesson counts phonons with Bose-Einstein statistics, defines crystal momentum and the normal versus Umklapp distinction in momentum conservation, builds the density of states with its van Hove singularities, and shows how inelastic neutron scattering measures a dispersion curve point by point.\n",{"path":5273,"title":5274,"module":5266,"summary":5275},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fdebye-einstein-heat-capacity","Thermal Properties — Einstein and Debye Models","The lattice heat capacity follows the classical Dulong-Petit value at high temperature but collapses toward zero as T approaches zero, a purely quantum effect. This lesson derives that behavior from the Einstein model of a single frequency, then the Debye model of a linear phonon spectrum with a cutoff, obtaining the Debye T-cubed law at low temperature and the Debye interpolation across all temperatures, and closes with thermal expansion and the Gruneisen parameter.\n",{"path":5277,"title":5278,"module":5266,"summary":5279},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fanharmonicity-and-thermal-transport","Anharmonicity, Thermal Expansion, and Heat Conduction","A perfectly harmonic crystal neither expands when heated nor resists heat flow. Both effects come from the cubic and higher terms the harmonic approximation discards. This lesson derives thermal expansion from an asymmetric interatomic potential, treats phonon-phonon scattering as the decay channel these terms open, shows why Umklapp processes are what make lattice thermal conductivity finite, and traces the temperature dependence of the conductivity and the phonon mean free path.\n",{"path":5281,"title":5282,"module":5283,"summary":5284},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ffree-electron-gas-and-conduction","Conduction and the Free-Electron Gas","Free-Electron Fermi Gas","Drude's classical free-electron model gets Ohm's law right but the resistivity, its temperature dependence, and the heat capacity wrong. Replacing the Maxwell-Boltzmann distribution with the Fermi-Dirac distribution and treating electron-lattice collisions as wave scattering repairs all three: the Fermi energy, Fermi speed, and a mean free path set by thermal lattice vibrations.\n",{"path":5286,"title":5287,"module":5283,"summary":5288},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fsommerfeld-model-and-heat-capacity","The Sommerfeld Model: Ground State and Heat Capacity","Quantizing the free-electron gas in a box fills a Fermi sphere in k-space. The density of states grows as the square root of energy in three dimensions, and the Fermi energy, temperature, and wavevector follow for real metals. The Sommerfeld expansion shows only a thermal shell of width k_BT near E_F is excited, giving an electronic heat capacity linear in T that sits beneath the phonon T-cubed term.\n",{"path":5290,"title":5291,"module":5283,"summary":5292},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ftransport-and-the-hall-effect","Transport, Wiedemann–Franz, and the Hall Effect","The relaxation-time picture displaces the Fermi sphere under an applied field and gives the electrical conductivity ne-squared-tau over m. The same electrons carry heat, and their ratio yields the Wiedemann–Franz law with the universal Lorenz number. A magnetic field bends the carriers into cyclotron orbits and produces the Hall voltage, whose sign reveals the charge of the carriers.\n",{"path":5294,"title":5295,"module":5283,"summary":5296},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fscreening-and-plasmons","Screening, Plasmons, and the Limits of Free Electrons","A mobile electron gas rearranges to screen any foreign charge, turning the bare Coulomb potential into a short-ranged Yukawa form over the Thomas–Fermi length. Displaced collectively, the gas rings at the plasma frequency, whose quantum is the plasmon and whose value sets the reflectivity edge of metals. A ledger of free-electron successes and failures then motivates band theory.\n",{"path":5298,"title":5299,"module":5300,"summary":5301},"\u002Fcondensed-matter\u002Fband-theory\u002Fblochs-theorem-and-energy-bands","Bloch's Theorem and Energy Bands","Band Theory","An electron in a periodic potential has stationary states that are plane waves modulated by a lattice-periodic envelope. This lesson proves Bloch's theorem two ways, defines crystal momentum and the band index, counts the allowed wavevectors from Born–von Kármán boundary conditions, and sets up the extended, reduced, and repeated-zone descriptions of a band.\n",{"path":5303,"title":5304,"module":5300,"summary":5305},"\u002Fcondensed-matter\u002Fband-theory\u002Fnearly-free-electron-model","The Nearly-Free-Electron Model","A weak periodic potential leaves the free-electron parabola almost intact except near Brillouin-zone boundaries, where two nearly degenerate plane waves mix. This lesson solves the resulting two-by-two secular problem, shows the gap of size twice the potential component opening at each boundary, identifies the two standing waves that pile charge on and between the ions, and works the exactly solvable Kronig–Penney model.\n",{"path":5307,"title":5308,"module":5300,"summary":5309},"\u002Fcondensed-matter\u002Fband-theory\u002Ftight-binding-method","The Tight-Binding Method","The opposite limit to nearly-free electrons builds bands from atomic orbitals. A Bloch sum of one orbital per site gives a dispersion set by the hopping integral between neighbours; the band widens from a sharp atomic level as the atoms approach. This lesson derives the s-band cosine dispersion, extends it to p-bands, and introduces Wannier functions as the localized dual of Bloch states.\n",{"path":5311,"title":5312,"module":5300,"summary":5313},"\u002Fcondensed-matter\u002Fband-theory\u002Ffermi-surfaces-and-semiclassical-dynamics","Fermi Surfaces, Effective Mass, and Metals vs Insulators","Filling the bands settles which crystals conduct. A filled band carries no current, so a crystal with filled bands and a gap is an insulator, while a partly filled band makes a metal. This lesson derives the no-current theorem for a filled band, defines the Fermi surface and Harrison's construction, introduces holes and the effective mass from band curvature, and states the semiclassical equations of motion that lead to Bloch oscillations.\n",{"path":5315,"title":5316,"module":5317,"summary":5318},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fsemiconductor-bands-and-junctions","Band Theory and Semiconductors","Semiconductors","The periodic lattice splits atomic levels into allowed energy bands separated by forbidden gaps. Whether the highest occupied band is full or partly full, and how wide the gap above it is, sorts every solid into conductor, insulator, or semiconductor. Doping adds donor or acceptor levels inside the gap, and a p-n junction built from doped regions gives the diode, the solar cell, the LED, and the transistor.\n",{"path":5320,"title":5321,"module":5317,"summary":5322},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fintrinsic-and-extrinsic-semiconductors","Carrier Statistics: Intrinsic and Extrinsic Semiconductors","The number of mobile electrons and holes in a semiconductor follows from the density of states near each band edge and the Fermi-Dirac tail that reaches into it. This lesson derives the effective densities of states, the intrinsic concentration and its exponential gap dependence, the law of mass action, the temperature march of the Fermi level, and the freeze-out, saturation, and intrinsic regimes of a doped crystal.\n",{"path":5324,"title":5325,"module":5317,"summary":5326},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fcarrier-transport-and-recombination","Carrier Transport and Recombination","Carriers move by drift in a field and by diffusion down a concentration gradient, the two tied together by the Einstein relation. This lesson derives mobility and its scattering-limited temperature dependence, the drift and diffusion currents, the continuity equations, band-to-band and trap-assisted recombination, and the minority-carrier lifetime and diffusion length that set the length scale of every junction device.\n",{"path":5328,"title":5329,"module":5317,"summary":5330},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fthe-pn-junction","The p-n Junction in Depth","Joining p-type and n-type silicon aligns their Fermi levels and leaves a depletion region of fixed charge with a built-in potential. This lesson derives the space-charge field and potential from Poisson's equation in the depletion approximation, the built-in voltage from Fermi-level alignment, the Shockley diode equation from minority-carrier diffusion, junction and diffusion capacitance, and the avalanche and Zener breakdown mechanisms.\n",{"path":5332,"title":5333,"module":5317,"summary":5334},"\u002Fcondensed-matter\u002Fsemiconductors\u002Ftransistors-and-optoelectronics","Transistors and Optoelectronic Devices","Two junctions in series make a bipolar transistor whose thin base gives current gain; a gate over an oxide makes a MOSFET whose inversion channel switches digital logic. Run in reverse, a junction converts photons to current. This lesson derives the transistor current gain and the MOSFET channel current, then treats the LED, the diode laser, and the illuminated solar-cell characteristic.\n",{"path":5336,"title":5337,"module":5338,"summary":5339},"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fdielectrics-and-polarization","Dielectrics, Polarization, and the Local Field","Dielectrics and Ferroelectrics","An insulator responds to an electric field by polarizing. This lesson builds the macroscopic polarization and the dielectric constant, sorts the microscopic response into electronic, ionic, and orientational polarizability, and corrects the field an atom actually feels to the Lorentz local field E + P\u002F3 epsilon-0. The Clausius-Mossotti relation links the measured permittivity to the atomic polarizability, and the frequency dependence of each mechanism explains why the static and optical dielectric constants differ.\n",{"path":5341,"title":5342,"module":5338,"summary":5343},"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fferroelectrics-and-piezoelectrics","Ferroelectrics, Piezoelectrics, and Structural Transitions","Some crystals carry a polarization with no applied field and switch it under a reversing field, tracing a hysteresis loop. This lesson develops the ferroelectric transition through the perovskite BaTiO3 displacive instability and its soft transverse-optical mode, builds the Landau free-energy theory of first- and second-order polar transitions, derives the Curie-Weiss divergence of the dielectric constant, and closes with piezoelectricity and pyroelectricity and their devices.\n",{"path":5345,"title":5346,"module":5347,"summary":5348},"\u002Fcondensed-matter\u002Fmagnetism\u002Fdiamagnetism-and-paramagnetism","Diamagnetism and Paramagnetism","Magnetism in Solids","Every solid responds to a magnetic field. Filled shells give a small negative diamagnetic susceptibility from induced Larmor currents; localized moments give a positive Curie paramagnetism described by the Brillouin function, with the ground-state moment fixed by Hund's rules. The conduction electrons add a temperature-independent Pauli paramagnetism from the thermal shell near the Fermi surface, partly cancelled by Landau diamagnetism of their orbital motion.\n",{"path":5350,"title":5351,"module":5347,"summary":5352},"\u002Fcondensed-matter\u002Fmagnetism\u002Fexchange-and-ferromagnetism","Exchange and Ferromagnetism","Magnetic ordering at hundreds of kelvin cannot be dipolar; it is an exchange effect, the Coulomb repulsion sorted by the Pauli principle into a spin-dependent energy captured by the Heisenberg Hamiltonian. Weiss molecular-field theory replaces the exchange field by an average proportional to the magnetization, giving a self-consistent equation whose solution is spontaneous magnetization below a Curie temperature and a Curie–Weiss susceptibility above it. Itinerant ferromagnetism follows from the Stoner criterion on the band density of states.\n",{"path":5354,"title":5355,"module":5347,"summary":5356},"\u002Fcondensed-matter\u002Fmagnetism\u002Fantiferromagnetism-and-domains","Antiferromagnetism, Ferrimagnetism, and Domains","A negative exchange coupling orders neighboring spins antiparallel. Two-sublattice molecular-field theory gives a Néel temperature marked by a cusp in the susceptibility, and unequal sublattices leave a net moment — ferrimagnetism, the magnetism of the ferrites. A ferromagnet breaks into domains to reduce its magnetostatic energy, separated by Bloch walls whose width is set by the competition between exchange and magnetocrystalline anisotropy, and the irreversible motion of those walls produces the hysteresis loop.\n",{"path":5358,"title":5359,"module":5347,"summary":5360},"\u002Fcondensed-matter\u002Fmagnetism\u002Fspin-waves-and-magnons","Spin Waves and Magnons","The lowest excitations of a ferromagnet are not single flipped spins but collective precessions in which every moment tips slightly and its phase advances along the crystal. These spin waves have a quadratic dispersion at long wavelength, quantize into magnons obeying Bose statistics, and their thermal population removes magnetization as the Bloch T-to-the-three-halves law. Antiferromagnetic magnons disperse linearly, and inelastic neutron scattering measures both.\n",{"path":5362,"title":5363,"module":5364,"summary":5365},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fsuperconductivity-phenomenology","Superconductivity: Phenomenology and BCS","Superconductivity","Below a critical temperature some materials lose all resistance and expel magnetic flux — the Meissner effect that defines the state. The isotope effect points to lattice vibrations, and BCS theory binds electrons into Cooper pairs through phonon exchange. The paired condensate opens an energy gap, quantizes magnetic flux, and drives the Josephson effects.\n",{"path":5367,"title":5368,"module":5364,"summary":5369},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Flondon-theory-and-the-meissner-effect","London Theory and the Meissner Effect","A perfect conductor freezes the field it was cooled in; a superconductor expels it. The distinction needs a constitutive law beyond zero resistance — the two London equations — whose solution is exponential flux decay over the penetration depth. The same rigidity follows from a macroscopic condensate wave function, and the thermodynamics of the critical field fixes the condensation energy, the latent heat, and the specific-heat jump.\n",{"path":5371,"title":5372,"module":5364,"summary":5373},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fginzburg-landau-theory","Ginzburg–Landau Theory, Vortices, and Type-II","A complex order parameter and a free-energy expansion turn the superconducting transition into a Landau theory. Two lengths emerge — the coherence length and the penetration depth — whose ratio kappa sorts superconductors into type I and type II. Type-II materials admit flux as an Abrikosov lattice of vortices, each threading exactly one quantum h\u002F2e, between a lower and an upper critical field.\n",{"path":5375,"title":5376,"module":5364,"summary":5377},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fbcs-theory","Microscopic BCS Theory","A phonon-mediated attraction, however weak, binds two electrons above the Fermi sea — the Cooper problem shows the sea is unstable. The BCS variational ground state pairs all electrons near the Fermi surface and, through a self-consistent gap equation, opens an energy gap. Weak-coupling solution gives the exponential T_c and the universal ratios 2 Delta(0) = 3.53 k_B T_c and Delta C \u002F C_n = 1.43.\n",{"path":5379,"title":5380,"module":5364,"summary":5381},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fjosephson-and-high-tc","Josephson Effects and Unconventional Superconductors","Two superconductors joined by a thin barrier carry a supercurrent set by their phase difference — the dc Josephson effect — and oscillate at 2eV\u002Fh under a voltage. A two-junction loop turns flux quantization into a magnetometer of single-quantum sensitivity. The cuprates superconduct in CuO2 planes with a doping-dependent dome, d-wave pairing, and a pseudogap that lie outside the phonon picture.\n",{"path":5383,"title":5384,"module":5385,"summary":5386},"\u002Fcondensed-matter\u002Fnanostructures\u002Fquantum-wells-wires-and-dots","Quantum Wells, Wires, and Dots","Nanostructures","When a crystal is shrunk until one or more of its dimensions approaches the electron wavelength, the continuous bands of the bulk break into discrete subbands. Confining in one direction gives a quantum well with a step-like density of states, in two directions a quantum wire with inverse-square-root singularities, and in all three a quantum dot whose levels are sharp like an atom's. This lesson derives the density of states in each case and applies it to size-tunable dot emission and the Coulomb blockade of a single-electron transistor.\n",{"path":5388,"title":5389,"module":5385,"summary":5390},"\u002Fcondensed-matter\u002Fnanostructures\u002Finteger-quantum-hall-effect","The 2D Electron Gas and the Integer Quantum Hall Effect","A two-dimensional electron gas in a strong perpendicular magnetic field has its continuous density of states collapse into macroscopically degenerate Landau levels. As the field is swept, the Hall resistance locks onto exact plateaus at h over an integer times e squared, while the longitudinal resistance drops to zero. This lesson derives the Landau levels and their degeneracy, explains the plateaus through disorder-localized states and current-carrying edge channels, and states why the von Klitzing constant is now a resistance standard.\n",{"path":5392,"title":5393,"module":5385,"summary":5394},"\u002Fcondensed-matter\u002Fnanostructures\u002Ffractional-quantum-hall-and-topology","The Fractional Quantum Hall Effect and Topological Order","When the lowest Landau level is only partly filled, the non-interacting theory predicts no gap, yet a plateau appears at filling one-third. It is a many-body effect: Coulomb repulsion selects a correlated ground state, the Laughlin wavefunction, whose excitations carry a fraction of the electron charge. This lesson builds the Laughlin state, introduces composite fermions that map the fractional effect onto an integer one, and explains how the quantum Hall effect brought the Chern number and topology into condensed-matter physics.\n",{"path":5396,"title":5397,"module":5385,"summary":5398},"\u002Fcondensed-matter\u002Fnanostructures\u002Fgraphene-and-dirac-materials","Graphene and Dirac Materials","Graphene is one atomic layer of carbon on a honeycomb lattice. A tight-binding calculation on its two-atom basis gives valence and conduction bands that touch at the corners of the Brillouin zone, where the dispersion is linear and the electrons behave as massless two-dimensional Dirac particles with a fixed speed. This lesson derives the Dirac cones, the Berry phase of pi and the sublattice chirality, the anomalous half-integer quantum Hall effect that follows, and how opening a gap in a Dirac cone points toward topological insulators.\n",{"path":5400,"title":5401,"module":6,"summary":6},"\u002Fcondensed-matter","Condensed Matter Physics",{"path":5403,"title":5404,"module":1231,"summary":5405},"\u002Flogic\u002Ffoundations\u002Flogic-as-a-mathematical-model","Logic as a Mathematical Model of Deduction","Symbolic logic models deductive reasoning the way probability theory models chance: it keeps the form of a correct deduction and discards its content. A deduction is valid when its conclusion follows from the form of the premises alone, independent of what the non-logical words mean. Two models carry the subject — coarse sentential logic and fine first-order logic — and four questions organize it: logical consequence, methods of proof, the gap between provable and true, and the link between logic and computability. Tuples, relations, functions, equivalence classes, and cardinality supply the set-theoretic vocabulary every later chapter uses.\n",{"path":5407,"title":5408,"module":5409,"summary":5410},"\u002Flogic\u002Fsentential-logic\u002Fformal-languages-and-well-formed-formulas","Formal Languages and Well-Formed Formulas","Sentential Logic","The language of sentential logic has an alphabet of sentence symbols, five connectives, and two parentheses, with formation rules that pick out the well-formed formulas. The wffs are the least set of expressions closed under the five formula-building operations, and every such generated set carries an induction principle.\n",{"path":5412,"title":5413,"module":5409,"summary":5414},"\u002Flogic\u002Fsentential-logic\u002Ftruth-assignments-and-tautologies","Truth Assignments, Tautologies, and Consequence","A truth assignment fixes the sentence symbols true or false, and a recursion extends it uniquely to every formula. Satisfaction, tautologies, and tautological implication — one formula following semantically from others — rest on that extension, and the truth-table procedure decides implication for finite premise sets.\n",{"path":5416,"title":5417,"module":5409,"summary":5418},"\u002Flogic\u002Fsentential-logic\u002Funique-readability-and-parsing","Unique Readability and a Parsing Algorithm","Parentheses keep a formula from being read two ways. The parenthesis lemmas and a top-down parsing algorithm recover a formula's structure and yield unique readability: every wff has exactly one formation tree, which is what makes the truth recursion well defined.\n",{"path":5420,"title":5421,"module":5409,"summary":5422},"\u002Flogic\u002Fsentential-logic\u002Finduction-and-recursion","Induction and Recursion on Formulas","Two principles govern any set generated from initial elements by operations: prove a property of all its members by covering the initial elements and the closure steps, and define a function on it by recursion on structure. The recursion theorem needs the set to be freely generated, and unique readability supplies that condition for the well-formed formulas.\n",{"path":5424,"title":5425,"module":5409,"summary":5426},"\u002Flogic\u002Fsentential-logic\u002Fexpressive-completeness-and-normal-forms","Sentential Connectives and Normal Forms","Every formula computes a Boolean function of its atoms, and Post's theorem gives the converse: every Boolean function is realized by a wff in disjunctive normal form, so the five connectives are more than enough. Minimal complete sets follow, down to the single connectives NAND and NOR, together with a method for proving a set of connectives incomplete.\n",{"path":5428,"title":5429,"module":5409,"summary":5430},"\u002Flogic\u002Fsentential-logic\u002Fboolean-circuits","Switching Circuits","A memoryless two-valued circuit computes a Boolean function, so every formula names a gate network and every network a formula. Cost and delay are read off the formula by recursion, and tautological equivalence and normal forms design and simplify circuits realizing a given specification.\n",{"path":5432,"title":5433,"module":5409,"summary":5434},"\u002Flogic\u002Fsentential-logic\u002Fcompactness-and-effectiveness","Compactness and Effectiveness","The compactness theorem reduces satisfiability of an infinite set of formulas to its finite subsets, proved by extension to a maximal finitely satisfiable set and applied to color infinite graphs. Effectiveness fixes what \"decidable\" and \"effectively enumerable\" mean and settles the decidability of tautologyhood.\n",{"path":5436,"title":5437,"module":5438,"summary":5439},"\u002Flogic\u002Ffirst-order-languages\u002Ffirst-order-languages","First-Order Languages","First-Order Languages and Structures","Sentential logic cannot see inside a simple statement, so it misses valid arguments that turn on quantifiers and predicates. A first-order language adds a quantifier, variables, and a chosen vocabulary of predicate, function, and constant symbols. Terms and well-formed formulas are built by recursion over this alphabet, and a variable occurs free or bound according to the quantifiers that reach it.\n",{"path":5441,"title":5442,"module":5438,"summary":5443},"\u002Flogic\u002Ffirst-order-languages\u002Fstructures-truth-and-satisfaction","Structures, Truth, and Satisfaction","A structure interprets a language: a nonempty universe plus a meaning for every predicate, function, and constant symbol. Tarski's recursion defines when a structure satisfies a formula under a variable assignment, and hence when a sentence is true. From satisfaction we recover logical implication, validity, and logical equivalence for first-order logic.\n",{"path":5445,"title":5446,"module":5438,"summary":5447},"\u002Flogic\u002Ffirst-order-languages\u002Fdefinability-and-elementary-equivalence","Definability and Elementary Equivalence","Fix a structure and ask which relations a formula can pick out: the definable ones. A set of sentences picks out a class of structures, the elementary classes. Homomorphisms and isomorphisms compare structures, and the homomorphism theorem shows isomorphic structures satisfy the same sentences. Automorphisms bound what first-order logic can distinguish, giving a tool for proving relations undefinable.\n",{"path":5449,"title":5450,"module":5438,"summary":5451},"\u002Flogic\u002Ffirst-order-languages\u002Fterms-substitution-and-parsing","Parsing, Substitution, and Substitutability","Every recursion on first-order syntax rests on unique readability. A parenthesis-counting function proves that terms and formulas decompose in exactly one way, and a parsing algorithm recovers the decomposition. Substituting a term for a free variable can capture it under a quantifier; the substitutability condition rules that out, and the substitution lemma trades syntactic substitution for a change of assignment.\n",{"path":5453,"title":5454,"module":5455,"summary":5456},"\u002Flogic\u002Fdeductive-calculus\u002Fa-deductive-calculus","A Deductive Calculus for First-Order Logic","The Deductive Calculus and Its Metatheorems","A proof must be finite and mechanically checkable. A Hilbert-style calculus meets both demands: six schemas of logical axioms, a single rule of inference (modus ponens), and the syntactic consequence relation they generate. Substitution and substitutability are defined by recursion, and the bridge theorem reduces deducibility to tautological implication from the axioms.\n",{"path":5458,"title":5459,"module":5455,"summary":5460},"\u002Flogic\u002Fdeductive-calculus\u002Fdeduction-theorem-and-derived-rules","The Deduction Theorem and Derived Rules","Raw deductions from axioms are unusable by hand. The generalization theorem, the deduction theorem, contraposition, reductio ad absurdum, and rule T reduce the calculus to the moves of ordinary mathematics, each proved once to license a block of axiom-level steps. Generalization on constants and alphabetic variants handle the quantifier and substitution bookkeeping.\n",{"path":5462,"title":5463,"module":5455,"summary":5464},"\u002Flogic\u002Fdeductive-calculus\u002Fsoundness","The Soundness Theorem","Soundness is the easy half of the match between proof and truth. Whatever the calculus deduces is logically implied, by an induction on deduction length that rests on one lemma: every logical axiom is valid. The only hard case, quantifier instantiation, needs the substitution lemma. The contrapositive corollary states that every satisfiable set is consistent.\n",{"path":5466,"title":5467,"module":5455,"summary":5468},"\u002Flogic\u002Fdeductive-calculus\u002Fcompleteness-and-consistency","The Completeness Theorem","Gödel's completeness theorem is the deep converse of soundness: whatever is logically implied can be deduced. Equivalently, every consistent set has a model. The Henkin proof manufactures that model out of syntax alone: add witnessing constants, extend to a maximal consistent set, and read a term model off the formulas it contains. Compactness and the enumerability theorem drop out.\n",{"path":5470,"title":5471,"module":5472,"summary":5473},"\u002Flogic\u002Fmodels-and-theories\u002Fcompactness-and-lowenheim-skolem","Compactness and the Löwenheim–Skolem Theorems","Models, Compactness, and Theories","A set of first-order sentences has a model whenever each of its finite subsets does. This compactness theorem follows from completeness and yields the finiteness limitation, the downward and upward Löwenheim–Skolem theorems, models of every infinite cardinality, and nonstandard models of arithmetic.\n",{"path":5475,"title":5476,"module":5472,"summary":5477},"\u002Flogic\u002Fmodels-and-theories\u002Ftheories-elementary-classes-and-categoricity","Theories, Elementary Classes, and Categoricity","A theory is a set of sentences closed under logical consequence. Theories correspond to classes of models; a theory may be complete, axiomatizable, or finitely axiomatizable, and completeness together with axiomatizability yields decidability. The Łoś–Vaught test derives completeness from categoricity in a cardinal, applied to dense linear orders and to algebraically closed fields.\n",{"path":5479,"title":5480,"module":5472,"summary":5481},"\u002Flogic\u002Fmodels-and-theories\u002Finterpretations-between-theories","Interpretations Between Theories","An interpretation translates the vocabulary of one theory into formulas of another, relativizing quantifiers to a definable domain and mapping symbols to defining formulas. Defined function symbols meet a noncreativity criterion; the syntactic translation of formulas carries theoremhood forward, and a faithful interpretation transfers decidability and undecidability between theories.\n",{"path":5483,"title":5484,"module":5472,"summary":5485},"\u002Flogic\u002Fmodels-and-theories\u002Fnonstandard-analysis","Nonstandard Analysis","Compactness builds a model of the real ordered field containing infinite elements and nonzero infinitesimals. The transfer principle carries every first-order truth from the reals to this extension, the standard-part map collapses finite hyperreals back onto the reals, and continuity and the derivative are rederived by working with infinitely small quantities directly.\n",{"path":5487,"title":5488,"module":5489,"summary":5490},"\u002Flogic\u002Farithmetic-and-definability\u002Fdefinability-in-arithmetic","The Structure of Arithmetic and Definability","Number Theory and Definability","Number theory is the theory of one fixed structure, the natural numbers under successor, order, addition, multiplication, and exponentiation. Every number is named by a numeral, and a relation is definable when a single formula picks out exactly its tuples. The central gap separates the sentences true in that structure from those any reasonable set of axioms can prove.\n",{"path":5492,"title":5493,"module":5489,"summary":5494},"\u002Flogic\u002Farithmetic-and-definability\u002Fnatural-numbers-with-successor","Natural Numbers with Successor","The weakest reduct keeps only zero and successor. Its models are a standard chain together with disjoint copies of the integers, which makes the theory categorical in every uncountable power, hence complete and decidable. A quantifier-elimination procedure gives a practical decision method and shows a subset is definable if and only if it is finite or cofinite.\n",{"path":5496,"title":5497,"module":5489,"summary":5498},"\u002Flogic\u002Farithmetic-and-definability\u002Fpresburger-and-reducts","Reducts: Order, Addition, and Multiplication","Adding order to the successor reduct keeps decidability and makes the theory finitely axiomatizable; adding addition gives Presburger arithmetic, still decidable by quantifier elimination once congruence predicates are included, with definable sets exactly the eventually periodic ones. Multiplication is the break point: neither addition nor order can define it, and once it joins addition the theory stops being decidable.\n",{"path":5500,"title":5501,"module":5489,"summary":5502},"\u002Flogic\u002Farithmetic-and-definability\u002Fa-subtheory-and-representability","A Subtheory of Number Theory and Representability","A finite set of eleven axioms, the recursion equations for successor, order, addition, multiplication, and exponentiation, already proves every true quantifier-free and existential sentence. Representability asks a theory to prove the right instances of a formula rather than merely make them true, and a relation is defined to be recursive exactly when some consistent finite theory represents it. Church's thesis identifies that with decidability, and closure under composition, minimization, and primitive recursion builds the catalog the incompleteness proofs need.\n",{"path":5504,"title":5505,"module":5506,"summary":5507},"\u002Flogic\u002Fincompleteness\u002Farithmetization-of-syntax","Arithmetization of Syntax","Arithmetization and the Incompleteness Theorems","Gödel numbering assigns a natural number to every symbol, expression, formula, and deduction, turning statements about syntax into statements about numbers. The syntactic operations — substitution, \"is a wff\", \"is an axiom\", \"d codes a deduction of a\" — come out primitive recursive and hence representable in the subtheory, which lets a formula of arithmetic talk about formulas, including itself.\n",{"path":5509,"title":5510,"module":5506,"summary":5511},"\u002Flogic\u002Fincompleteness\u002Fincompleteness-and-undecidability","Incompleteness, Undecidability, and Church's Theorem","The fixed-point lemma manufactures a sentence that talks about its own Gödel number. Pointed at truth it gives Tarski's theorem — arithmetic truth is not arithmetically definable; pointed at provability it gives Gödel's first incompleteness theorem and the undecidability of the theory of the natural numbers, and, applied to validity, Church's theorem that first-order logic is undecidable. The set of theorems of a recursive theory is only recursively enumerable — the gap between provable and true.\n",{"path":5513,"title":5514,"module":5506,"summary":5515},"\u002Flogic\u002Fincompleteness\u002Fsecond-incompleteness-theorem","The Second Incompleteness Theorem","Consistency of a recursively axiomatized theory is itself an arithmetic sentence, built from a provability predicate. When the theory is strong enough to formalize its own reflection and modus ponens — the Hilbert–Bernays–Löb derivability conditions — it cannot prove that sentence unless it is inconsistent. Löb's theorem is the companion result, and set theory is the case that closes Hilbert's program.\n",{"path":5517,"title":5518,"module":5519,"summary":5520},"\u002Flogic\u002Fcomputability-and-representability\u002Frecursive-functions","Recursive Functions and Church's Thesis","Recursive Functions and Representability","The recursive functions are the formal counterpart of the effectively computable ones: built from three initial functions by composition, primitive recursion, and minimization, and equivalently the functions representable in a finitely axiomatized arithmetic. Church's thesis identifies the class with effective calculability; Kleene's normal form theorem and the unsolvable halting problem place the recursive sets strictly inside the recursively enumerable ones.\n",{"path":5522,"title":5523,"module":5519,"summary":5524},"\u002Flogic\u002Fcomputability-and-representability\u002Frepresenting-exponentiation","Representing Exponentiation and the β-Function","Coding finite sequences by prime-power exponents already assumes exponentiation, so representing exponentiation from addition and multiplication alone needs a different encoder. Gödel's β-function, built from a pairing function and the Chinese remainder theorem, reads back arbitrary finite sequences using only plus and times. This represents exponentiation in the addition-multiplication arithmetic and closes the last gap in the representability of every recursive syntactic operation.\n",{"path":5526,"title":5527,"module":5528,"summary":5529},"\u002Flogic\u002Fsecond-order-logic\u002Fsecond-order-languages","Second-Order Languages","Second-Order Logic and Beyond","Second-order logic quantifies over relations and functions, not just individuals. Second-order Peano arithmetic and the second-order theory of the reals become categorical, and finiteness is definable by a single sentence. Compactness, completeness, and the Löwenheim–Skolem theorems all fail for the standard semantics.\n",{"path":5531,"title":5532,"module":5528,"summary":5533},"\u002Flogic\u002Fsecond-order-logic\u002Fskolem-functions-and-many-sorted-logic","Skolem Functions and Many-Sorted Logic","Skolem functions replace existential quantifiers with named witnesses, putting any first-order formula into a prenex form with all existentials — now over functions — pulled to the front. The Skolemized formula is equisatisfiable with the original, which reduces satisfiability to universal sentences and, through Herbrand expansions, to sentential logic. Many-sorted logic then adds several universes at once and reduces cleanly to ordinary one-sorted logic.\n",{"path":5535,"title":5536,"module":5528,"summary":5537},"\u002Flogic\u002Fsecond-order-logic\u002Fgeneral-structures","General (Henkin) Structures","General semantics reinterprets second-order logic by letting the predicate and function quantifiers range over a designated collection of relations and functions rather than all of them. Recast as many-sorted first-order logic with comprehension axioms, general second-order logic recovers a sound and complete calculus together with compactness and Löwenheim–Skolem, giving up the categoricity of the standard semantics. The ω-models of analysis show the trade.\n",{"path":5539,"title":5540,"module":6,"summary":6},"\u002Flogic","Logic",{"path":5542,"title":5543,"module":1231,"summary":5544},"\u002Freinforcement-learning\u002Ffoundations\u002Fwhat-is-reinforcement-learning","What Is Reinforcement Learning?","Reinforcement learning is learning what to do — how to map situations to actions — so as to maximize a numerical reward signal, discovered by trial and error rather than told. We set up the agent–environment loop, separate it from supervised and unsupervised learning, name the four elements (policy, reward, value, and an optional model), and train a tic-tac-toe player with a temporal-difference value update.\n",{"path":5546,"title":5547,"module":1231,"summary":5548},"\u002Freinforcement-learning\u002Ffoundations\u002Fa-brief-history-of-rl","A Brief History of Reinforcement Learning","The origins of reinforcement learning. Three threads — trial-and-error learning from animal psychology, optimal control and dynamic programming, and temporal-difference learning — ran independently for decades and merged around 1989 into the modern field. Replacing the lookup table with a neural network then produced deep reinforcement learning: DQN, AlphaGo, AlphaZero, MuZero, and RLHF.\n",{"path":5550,"title":5551,"module":1231,"summary":5552},"\u002Freinforcement-learning\u002Ffoundations\u002Fmulti-armed-bandits","Multi-Armed Bandits","A bandit is reinforcement learning stripped to a single decision, repeated: no state, no consequences, only the tension between exploiting the arm that looks best and exploring the ones that might be better. We build up the whole toolkit — sample-average value estimates, the incremental update rule, ε-greedy, optimistic initialization, UCB, and gradient bandits — and use it to study exploration in isolation, the one problem that carries over to the full setting.\n",{"path":5554,"title":5555,"module":1231,"summary":5556},"\u002Freinforcement-learning\u002Ffoundations\u002Fbandit-exploration-algorithms","Bandit Exploration Algorithms","Better ways to explore than picking at random. Upper-confidence-bound selection explores by optimism about what it hasn't measured; gradient bandits learn action preferences by stochastic gradient ascent on reward. We then add context to get the contextual bandit, the bridge to full RL, and measure everything by regret — where UCB1 and Thompson sampling reach the logarithmic optimum that fixed-ε greedy cannot.\n",{"path":5558,"title":5559,"module":1231,"summary":5560},"\u002Freinforcement-learning\u002Ffoundations\u002Fmarkov-decision-processes","Markov Decision Processes","A Markov decision process is the formal interface between an agent and its environment: at each step the agent reads a state, chooses an action, and receives a reward and a next state. We fix that loop, the dynamics function that governs it, and the Markov property that makes the state sufficient; then turn goals into a scalar reward and rewards into a discounted return, with one notation that covers both episodic and continuing tasks.\n",{"path":5562,"title":5563,"module":1231,"summary":5564},"\u002Freinforcement-learning\u002Ffoundations\u002Fvalue-functions-and-optimality","Value Functions and Optimality","A value function scores how good a state (or state–action pair) is under a policy: the expected return from there onward. Its defining property is the Bellman equation, a self-consistency condition linking a state's value to its successors' values, which we derive from the return and the dynamics. Pushing the same idea to the best-achievable value gives the Bellman optimality equations, whose solution yields an optimal policy — and whose intractability is what the rest of the course is about.\n",{"path":5566,"title":2386,"module":5567,"summary":5568},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdynamic-programming","Tabular Solution Methods","Dynamic programming computes optimal policies when a perfect model of the MDP is given, by turning the Bellman equations into assignment statements. We build up iterative policy evaluation (the expected update), the policy improvement theorem, and the two classic algorithms that alternate them — policy iteration and value iteration — worked on the gridworld, a two-state MDP, Jack's car rental, and the gambler's problem.\n",{"path":5570,"title":5571,"module":5567,"summary":5572},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdp-async-and-gpi","Dynamic Programming: Asynchronous DP and Generalized Policy Iteration","Policy and value iteration both sweep the entire state set on every pass, which is impossible once the state space is huge. This lesson loosens the schedule: asynchronous DP updates states in any order, generalized policy iteration names the alternation of evaluation and improvement that underlies nearly every RL method, and a look at efficiency and the curse of dimensionality places DP among the alternatives. We close past Sutton & Barto with prioritized sweeping, neuro-dynamic programming, value-iteration networks, and MuZero.\n",{"path":5574,"title":5575,"module":5567,"summary":5576},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-methods","Monte Carlo Methods","Monte Carlo methods learn value functions and optimal policies from complete sampled episodes, with no model of the environment: they simply average the returns that actually followed each state. We build prediction (first-visit and every-visit averaging), see why estimating action values forces the exploration question, and answer it two ways on-policy — exploring starts and epsilon-soft control. Throughout, Monte Carlo samples one whole trajectory to termination and never bootstraps.\n",{"path":5578,"title":5579,"module":5567,"summary":5580},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-off-policy","Monte Carlo Methods: Off-Policy Learning","On-policy Monte Carlo can only reach the best exploring policy, not the true optimum. Off-policy methods remove that ceiling by learning about a greedy target policy from data generated by a soft behavior policy, corrected with importance sampling. We derive the importance-sampling ratio, weigh ordinary against weighted estimators on real numbers, give the incremental off-policy algorithm, sharpen it with discounting-aware sampling, and close by placing Monte Carlo on the model\u002Fbootstrap map beside DP and temporal-difference learning.\n",{"path":5582,"title":5583,"module":5567,"summary":5584},"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftemporal-difference-learning","Temporal-Difference Learning","Temporal-difference learning is the one idea most central to reinforcement learning: learn a value directly from experience, like Monte Carlo, but update each guess toward the next guess before the episode ends, like dynamic programming. We derive the TD(0) prediction rule and its reward-prediction error, contrast its one-step backup with MC and DP, work the driving-home and random-walk examples, and show the batch-updating optimality that makes TD approximate the certainty-equivalence estimate.\n",{"path":5586,"title":5587,"module":5567,"summary":5588},"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftd-control-sarsa-and-q-learning","TD Control: Sarsa, Q-learning, and Double Learning","With TD prediction in hand, control follows the generalized-policy-iteration pattern with TD as the evaluation step. We build Sarsa (on-policy), Q-learning (off-policy, targeting the optimal policy), and Expected Sarsa that spans the two, then confront the maximization bias every max-based method inherits and fix it with Double Q-learning. We close past Sutton & Barto, following each one-step tabular update into its deep-RL descendant — DQN, Double DQN, and Rainbow.\n",{"path":5590,"title":5591,"module":5567,"summary":5592},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-bootstrapping","n-Step Bootstrapping","Monte Carlo waits for the full return; one-step TD bootstraps after a single reward. Between them lies a whole spectrum, indexed by one integer n: look ahead n real rewards, then bootstrap from the value n steps out. The n-step return unifies the previous two lessons, and — on the random walk — an intermediate n beats both extremes. We build the n-step return, the n-step TD update, the backup-diagram spectrum, and n-step Sarsa for control.\n",{"path":5594,"title":5595,"module":5567,"summary":5596},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-off-policy-methods","n-Step Bootstrapping: Off-Policy Methods","Taking the n-step family off-policy raises the same importance-sampling questions Monte Carlo did, now over a window of exactly n actions. We reweight n-step returns by the policy ratio, watch the ratio product inflate variance on real numbers, then build the tree-backup algorithm that learns off-policy with no ratios at all — and finally n-step Q(sigma), one algorithm whose per-step switch recovers Sarsa, tree backup, and Expected Sarsa as special cases.\n",{"path":5598,"title":5599,"module":5567,"summary":5600},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-and-learning","Planning and Learning","Planning and learning are the same operation run on two kinds of experience. A model turns states and actions into simulated transitions; planning backs up values over that simulated experience exactly as learning backs them up over real experience. We build the Dyna architecture that interleaves acting, model-learning, direct RL, and planning in one loop, trace a single Dyna-Q step by hand, and patch the architecture for when the model goes stale.\n",{"path":5602,"title":5603,"module":5567,"summary":5604},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-focusing-and-decision-time","Planning: Focusing Updates and Decision-Time Search","Dyna plans by replaying remembered transitions, but sampling them uniformly wastes most of the effort. This lesson sharpens planning: prioritized sweeping works backward from states whose value just changed, expected versus sample updates weigh thoroughness against cost, and trajectory sampling and real-time DP focus updates on the states the policy actually visits. We trace Dyna forward to model-based deep RL, then turn to decision-time planning — heuristic search, rollouts, and Monte Carlo Tree Search.\n",{"path":5606,"title":5607,"module":5567,"summary":5608},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdecision-time-planning","Decision-Time Planning","Planning need not build a global policy. Decision-time planning runs a fresh lookahead every time a state arrives and returns just one action, then throws the work away. We start from real-time dynamic programming — asynchronous value iteration on the states the agent actually visits — then move through heuristic search and rollout algorithms, each a one-step policy improvement applied on the fly to the current state.\n",{"path":5610,"title":5611,"module":5567,"summary":5612},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-tree-search","Monte Carlo Tree Search","Monte Carlo Tree Search is a rollout algorithm with memory: it accumulates value estimates across simulations and steers later ones toward promising branches. We work through the four steps — selection, expansion, simulation, backup — the UCT selection rule computed on real numbers, the asymmetric growing tree, and the full pseudocode. We close past Sutton & Barto with the lineage from UCT to AlphaGo, AlphaZero, and MuZero, where a learned network stands in for the leaf value and the rollout.\n",{"path":5614,"title":5615,"module":5616,"summary":5617},"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-prediction","On-Policy Prediction with Approximation","Approximate Solution Methods","Every tabular method so far stored one number per state, which fails once the state space is large or continuous. We replace the table with a parameterized value function $\\hat v(s,\\mathbf{w})$, define the mean squared value error it should minimize under the on-policy distribution, and derive stochastic- and semi-gradient learning rules — the semi-gradient TD(0) update that bootstraps and so is not a true gradient. Linear methods make the analysis clean and give the TD fixed point; feature construction (polynomials, Fourier basis, coarse and tile coding, RBFs) supplies the vectors $\\mathbf{x}(s)$, and neural networks are the nonlinear bridge to deep RL.\n",{"path":5619,"title":5620,"module":5616,"summary":5621},"\u002Freinforcement-learning\u002Fapproximation\u002Ffeature-construction-and-nonlinear","Feature Construction and Nonlinear Approximation","Linear methods are only as good as the feature vectors $\\mathbf{x}(s)$ fed to them, and this lesson builds those vectors. Polynomials and the Fourier basis turn a state's coordinates into smooth global features; coarse coding, tile coding, and radial basis functions cover a continuous space with overlapping local receptive fields whose size sets the reach of generalization. Then we stop designing features by hand: a neural network learns the representation itself by gradient descent, trading the convergence guarantees of the linear case for expressiveness — the bridge to deep reinforcement learning.\n",{"path":5623,"title":5624,"module":5616,"summary":5625},"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-control","On-Policy Control with Approximation","Prediction learned a value function from features; control learns to act. We carry semi-gradient methods over to action values $\\hat q(s,a,\\mathbf{w})$, giving episodic semi-gradient Sarsa and its n-step form, and solve Mountain Car by descending a cost-to-go surface. In the continuing case, function approximation makes discounting unable to affect which policy is best, so we replace it with the average-reward setting — the differential return, differential value functions, and differential semi-gradient Sarsa.\n",{"path":5627,"title":5628,"module":5616,"summary":5629},"\u002Freinforcement-learning\u002Fapproximation\u002Faverage-reward-control","Average-Reward Control for Continuing Tasks","With function approximation, discounting has no effect on a continuing task: averaged over the on-policy distribution, the discounted objective equals the average reward times a policy-independent constant, so $\\gamma$ cannot change which policy is best. This lesson replaces discounting with the average-reward setting — the long-run reward rate $r(\\pi)$, the differential return that measures each state's transient advantage over that rate, differential value functions and TD error, and differential semi-gradient Sarsa, the control method for continuing tasks that never invokes a discount factor.\n",{"path":5631,"title":5632,"module":5616,"summary":5633},"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-and-the-deadly-triad","Off-Policy Methods and the Deadly Triad","Off-policy learning with function approximation is where the convergence guarantees of reinforcement learning fail. We extend the tabular off-policy updates to semi-gradient form with per-step importance sampling, show Baird's counterexample driving the weights to infinity, and identify the cause: the deadly triad of function approximation, bootstrapping, and off-policy training — any two are safe, all three can diverge. The divergence is not caused by sampling noise: a fully synchronous dynamic-programming update blows up just the same, which is what makes the triad a structural hazard rather than a fluke.\n",{"path":5635,"title":5636,"module":5616,"summary":5637},"\u002Freinforcement-learning\u002Fapproximation\u002Fbellman-error-and-gradient-td","Value-Function Geometry and Gradient-TD Methods","Why does the deadly triad diverge, and how do you stop it? This lesson develops the geometry that explains the failure: value functions as vectors, the projection operator onto the representable subspace, and the split between the Bellman error, the value error, and the projected Bellman error: the three objectives have different minimizers. The projected Bellman error is the learnable one, and Gradient-TD methods (GTD2, TDC) do true stochastic gradient descent on it, staying stable even off-policy at $O(d)$ cost. Emphatic TD reweights states instead, and a survey of variance-reduction techniques closes the gap between stability and usable learning.\n",{"path":5639,"title":5640,"module":5616,"summary":5641},"\u002Freinforcement-learning\u002Fapproximation\u002Feligibility-traces","Eligibility Traces","n-step methods unify TD and Monte Carlo by storing the last n feature vectors; eligibility traces do the same job with a single short-term memory vector. The λ-return averages every n-step return under a geometric weighting; the forward view looks ahead to that average, and the backward view produces nearly the same updates online through a decaying trace vector. We build the λ-return, TD(λ) with its trace, the two ways λ recovers TD(0) and Monte Carlo, a note on the exact equivalence of true online TD(λ), and Sarsa(λ) for control.\n",{"path":5643,"title":5644,"module":5616,"summary":5645},"\u002Freinforcement-learning\u002Fapproximation\u002Ftrue-online-and-sarsa-lambda","True Online TD(λ) and Sarsa(λ)","Plain TD(λ) makes the forward and backward views nearly agree; this lesson closes the gap. True online TD(λ) uses a dutch trace and a small correction term to produce exactly the same weight sequence as the online λ-return algorithm, at the same memory and only a constant factor more compute — the sharpest statement of the forward\u002Fbackward duality. The whole apparatus then lifts to control unchanged: Sarsa(λ) threads a single delayed reward back along an entire trajectory in one sweep, and the λ-weighting reappears in modern deep RL as generalized advantage estimation.\n",{"path":5647,"title":5648,"module":5616,"summary":5649},"\u002Freinforcement-learning\u002Fapproximation\u002Fpolicy-gradient-methods","Policy Gradient Methods","Every method so far learned values and read a policy off them. Policy gradient methods drop the intermediary: parameterize the policy directly and climb the performance gradient. We build the softmax-in-preferences parameterization, prove the policy gradient theorem that makes the gradient computable without the unknown state distribution, and derive REINFORCE and its variance-cutting state-value baseline — the launch point for the bootstrapping actor-critic that follows.\n",{"path":5651,"title":5652,"module":5616,"summary":5653},"\u002Freinforcement-learning\u002Fapproximation\u002Factor-critic-and-continuous-actions","Actor-Critic Methods and Continuous Actions","REINFORCE with a baseline learns a value function but never bootstraps; this lesson adds the bootstrapping critic that completes the actor-critic architecture. The critic scores each transition into a single TD error that steers both the actor's policy step and its own value step, trading a little bias for much lower variance and fully online, continuing-task learning. The policy gradient theorem carries over unchanged to the average-reward setting, a Gaussian policy handles real-valued actions with self-tuning exploration, and the natural policy gradient leads straight to TRPO, PPO, and the deep actor-critic methods that train today's agents.\n",{"path":5655,"title":5656,"module":5616,"summary":5657},"\u002Freinforcement-learning\u002Fapproximation\u002Fleast-squares-and-memory-based-methods","Least-Squares TD","Semi-gradient TD spends one cheap step per example and needs many examples; this lesson makes the opposite tradeoff. Least-Squares TD (LSTD) accumulates the matrices $\\mathbf{A}$ and $\\mathbf{b}$ and solves the TD fixed point $\\mathbf{w} = \\mathbf{A}^{-1}\\mathbf{b}$ directly, using the Sherman-Morrison identity to maintain the inverse in $O(d^2)$ — the most data-efficient linear TD method, at a quadratic cost. We work a solve by hand, weigh the quadratic cost against semi-gradient TD's cheap steps, and note that LSTD never forgets — a problem in control, where least-squares policy iteration is the natural extension.\n",{"path":5659,"title":5660,"module":5616,"summary":5661},"\u002Freinforcement-learning\u002Fapproximation\u002Fmemory-and-kernel-methods","Memory-Based and Kernel Methods","Least-squares TD spent more compute to extract more from each example; this lesson drops the parametric form entirely. Memory-based methods store training examples untouched and answer a query locally at retrieval time — nearest neighbor, weighted average, locally weighted regression — so accuracy grows with the data and effort concentrates where the agent actually goes. Kernel-based methods weight stored examples by a similarity kernel $k(s,s')$, and every linear method turns out to be a kernel method. Interest and emphasis, finally, make the on-policy weighting itself a design choice, aiming scarce approximation capacity at the states that matter.\n",{"path":5663,"title":5664,"module":5616,"summary":5665},"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-eligibility-traces","Off-Policy Eligibility Traces","Eligibility traces meet off-policy learning and function approximation — the corner where stability gets hard. We first let the bootstrapping and discounting parameters vary with state, so a single generalized return covers episodic and continuing tasks and folds termination into the discount. Then we fold the per-decision importance ratio into the trace with a control-variate correction, and build Watkins's Q(λ) and its importance-sampling-free successor Tree-Backup(λ) — all correct in expectation, but still semi-gradient, so the deadly triad and its fixes wait for the next lesson.\n",{"path":5667,"title":5668,"module":5616,"summary":5669},"\u002Freinforcement-learning\u002Fapproximation\u002Fstable-off-policy-traces","Stable Off-Policy Methods with Traces","Off-policy traces get the expected target right, but with $\\lambda \u003C 1$ they bootstrap, so off-policy plus bootstrapping plus function approximation is the deadly triad and the weights can diverge. This lesson carries the two one-step fixes to traces: GTD(λ) and GQ(λ) add a second weight vector and a gradient correction for true gradient descent on the projected Bellman error, while Emphatic TD(λ) reweights updates through a followon trace and interest to recover the on-policy stability. It closes with the implementation reality that traces are cheap because they are sparse, and with Retrace and V-trace — the clipped-ratio descendants that make off-policy traces work at deep-RL scale.\n",{"path":5671,"title":4989,"module":5672,"summary":5673},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdeep-q-networks","Deep Reinforcement Learning","Deep Q-networks replace the linear value function with a neural network $Q(s,a;\\mathbf{w})$ and confront the fact that a nonlinear approximator, off-policy bootstrapping, and correlated online data — the deadly triad — make naive Q-learning diverge. DQN counters this empirically with two stabilizers: an experience replay buffer that decorrelates and reuses samples, and a periodically-frozen target network that fixes the bootstrap target. We derive the DQN loss and gradient, walk through the Atari convolutional architecture and its results, and then add the three refinements that define modern value-based deep RL — Double DQN, dueling networks, and prioritized experience replay.\n",{"path":5675,"title":5676,"module":5672,"summary":5677},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdqn-improvements","DQN Improvements: Double, Dueling, and Prioritized Replay","Three refinements that turn plain DQN into the standard modern value-based agent, each touching a different part of the system. Double DQN fixes the maximization bias in the target by splitting action selection from evaluation; dueling networks restructure the network around a state value and per-action advantages; prioritized replay changes which transitions are learned from. We close with Rainbow, which combines them, and the distributional view that predicts the whole return distribution rather than its mean.\n",{"path":5679,"title":5680,"module":5672,"summary":5681},"\u002Freinforcement-learning\u002Fdeep-rl\u002Factor-critic-and-ppo","Actor–Critic and GAE","Make the actor and the critic deep networks and the policy-gradient architecture becomes modern deep RL. We build the neural actor-critic, the advantage estimate that replaces the raw return, and Generalized Advantage Estimation as a λ-blend of n-step advantages, then the parallel-worker methods A3C and A2C that decorrelate on-policy data. The step-size constraints — trust regions, PPO, and the continuous-control family — follow in the next lesson.\n",{"path":5683,"title":5684,"module":5672,"summary":5685},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fppo-and-continuous-control","PPO and Continuous Control","Keeping the policy-gradient step from destroying the policy, and the algorithms that result. Trust-region optimization bounds each update by a KL constraint; PPO keeps that goal but replaces the second-order machinery with a first-order clip on the probability ratio, which is why it is the modern default and the optimizer inside RLHF. We then tour the off-policy continuous-control family — DDPG, TD3, and SAC — and where actor-critic went at scale, from OpenAI Five to language-model alignment.\n",{"path":5687,"title":5688,"module":5672,"summary":5689},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fcase-studies","Case Studies: Learning to Play","The game-playing systems that turned reinforcement learning from a theory into a track record: Samuel's checkers player, TD-Gammon, Watson's Daily-Double wagering, a reinforcement-learning memory controller, DQN, and AlphaGo through AlphaGo Zero. Read as a set they draw one line — a value function, learned by self-play or interaction, refined by search, carried by a deep network — that runs from a 1959 checkers program to superhuman Go.\n",{"path":5691,"title":5692,"module":5672,"summary":5693},"\u002Freinforcement-learning\u002Fdeep-rl\u002Frl-beyond-games","Reinforcement Learning Beyond Games","The same value-and-reward machinery, pointed at problems with no opponent. Web personalization as a contextual bandit and then a full MDP for life-time value; thermal soaring, where a glider learns to climb on turbulent air and reward design does most of the work; and the industrial-scale systems that carried the same design past Sutton & Barto — AlphaStar, OpenAI Five, GT Sophy, and RLHF, where the reward itself is learned from human preference.\n",{"path":5695,"title":5696,"module":5672,"summary":5697},"\u002Freinforcement-learning\u002Fdeep-rl\u002Ffrontiers","Frontiers: Beyond the Standard MDP","The standard MDP fixes three things — state, reward, and single-step actions — and this lesson loosens two of them. We generalize the value function into a general value function that predicts any signal, and use those predictions as auxiliary tasks that shape representations; we extend actions in time with the options framework; and we treat state as a construction the agent builds from a stream of observations. Reward design and the open problems follow in the next lesson.\n",{"path":5699,"title":5700,"module":5672,"summary":5701},"\u002Freinforcement-learning\u002Fdeep-rl\u002Freward-design-and-open-problems","Reward Design and Open Problems","How to design a reward signal that encodes the intended goal — sparse reward, shaping, and reward hacking — and the problems the whole tabular, approximate, and deep arc leaves unsolved. We close with how the frontiers were pushed after Sutton & Barto: auxiliary tasks, learned options, intrinsic-motivation bonuses, learned world models, and offline RL, then the two concerns of reward hacking and safety that any real-world agent must address.\n",{"path":5703,"title":5704,"module":5705,"summary":5706},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow","Sharpening DQN: Improvements and the Distributional Idea","Modern Deep Reinforcement Learning","In the years after the 2015 DQN paper, a stream of focused improvements each fixed one weakness of the baseline without disturbing its frame. This lesson recaps five that keep the scalar $Q$-value — Double DQN, multi-step returns, dueling networks, prioritized replay, and NoisyNets, each changing a different slot of the same Q-learning loop — then develops the sixth, distributional RL, which changes the objective itself: learn the whole return distribution $Z(s,a)$. We build the distributional Bellman equation and the C51 categorical algorithm, projection step and all, worked end to end on real numbers. A companion lesson takes up QR-DQN, Rainbow, and the modern distributional line.\n",{"path":5708,"title":5709,"module":5705,"summary":5710},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow-part-2","Distributional RL and Rainbow","A companion to the DQN improvements lesson. C51 fixed the return atoms and learned their probabilities; QR-DQN does the reverse — fix the probabilities, learn the values — which removes the projection and trains with a quantile loss. We cover why the distribution helps even when you act on the mean, then assemble Rainbow: all six improvements in one Q-learning loop, with the component ablation that shows each one's real weight. The distributional line then runs on through IQN, FQF, and Agent57, the first agent to beat the human baseline on all 57 Atari games.\n",{"path":5712,"title":5713,"module":5705,"summary":5714},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control","Continuous Control: DDPG and TD3","When actions are real-valued, the $\\arg\\max_a Q(s,a)$ in Q-learning becomes an optimization problem on every step. This lesson builds the off-policy actor-critic family that sidesteps it: the deterministic policy gradient and DDPG, which replaces the max with a learned actor, and the three fixes of TD3 that counter the value overestimation DDPG inherits. A companion lesson takes up SAC's maximum-entropy objective and the methods built on this template.\n",{"path":5716,"title":5717,"module":5705,"summary":5718},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control-part-2","Continuous Control: SAC and Beyond","A companion to the DDPG and TD3 lesson. Where those actors are deterministic and explore with bolted-on noise, soft actor-critic (SAC) changes the objective itself: maximize return plus the entropy of the policy, so exploration becomes intrinsic and the agent stays robust. We develop the maximum-entropy objective, the reparameterized squashed-Gaussian actor, and automatic temperature tuning, then survey the methods built on this off-policy template — distributional critics (D4PG), critic ensembles (REDQ), and control from pixels (DrQ, RAD).\n",{"path":5720,"title":5721,"module":5705,"summary":5722},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl","Model-Based Deep RL: Sample Efficiency and PETS","A model turns experience into imagined planning. This lesson makes the sample-efficiency case for learning a dynamics model, works through why a learned model's errors compound over the planning horizon, and builds the most direct model-based method: PETS plans online with a probabilistic ensemble under model-predictive control, distrusting the model exactly where its members disagree. A companion lesson takes up latent world models (Dreamer) and MuZero.\n",{"path":5724,"title":5725,"module":5705,"summary":5726},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl-part-2","Model-Based Deep RL: World Models, Dreamer, and MuZero","A companion to the PETS lesson. PETS plans in the environment's native state space; these methods change what the model represents. World Models and Dreamer learn a compact latent state and do almost all their learning by imagining inside it, with value gradients flowing through the differentiable dynamics. MuZero predicts neither states nor pixels — only the reward, value, and policy that MCTS reads — and plans with search against that learned model, AlphaZero without the rules. We close with MBPO, TD-MPC, and EfficientZero.\n",{"path":5728,"title":5729,"module":5705,"summary":5730},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration","Exploration in Deep RL: Novelty as Reward","When the state space is enormous and reward is rare, ε-greedy amounts to a random walk that almost never reaches the first reward. This lesson scales the bandit's exploration ideas up to deep RL through the dominant approach — manufacture a reward for novelty and let the agent chase it: optimism and pseudo-counts from density models, and intrinsic motivation and curiosity (the Intrinsic Curiosity Module and Random Network Distillation). A companion lesson takes up posterior sampling, Go-Explore, and the modern methods.\n",{"path":5732,"title":5733,"module":5705,"summary":5734},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration-part-2","Exploration in Deep RL: Posterior Sampling and Go-Explore","A companion to the novelty-as-reward lesson. Pseudo-counts and curiosity reward the unfamiliar after the agent stumbles into it; this lesson covers two ideas that go further. Bootstrapped DQN keeps an ensemble that approximates a posterior over value functions and explores by committing to one sampled hypothesis per episode — the deep, directed exploration ε-greedy cannot manage. Go-Explore remembers and returns to the frontier, defeating detachment and derailment to solve Montezuma's Revenge. We close with episodic memory (Never Give Up), Agent57, and model-based exploration.\n",{"path":5736,"title":5737,"module":5705,"summary":5738},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl","Offline RL: The Problem and Value-Based Fixes","Offline reinforcement learning learns a policy from a fixed logged dataset with no further environment interaction — off-policy learning pushed to the extreme, and it breaks for the extreme version of the same reason. Bootstrapping queries the value function at out-of-distribution actions the data never covers, those errors are optimistic, and with no online feedback to correct them they compound through the Bellman backup. This lesson sets up the failure and off-policy evaluation, then builds the first two families of pessimistic fixes: policy constraint (BCQ) and conservative value estimation (CQL). A companion lesson takes up implicit methods, model-based offline RL, and Decision Transformer.\n",{"path":5740,"title":5741,"module":5705,"summary":5742},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl-part-2","Offline RL: Implicit Methods, Sequence Models, and Beyond","A companion to the offline-RL problem lesson. Policy constraint and conservative value estimation both still query a learned value function; implicit methods (IQL) avoid querying it off the data at all, using an in-sample expectile backup. We then build pessimism into a learned model (MOPO, COMBO) and drop bootstrapping entirely with Decision Transformer's return-conditioned sequence modeling, closing with offline-to-online fine-tuning, diffusion planners, and the offline view of RLHF. The one rule throughout: without online correction, be pessimistic about what you cannot verify.\n",{"path":5744,"title":5745,"module":5705,"summary":5746},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl","Imitation Learning: Cloning, DAgger, and Inverse RL","When a reward is hard to specify but an expert is easy to watch, learn from demonstrations instead. Behavioral cloning treats control as supervised learning of the expert's state-to-action map, and fails through compounding error: small mistakes carry the agent off the expert's distribution, where it was never trained. DAgger fixes the mismatch by querying the expert on the learner's own states. Inverse RL instead recovers the reward the expert seems to optimize — an ill-posed problem that maximum-entropy IRL disambiguates. A companion lesson casts imitation as adversarial occupancy matching (GAIL, AIRL).\n",{"path":5748,"title":5749,"module":5705,"summary":5750},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl-part-2","Imitation as Adversarial Matching: GAIL and AIRL","A companion to the imitation-learning lesson. If the point of recovering a reward is only to re-run RL and match the expert, you can skip the reward and match the behavior directly. GAIL casts imitation as a GAN — a discriminator separating expert from learner state-action pairs supplies the reward a policy-gradient method optimizes — matching occupancy measures without ever naming a reward. AIRL reads a transferable reward back out of the discriminator. We compare all four methods and close with reward models in RLHF, scaled cloning, and diffusion policies.\n",{"path":5752,"title":5753,"module":5705,"summary":5754},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl","Multi-Agent RL: Markov Games and Centralized Training","With more than one learning agent in an environment, each agent's world becomes non-stationary because the others are changing too. This lesson builds the Markov-game generalization of the MDP, diagnoses non-stationarity as the central obstacle, shows why the naive baselines fail, and develops the dominant fix — centralized training with decentralized execution (MADDPG, VDN, QMIX). A companion lesson takes up self-play, the landmark game-playing systems, and the equilibrium concepts that define what \"solved\" means.\n",{"path":5756,"title":5757,"module":5705,"summary":5758},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl-part-2","Multi-Agent RL: Self-Play and Solution Concepts","A companion to the Markov-games lesson. In the purely competitive setting, an agent can generate its own training curriculum by playing against copies of itself — self-play, the method behind AlphaGo, OpenAI Five, and AlphaStar. We develop why self-play produces an ever-improving opponent, the systems it built, and then the equilibrium solution concepts (Nash, correlated, coarse-correlated) that define what \"solved\" means once there is an opponent, closing with PSRO, MAPPO, and the language-model-agent frontier.\n",{"path":5760,"title":5761,"module":5705,"summary":5762},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl","Hierarchical RL: Options and the Option-Critic","Flat RL cannot explore a long horizon: reaching reward through hundreds of primitive actions is exponentially unlikely, and every credit-assignment update crawls one step at a time. Hierarchy breaks one hard long-horizon problem into many short ones. This lesson develops temporal abstraction — the options framework and its semi-Markov view, and learning options end to end with the option-critic. A companion lesson takes up goal-conditioned manager\u002Fworker hierarchies (FeUdal Networks and HIRO), hindsight relabeling, and unsupervised skill discovery.\n",{"path":5764,"title":5765,"module":5705,"summary":5766},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl-part-2","Hierarchical RL: Goal-Conditioned Hierarchies and Skills","A companion to the options lesson. Options package a behavior; goal-conditioned hierarchies instead give the top level an explicit language of goals — a manager proposes a target state or a latent direction, and a worker is rewarded for reaching it (FeUdal Networks, HIRO). We develop that architecture, the hindsight relabeling that lets it learn from sparse reward, and unsupervised skill discovery (DIAYN) that learns a repertoire of behaviors with no reward at all. The shared idea throughout: shorten the horizon by inserting a level that decides less often.\n",{"path":5768,"title":5769,"module":5705,"summary":5770},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Frlhf-and-language-models","RLHF and Language Models","A language model trained to predict the next token is fluent but not helpful, honest, or harmless — the objective it was optimized for is not the objective we want. RLHF closes that gap by turning the one thing humans do reliably, comparing two outputs, into a reward. We build the three-stage pipeline: supervised fine-tuning, a Bradley-Terry reward model fit to preference pairs, then PPO against that reward with a KL penalty keeping it near the reference policy. We then cover reward hacking and why the KL penalty matters, Direct Preference Optimization, which folds the reward model into a single classification loss, and the RLAIF and verifiable-reward variants. This pipeline is what makes the largest models usable as assistants.\n",{"path":5772,"title":5773,"module":5705,"summary":5774},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps","Partial Observability: POMDPs and the Belief State","Drop the assumption that the agent sees the state. It sees an observation, a partial and noisy function of a hidden state, and one observation is no longer a Markov signal. This lesson builds the POMDP tuple, shows that the belief state — the posterior over hidden states — is a sufficient statistic that turns a POMDP back into an MDP over beliefs, and works the Bayes-filter belief update step by step. A companion lesson explains why exact planning is intractable and develops the deep-RL answer of recurrent, history-based policies.\n",{"path":5776,"title":5777,"module":5705,"summary":5778},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps-part-2","Partial Observability: Planning and Recurrent Policies","A companion to the belief-state lesson. In principle a POMDP reduces to an MDP over beliefs; in practice two obstacles block that. Exact planning over the belief simplex is intractable — the value function is piecewise-linear-and-convex with a number of pieces that can explode — and computing the belief needs a model the agent rarely has. This lesson develops the intractability, the point-based approximations that address it, and the deep-RL answer: make the policy a function of history with a recurrent network (DRQN, R2D2), with frame-stacking, attention, and world-model latents as learned beliefs.\n",{"path":5780,"title":5781,"module":5705,"summary":5782},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl","Safe and Constrained RL: The CMDP and Policy Methods","Maximizing a scalar reward is not the same as behaving well: a capable optimizer will find and exploit any gap between the reward and what its designer actually meant, a failure called specification gaming or reward hacking. The remedy is to add explicit cost constraints — the constrained MDP — maximizing return subject to an expected-cost budget. This lesson builds the core toolkit: the CMDP itself, Lagrangian primal-dual methods that learn a multiplier on the constraint (RCPO), and constrained policy optimization (CPO) with its trust-region cost bound. A companion lesson covers risk-sensitivity, safe exploration, and the alignment framing.\n",{"path":5784,"title":5785,"module":5705,"summary":5786},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl-part-2","Safe RL: Risk, Safe Exploration, and Alignment","A companion to the constrained-MDP lesson. Constraining the mean cost is not enough: a policy safe on average can be catastrophic in the tail, and a policy safe at convergence can violate its limits wildly while learning. This lesson optimizes the tail with risk-sensitive objectives (CVaR), then makes exploration itself safe with shields, Lyapunov methods, and safety layers that project unsafe actions onto the feasible set — closing with benchmarks, safe RLHF, robustness, and the alignment framing that ties safety back to the problem of incompletely specified reward.\n",{"path":5788,"title":5789,"module":5705,"summary":5790},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmeta-rl-and-generalization","Meta-RL and Generalization","An agent that masters one task often fails on the next; it has overfit to a single environment. This lesson treats fast adaptation as a meta-problem over a distribution of tasks: meta-train so that a few episodes at meta-test time suffice. We cover the two families — optimization-based (MAML learns an initialization) and context-based (RL-squared and PEARL infer a latent task) — the exploration cost of adaptation, and the parallel problem of generalization: why deep RL memorizes environments and what fixes it (domain randomization, procedural generation, augmentation, regularization). It closes on foundation models and sequence-model agents as the generalist endpoint.\n",{"path":5792,"title":5793,"module":5794,"summary":5795},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fpsychology-of-reinforcement","The Psychology of Reinforcement","Reinforcement Learning in Minds and Brains","Reinforcement learning is both an engineering method and a theory of how animals learn. The prediction\u002Fcontrol split of the algorithms mirrors the psychologist's split between classical and instrumental conditioning. We trace the correspondence: the Rescorla–Wagner model as a prediction-error rule that explains blocking, its real-time TD extension, Thorndike's Law of Effect behind trial-and-error control, and the habitual\u002Fgoal-directed distinction that maps onto model-free versus model-based learning.\n",{"path":5797,"title":5798,"module":5794,"summary":5799},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Finstrumental-conditioning-and-control","The Psychology of Reinforcement: Instrumental Control","Classical conditioning was prediction; instrumental conditioning is control. Thorndike's Law of Effect is trial-and-error control — selection plus association, search plus memory — and Skinner's shaping and schedules are reward engineering. The habitual\u002Fgoal-directed distinction maps onto model-free versus model-based control, dissociated by outcome devaluation and arbitrated by uncertainty. Delayed reinforcement is the credit-assignment problem, and the stimulus traces and secondary reinforcers of animal-learning theory are eligibility traces and value functions.\n",{"path":5801,"title":5802,"module":5794,"summary":5803},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-and-td-error","Dopamine and the TD Error","The TD error was invented as an algorithm; a decade later it turned out to closely describe the firing of the brain's dopamine neurons. We follow Schultz's experiments — dopamine fires at an unpredicted reward, shifts to the earliest predictive cue, and dips below baseline when a predicted reward is withheld — and match each result to the TD error term by term. We then read the basal ganglia as a neural actor–critic with dopamine as its shared training signal, and close on addiction as a hijacking of that signal.\n",{"path":5805,"title":5806,"module":5794,"summary":5807},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-in-the-brain","Dopamine in the Brain: The Neural Actor–Critic","If phasic dopamine is a TD error, where does it go and what does it change? We follow the axons into the basal ganglia, read the corticostriatal synapse as the place where state, action, and error meet, and map the ventral and dorsal striatum onto the critic and the actor of an actor–critic. Addiction becomes a broken cancellation in the same learning signal, and distributional dopamine extends the scalar RPE into a population code.\n",{"path":5809,"title":5810,"module":5794,"summary":5811},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fanimal-learning-and-cognition","Animal Learning and Cognition","Three classic associative phenomena turn out to be reinforcement-learning mechanisms seen in behavior. Blocking says learning is driven by prediction error, not co-occurrence, and reduces to least-squares regression fitting a collinear feature. Higher-order conditioning and conditioned reinforcement make a value estimate a secondary reinforcer — bootstrapping in an animal. Delayed reinforcement is the credit-assignment problem, and the stimulus traces and goal gradients of Pavlov and Hull are eligibility traces and TD-learned value functions.\n",{"path":5813,"title":5814,"module":5794,"summary":5815},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fcognitive-maps-and-planning","Cognitive Maps and Model-Based Learning","Tolman's rats learned the layout of a maze with no reward, then used it the moment food appeared — latent learning, a cognitive map, and the behavioral face of model-based reinforcement learning. The map is learned by system identification (stimulus–stimulus associations), which fills in whether or not reward is present, and queried by planning, which re-solves a route from a single changed reward. The successor representation sits between cache and model, and hippocampal predictive maps and scaled-up world models carry the same idea into brain and machine.\n",{"path":5817,"title":5818,"module":5794,"summary":5819},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fneuroscience-of-reinforcement","The Neuroscience of Reinforcement","The dopamine story is one contact point between reinforcement learning and the brain; this lesson fills in the surrounding neuroscience so the mapping stands on its own. We build a working primer of neurons, synapses, and neuromodulation; separate four signals that casual usage conflates — reward, reinforcement, value, and prediction error; and read the actor and critic as corticostriatal synapses updated by two- and three-factor rules, grounded in spike-timing-dependent and reward-modulated plasticity.\n",{"path":5821,"title":5822,"module":5794,"summary":5823},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fseveral-learning-systems","The Brain's Several Learning Systems","The actor's three-factor rule has an ancestor in Klopf's hedonistic neuron — a single cell as a reinforcement-seeking agent — and a bacterium's run-and-twiddle shows the Law of Effect with no synapses at all. Teams of such neurons implement policy gradient collectively, the broadcast reward replacing backpropagation. And the brain is not only model-free: outcome devaluation, prefrontal value coding, and hippocampal forward sweeps localize a model-based system. The recurring conclusion is that the brain is several interacting learning systems, not one algorithm.\n",{"path":5825,"title":4981,"module":6,"summary":6},"\u002Freinforcement-learning",{"path":5827,"title":5828,"module":1231,"summary":5829},"\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai","What Is Artificial Intelligence?","Eight definitions of AI fall into a two-by-two grid: think versus act, and measure success against human performance versus an ideal standard of rationality. We work through all four schools — the Turing test, cognitive modelling, the laws of thought, and the rational agent — and adopt the last as the frame for the whole course: AI is the study and design of rational agents.\n",{"path":5831,"title":5832,"module":1231,"summary":5833},"\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai","The Foundations of AI","Where the rational-agent idea came from and what surrounds it. AI inherited its core tools from eight older disciplines — philosophy, mathematics, economics, neuroscience, psychology, computer engineering, control theory, and linguistics. Its history runs in cycles of boom and winter, from the 1956 Dartmouth workshop through expert systems to the statistical turn. And the deep-learning era — AlexNet, the Transformer, GPT-3, AlphaGo — is a new way of computing the agent function at scale, not a new definition of AI.\n",{"path":17,"title":18,"module":1231,"summary":5835},"An agent perceives an environment through sensors and acts on it through actuators; its behavior is an agent function mapping percept sequences to actions. A rational agent chooses, for each percept sequence, the action that maximizes its expected performance measure given its knowledge. We build the first half of the vocabulary the whole course rests on — the agent function, rationality, PEAS task specifications, and the six axes along which task environments vary.\n",{"path":1233,"title":5,"module":1231,"summary":1249},{"path":684,"title":5838,"module":5839,"summary":5840},"Uninformed Search","Search","A goal-based agent that cannot see which action is best turns the problem into a state space — an initial state, a set of actions, a transition model, a goal test, and a path cost — and searches for a sequence of actions reaching the goal. We build the state-space formulation on the 8-puzzle and route-finding, give the one TREE-SEARCH \u002F GRAPH-SEARCH skeleton every algorithm specializes, and measure strategies by completeness, optimality, and complexity. This lesson develops the first two frontier disciplines — breadth-first and uniform-cost search; the rest follow in the next lesson.\n",{"path":5842,"title":5843,"module":5839,"summary":5844},"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared","Search Strategies Compared","Breadth-first and uniform-cost search pay for optimality in memory. This lesson develops the strategies that trade memory for depth: depth-first search, which keeps only the current path; depth-limited and iterative-deepening search, which fix DFS's failure on infinite paths; and bidirectional search, which meets in the middle for a square-root saving. It closes by lining up all six uninformed strategies against completeness, optimality, and complexity, and tracing where the algorithms came from and where they went.\n",{"path":5846,"title":5847,"module":5839,"summary":5848},"\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search","Informed Search and A*","An informed search uses a heuristic $h(n)$, an estimate of the cost from a node to the goal, to decide what to expand next. Greedy best-first search follows the heuristic blindly and gives up optimality; A* corrects it by ranking nodes on $f(n) = g(n) + h(n)$, and is optimal when the heuristic is admissible (tree search) or consistent (graph search). This lesson defines the heuristic, builds best-first search, and proves why A* is optimal, with the contour picture that explains its pruning. Where good heuristics come from is the next lesson.\n",{"path":5850,"title":5851,"module":5839,"summary":5852},"\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions","Heuristic Functions and Memory-Bounded Search","A* is only as good as its heuristic, so this lesson answers where good heuristics come from: relaxed problems, whose exact solution cost is an admissible heuristic, and pattern databases, which precompute subproblem costs. It measures heuristic quality with dominance and the effective branching factor, then tackles A*'s memory problem with IDA*, RBFS, and SMA*. It closes with modern heuristic search — weighted A*, learned and disjoint pattern-database heuristics, and bidirectional A*.\n",{"path":5854,"title":5855,"module":5839,"summary":5856},"\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search","Local Search and Optimization","When the path to a goal is irrelevant and only the final state matters, we can discard the search tree entirely and keep just the current state, moving to a better neighbor at each step. This lesson builds the state-space landscape metaphor, works through hill climbing and the three obstacles that defeat it (local maxima, ridges, plateaus), then develops the first escapes: random restarts and simulated annealing with its temperature schedule. The population-based methods and continuous-space calculus follow in the next lesson.\n",{"path":5858,"title":5859,"module":5839,"summary":5860},"\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search","Population and Continuous Search","Single-state local search escapes a trap by restarting or tolerating downhill moves. This lesson develops the alternatives that keep several states at once — local beam search, which shares successors across parallel threads, and genetic algorithms, which recombine two parents through crossover and mutation — then crosses into continuous spaces, where calculus replaces the finite neighbor set: gradient ascent, line search, and Newton's method. It closes with the industrial descendants of these methods and the loop they all share.\n",{"path":5862,"title":5863,"module":5839,"summary":5864},"\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search","Adversarial Search and Games","When another agent plans against you, search becomes a game. We formalize two-player, zero-sum, perfect-information games as search problems, define the minimax value that optimal play backs up through the game tree, and give the MINIMAX algorithm that computes it. Alpha–beta pruning then cuts the cost of that search roughly in half in the exponent without changing the answer, and a heuristic evaluation function plus a cutoff test turns the exact algorithm into a real-time player that copes with the horizon effect.\n",{"path":5866,"title":5867,"module":5839,"summary":5868},"\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information","Games of Chance and Imperfect Information","Minimax and alpha–beta assume a deterministic game both players can see in full. Drop either assumption and search must change. This lesson adds chance nodes and the expectiminimax value for games with dice, then belief-state reasoning for partially observable games — Kriegspiel and card games — where averaging over clairvoyance both helps and misleads. It closes with the line from Deep Blue's alpha–beta to AlphaGo's learned evaluation and Monte Carlo tree search, and the provable-pruning and self-play research around each end of that story.\n",{"path":1058,"title":5870,"module":5839,"summary":5871},"Constraint Satisfaction Problems","A constraint satisfaction problem replaces the black-box state with a factored one: variables, domains, and constraints. That structure supports inference before any search runs. This lesson defines the CSP on map coloring, Sudoku, and scheduling, then develops constraint propagation: node and arc consistency, the AC-3 algorithm that makes a whole network arc-consistent, and the way one deleted value cascades across the graph to prune impossible options ahead of search.\n",{"path":5873,"title":5874,"module":5839,"summary":5875},"\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure","CSP Search and Structure","Propagation prunes a CSP but rarely finishes it, so we search. This lesson builds backtracking search over partial assignments and the general-purpose heuristics that make it fast — MRV, degree, least-constraining-value, forward checking, MAC, and intelligent backtracking. It then shows how the shape of the constraint graph controls difficulty: tree-structured problems fall in linear time, cutset conditioning handles the rest, and min-conflicts local search solves a million queens in a constant number of steps.\n",{"path":5877,"title":5878,"module":5839,"summary":5879},"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty","Search Under Uncertainty","Classical search assumes the agent knows the state it is in and exactly what each action does. Drop the second assumption and a plan can no longer be a fixed sequence of actions. This lesson develops the first response: AND-OR search over nondeterministic actions, which returns a branching contingency plan rather than a straight line. We build it on the erratic vacuum world, show how OR nodes (the agent's choices) alternate with AND nodes (nature's outcomes), trace the recursion that finds a plan, and handle the case where the only solution is a cyclic \"try, try again.\"\n",{"path":5881,"title":5882,"module":5839,"summary":5883},"\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search","Belief-State and Online Search","When the agent cannot see the full state, a plan can no longer test where it actually is — it must reason over the set of states it might be in. This lesson develops belief-state search, from sensorless (conformant) planning that coerces an unknown world into a goal, through the predict-observe-update cycle of contingent planning with percepts, to online search in unknown environments, where the agent must act in order to learn. It closes with LRTA*, which refines its own heuristic as it explores, one step from reinforcement learning.\n",{"path":1063,"title":5885,"module":5886,"summary":5887},"Logical Agents and Propositional Logic","Logic and Planning","A knowledge-based agent keeps a store of sentences and acts by asking it what to do. To make \"asking\" mean something we need entailment — the relation $KB \\models \\alpha$ that holds when every model of the knowledge base is a model of the query. Propositional logic gives a syntax and a truth-table semantics for which entailment is decidable. This first part builds the foundations: the agent loop, the Wumpus World, models and entailment, the connectives and truth tables, theorem proving by refutation, and the resolution rule with its CNF conversion — a single complete inference procedure for all of propositional logic.\n",{"path":5889,"title":5890,"module":5886,"summary":5891},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference","Propositional Inference and Logical Agents","Model checking and resolution decide entailment, but both can blow up. This part turns propositional logic into a practical engine and a working agent. Horn clauses give linear-time forward and backward chaining — the basis of logic programming. DPLL and WalkSAT make satisfiability testing fast in the common case. Then we make the agent situated: time-indexed fluents, the frame problem and its solution by successor-state axioms, a hybrid agent that deduces a safe map and plans a route through it, and SATPlan, which finds a plan by asking a SAT solver for a satisfying model.\n",{"path":1077,"title":5893,"module":5886,"summary":5894},"First-Order Logic","Propositional logic can only say that facts hold; it cannot talk about the objects a fact is about, or state a rule once and have it cover every object. First-order logic fixes this by committing to a world of objects, relations, and functions. This first part builds the language from the ground up: the ontology it commits to, the model that gives a sentence a truth value, the syntax of terms and sentences, the two quantifiers with their standard mistakes, and equality.\n",{"path":5896,"title":5897,"module":5886,"summary":5898},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use","First-Order Logic in Use","With the language of first-order logic in hand, this part is about using it well. Database semantics trades expressive power for the convenience of a single intended model; higher-order logic shows what first-order logic gives up for decidability. Then we put the language to work: the Tell\u002FAsk interface, the kinship domain axiomatized from scratch, and the seven-step knowledge-engineering process applied to a digital circuit.\n",{"path":5900,"title":5901,"module":5886,"summary":5902},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution","Inference in First-Order Logic","Propositional inference lifts to first-order logic once we can make terms match. Unification is that machinery: the algorithm that finds the substitution making two expressions identical, and the basis of generalized modus ponens. This first part builds the lifted inference rules and the two chaining algorithms they drive — forward chaining, the data-driven procedure behind production systems and Datalog, and backward chaining, the goal-driven procedure behind Prolog.\n",{"path":5904,"title":5905,"module":5886,"summary":5906},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution","First-Order Resolution","Chaining is complete only for Horn knowledge bases. General first-order sentences — with disjunctive conclusions and negations — need a single sound and complete rule: resolution. This part converts arbitrary sentences to CNF by skolemizing away the existentials, lifts the resolution rule with unification, and proves entailment by refuting the negated goal. The result is the proof procedure Gödel's completeness theorem guarantees will find any entailment, together with the search strategies that make it usable.\n",{"path":688,"title":5908,"module":5886,"summary":5909},"Classical Planning","Classical planning represents a problem in a factored language, PDDL: states are sets of ground fluents, and actions are lifted schemas with a precondition and an effect. That structure turns planning into search — forward through states or backward through goals — and lets a program read heuristics straight off the schemas by relaxing the problem. This first part develops the representation, the two search directions, and the domain-independent heuristics that come from ignoring preconditions or delete lists.\n",{"path":5911,"title":5912,"module":5886,"summary":5913},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan","Planning Heuristics and GraphPlan","Every relaxation heuristic can be inaccurate, and none can tell how far apart subgoals sit. The planning graph is a polynomial-size structure that does better: leveled off the problem, it yields admissible distance estimates and a record of which actions and fluents cannot coexist. This part builds the graph, reads heuristics from it, extracts plans with GraphPlan, and closes with the other classical approaches — SATPlan and partial-order planning — and the representational trade that makes all of it work.\n",{"path":5915,"title":5916,"module":5886,"summary":5917},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world","Planning and Acting in the Real World","Classical planning's clean theory rests on four assumptions: time is ignored, actions are atomic, the world is deterministic and fully observable, and the agent is alone. This first part drops the first two. We add durations and resource constraints — turning a plan into a schedule, solved by the critical-path method and, once resources contend, by NP-hard job-shop scheduling — and let a planner reason at multiple levels of abstraction through high-level actions and their angelic reachable sets.\n",{"path":5919,"title":5920,"module":5886,"summary":5921},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty","Planning Under Uncertainty","Classical planning assumed the world was deterministic, fully observable, and the agent alone. This part drops the last two assumptions. When the agent cannot see or predict the world, planning moves into belief-state space: sensorless plans that coerce the world into the goal without sensing, contingent plans that branch on what is sensed, and online agents that monitor and replan when execution diverges. Then we add other agents — joint plans, the coordination problem, and the conventions that let a team act without constant negotiation.\n",{"path":5923,"title":5924,"module":5886,"summary":5925},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation","Knowledge Representation","First-order logic gives you the language; this lesson is about what to say in it. This first part builds the content: a general upper ontology from the top down, categories as first-class objects with taxonomies and inheritance, physical composition and the count-noun\u002Fmass-noun split, events and time reified through the event calculus, and belief modeled with modal logic — the machinery for representing the world an agent reasons about.\n",{"path":5927,"title":5928,"module":5886,"summary":5929},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults","Reasoning Systems and Default Logic","Having represented the world, this part is about reasoning with it at scale. Semantic networks give a graphical notation with fast inheritance; description logics keep subsumption and classification tractable by design. Then we confront the fact that most useful rules hold only by default: circumscription and default logic give a logical account of nonmonotonic reasoning, and truth maintenance systems retract conclusions cleanly when the beliefs beneath them change.\n",{"path":5931,"title":5932,"module":5933,"summary":5934},"\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes","Quantifying Uncertainty","Uncertainty","Logic breaks down in any domain where the rules have exceptions you cannot enumerate — the qualification problem. Probability replaces truth values with degrees of belief that obey Kolmogorov's axioms, and the full joint distribution becomes a knowledge base from which any query is answered by summing entries: marginalization, conditioning, and normalization. Independence factors that joint into smaller pieces — the first step toward a calculus of rational belief that an agent can actually compute with.\n",{"path":5936,"title":5937,"module":5933,"summary":5938},"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes","Bayes' Rule and Naive Bayes","Bayes' rule inverts a causal model into a diagnostic one, turning \"how a cause produces its symptoms\" into \"which cause explains what I observed.\" Ignoring the prior is the base-rate fallacy behind overconfident test results. Conditional independence then lets several pieces of evidence combine by multiplying likelihood ratios instead of building an exponential joint, giving the naive Bayes model and pointing directly at Bayesian networks.\n",{"path":1068,"title":5940,"module":5933,"summary":5941},"Bayesian Networks","A Bayesian network is a directed acyclic graph of random variables in which each node carries a conditional probability table for itself given its parents. That structure factors the full joint distribution into a product of local terms, turning an exponential table into a linear one, and it makes the conditional independences of the domain explicit. We build the canonical burglary–alarm network, read compactness and d-separation off the graph, run exact inference by variable elimination, and, where that is intractable, estimate answers by sampling.\n",{"path":5943,"title":5944,"module":5933,"summary":5945},"\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks","Bayesian Networks: Inference and Relational Models","When exact inference is intractable, sampling estimates the posterior instead: prior and rejection sampling, likelihood weighting, and Gibbs\u002FMCMC, whose error shrinks as one over the square root of the sample count. The same graphical idea then lifts from a fixed set of variables to whole populations — relational and open-universe probability models write dependencies once and unroll them over objects — and we close by placing probability against the rule-based, Dempster–Shafer, and fuzzy alternatives it displaced.\n",{"path":5947,"title":5948,"module":5933,"summary":5949},"\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time","Probabilistic Reasoning over Time","A world that changes needs a state variable at every point in time. The Markov assumption cuts the dependence on history down to the previous slice, leaving a transition model and a sensor model that define a temporal Bayesian network. Four recursive tasks fall out — filtering, prediction, smoothing, and the most likely explanation — each a message passed along the sequence. We ground them in hidden Markov models and their matrix form, sketch the Kalman filter for continuous state, and reach dynamic Bayesian networks with particle filtering as the general approximate method.\n",{"path":5951,"title":5952,"module":5933,"summary":5953},"\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association","Reasoning over Time: Tracking and Data Association","Dynamic Bayesian networks generalize HMMs and Kalman filters to arbitrarily many state variables per slice, and when exact inference blows up, particle filtering approximates the belief state with a population of weighted samples that propagate, reweight, and resample. Tracking several objects at once adds the data-association problem — which observation came from which object — whose combinatorics defeat any exact filter, so particle filters and MCMC keep many hypotheses alive. We close with SLAM and learned state-space models.\n",{"path":963,"title":5955,"module":5933,"summary":5956},"Making Decisions: Utility Theory","A rational agent chooses the action that maximizes expected utility — the probability of each outcome weighted by how much the agent wants it. We derive the utility function from six axioms on preferences, so maximizing expected utility is forced by consistency rather than assumed; look at risk aversion in the utility-of-money curve; package one-shot choices into decision networks; and quantify what an observation is worth with the value of information.\n",{"path":5958,"title":5559,"module":5933,"summary":5959},"\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes","When an agent must act repeatedly in a stochastic world, a fixed plan is useless — it needs a policy, an action for every state. The Markov decision process makes this precise with a transition model, a reward, and a discount factor; the Bellman equation characterizes the optimal state utilities, and value iteration and policy iteration solve it. Partial observability lifts the problem to belief states, and bandits, Monte-Carlo tree search, and scalable POMDP solvers extend it — this is the model-known half of reinforcement learning.\n",{"path":5961,"title":5962,"module":5933,"summary":5963},"\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory","Decision Analysis: Multi-Attribute Utility and Decision Networks","Decision analysis takes the single-agent utility framework and makes it practical: utility over several attributes, dominance and additive value functions, influence diagrams that fold Bayesian networks together with decision and utility nodes, and the value of information that tells an agent which questions are worth asking. Structure in an agent's preferences — dominance, preferential and utility independence — collapses an exponential utility table into a few one-dimensional functions, the same move that made Bayesian networks compact.\n",{"path":5965,"title":5966,"module":5933,"summary":5967},"\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design","Game Theory and Mechanism Design","When outcomes depend on other rational agents, single-agent utility maximization no longer suffices. Game theory studies decisions among agents — normal-form games, dominant strategies, Nash and maximin equilibria, and repeated games — and mechanism design runs the logic backwards, engineering rules (auctions, VCG) so that self-interested play produces a good collective outcome. Algorithmic game theory then asks whether equilibria can be computed, what selfishness costs society, and how the mechanisms deployed at internet scale actually behave.\n",{"path":5969,"title":5970,"module":5971,"summary":5972},"\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples","Learning from Examples","Learning","An agent that improves with experience does not need its designer to anticipate every situation. Inductive learning takes that ambition and narrows it to one tractable problem: from labelled input-output pairs, recover a function that predicts the output for inputs never seen. This first part builds the foundation around a single organizing question — generalization — through decision trees and information gain, and the training\u002Fvalidation\u002Ftest discipline for evaluating and choosing hypotheses. A second part takes up the theory of learning and the main model families.\n",{"path":5974,"title":5975,"module":5971,"summary":5976},"\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families","The Theory of Learning and Model Families","Cross-validation measures generalization but does not explain it. This part supplies the theory — PAC learning, sample complexity, and the VC dimension — that says when a hypothesis consistent with enough data is probably approximately correct, and why an unrestricted hypothesis space can never generalize. It then surveys the model families a practitioner reaches for: linear regression and gradient descent, the perceptron and logistic regression, support vector machines and the kernel trick, and ensembles by bagging and boosting — closing with what deep learning changed about the classical picture.\n",{"path":5978,"title":5979,"module":5971,"summary":5980},"\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning","Learning Probabilistic Models","A [Bayesian network](\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks) is useless until its numbers are filled in, and those numbers come from data. This first part casts learning itself as probabilistic inference: hypotheses carry a prior, data update it to a posterior, and predictions average over what remains. From that frame fall the standard estimators — maximum likelihood by counting, MAP with a conjugate prior, full Bayesian updating — for the case where every variable is observed. A second part takes up the harder case of hidden variables and the EM algorithm.\n",{"path":5982,"title":5983,"module":5971,"summary":5984},"\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization","Learning with Hidden Variables: The EM Algorithm","Complete data can be learned by counting; real data usually hide some variables — the disease behind the symptoms, the cluster behind the points. This part develops the expectation-maximization algorithm, which learns those models by alternating an expected completion of the missing data with a re-estimation of the parameters. It works the idea through mixtures of Gaussians, Bayesian networks, and hidden Markov models, proves the monotone-likelihood guarantee from the evidence lower bound, and traces the line from EM to variational inference and the variational autoencoder.\n",{"path":1020,"title":4981,"module":5971,"summary":5986},"Reinforcement learning is an MDP with the model unknown: the agent knows neither how its actions move the world nor which states are rewarded, and must recover good behaviour from experienced transitions and rewards alone. This first part builds the classical tabular theory — passive learning (fix a policy, learn its value, by direct estimation, adaptive dynamic programming, and temporal differences) and active learning (choose actions, trade exploration against exploitation, and learn control with Q-learning and SARSA). A second part lifts it off the lookup table with function approximation and policy search.\n",{"path":5988,"title":5989,"module":5971,"summary":5990},"\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search","Reinforcement Learning: Generalization and Policy Search","Tabular reinforcement learning stores one number per state, which is hopeless for backgammon or chess. This part lifts RL off the lookup table with function approximation, so that updating one state generalizes to related ones, then turns to policy search — representing and optimizing the policy directly, up to the REINFORCE policy gradient and correlated sampling. It closes with the bridge to deep reinforcement learning (deep Q-networks, actor-critic, PPO), the classic applications, and the hand-off to the dedicated RL subject.\n",{"path":5992,"title":5993,"module":5971,"summary":5994},"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning","Knowledge in Learning","Pure induction learns a function from labelled examples while knowing almost nothing to begin with. This first part brings prior knowledge into the loop by recasting learning as logical inference — hypotheses, examples, and classifications as sentences. It develops current-best-hypothesis search, the version space and its general\u002Fspecific boundary maintained by candidate elimination, and states the three entailment constraints that fix how background knowledge enters. A second part builds the three knowledge-based methods those constraints define.\n",{"path":5996,"title":5997,"module":5971,"summary":5998},"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods","Knowledge-Based Learning: EBL, Relevance, and ILP","Once learning is cast as logical inference, three methods follow from the three ways prior knowledge can enter. Explanation-based learning generalizes a single example by explaining it with the domain theory, gaining speed but nothing new. Relevance-based learning uses determinations to shrink the hypothesis space and converge from fewer examples. Inductive logic programming learns genuinely new first-order rules — top-down with FOIL, bottom-up by inverting resolution, even inventing new predicates — and connects to modern statistical relational and neuro-symbolic learning.\n",{"path":6000,"title":6001,"module":6002,"summary":6003},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception","Vision and Perception","Frontiers","Perception connects an agent to the physical world. We follow one modality — vision — from the physics of image formation (the pinhole camera, perspective projection, lenses, shading, color) through the early operations that turn a pixel array into edges, texture, and motion, and into recognition by appearance. The recurring problem is inversion: a camera collapses a 3-D world onto a 2-D grid, and an agent that wants to act must build the scene back up. Rebuilding the scene is the subject of the companion lesson.\n",{"path":6005,"title":6006,"module":6002,"summary":6007},"\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world","Vision: Reconstructing the 3D World","A camera collapses a three-dimensional world onto a flat grid; this lesson inverts that collapse. We build the camera projection matrix (intrinsics and extrinsics), triangulate a point from two views, then work through the toolbox of depth cues — motion parallax, binocular stereopsis, multiple views, texture, shading, and contour — that turn an ambiguous image back into a scene. We add structural recognition (pictorial-structure \"cardboard people\"), the task-driven use of vision in cars and robots, and the shift from hand-built pipelines to learned deep-vision networks.\n",{"path":6009,"title":6010,"module":6002,"summary":6011},"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics","Robotics","A robot is an agent with a body: sensors that read the physical world and effectors that push back on it. This lesson grounds the abstract AI machinery in that body. We build up the hardware (range finders, proprioception, degrees of freedom), then cast perception as probabilistic filtering — the kinematic motion and sensor models, Monte Carlo localization, the extended Kalman filter, and simultaneous localization and mapping (SLAM). The companion lesson takes the estimated pose forward into planning and control.\n",{"path":6013,"title":6014,"module":6002,"summary":6015},"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control","Robotics: Planning and Control","A robot that knows where it is still has to decide how to move, and then make a slipping, sensing-imperfect body actually go there. This lesson takes the pose estimate forward: planning motion in configuration space with cell decomposition and sampling-based roadmaps (PRMs and RRTs), planning under uncertainty with most-likely-state and online replanning, closing the loop with P\u002FPD\u002FPID control and potential fields, and finally the software architectures — subsumption, three-layer, and pipeline — that assemble it all, plus the learning-based turn in modern robotics.\n",{"path":6017,"title":6018,"module":6002,"summary":6019},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai","Natural Language for AI Agents","Language is how agents acquire the knowledge already written down and how they communicate with the humans they serve. This lesson gives the classical AI account of language as a source of information: n-gram language models and the information-seeking tasks built on them — text classification, information retrieval (BM25, the inverted index, PageRank), and information extraction with finite-state templates and hidden Markov models. Throughout, we point to the dedicated NLP subject for the modern deep-learning treatment; the companion lesson takes up grammar, translation, and speech.\n",{"path":6021,"title":6022,"module":6002,"summary":6023},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech","Language for AI Agents: Grammar, Translation, and Speech","N-gram models see only a local window; they cannot say why \"black dog\" is well-formed English and \"dog black\" is not, because that is a fact about structure. This lesson takes up structure: phrase-structure and probabilistic context-free grammars, syntactic analysis by chart parsing and CYK, augmented grammars and compositional semantics, then the two major statistical successes — machine translation and speech recognition — cast as noisy-channel problems. It closes with the bridge from n-grams to transformers and where the classical account sits relative to modern NLP.\n",{"path":6025,"title":6026,"module":6002,"summary":6027},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future","Philosophy, Ethics, and the Future of AI","Two questions have shadowed the field since its founding: can machines act intelligently (weak AI), and can they really think (strong AI)? We work through Turing's objections and their rebuttals — the arguments from disability, mathematics, and informality — then the strong-AI debate: the mind-body problem, functionalism and the brain prosthesis, Searle's Chinese Room and the systems reply, and consciousness and qualia. The companion lesson turns from what AI can do to what it should, and closes the course.\n",{"path":6029,"title":6030,"module":6002,"summary":6031},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future","The Ethics and Future of AI","Having asked whether machines can act intelligently and really think, we turn to whether we should build them at all. This lesson works through the six ethical risks — lost jobs, autonomous weapons, surveillance and privacy, biased decisions, the safety of superintelligence, and the erosion of accountability — then the value-alignment problem in the LLM era, and where the classical agent components could go next. It closes the course by tying search, logic, probability, and learning into a single picture of intelligence as rational agency.\n",{"path":6033,"title":6034,"module":6,"summary":6},"\u002Fartificial-intelligence","Artificial Intelligence",{"path":6036,"title":6037,"module":6038,"summary":6039},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart","Nuclear Composition and Ground-State Properties","Nuclear Properties","The nucleus is a bound assembly of Z protons and N neutrons packed to a radius R = R0 A^(1\u002F3) at a nearly constant density of about 10^17 kg\u002Fm^3. We fix the vocabulary of nuclides, derive nuclear size from mirror-nuclide and electron-scattering data, read the binding-energy-per-nucleon curve, and model it with the liquid-drop semiempirical mass formula.\n",{"path":6041,"title":6042,"module":6038,"summary":6043},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions","Nuclear Size, Shape, and Charge Distributions","Elastic electron scattering resolves the nucleus by its de Broglie wavelength. The measured cross section is the Mott point-charge cross section modulated by a form factor, and that form factor is the Fourier transform of the charge density. Diffraction minima fix the radius, the small-angle slope fixes the mean-square radius, and the fitted Woods-Saxon profile gives a central density and a skin thickness. Mirror-nucleus Coulomb energies, muonic-atom X-rays, and optical isotope shifts give independent radii that all track R = R0 A^(1\u002F3).\n",{"path":6045,"title":6046,"module":6038,"summary":6047},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy","Nuclear Masses, Mass Excess, and Separation Energies","The atomic mass unit fixes the scale, and the mass excess collects the small binding-driven deviation from the integer mass number. Penning-trap cyclotron frequencies now measure masses to parts in a billion, and every decay and reaction Q-value is a difference of these masses. One- and two-nucleon separation energies read the binding difference between neighbouring nuclides directly, showing the even-odd pairing stagger and the sharp drops at magic numbers, and their vanishing marks the neutron and proton drip lines that bound the chart of the nuclides.\n",{"path":6049,"title":6050,"module":6038,"summary":6051},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula","The Semi-Empirical Mass Formula and the Valley of Stability","Five physical terms reproduce nuclear binding across the chart: a volume term from saturation, a surface term from the deficit of edge neighbours, a Coulomb term from the electrostatic self-energy of a charged sphere, an asymmetry term from the Pauli cost of unequal proton and neutron filling, and a pairing term. The formula is quadratic in Z at fixed A, so isobars lie on a mass parabola whose minimum sets the most stable charge and whose slope dictates the direction of beta decay. The same competition between surface and Coulomb energy defines the fissility parameter and the onset of fission.\n",{"path":6053,"title":6054,"module":6038,"summary":6055},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles","Nuclear Spin, Magnetic Dipole, and Electric Quadrupole Moments","The ground state of a nucleus carries a definite spin and parity, a magnetic dipole moment of order the nuclear magneton, and, when its spin exceeds one-half, an electric quadrupole moment that measures its shape. The single-particle Schmidt lines predict the magnetic moment of an odd-A nucleus from the last unpaired nucleon, and the measured moments fall between them. The quadrupole moment distinguishes prolate from oblate deformation, and hyperfine structure is the experimental handle that fixes the spin and the moments from an atomic spectrum.\n",{"path":6057,"title":6058,"module":6059,"summary":6060},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview","The Nuclear Force and the Shell Model","The Nuclear Force","The strong force between nucleons is short-range, charge-independent, saturated, and repulsive at its core, about a hundred times stronger than Coulomb. Yukawa explained it as an exchange of massive mesons, tying the force's range to the meson mass through the uncertainty principle. Layered on top, an independent-particle shell model with strong spin-orbit coupling reproduces the magic numbers 2, 8, 20, 28, 50, 82, 126.\n",{"path":6062,"title":6063,"module":6059,"summary":6064},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron","The Deuteron and the Tensor Force","The deuteron is the only bound two-nucleon state: one shallow level at 2.22 MeV, no excited states. A square-well fit fixes a depth near 35 MeV over a 2 fm range, yet the wavefunction leaks so far past the edge that most of the probability lies outside the force. Its spin-1 ground state, magnetic moment close to the sum of the free-nucleon moments, and small but nonzero electric quadrupole moment together force a D-state admixture and a non-central tensor force.\n",{"path":6066,"title":6067,"module":6059,"summary":6068},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering","Nucleon-Nucleon Scattering and the Interaction's Structure","Scattering probes the nuclear force above threshold. Partial-wave analysis reduces low-energy data to a single s-wave phase shift, and the effective-range expansion packages that into a scattering length and an effective range. The triplet channel binds (the deuteron) while the singlet is only virtual, which together explain the anomalously large free neutron-proton cross section. Comparing pp, nn, and np results establishes charge symmetry and charge independence, and polarization experiments expose the spin-orbit and tensor pieces.\n",{"path":6070,"title":6071,"module":6059,"summary":6072},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin","Meson Exchange, the Yukawa Potential, and Isospin","Yukawa's massive-field propagator turns the range of the nuclear force into a meson mass: the exchanged quantum's Compton wavelength is the range. One-pion exchange fixes the long-range tail, complete with the tensor structure the deuteron demanded, while heavier mesons build the intermediate attraction and the repulsive core. Charge independence becomes an isospin symmetry, the force is diagonalized by the total isospin through a tau-dot-tau interaction, and the whole picture sits inside QCD as a residual color force between color-neutral nucleons.\n",{"path":6074,"title":6075,"module":6076,"summary":6077},"\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model","The Fermi Gas Model","Nuclear Models","Treating the nucleus as two degenerate Fermi gases of protons and neutrons confined in a common well fixes the Fermi momentum near 250 MeV\u002Fc and the Fermi energy near 33 MeV from the nuclear density alone. The average kinetic energy per nucleon is about 20 MeV, the well depth is the Fermi energy plus the separation energy, and unequal proton and neutron Fermi levels reproduce the asymmetry term of the mass formula.\n",{"path":6079,"title":6080,"module":6076,"summary":6081},"\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates","The Liquid-Drop Model and Collective Deformation","Deforming a charged liquid drop into a spheroid raises its surface energy and lowers its Coulomb energy; the two effects compete through the deformation parameter to set a stability minimum and a fission barrier. The ratio of Coulomb to twice the surface energy is the fissility Z-squared over A, which crosses one near 49 and marks the point where the sphere is unstable. The same surface tension that restores small deformations quantizes into collective vibrations, carrying the static mass formula into dynamic collective motion.\n",{"path":6083,"title":6084,"module":6076,"summary":6085},"\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle","The Shell Model: Single-Particle States and Spin-Orbit Coupling","A harmonic-oscillator well reproduces the first three magic numbers but fails above twenty; adding a strong inverted spin-orbit term that drives the stretched j equals l plus one-half level down closes the gaps at 28, 50, 82, and 126. The filled shells couple to zero, so the last unpaired nucleon fixes the ground-state spin and parity, and its single-particle magnetic moment falls on the Schmidt lines. Configuration mixing sets the limits of the extreme single-particle model.\n",{"path":6087,"title":6088,"module":6076,"summary":6089},"\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations","The Collective Model: Rotations, Vibrations, and Deformed Nuclei","Deformed nuclei rotate with energies proportional to I times I plus one, giving the ground-state band its characteristic level ratios, while near-spherical nuclei vibrate in quantized surface phonons that build one- and two-phonon multiplets. The Nilsson model tracks single-particle levels as the well deforms, moments of inertia fall between the rigid and irrotational limits, backbending marks the sudden alignment of a broken pair, and giant resonances are the bulk dipole and quadrupole modes of the whole nucleus.\n",{"path":6091,"title":6092,"module":6093,"summary":6094},"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes","Radioactivity and Decay Modes","Radioactive Decay","Unstable nuclei decay at a rate proportional to how many remain, giving the exponential law N(t) = N0 e^(-lambda t) with half-life t = 0.693\u002Flambda. We work through the three common modes: alpha decay as Coulomb-barrier tunneling with the Geiger-Nuttall rule, beta decay whose continuous spectrum demands the neutrino, and gamma de-excitation, and follow a decay chain across the chart of nuclides.\n",{"path":6096,"title":6097,"module":6093,"summary":6098},"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium","Serial Decay, the Bateman Equations, and Radioactive Equilibrium","A radioactive parent that decays into a radioactive daughter obeys a coupled pair of rate equations whose solution is the Bateman formula. Depending on the half-life ordering the chain settles into secular equilibrium (equal activities), transient equilibrium (a fixed activity ratio), or no equilibrium. Constant production under irradiation drives the activity toward a saturation value equal to the production rate, competing decay modes split the total decay constant into partial constants, and the natural decay series in secular equilibrium underpin radiometric dating.\n",{"path":6100,"title":6101,"module":6102,"summary":6103},"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory","Alpha Decay and the Gamow Theory of Tunneling","Alpha Decay","The alpha Q-value turns positive above mass number 150 because the emitted helium-4 is exceptionally tightly bound. Emission proceeds by quantum tunneling through the Coulomb barrier: a WKB integral from the nuclear surface to the outer turning point gives the Gamow factor, and multiplying its penetrability by the assault frequency yields half-lives spanning more than twenty orders of magnitude. The leading term reproduces the Geiger-Nuttall relation, log t½ proportional to the daughter charge over the square root of Q.\n",{"path":6105,"title":6106,"module":6102,"summary":6107},"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance","Fine Structure, Angular Momentum, and Hindrance Factors","A single parent emits several alpha groups of slightly different energy, each feeding a distinct level of the daughter, so the alpha spectrum maps the daughter's low-lying states. Emission with orbital angular momentum L raises the barrier by a centrifugal term and is allowed only when angular-momentum and parity selection rules permit. Comparing the measured partial half-life to the Gamow estimate defines a hindrance factor near unity for even-even ground-state transitions and large for odd-A decays that must rearrange the unpaired nucleon.\n",{"path":6109,"title":6110,"module":6111,"summary":6112},"\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino","Beta Decay Energetics and the Neutrino","Beta Decay and the Weak Interaction","Beta decay converts a neutron into a proton or the reverse, adjusting Z at fixed A along an isobaric mass parabola. We write the three processes (beta-minus, beta-plus, electron capture), reduce every Q-value to a difference of neutral atomic masses, and read the continuous electron spectrum as the fingerprint of a third, nearly massless particle. Pauli's neutrino, its detection by Reines and Cowan, and the endpoint bound on its mass close the lesson.\n",{"path":6114,"title":6115,"module":6111,"summary":6116},"\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay","Fermi's Theory: Kurie Plots and ft Values","Fermi treated beta decay as a point-contact weak transition and read its rate from the golden rule. The electron spectrum then follows from phase space and the Coulomb Fermi function; the Kurie plot straightens it to a line whose intercept is the endpoint. Integrating the spectrum gives the comparative half-life ft, whose logarithm sorts transitions into superallowed, allowed, and forbidden classes governed by the Fermi and Gamow-Teller selection rules.\n",{"path":6118,"title":6119,"module":6111,"summary":6120},"\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation","The Weak Interaction and Parity Violation","Beta decay violates mirror symmetry. The Wu experiment on polarized cobalt-60 showed electrons emitted preferentially against the nuclear spin, a pseudoscalar correlation forbidden if parity were conserved. The result fixes the weak charged current as left-handed V minus A, forces neutrinos to be left-handed and antineutrinos right-handed (measured by Goldhaber), and places beta decay within the electroweak theory as W-boson exchange turning a down quark into an up quark.\n",{"path":6122,"title":6123,"module":6111,"summary":6124},"\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass","Double Beta Decay and Neutrino Mass","For even-A isobars the pairing term splits the mass parabola into two curves, and a handful of even-even nuclides sit below their odd-odd neighbor yet above the next even-even one: single beta decay is forbidden but second-order double beta decay is allowed. The two-neutrino mode is a standard-model process with the longest measured lifetimes in nature; the neutrinoless mode would require the neutrino to be its own antiparticle and its rate measures the effective Majorana mass, the sharpest probe of the absolute neutrino mass scale.\n",{"path":6126,"title":6127,"module":6128,"summary":6129},"\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation","Multipole Radiation and Selection Rules","Gamma Decay","Gamma decay carries a nucleus from an excited state to a lower one by emitting a photon of definite angular momentum and parity. We correct the photon energy for nuclear recoil, expand the radiation field into electric and magnetic multipoles, and read off how the transition rate collapses with each increase in multipole order. The Weisskopf single-particle estimates set the scale, and angular-momentum and parity conservation fix which multipole dominates.\n",{"path":6131,"title":6132,"module":6128,"summary":6133},"\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers","Internal Conversion and Isomers","A nucleus can shed excitation energy without emitting a photon by handing it directly to an atomic electron. We define the internal-conversion coefficient, trace its growth with atomic number, multipole order, and decreasing energy, and treat the electron-only E0 transitions and internal pair formation. When the lowest allowed multipole is high and the energy low, the gamma rate falls so far that the excited state survives as a metastable isomer.\n",{"path":6135,"title":6136,"module":6128,"summary":6137},"\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer","Angular Correlations and the Mössbauer Effect","Two gammas emitted in cascade are not independent in direction: detecting the first selects magnetic substates of the intermediate level and makes the second anisotropic, so the correlation function fixes the intermediate spin. The same nuclear resonance that recoil normally destroys is recovered when the emitter is locked in a lattice, giving the Mössbauer effect and its part-in-a-trillion resolution of isomer shifts and hyperfine fields.\n",{"path":6139,"title":6140,"module":6141,"summary":6142},"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections","Nuclear Reactions, Fission, and Fusion","Nuclear Reactions","A nuclear reaction X(x, y)Y is governed by its Q value and its cross section, the effective target area for a given process. Splitting the curve of binding energy near iron in either direction releases energy: fission of heavy nuclei by neutron capture and a chain reaction, and fusion of light nuclei that powers the Sun and needs Lawson's density-confinement criterion to be practical.\n",{"path":6144,"title":6145,"module":6141,"summary":6146},"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances","The Compound Nucleus and Resonance Reactions","Low-energy reactions proceed through a long-lived intermediate state whose decay forgets how it formed. Bohr's independence hypothesis factorizes the cross section into a formation step and a branching ratio, an isolated level gives the single-level Breit-Wigner line shape with total width Γ tied to the lifetime by Γτ = ħ, and at high excitation overlapping levels merge into a statistical continuum described by evaporation spectra and the Hauser-Feshbach average.\n",{"path":6148,"title":6149,"module":6141,"summary":6150},"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model","Direct Reactions and the Optical Model","A complex optical potential replaces the many-body target by a single particle moving in an average field whose imaginary part removes flux into non-elastic channels, reproducing the diffraction pattern of elastic scattering. Direct reactions bypass the compound nucleus, transferring a nucleon in one step: stripping and pickup deposit or remove a single nucleon, the angle of the first peak in the distorted-wave angular distribution fixes the transferred orbital angular momentum, and its magnitude gives the spectroscopic factor.\n",{"path":6152,"title":6153,"module":6154,"summary":6155},"\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics","The Fission Barrier and Fragment Energetics","Nuclear Fission","Fission is the large-amplitude collective deformation of a heavy nucleus into two fragments. The liquid-drop model sets a barrier from the competition between rising surface energy and falling Coulomb energy under quadrupole deformation, with the fissility parameter Z²\u002FA measuring how close a nucleus is to instability. Bohr-Wheeler theory separates spontaneous from neutron-induced fission, the fragment mass yield is double-humped and asymmetric, about 200 MeV is released per event, and shell corrections add a second minimum that produces fission isomers.\n",{"path":6157,"title":6158,"module":6154,"summary":6159},"\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics","Chain Reactions and Reactor Physics","A self-sustaining chain reaction is a fixed point of neutron bookkeeping: the multiplication factor k counts the neutrons in one generation per neutron in the last, and criticality is k = 1. The four-factor formula tracks a neutron through fast fission, resonance escape, thermal utilization, and reproduction; moderation slows fission neutrons to the thermal energies where the fission cross section is largest; and the small delayed-neutron fraction sets the timescale that makes a reactor controllable. Breeding converts fertile U-238 and Th-232 into new fissile fuel.\n",{"path":6161,"title":6162,"module":6163,"summary":6164},"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement","Fusion Reactions and Confinement","Fusion and Nucleosynthesis","Light nuclei release energy when they fuse because binding per nucleon rises steeply toward the iron peak, but the Coulomb barrier suppresses the rate at reactor temperatures. The thermonuclear rate is a convolution of the Maxwell distribution with the tunneling probability, sharply peaked at the Gamow energy. The deuterium-tritium reaction has the lowest barrier and largest cross section; sustained energy gain requires the Lawson triple product of density, temperature, and confinement time, reached by magnetic or inertial confinement.\n",{"path":6166,"title":6167,"module":6163,"summary":6168},"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis","Stellar Nucleosynthesis","Main-sequence stars burn hydrogen to helium through the proton-proton chain and the CNO cycle, both releasing 26.7 MeV per helium nucleus. Helium burning bridges the mass-5 and mass-8 gaps by the triple-alpha process through the Beryllium-8 and Hoyle resonances, and successive carbon-to-silicon burning stages climb to the iron peak, where fusion stops. The elements beyond iron are built by slow and rapid neutron capture, and the solar neutrino flux confirms the reactions directly.\n",{"path":6170,"title":6171,"module":6163,"summary":6172},"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis","Big-Bang Nucleosynthesis","In the first three minutes the expanding universe forged the light elements. The weak interaction froze the neutron-to-proton ratio near one in six when the reaction rate fell below the expansion rate, and free-neutron decay lowered it to about one in seven before the deuterium bottleneck broke. Almost every surviving neutron ended in helium-4, fixing the primordial helium mass fraction near 0.25, with trace deuterium, helium-3, and lithium-7. The deuterium abundance measures the cosmic baryon density.\n",{"path":6174,"title":6175,"module":6176,"summary":6177},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power","Stopping Power and the Range of Charged Particles","Radiation and Applications","A heavy charged particle loses energy in a dense sequence of small Coulomb collisions with atomic electrons, at a rate the Bethe-Bloch formula fixes from the particle's charge and speed and the medium's electron density and mean excitation energy. The rate scales as the inverse square of the speed, so most energy is deposited at the end of the track in the Bragg peak, and integrating the reciprocal rate gives a sharp range. Electrons differ: they also radiate, and above a critical energy bremsstrahlung dominates. Fast particles above the phase velocity of light in the medium emit Cherenkov radiation.\n",{"path":6179,"title":6180,"module":6176,"summary":6181},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions","Interactions of Photons and Neutrons","Photons are removed from a beam in single events, so their intensity falls exponentially with a linear attenuation coefficient built from three processes: the photoelectric effect at low energy, Compton scattering at intermediate energy, and pair production above twice the electron rest energy, each with its own atomic-number and energy dependence. Neutrons carry no charge and interact only with nuclei, moderating by elastic scattering and being captured with a cross section that rises as one over speed away from resonances.\n",{"path":6183,"title":6184,"module":6176,"summary":6185},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors","Radiation Detectors and Nuclear Spectroscopy","Every detector converts the energy a radiation deposits into a measurable electrical signal. Gas counters read the ionization directly, in three operating regions set by the applied voltage; scintillators convert the energy to light read out by a photomultiplier; semiconductor detectors collect electron-hole pairs and give the best energy resolution because so many carriers are made per event. The resolution is governed by the number of independent charge carriers, and the pulse-height spectrum of a gamma line shows a full-energy photopeak, a Compton continuum with its edge, and escape peaks.\n",{"path":6187,"title":6188,"module":6176,"summary":6189},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology","Dosimetry, Radiation Biology, and Protection","Absorbed dose is the energy deposited per unit mass, measured in gray. Equal absorbed doses do unequal biological damage because densely ionizing radiation deposits its energy along short tracks: weighting the dose by a radiation factor gives the equivalent dose, and weighting by tissue sensitivity gives the effective dose, both in sieverts. Deterministic effects have a threshold and a severity that grows with dose; stochastic effects are assumed to follow a linear-no-threshold probability. Natural background dominates the dose to the population, and protection rests on time, distance, and shielding.\n",{"path":6191,"title":6192,"module":6176,"summary":6193},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine","Applications — Dating, Analysis, and Nuclear Medicine","Charged particles lose energy continuously and stop at a well-defined range with a Bragg peak, while gamma rays are attenuated exponentially. These interactions define radiation detectors and dosimetry (gray and sievert) and drive the applications: neutron activation analysis, magnetic resonance imaging, PET, and radiometric dating with carbon-14 and long-lived rock clocks.\n",{"path":6195,"title":6196,"module":6,"summary":6},"\u002Fnuclear-physics","Nuclear Physics",{"path":6198,"title":6199,"module":1231,"summary":6200},"\u002Fnatural-language-processing\u002Ffoundations\u002Fwhat-is-nlp","What Is Natural Language Processing?","Natural language processing is the computational treatment of human language: reading it, representing it, and generating it. We set up why the problem is hard — ambiguity at every level, from sound to intent — trace the field from ELIZA's pattern-matching through statistical methods to today's neural models, lay out the linguistic levels and task families the course covers, and fix the vocabulary of tokens, types, and corpora the rest of the notes rely on.\n",{"path":6202,"title":6203,"module":1231,"summary":6204},"\u002Fnatural-language-processing\u002Ffoundations\u002Fregex-and-text-normalization","Regular Expressions and Text Normalization","Before any model touches text, the text has to be found and cleaned. Regular expressions give an algebra for describing string patterns; tokenization, case folding, and stemming turn raw characters into the units a model counts; and byte-pair encoding builds a subword vocabulary that spells out any word. Measuring how far apart two strings are — minimum edit distance — is the next lesson.\n",{"path":6206,"title":6207,"module":1231,"summary":6208},"\u002Fnatural-language-processing\u002Ffoundations\u002Fminimum-edit-distance","Minimum Edit Distance","Much of language processing needs to measure how similar two strings are — a speller ranking corrections, a diff tool, a coreference resolver. Minimum edit distance counts the insertions, deletions, and substitutions that turn one string into another, computed by a dynamic-programming table. We fill the table for intention to execution, backtrace to recover the alignment, and see how the same machinery generalizes to weighted edits, Viterbi, and biological sequence alignment.\n",{"path":6210,"title":6211,"module":1231,"summary":6212},"\u002Fnatural-language-processing\u002Ffoundations\u002Fn-gram-language-models","N-Gram Language Models","A language model assigns a probability to a sequence of words and, equivalently, predicts the next word from its history. The n-gram model makes this tractable by truncating the history to the last few words, estimates the resulting conditional probabilities by counting, and is scored by perplexity. We build the model from the chain rule, work a bigram example on a small corpus, and read perplexity as a branching factor. The next lesson covers the zero counts that break this model and the smoothing that repairs them.\n",{"path":6214,"title":6215,"module":1231,"summary":6216},"\u002Fnatural-language-processing\u002Ffoundations\u002Fsmoothing-and-backoff","Smoothing and Backoff","Every finite corpus is missing good word sequences it simply never saw, so a raw n-gram model assigns them probability zero and breaks. Smoothing repairs the zeros: add-one and add-k shave mass off seen events, backoff and interpolation fall back on shorter contexts, and Kneser-Ney — worked here by hand — replaces raw frequency with how many contexts a word completes. We close on web-scale stupid backoff and the neural models that dissolve the zero problem rather than patch it.\n",{"path":6218,"title":6219,"module":6220,"summary":6221},"\u002Fnatural-language-processing\u002Fclassification\u002Fnaive-bayes-and-sentiment","Naive Bayes and Sentiment Classification","Text Classification","Text classification assigns a category to a document — positive or negative, spam or not, one topic among many. Naive Bayes is a generative solution: apply Bayes' rule, assume the words are conditionally independent given the class, and the winning class is the one maximizing the product of a prior and per-word likelihoods. We train it by counting with add-one smoothing, work a full sentiment example by hand, sharpen it for sentiment (binary counts, negation, lexicons), and place it among the transformer classifiers that came after.\n",{"path":6223,"title":6224,"module":6220,"summary":6225},"\u002Fnatural-language-processing\u002Fclassification\u002Fevaluating-classifiers","Evaluating Classifiers","A trained classifier is only useful once we can measure how good it is. We build the confusion matrix, see why accuracy misleads on unbalanced data, and define precision, recall, and the F-measure that balances them. Multi-class tasks need macro- versus micro-averaging; reliable estimates need cross-validation. We close on statistical significance — the paired bootstrap test for whether one system's lead over another is significant.\n",{"path":6227,"title":6228,"module":6220,"summary":6229},"\u002Fnatural-language-processing\u002Fclassification\u002Flogistic-regression","Logistic Regression","Logistic regression is the discriminative counterpart to naive Bayes: instead of modelling how a document is generated, it learns weights that directly separate the classes. We build it from the sigmoid, derive the cross-entropy loss from maximum likelihood, learn the weights by stochastic gradient descent, regularize to curb overfitting, and generalize to many classes with the softmax. The two-class model is already a one-neuron network, so this is the bridge to neural language models.\n",{"path":6231,"title":6232,"module":6220,"summary":6233},"\u002Fnatural-language-processing\u002Fclassification\u002Fsentiment-and-affect-lexicons","Sentiment and Affect Lexicons","A sentiment lexicon is a list of words annotated with the affective meaning they carry — positive or negative, or scores along valence, arousal, and dominance. We fix what \"emotion\" means (basic-emotion versus dimensional models), survey the standard lexicons, and then build lexicons three ways: by human labeling with best-worst scaling, by semi-supervised induction from seed words over an embedding space, and by supervised learning from starred reviews. We close on connotation frames, which record the sentiment a verb implies about each of its arguments.\n",{"path":6235,"title":6236,"module":6237,"summary":6238},"\u002Fnatural-language-processing\u002Fsemantics\u002Fvector-semantics-and-embeddings","Vector Semantics and Embeddings","Semantics","Vector semantics represents a word's meaning as a point in space, derived from the company the word keeps. This first part builds the count-based side: the distributional hypothesis, co-occurrence matrices in their term-document and word-word forms, cosine as the similarity measure, and the two weightings — tf-idf and PPMI — that fix what raw counts get wrong. The result is a sparse, interpretable vector for every word, and the setup for the dense embeddings of the next lesson.\n",{"path":6240,"title":6241,"module":6237,"summary":6242},"\u002Fnatural-language-processing\u002Fsemantics\u002Fstatic-word-embeddings","Static Word Embeddings: word2vec and After","Count-based vectors are long and sparse; embeddings are the short, dense alternative. This lesson builds them with word2vec's skip-gram and negative sampling — a classifier whose learned weights are the vectors — derives its gradient, and works one update by hand. It then reads relations off the analogy parallelogram, surveys the papers that framed the static-embedding era (word2vec, GloVe, the SGNS-as-PPMI equivalence, fastText, ELMo), and closes on the biases embeddings inherit and the single-vector-per-word ceiling that contextual models break.\n",{"path":6244,"title":6245,"module":6237,"summary":6246},"\u002Fnatural-language-processing\u002Fsemantics\u002Fneural-language-models","Neural Networks and Neural Language Models","A neural network is a stack of units, each a weighted sum passed through a non-linearity — a single unit on its own is logistic regression. We build the network up from that unit: the activation functions that give it power, the XOR problem that forces a hidden layer, the feedforward forward pass in matrix form, and the Bengio-style feedforward neural language model that concatenates word embeddings and predicts the next word with a softmax. Training is cross-entropy minimized by gradient descent, with backpropagation supplying the gradient. Embeddings let the model share statistical strength across similar words, avoiding the sparsity that limits n-gram models.\n",{"path":6248,"title":6249,"module":2633,"summary":6250},"\u002Fnatural-language-processing\u002Fsequences\u002Fsequence-labeling","Sequence Labeling: POS and NER","Sequence labeling assigns one tag to every token in a sentence. This first part sets up the task through its two canonical cases — part-of-speech tagging over the Penn Treebank tagset, and named-entity recognition reframed as token labeling with the BIO scheme — then builds the hidden Markov model, the classic probabilistic tagger. The HMM tags by Bayesian inference: transition and emission probabilities under two Markov assumptions, reducing tagging to an argmax over tag sequences. That argmax is exponential to enumerate, which sets up the Viterbi decoder, the CRF, and neural taggers of the next lesson.\n",{"path":6252,"title":6253,"module":2633,"summary":6254},"\u002Fnatural-language-processing\u002Fsequences\u002Fcrfs-and-neural-taggers","Viterbi Decoding, CRFs, and Neural Taggers","The HMM reduced tagging to an argmax over exponentially many tag sequences. This lesson builds the decoder that makes it tractable — the Viterbi dynamic program, worked through a full numeric trace on real WSJ probabilities — then keeps that same decoder while replacing the HMM's rigid tables. The linear-chain conditional random field is a discriminative log-linear model whose global feature functions can inspect any part of the input, which is why CRFs win for NER. Finally it traces the shift to neural taggers (biLSTM-CRF, character-aware NER, ELMo), where hand-built features become learned representations while the Viterbi decoder carries over unchanged.\n",{"path":6256,"title":6257,"module":2633,"summary":6258},"\u002Fnatural-language-processing\u002Fsequences\u002Frnns-and-lstms","RNNs and LSTMs","A feedforward neural language model sees a fixed window of words and can look no further back. The recurrent neural network removes that limit: it carries a hidden state across time, so each word is read in the context of everything before it. We build the RNN from its one recurrent equation, use it as a language model, train it by backpropagation through time, and diagnose the vanishing-gradient problem that makes plain RNNs forget. The LSTM fixes the forgetting with a cell state and three gates, and the encoder-decoder stacks two RNNs into a sequence-to-sequence model — and its single-vector bottleneck is the problem attention was invented to remove.\n",{"path":6260,"title":6261,"module":3115,"summary":6262},"\u002Fnatural-language-processing\u002Ftransformers\u002Ftransformers-and-attention","Transformers and Self-Attention","Recurrence forced language models to read one word at a time and to squeeze every dependency through a chain of hidden states. Self-attention removes the recurrence: at every layer each position compares itself to every other and reads a weighted mixture of them, in a single parallel step. This first part builds the attention operation from the ground up — the soft lookup, queries and keys and values, the scaled dot-product, the numeric trace, the matrix form, and the causal mask — and sets up the full transformer architecture that follows.\n",{"path":6264,"title":4827,"module":3115,"summary":6265},"\u002Fnatural-language-processing\u002Ftransformers\u002Fthe-transformer-architecture","This part takes the scaled dot-product attention of the previous lesson and assembles the full transformer architecture around it: multi-head attention so several relations can be read at once, the transformer block of residual connections and layer norm that makes deep stacks trainable, positional embeddings that restore word order, the decoder-only language model, and the encoder, decoder, and encoder-decoder shapes — closing with the 2017 paper and the pre-norm, FlashAttention, and RoPE refinements that scaled it up.\n",{"path":6267,"title":4935,"module":3115,"summary":6268},"\u002Fnatural-language-processing\u002Ftransformers\u002Flarge-language-models","A large language model is a decoder-only transformer trained on one objective — predict the next token. This first part assembles the inference side: the language-modeling head that turns a hidden state into a distribution over the vocabulary, autoregressive generation, and the decoding strategies — greedy, beam, and sampling with temperature, top-k, and nucleus — that read text back out of that distribution. Training the distribution at web scale comes next.\n",{"path":6270,"title":6271,"module":3115,"summary":6272},"\u002Fnatural-language-processing\u002Ftransformers\u002Fllm-pretraining-and-scaling","Large Language Models: Pretraining and Scaling","A language model's next-token distribution is only as good as the parameters behind it. This part is where those parameters come from: self-supervised pretraining on web-scale text with teacher forcing and cross-entropy, the scaling laws that make test loss a predictable power law in parameters, data, and compute, the KV cache that keeps long-context inference affordable, and how a finished model is evaluated by perplexity and benchmarks — closing with the Kaplan, Chinchilla, GPT-3, and emergence papers behind the scaling story.\n",{"path":6274,"title":6275,"module":3115,"summary":6276},"\u002Fnatural-language-processing\u002Ftransformers\u002Ffine-tuning-and-prompting","Fine-Tuning and Prompting","A pretrained transformer is a general-purpose knowledge source; a task is what you do with it. There are two ways to adapt one, and this first part covers the one that updates the weights: fine-tuning. A bidirectional encoder like BERT is pretrained by masked language modeling, then a small task head is bolted on and the whole thing is trained on labelled data for classification, sequence labeling, or span-based question answering — with parameter-efficient variants (adapters, LoRA) that touch only a sliver of the weights. Prompting, the family that leaves the weights frozen, comes next.\n",{"path":6278,"title":6279,"module":3115,"summary":6280},"\u002Fnatural-language-processing\u002Ftransformers\u002Fprompting-and-alignment","Prompting and Alignment","Fine-tuning adapts a model by changing its weights. The second family of adaptation changes nothing: a large frozen model performs a task from an instruction and a few examples placed in its context. This part covers prompting and in-context learning, chain-of-thought that elicits reasoning, and the two training stages — instruction tuning and RLHF — that turn a fluent base predictor into an aligned assistant, closing with the BERT, LoRA, chain-of-thought, InstructGPT, and retrieval-augmentation papers behind the modern adaptation pipeline.\n",{"path":6282,"title":6283,"module":6284,"summary":6285},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-parsing","Constituency Parsing","Linguistic Structure","A constituency parse groups a sentence into nested phrases described by a context-free grammar. We build the CFG formalism, read the phrase structure of English off a treebank, confront the structural ambiguity that makes parsing hard, convert to Chomsky normal form, and then solve it with CKY — the dynamic-programming chart that fills a triangular table bottom-up. Probabilistic and neural span parsers, evaluation, and shallow parsing follow in the companion lesson.\n",{"path":6287,"title":6288,"module":6284,"summary":6289},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcky-scoring-and-evaluation","CKY Scoring, Evaluation, and Shallow Parsing","The CKY chart returns every parse but does not say which is correct. Disambiguation needs a score on trees. This lesson attaches probabilities to a grammar (the PCFG and lexicalization), replaces the grammar with a neural span scorer over a pretrained encoder, states the self-attentive results that made it the state of the art, evaluates parsers against a treebank with PARSEVAL, and closes with chunking and shallow parsing for tasks that need only the flat phrases.\n",{"path":6291,"title":6292,"module":6284,"summary":6293},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdependency-parsing","Dependency Parsing","A dependency parse throws away phrases and keeps only directed, labeled arcs from heads to their dependents, so the subject and object of a verb hang off the verb directly. We fix the formalism (rooted trees, typed Universal-Dependency relations, projectivity), then build the first parser family: transition-based arc-standard and arc-eager parsing, a greedy stack-and-buffer machine trained from an oracle. Graph-based and neural dependency parsing follow in the companion lesson.\n",{"path":6295,"title":6296,"module":6284,"summary":6297},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fgraph-based-and-neural-dependency-parsing","Graph-Based and Neural Dependency Parsing","Greedy transition parsing commits locally; the graph-based family scores whole trees instead. This lesson scores every candidate head-dependent edge and extracts the maximum spanning tree with Chu-Liu\u002FEdmonds, develops the biaffine neural scorer that made graph-based parsing the accuracy leader, evaluates parsers with the unlabeled and labeled attachment scores (UAS and LAS), and closes on where the two parser families sit and what they feed downstream.\n",{"path":6299,"title":6300,"module":6284,"summary":6301},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fword-senses-and-wsd","Word Senses and Disambiguation","A word is not an atom of meaning: \"bass\" names a fish, a voice, and an instrument, and one static embedding blurs them into a single point. This lesson pulls those senses apart. We define polysemy and the relations that organize senses — synonymy, antonymy, hyponymy, meronymy — build them into WordNet's synset graph, measure similarity along that graph, and then solve the core of word sense disambiguation: the most-frequent-sense baseline, the Lesk gloss-overlap algorithm, feature-based classifiers, and the nearest-neighbor method over BERT embeddings. WSD variants, embeddings, and evaluation follow in the companion lesson.\n",{"path":6303,"title":6304,"module":6284,"summary":6305},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fwsd-in-practice-and-induction","WSD in Practice and Word Sense Induction","Beyond core word sense disambiguation lie the variants and loose ends: the sense-inventory-free Word-in-Context task, retrofitting static embeddings to a thesaurus, discovering senses without a fixed inventory (word sense induction), the gloss-aware and bi-encoder neural systems that hold the state of the art, and how WSD and its cousins are evaluated. Together they connect one-vector-per-word embeddings to sense-aware contextual representations.\n",{"path":6307,"title":6308,"module":6284,"summary":6309},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-roles-and-information-extraction","Semantic Roles and Information Extraction","Semantic roles answer \"who did what to whom\" for a single event, abstracting away the syntax that expresses it. We show why syntax alone is not enough, generalize over diathesis alternations with thematic roles, number a predicate's arguments with PropBank and group predicates into frames with FrameNet, tag each argument automatically with semantic role labeling, and factor predicates into primitives. Information extraction scales the idea to a corpus in the companion lesson.\n",{"path":6311,"title":6312,"module":6284,"summary":6313},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Frelations-events-and-templates","Relations, Events, and Templates","Semantic roles answer \"who did what\" for one predicate; information extraction scales the idea to a whole corpus. This lesson turns unstructured text into structured data: relation extraction pulls entity-relation-entity triples out of sentences by patterns, supervision, and distant supervision; event and temporal extraction place those facts on a timeline; and template filling and knowledge-base population assemble them into a database a downstream system can query.\n",{"path":6315,"title":6316,"module":6284,"summary":6317},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoreference-and-discourse","Coreference and Discourse","A text is more than a bag of sentences: entities recur under different names. Coreference resolution links every mention to the discourse entity it evokes — the linguistic background of pronouns, definite NPs, and names; mention detection; the mention-pair, mention-ranking, and entity-based architectures; a neural end-to-end span model that scores candidate antecedents; features, evaluation by the CoNLL F1, gender bias, and the neural coreference lineage. Discourse coherence follows in the companion lesson.\n",{"path":6319,"title":6320,"module":6284,"summary":6321},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoherence-and-discourse-structure","Coherence and Discourse Structure","Coherence is what makes a run of sentences a discourse rather than an arbitrary collection. This lesson develops coherence relations and Rhetorical Structure Theory trees, discourse-structure parsing, Centering and the entity grid for entity-based coherence, and representation-learning models of local coherence, measured in part over the coreference chains recovered in the companion lesson.\n",{"path":6323,"title":6324,"module":6284,"summary":6325},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Flogical-semantics","Logical Representations of Meaning","A meaning representation turns a sentence into a formal structure a machine can check against a world and reason over. We set the desiderata a good representation must meet, ground truth in a model, build up first-order logic for sentences with its connectives, quantifiers, and inference, and reify events with the neo-Davidsonian event variable to escape fixed predicate arity. The compositional lambda calculus, quantifier scope, and description logics follow in the companion lesson.\n",{"path":6327,"title":6328,"module":6284,"summary":6329},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcompositional-semantics-and-description-logics","Compositional Semantics and Description Logics","How do you compute a logical form from a sentence automatically? This lesson builds the compositional machinery: the lambda calculus that assembles a formula from a parse tree one beta-reduction at a time, the quantifier-scope ambiguity a single syntax tree leaves open, and the decidable description logics — TBox, ABox, subsumption, role restrictions — behind the Web Ontology Language, closing with how the map from string to logical form can be learned.\n",{"path":6331,"title":6332,"module":6284,"summary":6333},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-parsing","Semantic Parsing","Turning a sentence into a structured, executable meaning, the grammar-based way. We take the logical forms defined earlier and build them compositionally: a rule-based parser that walks a syntax tree applying lambda terms, then Combinatory Categorial Grammar (CCG), which fuses syntax and semantics so one lexicalized derivation produces both — including supertagging and A* parsing. Learned and neural semantic parsers follow in the companion lesson.\n",{"path":6335,"title":6336,"module":6284,"summary":6337},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fneural-semantic-parsing","Learned and Neural Semantic Parsing","Hand-writing a lexicon of lambda terms does not scale, so this lesson learns the parser instead. We cover the two supervision regimes (from logical forms and from denotations), Abstract Meaning Representation as a rooted concept graph, neural sequence-to-sequence parsing with constrained decoding and copy mechanisms, executable text-to-SQL and knowledge-based question answering, the practical systems that made learned parsers accurate, and how the task is evaluated.\n",{"path":6339,"title":6340,"module":6284,"summary":6341},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Finformation-extraction","Information Extraction","Information extraction turns free text into a database, and the first step is relation extraction: pulling entity-relation-entity triples out of sentences. We cover all five families — hand-built patterns, supervised classifiers, semi-supervised bootstrapping, distant supervision, and unsupervised Open IE — with worked bootstrapping and distant-supervision traces, then the neural and LLM systems that extended them. Times, events, and templates follow in the companion lesson.\n",{"path":6343,"title":6344,"module":6284,"summary":6345},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftimes-events-and-templates","Extracting Times, Events, and Templates","Once relation extraction has produced typed triples, the information-extraction pipeline still has to place facts in time and assemble them into records. This lesson detects and normalizes temporal expressions to ISO 8601 values, detects events and orders them on a timeline with the 13 Allen relations, and fills slot-and-filler templates — flat and hierarchical — for stereotyped situations, closing the loop from text to a queryable database.\n",{"path":6347,"title":6348,"module":6284,"summary":6349},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdiscourse-coherence","Discourse Coherence","A text is more than a set of sentences. What binds a run of sentences into a discourse is coherence, and one of its sources is structured relations between clauses. This lesson develops relational coherence — RST and the PDTB models of coherence relations — and discourse-structure parsing: EDU segmentation and shift-reduce RST parsing, then PDTB relation classification. Entity-based and global coherence follow in the companion lesson.\n",{"path":6351,"title":6352,"module":6284,"summary":6353},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fentity-based-and-global-coherence","Entity-Based and Global Coherence","A text coheres not only through relations between clauses but by staying about the same entities and the same topic, and by obeying the macro-structure of its genre. This lesson develops Centering Theory and the entity grid for entity-based coherence, representation-learning models of local coherence, and global coherence — topic segmentation, narrative and argumentation structure, and scientific discourse — then the neural models that learn each.\n",{"path":6355,"title":6356,"module":6284,"summary":6357},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-grammars","Constituency Grammars","A constituency grammar is the declarative theory of sentence structure that a parser operates on. We build the context-free grammar formalism from its four parts, show how derivations become parse trees, and work through the phrase structure of English — noun phrases, verb phrases and their subcategorization frames, agreement, coordination, and long-distance dependencies. The treebank, normal-form, and lexicalized views follow in the companion lesson.\n",{"path":6359,"title":6360,"module":6284,"summary":6361},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftreebanks-and-lexicalized-grammars","Treebanks and Lexicalized Grammars","Where does a grammar come from, and how is it prepared for a parser? We read a context-free grammar off the Penn Treebank, normalize it to Chomsky Normal Form for the CKY chart, then invert the phrase-structure emphasis with lexicalized grammars — Combinatory Categorial Grammar and its slash categories — and close with the grammar's fate in the neural era: span scoring, self-attention, and grammar induction.\n",{"path":6363,"title":6364,"module":4923,"summary":6365},"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation","Machine Translation","Machine translation is the task that built the modern toolkit: the encoder-decoder was invented for it, attention was invented to fix its fixed-context bottleneck, and both were later folded into the general transformer. We work through why translation is hard (word order, morphology, lexical and structural divergences), the sequence-to-sequence model and its attention mechanism, transformer-based NMT with cross-attention, subword tokenization with a shared vocabulary, beam-search decoding, and evaluation by BLEU and its successors chrF, BERTScore, and COMET — closing on multilingual and low-resource translation and backtranslation.\n",{"path":6367,"title":6368,"module":4923,"summary":6369},"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation-decoding-and-evaluation","Machine Translation: Decoding, Evaluation, and Scale","Having built the transformer translation model, we now decode from it and measure the output. Beam search turns the decoder's per-step distributions into a single output string; length normalization keeps it from favoring short translations. We then score translations automatically — BLEU with its n-gram precision, clipping, and brevity penalty, worked through by hand, then its successors chrF, BERTScore, and COMET — and close on the parts of MT that scale beyond one language pair: multilingual and low-resource translation, backtranslation, gender bias, and the lineage from the Transformer to massively multilingual models like NLLB-200.\n",{"path":6371,"title":6372,"module":4923,"summary":6373},"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering","Question Answering","A question-answering system takes a natural-language question and returns an answer, not a ranked list of documents. Almost every modern system is built on one pattern: retrieve then read. We start with the information-retrieval machinery that finds candidate text — tf-idf and BM25 term weighting, a worked ranking example, the inverted index, and dense embedding retrieval — then build the retriever-reader pipeline that extracts an answer span with BERT and trace a full retrieve-and-read example end to end.\n",{"path":6375,"title":6376,"module":4923,"summary":6377},"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering-knowledge-and-llms","Question Answering: Knowledge Bases and Language Models","The retrieve-and-read pipeline extracts an answer span from prose, but not all knowledge lives in prose. This part covers the rest of the QA stack: entity linking (Wikification) that grounds a question's entities to a knowledge base, knowledge-based QA by semantic parsing a question into an executable query, and the modern default — closed-book QA and retrieval-augmented generation with a large language model — closing on the DPR\u002FRAG\u002Ffusion-in-decoder lineage and how factoid answers are scored by exact match and F1.\n",{"path":6379,"title":6380,"module":4923,"summary":6381},"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-and-chatbots","Dialogue and Chatbots","Conversation is the most natural interface to a machine and one of the hardest to build. We set up what makes human dialogue work — turns, speech acts, grounding, and the local structure of adjacency pairs — then trace the two traditions that answer it: chatbots built to chat (ELIZA's pattern-matching, corpus retrieval, and seq2seq generation with its blandness problem) and task-oriented systems built to get something done (the GUS frame-and-slot architecture and the modern NLU \u002F state-tracker \u002F policy \u002F NLG pipeline that accumulates a frame across turns).\n",{"path":6383,"title":6384,"module":4923,"summary":6385},"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-systems-and-assistants","Dialogue Systems: LLM Assistants, Evaluation, and Design","Two dialogue traditions — chatbots built to chat and task-oriented frame systems built to get something done — met in the aligned LLM assistant. Instruction tuning plus RLHF fold chit-chat and task dialogue into one model; the LaMDA \u002F InstructGPT \u002F ChatGPT lineage fills in how. The lesson then turns to evaluation (human ratings and acute-eval for chatbots, task success and slot error rate for task systems), user-centered design with Wizard-of-Oz prototyping, and the ethical stakes of building agents people talk to.\n",{"path":6387,"title":6388,"module":4923,"summary":6389},"\u002Fnatural-language-processing\u002Fapplications\u002Ftext-summarization","Text Summarization","Summarization compresses a document to its essential meaning, by either selecting sentences to keep (extractive) or writing new ones (abstractive). This part fixes the task and its flavors — single vs. multi-document, generic vs. query-focused, extractive vs. abstractive — then works through extractive summarization in full: scoring by position and centrality, the TextRank\u002FLexRank graph algorithm run as PageRank over a sentence-similarity graph with a worked iteration, and supervised sentence selection.\n",{"path":6391,"title":6392,"module":4923,"summary":6393},"\u002Fnatural-language-processing\u002Fapplications\u002Fabstractive-summarization-and-evaluation","Abstractive Summarization and Evaluation","Extractive methods can only reuse the source's own sentences; to compress within a sentence or paraphrase, a summarizer has to generate. This part covers abstractive summarization: the sequence-to-sequence approach, the pointer-generator's copy switch and coverage mechanism, pretrained summarizers (BART, PEGASUS) and zero-shot LLM prompting, the long-document and factuality problems, and ROUGE evaluation with a worked example and its limits — closing on the abstractive lineage from See 2017 through faithfulness metrics.\n",{"path":6395,"title":6396,"module":6397,"summary":6398},"\u002Fnatural-language-processing\u002Fspeech\u002Fphonetics","Phonetics","Speech","Before a recognizer can read speech it has to know what speech is. This first part covers the linguistic substrate: phones and their transcription in the IPA and ARPAbet; articulatory phonetics — how the vocal tract shapes airflow into consonants and vowels; and prosody — stress, tune, and the F0 contour. The acoustic side — the waveform, its spectrum, formants, and the spectrogram — is the second part.\n",{"path":6400,"title":6401,"module":6397,"summary":6402},"\u002Fnatural-language-processing\u002Fspeech\u002Facoustic-phonetics","Acoustic Phonetics","Articulation is the cause; the acoustic signal is the effect, and the effect is all a microphone ever gets. This part follows the sound out of the mouth: waves, sampling and the Nyquist limit, F0 and the pitch track, the mel scale, the spectrum and Fourier analysis, the source-filter model that explains why each vowel carries its own formants, and the spectrogram the log-mel front end of every ASR system sits directly on top of — closing with neural TTS, wav2vec, HuBERT, and Whisper, where phonetics went in neural speech.\n",{"path":6404,"title":6405,"module":6397,"summary":6406},"\u002Fnatural-language-processing\u002Fspeech\u002Fautomatic-speech-recognition","Automatic Speech Recognition","Speech recognition maps an acoustic waveform to a string of words, and once the waveform is turned into a sequence of log-mel spectrogram frames the problem is the same sequence-to-sequence transduction the rest of the course already solved. This first part builds the feature front end (framing, the DFT, the mel filterbank, the log), then the modern architectures: the attention-based encoder-decoder, the CTC alignment trick that collapses repeated and blank frames, and RNN-T for streaming. Training-data advances, evaluation, TTS, and the other speech tasks come next.\n",{"path":6408,"title":6409,"module":6397,"summary":6410},"\u002Fnatural-language-processing\u002Fspeech\u002Fasr-evaluation-and-applications","ASR Evaluation and Speech Applications","A recognizer turns a waveform into text; this part scores that text and puts the same machinery to other uses. It opens with the self-supervised and weakly- supervised systems (wav2vec 2.0, HuBERT, Whisper) that made ASR error rates fall. Word error rate reuses the edit distance from the first module, run over words. Text-to-speech runs the whole pipeline in reverse — text to mel spectrogram to waveform. And a family of smaller tasks — wake-word detection, speaker recognition and diarization, language identification — reuse the same log-mel front end without the decoder.\n",{"path":6412,"title":6413,"module":6,"summary":6},"\u002Fnatural-language-processing","Natural Language Processing",{"path":6415,"title":6416,"module":1231,"summary":6417},"\u002Fparticle-physics\u002Ffoundations\u002Fhistorical-overview-particle-zoo","From the Electron to the Particle Zoo","A timeline of the subject, from J. J. Thomson's electron in 1897 to the Higgs boson in 2012. The electron, photon, nucleus, proton, and neutron gave a tidy picture that Yukawa's meson prediction and the muon–pion confusion complicated; strange particles in cosmic rays and the accelerator-era flood of hadrons then produced a \"particle zoo\" that only the quark model organized.\n",{"path":6419,"title":6420,"module":1231,"summary":6421},"\u002Fparticle-physics\u002Ffoundations\u002Fparticle-physics-basic-concepts","Basic Concepts and Particle Classification","Every particle has an antiparticle of equal mass and opposite charge, a consequence of the Dirac equation confirmed by the positron. Feynman diagrams track interactions in spacetime; the material particles sort into leptons and the composite hadrons built from quarks, with baryons carrying three quarks and mesons a quark-antiquark pair.\n",{"path":6423,"title":6424,"module":1231,"summary":6425},"\u002Fparticle-physics\u002Ffoundations\u002Ffundamental-interactions-force-carriers","Fundamental Interactions and Force Carriers","Four interactions account for every force in nature: strong, electromagnetic, weak, and gravitational, in decreasing strength. Each is carried by a boson — the gluon, photon, W and Z, and the graviton — with a range fixed by the carrier's mass through the Yukawa relation, and a coupling constant that itself varies with distance.\n",{"path":6427,"title":6428,"module":6429,"summary":6430},"\u002Fparticle-physics\u002Funits-kinematics\u002Fnatural-units-and-scales","Natural Units and Scales","Units and Kinematics","Setting $\\hbar = c = 1$ collapses mass, momentum, and energy into a single unit, the GeV, and turns lengths and times into inverse energies through the conversion $\\hbar c = 197.3$ MeV·fm. This lesson fixes the natural-unit conventions used for the rest of the course, converts cross sections between barns and GeV$^{-2}$, and shows how to restore factors of $\\hbar$ and $c$ by dimensional analysis.\n",{"path":6432,"title":6433,"module":6429,"summary":6434},"\u002Fparticle-physics\u002Funits-kinematics\u002Ffour-vectors-invariant-mass","Four-Vectors and Invariant Mass","The energy and momentum of a particle form a four-vector whose square is the frame-independent quantity $p^2 = m^2$. This lesson develops the metric and four-vector products, the invariant mass of a multiparticle system, the center-of-momentum and laboratory frames, and the description of collinear boosts by rapidity, whose additivity replaces the awkward velocity-addition law.\n",{"path":6436,"title":6437,"module":6429,"summary":6438},"\u002Fparticle-physics\u002Funits-kinematics\u002Fdecay-scattering-kinematics-mandelstam","Decay, Scattering, and Mandelstam Variables","Two-body decay in the rest frame fixes the daughter momenta from the three masses alone; production thresholds follow from the minimum invariant mass. This lesson works both, then introduces the Mandelstam invariants $s$, $t$, $u$ for $2\\to2$ scattering, proves the identity $s+t+u=\\sum m_i^2$, and maps the physical regions and the crossing that relates channels.\n",{"path":6440,"title":6441,"module":6429,"summary":6442},"\u002Fparticle-physics\u002Funits-kinematics\u002Fcross-sections-golden-rule","Cross Sections and the Golden Rule","The cross section measures how often a scattering happens and the decay width how fast a particle disintegrates. This lesson defines both, relates event rate to luminosity through $R=\\mathcal L\\,\\sigma$ and lifetime to width through $\\tau=\\hbar\u002F\\Gamma$, and states Fermi's golden rule with Lorentz-invariant phase space, giving the master formulas that turn an amplitude $\\mathcal M$ into a measurable rate for $1\\to2$ decay and $2\\to2$ scattering.\n",{"path":6444,"title":6445,"module":6446,"summary":6447},"\u002Fparticle-physics\u002Fsymmetries\u002Fconservation-laws-symmetries","Conservation Laws and Symmetries","Symmetries and Conservation Laws","Which decays occur is decided by conservation laws, each tied by Noether's theorem to a symmetry of physical law. Energy, charge, baryon number, and lepton number are conserved universally; strangeness, isospin, and parity hold in the strong and electromagnetic interactions but break in the weak one, whose parity and CP violation distinguish matter from antimatter.\n",{"path":6449,"title":6450,"module":6446,"summary":6451},"\u002Fparticle-physics\u002Fsymmetries\u002Fdiscrete-symmetries-cpt","Discrete Symmetries — C, P, T, and CPT","Parity reflects space, charge conjugation swaps particle for antiparticle, and time reversal runs the clock backward. Each assigns multiplicative quantum numbers that act as selection rules — intrinsic parities, the photon's C = −1, the C-parity argument fixing the pion's two-photon decay. Their product CPT is a theorem of any local relativistic field theory, forcing particle and antiparticle to share mass and lifetime.\n",{"path":6453,"title":6454,"module":6446,"summary":6455},"\u002Fparticle-physics\u002Fsymmetries\u002Fparity-violation-weak","Parity Violation and the Weak Force","The tau–theta puzzle forced a choice: two particles with identical mass but opposite parity, or one particle whose decay violates parity. Lee and Yang proposed the latter, Wu's polarized cobalt-60 confirmed it, and the violation proved maximal. The charged weak force couples only to left-handed chirality — the Goldhaber experiment showed the neutrino is left-handed — which is why the mirror image of a weak decay is something nature never produces.\n",{"path":6457,"title":6458,"module":6446,"summary":6459},"\u002Fparticle-physics\u002Fsymmetries\u002Fsu2-su3-flavor-symmetry","Isospin, SU(2), and Flavor SU(3)","The near-equal masses of the proton and neutron, and of the three pions, signal a continuous internal symmetry of the strong force: isospin, an SU(2) whose ladder operators move between the members of a multiplet. Adding strangeness enlarges it to an approximate SU(3) flavor symmetry, and the Gell-Mann–Nishijima relation Q = I3 + Y\u002F2 places every hadron on a weight diagram in the isospin–hypercharge plane — the language in which the quark model is written.\n",{"path":6461,"title":6462,"module":6463,"summary":6464},"\u002Fparticle-physics\u002Fquark-model\u002Feightfold-way-su3","The Eightfold Way and SU(3) Flavor","The Quark Model","Gell-Mann and Ne'eman's classification of the hadrons into geometric multiplets, read as representations of an approximate flavor SU(3). The fundamental triplet (u, d, s) and its antitriplet combine into the meson nonet from 3⊗3̄ = 8⊕1 and the baryon octet and decuplet from 3⊗3⊗3, and the empty corner of the decuplet forecast the Ω⁻.\n",{"path":6466,"title":6467,"module":6463,"summary":6468},"\u002Fparticle-physics\u002Fquark-model\u002Fmeson-spectroscopy","Meson Multiplets and Quantum Numbers","Mesons as quark–antiquark bound states. The spin singlet and triplet, orbital excitations, and the assignment of J^PC from the quark spins and orbital angular momentum, giving the pseudoscalar and vector nonets. The η–η' and ω–φ mixing problems, and the charmonium and bottomonium spectra read as heavy-quark positronium.\n",{"path":6470,"title":6471,"module":6463,"summary":6472},"\u002Fparticle-physics\u002Fquark-model\u002Fbaryon-spectroscopy","Baryon Multiplets, Spin, and the Color Puzzle","Baryons as three-quark states, with a wavefunction factored into space, spin, flavor, and color. The spin-3\u002F2 Δ⁺⁺ = uuu forces a totally symmetric state that the Pauli principle forbids, and the resolution is an antisymmetric color factor — the first evidence for color. The octet and decuplet spin content, and baryon magnetic moments as a quantitative test of the model.\n",{"path":6474,"title":6475,"module":6463,"summary":6476},"\u002Fparticle-physics\u002Fquark-model\u002Fcolor-confinement-exotics","Color, Confinement, and Exotic Hadrons","Color as the gauged SU(3) charge, and the requirement that every physical hadron be a color singlet — which selects q-qbar mesons and qqq baryons as the simplest states. The R-ratio of e⁺e⁻ annihilation measures three colors directly. Beyond the simplest singlets lie glueballs, tetraquarks, and pentaquarks, and the recent XYZ states, read as either compact multiquarks or loose hadronic molecules.\n",{"path":6478,"title":6479,"module":6480,"summary":6481},"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fklein-gordon-equation","The Klein-Gordon Equation","Relativistic Wave Equations","Quantizing the relativistic energy relation $E^2 = p^2 + m^2$ produces the Klein-Gordon equation for a scalar field. Its plane-wave solutions come in positive- and negative-energy branches, and the conserved density it supplies is not positive-definite — the two difficulties that first drove physicists to seek a first-order equation. The static Klein-Gordon equation with a point source gives the Yukawa potential, and the free equation gives the scalar propagator that later modules attach to exchanged lines.\n",{"path":6483,"title":6484,"module":6480,"summary":6485},"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fdirac-equation-spinors","The Dirac Equation and Spinors","Dirac demanded a wave equation first order in time to fix the Klein-Gordon density problem. Factorizing $E^2 = p^2 + m^2$ into a linear form forces the coefficients to be anticommuting matrices — the gamma matrices of the Clifford algebra — so the wavefunction becomes a four-component spinor. The plane-wave solutions split into two particle and two antiparticle states, spin appears automatically with the correct $g = 2$ magnetic moment, and the chirality projectors that the weak interaction later needs fall straight out of the fifth gamma matrix.\n",{"path":6487,"title":6488,"module":6480,"summary":6489},"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fantiparticles-hole-theory","Antiparticles and Hole Theory","The negative-energy solutions of the Dirac equation refuse to go away, so they must mean something. Dirac read them as a filled sea of occupied negative-energy states whose holes are positive-energy antiparticles, predicting the positron before its discovery. The picture works for fermions but not bosons, and the Feynman-Stückelberg interpretation replaces it: an antiparticle is a negative-energy solution propagating backward in time, equivalent to a positive-energy antiparticle going forward. Crossing symmetry ties incoming particles to outgoing antiparticles in a single amplitude.\n",{"path":6491,"title":6492,"module":6493,"summary":6494},"\u002Fparticle-physics\u002Fqed\u002Ffeynman-rules-qed","Feynman Rules for QED","Quantum Electrodynamics","Quantum electrodynamics computes a process by summing diagrams, each a term in a power series in the coupling. Every diagram translates into an amplitude by a fixed dictionary: spinors and polarization vectors for external lines, propagators for internal lines, and the vertex factor $ie\\gamma^\\mu$ for each photon-fermion junction. Squaring the amplitude and feeding it to Fermi's golden rule produces a cross section or decay rate, with each extra vertex costing one power of $\\alpha$.\n",{"path":6496,"title":6497,"module":6493,"summary":6498},"\u002Fparticle-physics\u002Fqed\u002Fqed-tree-processes","Tree-Level QED Processes","The Feynman rules become numbers on the reference reactions of QED. Muon pair production $e^+e^-\\to\\mu^+\\mu^-$ sets the scale with its $1+\\cos^2\\theta$ distribution and $4\\pi\\alpha^2\u002F3s$ total cross section, and its ratio to hadron production counts colors. Compton scattering gives the Klein-Nishina formula and the Thomson limit; Bhabha scattering shows $s$- and $t$-channel interference. Casimir's trick turns every spin-averaged square into a trace of gamma matrices.\n",{"path":6500,"title":6501,"module":6493,"summary":6502},"\u002Fparticle-physics\u002Fqed\u002Frenormalization-running-coupling","Renormalization and the Running Coupling","Beyond tree level, QED loops diverge. The three primitive one-loop diagrams — vacuum polarization, electron self-energy, and vertex correction — carry ultraviolet divergences that regularization exposes as logarithms of a cutoff. Renormalization absorbs them into the measured mass, charge, and field normalization, leaving finite predictions. The surviving physical content is that the coupling runs: vacuum polarization screens charge, so $\\alpha$ grows from $1\u002F137$ at low energy to about $1\u002F128$ at the $Z$ mass.\n",{"path":6504,"title":6505,"module":6493,"summary":6506},"\u002Fparticle-physics\u002Fqed\u002Felectron-g-2","The Anomalous Magnetic Moment","The Dirac equation predicts $g=2$; loops shift it. Schwinger's one-loop vertex correction gives the anomaly $a=(g-2)\u002F2=\\alpha\u002F2\\pi$, and the QED series continues to five loops. The electron $a_e$ agrees with theory to better than a part in a billion, the most precise confrontation of theory and experiment in physics. The muon $a_\\mu$, heavier and so more sensitive to virtual heavy states, is dominated by hadronic uncertainty and sits at the center of a long-running comparison with the Standard Model prediction.\n",{"path":6508,"title":6509,"module":6510,"summary":6511},"\u002Fparticle-physics\u002Fweak-interaction\u002Fva-structure-weak","The V–A Charged Weak Current","The Weak Interaction","Fermi modelled beta decay as a four-fermion contact interaction, but a coupling with dimensions of inverse mass squared makes cross sections grow without bound and the theory fails near 300 GeV. The cure is a heavy mediator: the $W$ boson, whose propagator collapses to Fermi's contact term at low energy and fixes $G_F\u002F\\sqrt2 = g^2\u002F8M_W^2$. Parity violation dictates the current's form — vector minus axial-vector, coupling only to left-chiral fields — and universality of the coupling ties muon decay, beta decay, and pion decay to one constant. Pion decay's helicity suppression of the electron channel is the sharpest test.\n",{"path":6513,"title":6514,"module":6510,"summary":6515},"\u002Fparticle-physics\u002Fweak-interaction\u002Fw-z-bosons-decays","The W and Z Bosons","The contact theory hides a massive mediator. The charged $W^\\pm$ carries the current that changes flavour; the neutral $Z^0$ carries a current that does not. Both were found at CERN's proton–antiproton collider in 1983 at the masses the electroweak theory demanded. Their decay widths partition into leptonic and hadronic channels, and the $Z$ carries a decisive extra: an invisible width from decays to neutrinos that counts the number of light generations at exactly three. Beta decay and muon decay are re-read at the parton level as $W$ exchange.\n",{"path":6517,"title":6518,"module":6510,"summary":6519},"\u002Fparticle-physics\u002Fweak-interaction\u002Fckm-matrix","Quark Mixing and the CKM Matrix","The quark eigenstates the weak force acts on are not the mass eigenstates. Cabibbo captured this with one rotation angle; the GIM mechanism added a fourth quark to cancel dangerous flavour-changing neutral currents and predicted charm before its discovery. Three generations promote the rotation to the unitary Cabibbo–Kobayashi–Maskawa matrix — three angles and one irreducible complex phase, the sole source of Standard-Model CP violation. The Wolfenstein parametrization exposes its steep hierarchy, and unitarity closes into a triangle whose area measures the phase.\n",{"path":6521,"title":6522,"module":6510,"summary":6523},"\u002Fparticle-physics\u002Fweak-interaction\u002Fcp-violation-kaons-b-mesons","CP Violation in Kaons and B Mesons","The neutral kaon is its own laboratory for CP. Weak box diagrams mix $K^0$ and its antiparticle into short- and long-lived states that should be pure CP eigenstates decaying to two and three pions. In 1964 Cronin and Fitch caught the long-lived kaon decaying to two pions — CP is violated, at the two-per-mille level of $\\epsilon$. Direct violation ($\\epsilon'$) followed, and the $B$ factories turned the CKM phase into a large, clean time-dependent asymmetry measuring $\\sin 2\\beta$. The effect is real but far too small to explain why the universe is made of matter.\n",{"path":6525,"title":6526,"module":6527,"summary":6528},"\u002Fparticle-physics\u002Fqcd\u002Fcolor-su3-gluons","Color SU(3), Gluons, and the QCD Lagrangian","Quantum Chromodynamics","Color is the exact gauged SU(3) charge of the strong force. Gauging it forces eight massless gluons in the adjoint representation and, because the gauge group is non-abelian, three- and four-gluon self-couplings absent from QED. This lesson builds the QCD Lagrangian from the covariant derivative and the non-abelian field strength, states the Feynman rules with their color factors, and computes the Casimir invariants that set the strength of quark-gluon and gluon-gluon coupling.\n",{"path":6530,"title":6531,"module":6527,"summary":6532},"\u002Fparticle-physics\u002Fqcd\u002Fasymptotic-freedom-confinement","Asymptotic Freedom and Confinement","The QCD beta function is negative: gluon self-interaction antiscreens color, so the coupling weakens at short distance (asymptotic freedom) and strengthens at long distance (confinement). This lesson computes the one-loop beta coefficient, solves for the running of alpha_s and the emergent scale Lambda_QCD, and reads the strong-coupling regime as the linear quark-antiquark potential of a color flux tube that breaks by pair creation.\n",{"path":6534,"title":6535,"module":6527,"summary":6536},"\u002Fparticle-physics\u002Fqcd\u002Fdeep-inelastic-scattering-partons","Deep Inelastic Scattering and the Parton Model","Scattering electrons hard off a proton resolves pointlike constituents. This lesson sets up the deep-inelastic kinematics, defines the structure functions F1 and F2, and reads Bjorken scaling as the signature of free spin-half partons. The Callan-Gross relation fixes the parton spin, the structure function becomes a charge-weighted sum of parton distributions, and the slow logarithmic scaling violations expose the gluon through DGLAP evolution.\n",{"path":6538,"title":6539,"module":6527,"summary":6540},"\u002Fparticle-physics\u002Fqcd\u002Fjets-hadronization","Jets, Hadronization, and Testing QCD","Quarks and gluons produced in a collision fragment into collimated sprays of hadrons — jets — whose directions track the underlying partons. This lesson reads two-jet events as the quark and antiquark of electron-positron annihilation, three-jet events as direct evidence of the radiated gluon, and the hadronization step as the flux tube breaking into color singlets. Jet algorithms and event-shape variables turn the pattern into precision measurements of alpha_s.\n",{"path":6542,"title":6543,"module":6544,"summary":6545},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Felectroweak-su2-u1","The Electroweak Theory","Electroweak Unification and the Higgs","The electromagnetic and weak interactions are two faces of a single gauge theory built on $SU(2)_L \\times U(1)_Y$. Left-handed fermions sit in weak-isospin doublets and right-handed fermions in singlets, each carrying a hypercharge fixed by the Gell-Mann–Nishijima relation $Q = T_3 + Y\u002F2$. The four gauge fields $W^{1,2,3}$ and $B$ mix: the charged combinations $W^\\pm$ mediate the charged current, while $W^3$ and $B$ rotate through the Weinberg angle into the massless photon and the massive $Z$. The single angle $\\theta_W$ ties the couplings, the boson masses, and the neutral-current strengths together.\n",{"path":6547,"title":6548,"module":6544,"summary":6549},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fspontaneous-symmetry-breaking","Spontaneous Symmetry Breaking","A symmetry of the Lagrangian need not be a symmetry of the ground state. When the lowest-energy configuration sits away from the symmetric point, the symmetry is spontaneously broken and the vacuum is one of a degenerate family. Breaking a continuous global symmetry produces one massless scalar — a Goldstone boson — for every broken generator, the flat direction along the vacuum manifold. The Mexican-hat potential and the ferromagnet below its Curie point are the working pictures.\n",{"path":6551,"title":6552,"module":6544,"summary":6553},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-mechanism","The Higgs Mechanism","Gauging a spontaneously broken symmetry converts the would-be Goldstone bosons into the longitudinal polarizations of the gauge fields, which thereby acquire mass. Applied to $SU(2)_L \\times U(1)_Y$ with a single Higgs doublet, three of the four scalar degrees of freedom are eaten by the $W^\\pm$ and $Z$; the fourth survives as the physical Higgs boson, and the photon stays massless. Fermion masses come from Yukawa couplings to the same field, each mass proportional to its coupling times the vacuum expectation value $v \\approx 246$ GeV.\n",{"path":6555,"title":6556,"module":6544,"summary":6557},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-boson-discovery","The Higgs Boson","The Higgs boson is produced at the LHC chiefly through gluon fusion, with vector-boson fusion and associated production as cleaner but rarer channels. It decays most often to $b\\bar b$ and $WW^\\ast$, but the discovery rested on two rare clean modes, $H \\to \\gamma\\gamma$ and $H \\to ZZ^\\ast \\to 4\\ell$, whose narrow invariant-mass peaks emerged over smooth backgrounds. ATLAS and CMS announced a boson near 125 GeV in 2012; its measured spin-parity $0^+$ and its couplings, which scale with particle mass, identify it as the Standard Model Higgs.\n",{"path":6559,"title":6560,"module":6544,"summary":6561},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fstandard-model","The Standard Model","The Standard Model combines the quark model, quantum chromodynamics, and the electroweak theory. SU(3) symmetry sorts the hadrons and predicted the omega; color explains why only colorless quark combinations exist; QCD gives asymptotic freedom and confinement; and spontaneous symmetry breaking through the Higgs field gives the weak bosons their mass.\n",{"path":6563,"title":6564,"module":6565,"summary":6566},"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-oscillations","Neutrino Oscillations","Neutrino Physics","Neutrinos are produced and detected in flavour states, but they propagate as mass states, and the two bases are misaligned. A flavour therefore evolves coherently into a superposition of other flavours with a probability set by the mass-squared splitting and the ratio L\u002FE. This lesson derives the two-flavour oscillation formula, applies it to the solar and atmospheric neutrino deficits, shows how the SNO neutral-current measurement resolved the solar problem, and works out the MSW resonance that amplifies mixing inside the Sun.\n",{"path":6568,"title":6569,"module":6565,"summary":6570},"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-mass-pmns","Neutrino Mass and the PMNS Matrix","Three-flavour mixing promotes the single oscillation angle to the unitary Pontecorvo–Maki–Nakagawa–Sakata matrix, parametrised by three angles and a Dirac CP phase. This lesson decomposes the PMNS matrix into three rotations, records the measured angles and mass-squared splittings, lays out the normal and inverted mass orderings, contrasts the large leptonic mixing with the near-diagonal CKM matrix, and collects the absolute-mass bounds from beta decay and cosmology.\n",{"path":6572,"title":6573,"module":6565,"summary":6574},"\u002Fparticle-physics\u002Fneutrinos\u002Fdirac-majorana-experiments","Dirac, Majorana, and Neutrino Experiments","A neutral fermion can carry a mass term forbidden to every charged particle, so the neutrino may be its own antiparticle. This lesson contrasts the Dirac and Majorana mass terms and their state content, derives the seesaw mechanism that ties a tiny light mass to a heavy right-handed partner, presents neutrinoless double-beta decay as the decisive lepton-number test, surveys the reactor, accelerator, solar, and atmospheric sources on a baseline–energy map, and explains why neutrino mass is physics beyond the original Standard Model.\n",{"path":6576,"title":6577,"module":6578,"summary":6579},"\u002Fparticle-physics\u002Fexperiment\u002Faccelerators-luminosity","Accelerators, Colliders, and Luminosity","Accelerators and Detectors","Fixed-target machines waste energy in the center-of-mass motion of the whole system, so the reachable $\\sqrt s$ grows only as the square root of the beam energy, while colliders put the full beam energy into the collision. Circular electron machines are limited by synchrotron radiation scaling as $E^4\u002Fm^4R$; proton machines are limited by bending fields. Luminosity, set by beam current and focusing, converts a cross section into an event rate through $R=\\mathcal L\\,\\sigma$, and integrated luminosity sets the total event count.\n",{"path":6581,"title":6582,"module":6578,"summary":6583},"\u002Fparticle-physics\u002Fexperiment\u002Fdetectors-subsystems","Particle Detectors and Subsystems","A detector reads a collision by the energy particles deposit as they cross matter. Charged particles ionize at the Bethe-Bloch rate, radiate in the field of nuclei above a critical energy, and emit Cherenkov light above a velocity threshold; electrons and photons build electromagnetic showers over a radiation length, and hadrons build wider showers over a nuclear interaction length. The onion of tracker, electromagnetic and hadronic calorimeters, and outer muon chambers turns these processes into momentum, energy, and identity, with neutrinos inferred from missing transverse momentum.\n",{"path":6585,"title":6586,"module":6578,"summary":6587},"\u002Fparticle-physics\u002Fexperiment\u002Fhow-discoveries-are-made","From Collisions to Discoveries","A discovery is a peak that survives statistics. Events are reconstructed into invariant masses, a signal accumulates as a bump over a smooth background, and its significance is judged by a p-value; the field's threshold is five sigma. The expected yield is a product — luminosity times cross section times branching ratio times acceptance and efficiency — that must be balanced by a trigger and data-reduction chain against an overwhelming rate. Worked reconstructions of $Z\\to\\ell\\ell$, the $J\u002F\\psi$, and the Higgs show the same peak-over-background logic at three scales.\n",{"path":6589,"title":6590,"module":6590,"summary":6591},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fbeyond-standard-model","Beyond the Standard Model","The Standard Model leaves the four interactions ununified and the neutrinos massless, both now known to be wrong. Grand unification predicts the couplings merge near ten-to-the-sixteen GeV and the proton decays; supersymmetry pairs each particle with a superpartner; and the confirmed oscillation of neutrinos proves they carry mass, the first crack in the model.\n",{"path":6593,"title":6594,"module":6590,"summary":6595},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fgrand-unified-theories","Grand Unified Theories and Proton Decay","The Standard Model gauge group is a product of three factors with three independent couplings. A grand unified theory embeds them in a single simple group — SU(5) is the minimal choice — so that one coupling runs into all three and the fractional quark charges follow from a tracelessness condition. The same embedding places quarks and leptons in shared multiplets, mediates baryon-number violation through superheavy gauge bosons, and predicts the proton decays with a lifetime that Super-Kamiokande has pushed past ten-to-the-thirty-four years.\n",{"path":6597,"title":6598,"module":6590,"summary":6599},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fsupersymmetry","Supersymmetry","Supersymmetry relates fermions and bosons, pairing every Standard Model particle with a superpartner whose spin differs by one half. The pairing makes the scalar and fermion loop corrections to the Higgs mass cancel, removing the quadratic sensitivity to high scales; it sharpens the meeting of the three gauge couplings; and, when R-parity is conserved, it leaves the lightest superpartner stable and neutral, a natural dark-matter candidate. The LHC has excluded gluinos and light squarks below roughly two TeV.\n",{"path":6601,"title":6602,"module":6590,"summary":6603},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fhierarchy-problem-naturalness","The Hierarchy Problem and Naturalness","The electroweak scale sits sixteen orders of magnitude below the Planck scale, and nothing in the Standard Model protects that gap. The Higgs mass squared picks up quadratic corrections proportional to the highest scale in the theory, so keeping it at the observed value requires the bare mass and its counterterm to cancel to some thirty significant figures. Naturalness treats that cancellation as a symptom of missing physics. Supersymmetry, compositeness, and extra dimensions each remove the quadratic sensitivity, but the LHC has found none of them at the predicted scale.\n",{"path":6605,"title":6606,"module":6590,"summary":6607},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fdark-matter-candidates","Dark Matter and Particle Candidates","Flat galactic rotation curves, gravitational lensing, the cosmic microwave background, and structure formation all require about five times more matter than the visible baryons, none of it interacting electromagnetically. A stable weakly interacting particle of roughly weak-scale mass freezes out of the early universe with close to the observed abundance — the WIMP miracle — and is the leading candidate, with axions and sterile neutrinos as alternatives. Direct, indirect, and collider searches have so far only tightened the limits.\n",{"path":6609,"title":6610,"module":6590,"summary":6611},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fmatter-antimatter-open-questions","Matter-Antimatter Asymmetry and Open Questions","The universe is made of matter, with about one extra baryon for every billion photons and no antimatter regions. Sakharov identified the three conditions any dynamical explanation must meet: baryon-number violation, C and CP violation, and a departure from thermal equilibrium. The Standard Model contains all three in principle, but its CP violation falls short by some ten orders of magnitude, so baryogenesis requires new physics — leptogenesis being the leading route. A closing survey collects the open questions and the experiments aimed at them.\n",{"path":6613,"title":6614,"module":6,"summary":6},"\u002Fparticle-physics","Particle Physics",{"path":6616,"title":6617,"module":6618,"summary":6619},"\u002Fastrophysics-cosmology\u002Forientation\u002Fthe-sun-and-stars","The Sun and the Life of Stars","Orientation","The Sun is the one star close enough to study in detail: its luminosity fixes a surface temperature of 5780 K, and the proton-proton fusion cycle in its 1.5-million-kelvin core supplies its power. Measuring other stars needs the magnitude scale, parallax, and the distance ladder; plotting luminosity against temperature builds the Hertzsprung-Russell diagram, on which a star's mass sets its lifetime and its evolutionary track off the main sequence.\n",{"path":6621,"title":6622,"module":6618,"summary":6623},"\u002Fastrophysics-cosmology\u002Forientation\u002Fstellar-death-final-states","Cataclysmic Events and the Final States of Stars","A star's death is set by its mass. In close binaries, matter poured across the Roche lobe onto a white dwarf produces novae and, at the Chandrasekhar limit of 1.4 solar masses, a Type Ia supernova; a massive star fusing to an iron core collapses into a Type II supernova. The remnant is a white dwarf held by electron degeneracy, a neutron star held by neutron degeneracy, or, above the neutron-star limit, a black hole inside its Schwarzschild radius.\n",{"path":6625,"title":6626,"module":6618,"summary":6627},"\u002Fastrophysics-cosmology\u002Forientation\u002Fgalaxies-and-cosmology","Galaxies, Cosmology, and the Evolving Universe","Galaxies come in elliptical, spiral, and irregular forms, and their redshifts obey Hubble's law, evidence that space itself is expanding. The critical density and the density parameter decide whether the universe is open, flat, or closed; baryons, dark matter, and dark energy each contribute. The cosmic microwave background and primordial helium anchor the Big Bang, whose thermal history runs from inflation through nucleosynthesis to the atoms of today.\n",{"path":6629,"title":6630,"module":6631,"summary":6632},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fmagnitudes-fluxes-and-the-distance-modulus","Magnitudes, Fluxes, and the Distance Modulus","Observational Foundations","The brightness of a star reaches us as a radiant flux that falls off as the inverse square of distance. The magnitude scale encodes flux logarithmically through the Pogson ratio; the apparent and absolute magnitudes differ by the distance modulus, which converts a measured brightness into a distance. The bolometric correction folds a filtered magnitude into a total luminosity, and the difference of two magnitudes in different bands, the color index, measures surface temperature.\n",{"path":6634,"title":6635,"module":6631,"summary":6636},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fstellar-spectra-and-spectral-classification","Stellar Spectra and Spectral Classification","A stellar spectrum is a continuum crossed by absorption lines whose strengths are set by the temperature of the atmosphere. The Boltzmann factor governs how atoms populate excited states, and the Saha equation governs how they ionize; their product explains why each line, such as the hydrogen Balmer series, peaks in strength at a characteristic temperature. This behavior orders stars into the OBAFGKM sequence, and the luminosity classes of the MK system add a second dimension for surface gravity.\n",{"path":6638,"title":6639,"module":6631,"summary":6640},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Ftelescopes-and-detectors-across-the-spectrum","Telescopes and Detectors Across the Spectrum","A telescope collects light in proportion to its collecting area and resolves detail down to the diffraction limit set by its aperture and the observing wavelength. The atmosphere blurs and blocks large parts of the spectrum, which drives the choice between ground and space and between refractors, reflectors, and radio dishes. CCDs record the light with high quantum efficiency, and interferometry synthesizes an aperture as large as the separation of two telescopes.\n",{"path":6642,"title":6643,"module":6631,"summary":6644},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fthe-cosmic-distance-ladder","The Cosmic Distance Ladder","No single method measures distances from the nearest stars to the far reaches of the universe. Instead a ladder of overlapping techniques, each calibrated by the one below it, extends the scale rung by rung: trigonometric parallax, main-sequence fitting, pulsating variables, the tip of the red-giant branch, the Tully-Fisher relation, and Type Ia supernovae. Each rung inherits the uncertainty of every rung beneath it, so the whole chain sets the accuracy of the Hubble constant.\n",{"path":6646,"title":6647,"module":6648,"summary":6649},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fblackbody-radiation-and-specific-intensity","Blackbody Radiation and Specific Intensity","Radiation and Matter","Specific intensity is the fundamental measure of a radiation field: energy per unit area, time, frequency, and solid angle. It is conserved along a ray in empty space, and its angular moments give the mean intensity, flux, and radiation pressure. In thermal equilibrium the intensity equals the Planck function, whose limits and integrals reproduce the Rayleigh-Jeans law, the Wien law, Stefan-Boltzmann, and Wien's displacement law.\n",{"path":6651,"title":6652,"module":6648,"summary":6653},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fradiative-transfer-and-the-transfer-equation","Radiative Transfer and the Transfer Equation","Along a ray, matter adds intensity through emission and removes it through absorption. Measuring path length in optical depth turns this into the transfer equation, whose formal solution superposes an attenuated background on the source function integrated along the line of sight. In local thermodynamic equilibrium the source function is the Planck function, and the Eddington-Barbier relation shows that the emergent intensity samples the source function at optical depth of order unity, explaining absorption lines and solar limb darkening.\n",{"path":6655,"title":6656,"module":6648,"summary":6657},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fspectral-line-formation-and-broadening","Spectral-Line Formation and Broadening","A spectral line is a bound-bound transition whose strength is set by an oscillator strength and whose shape is set by three broadening mechanisms: the Lorentzian natural and collisional wings, the Gaussian thermal Doppler core, and their Voigt convolution. Equivalent width measures the total absorption, and the curve of growth relates it to the number of absorbers through a linear, saturated, and damping regime, turning line strengths into abundances.\n",{"path":6659,"title":6660,"module":6648,"summary":6661},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fopacity-and-the-rosseland-mean","Opacity Sources and the Rosseland Mean","Stellar opacity comes from four processes: bound-bound line absorption, bound-free photoionization, free-free absorption, and electron scattering. The bound-free and free-free terms follow a Kramers law, electron scattering sets a frequency-flat floor, and the negative hydrogen ion dominates cool photospheres. The Rosseland mean averages these harmonically, weighting transparent frequencies because they carry the flux, and its value fixes the radiative temperature gradient and decides where a star becomes convective.\n",{"path":6663,"title":6664,"module":6665,"summary":6666},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fhydrostatic-equilibrium-and-the-virial-theorem","Hydrostatic Equilibrium and the Virial Theorem","Stellar Structure","A star holds itself up by balancing the inward pull of gravity against an outward pressure gradient. This balance, hydrostatic equilibrium, fixes a lower bound on the central pressure and, combined with the gravitational potential energy, yields the virial theorem. The virial relation gives a star a negative heat capacity, so that losing energy makes it hotter, and sets the Kelvin-Helmholtz timescale over which contraction alone can power the Sun.\n",{"path":6668,"title":6669,"module":6665,"summary":6670},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equations-of-stellar-structure","The Equations of Stellar Structure","A static star is described by four coupled first-order differential equations in the interior mass or radius: mass conservation, hydrostatic equilibrium, energy generation, and energy transport. Closed with an equation of state, opacity, and reaction rates, and subject to central and surface boundary conditions, they determine the structure uniquely from mass and composition, the Vogt-Russell theorem. Energy moves by radiation until the temperature gradient exceeds the Schwarzschild limit, where convection takes over.\n",{"path":6672,"title":6673,"module":6665,"summary":6674},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equation-of-state-and-polytropes","The Equation of State and Polytropes","Stellar pressure comes from gas, radiation, and, at high density, degenerate electrons. When pressure depends on density as a power law, hydrostatic equilibrium reduces to the Lane-Emden equation, whose solutions describe polytropes of index n. The relativistic degenerate case, n equal to three, gives a mass independent of radius, the Chandrasekhar mass. Eddington's standard model treats a radiation-supported star as an n equal to three polytrope and yields the quartic relating radiation fraction to mass.\n",{"path":6676,"title":6677,"module":6665,"summary":6678},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-standard-solar-model","The Standard Solar Model","The standard solar model integrates the structure equations for one solar mass and calibrates the composition and convection parameter to reproduce the Sun's observed luminosity, radius, and age. Helioseismology tests the model's sound speed through the Sun's acoustic p-mode oscillations, and the model predicts a neutrino flux by production channel. The measured deficit, the solar-neutrino problem, is resolved by matter-enhanced flavor oscillation, confirmed when SNO measured the total flux across all flavors.\n",{"path":6680,"title":6681,"module":6682,"summary":6683},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fthermonuclear-reaction-rates-and-the-gamow-peak","Thermonuclear Reaction Rates and the Gamow Peak","Nuclear Astrophysics","Stellar fusion proceeds only by quantum tunneling through the Coulomb barrier, because thermal energies are a thousand times smaller than the barrier height. The reaction rate is an integral over the Maxwell–Boltzmann distribution and the tunneling probability, whose product is sharply peaked at the Gamow energy. The astrophysical S-factor isolates the nuclear physics from the barrier penetration, and the steep temperature dependence follows from the width and position of the Gamow peak.\n",{"path":6685,"title":6686,"module":6682,"summary":6687},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhydrogen-burning-pp-chains-and-cno","Hydrogen Burning: pp Chains and the CNO Cycle","Four protons fuse into one helium-4 nucleus, releasing 26.7 MeV, through two competing networks. The pp chain begins with a weak-interaction bottleneck and branches three ways; the CNO cycle uses carbon, nitrogen, and oxygen as catalysts and is limited by nitrogen-14 proton capture. Their steep and gentle temperature dependences cross near 1.8e7 K, which divides pp-powered lower-main-sequence stars from CNO-powered upper-main-sequence stars.\n",{"path":6689,"title":6690,"module":6682,"summary":6691},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhelium-burning-and-the-triple-alpha-process","Helium Burning and the Triple-Alpha Process","Helium fuses to carbon in two steps through the unbound beryllium-8 nucleus and a resonant excited state of carbon-12, the Hoyle state, whose existence was predicted from the observed carbon abundance. The rate scales as roughly the fortieth power of temperature, and in a degenerate low-mass core this drives the runaway helium flash. A competing alpha capture on carbon-12 sets the carbon-to-oxygen ratio and the composition of the resulting white dwarf.\n",{"path":6693,"title":6694,"module":6682,"summary":6695},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fadvanced-burning-and-neutron-capture-nucleosynthesis","Advanced Burning, the Iron Peak, and the s\u002Fr Processes","Massive stars burn carbon, neon, oxygen, and silicon in ever-shorter stages, building an onion-shell interior and reaching nuclear statistical equilibrium at the iron peak, where the binding-energy-per-nucleon curve turns over and fusion can release no more energy. Elements beyond iron form by neutron capture: the slow s-process in AGB stars tracks the valley of stability, while the rapid r-process in supernovae and neutron-star mergers builds the heaviest nuclei far from it.\n",{"path":6697,"title":6698,"module":6699,"summary":6700},"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fphases-of-the-interstellar-medium","The Phases of the Interstellar Medium","The Interstellar Medium","The gas between the stars separates into distinct thermal phases, from cold molecular clouds at 10 K to a diffuse million-degree corona, held near a common pressure by a balance of photoelectric heating and radiative cooling. Neutral hydrogen is traced by the 21-cm hyperfine line, dust reddens and extinguishes starlight along a characteristic wavelength law, and the ultraviolet output of hot stars carves ionized Strömgren spheres out of the surrounding gas.\n",{"path":6702,"title":6703,"module":6699,"summary":6704},"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fmolecular-clouds-and-gravitational-collapse","Molecular Clouds and Gravitational Collapse","Stars form in cold, dense molecular clouds when self-gravity overcomes thermal and magnetic support. The virial theorem fixes the Jeans mass and length at which a clump becomes unstable, the free-fall time sets how fast it collapses, and a fragmentation cascade — cut off at a minimum mass by the onset of opacity — turns one cloud into a whole cluster, imprinting the stellar initial mass function.\n",{"path":6706,"title":6707,"module":6699,"summary":6708},"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fprotostars-and-the-pre-main-sequence","Protostars and Pre-Main-Sequence Evolution","A collapsing core becomes optically thick and forms a protostar that grows by accretion through a disk while driving bipolar outflows. The newborn star appears on the birthline and contracts down the fully convective Hayashi track, then crosses the radiative Henyey track to the zero-age main sequence, powered by gravitational contraction until hydrogen ignites. Below about 0.08 solar masses degeneracy halts contraction before ignition, dividing stars from brown dwarfs.\n",{"path":6710,"title":6711,"module":6712,"summary":6713},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-main-sequence-and-its-structure","The Main Sequence and Its Structure","Stellar Evolution","A star settles onto the zero-age main sequence when core hydrogen ignition halts contraction. Homology scaling of the structure equations reproduces the mass–luminosity relation, and the burning mode splits the sequence into an upper branch with a convective core and a lower branch with a convective envelope. The main-sequence lifetime falls steeply with mass, and the turnoff of a coeval cluster serves as a clock.\n",{"path":6715,"title":6716,"module":6712,"summary":6717},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fpost-main-sequence-low-mass-evolution","Post-Main-Sequence Evolution of Low-Mass Stars","When a low-mass star exhausts core hydrogen, burning moves to a shell, the core contracts, and the envelope swells into a red giant. A degenerate helium core ignites in a flash, settles onto the horizontal branch, and after a second contraction the star climbs the asymptotic giant branch with two burning shells. Thermal pulses and dredge-up enrich the surface, and mass loss ejects a planetary nebula, leaving a carbon–oxygen white dwarf.\n",{"path":6719,"title":6720,"module":6712,"summary":6721},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-evolution-of-massive-stars","The Evolution of Massive Stars","Stars above about eight solar masses burn through hydrogen, helium, carbon, neon, oxygen, and silicon in stages that grow shorter as neutrino losses accelerate contraction. The interior becomes an onion of concentric burning shells around an inert iron core. Radiation pressure near the Eddington limit drives fierce winds that can strip the hydrogen envelope entirely, and silicon burning builds an iron core toward the threshold of collapse.\n",{"path":6723,"title":6724,"module":6712,"summary":6725},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fstellar-pulsation-and-the-instability-strip","Stellar Pulsation and the Instability Strip","Radial pulsation is a standing sound wave whose period scales inversely with the square root of the mean density. The kappa mechanism, an opacity valve seated in the helium partial-ionization zone, turns a star into a heat engine that pumps the oscillation. Stars in the instability strip pulsate as Cepheids, RR Lyrae, and Mira variables, and the Cepheid period–luminosity relation calibrates the distance ladder.\n",{"path":6727,"title":5156,"module":6728,"summary":6729},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fwhite-dwarfs-and-the-chandrasekhar-limit","Stellar Death and Compact Remnants","A white dwarf is held up by the degeneracy pressure of its electrons, a quantum-mechanical stiffness that survives to zero temperature. Filling the Fermi sea sets a pressure that scales as density to the five-thirds power when the electrons are slow and only four-thirds when they are relativistic. The softer relativistic law produces the inverted mass-radius relation and a maximum mass, the Chandrasekhar limit near 1.4 solar masses, above which no cold equilibrium exists. Cooling and crystallization then turn the white-dwarf population into a clock for the Galactic disk.\n",{"path":6731,"title":6732,"module":6728,"summary":6733},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fcore-collapse-supernovae","Core-Collapse Supernovae","When a massive star builds an iron core past the Chandrasekhar mass, degeneracy fails and the core collapses in less than a second. Photodisintegration and electron capture remove pressure support and neutronize the matter; the collapse halts abruptly at nuclear density, launching a shock that stalls and is revived by neutrino heating. The event is a Type II or stripped-envelope Ib\u002FIc supernova, and the neutrinos from SN 1987A confirmed the picture directly.\n",{"path":6735,"title":6736,"module":6728,"summary":6737},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fthermonuclear-supernovae-type-ia","Thermonuclear Supernovae","A carbon-oxygen white dwarf driven toward the Chandrasekhar mass ignites its degenerate fuel and unbinds itself in a thermonuclear runaway, the Type Ia supernova. The light curve is powered by the radioactive decay of nickel-56 to cobalt-56 to iron-56, and the Phillips relation between peak brightness and decline rate makes these events standardizable candles. Their near-uniform luminosity turns them into the distance indicators that revealed cosmic acceleration.\n",{"path":6739,"title":6740,"module":6728,"summary":6741},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fneutron-stars-and-pulsars","Neutron Stars and Pulsars","A neutron star is held up by neutron degeneracy and the repulsive nuclear force, with a maximum mass, the Tolman-Oppenheimer-Volkoff limit, set by an uncertain dense-matter equation of state. Its rotating magnetic dipole sweeps a beam past Earth as a pulsar, and magnetic braking traces a track across the period-period- derivative diagram. Millisecond pulsars, magnetars, glitches, and the orbital decay of the Hulse-Taylor binary follow from the same structure.\n",{"path":6743,"title":6744,"module":6728,"summary":6745},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fblack-holes-schwarzschild-and-kerr","Black Holes, Schwarzschild and Kerr","Above the neutron-star mass limit gravity wins completely and the remnant is a black hole. The Schwarzschild solution gives the event horizon, gravitational redshift, and time dilation; the innermost stable circular orbit sets the efficiency of accretion. Rotating Kerr black holes drag spacetime and carry an ergosphere. Stellar-mass black holes are found in X-ray binaries, and the Event Horizon Telescope has imaged the shadow of a supermassive one.\n",{"path":6747,"title":6748,"module":6749,"summary":6750},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fbinary-systems-and-mass-transfer","Binary Systems and Mass Transfer","Binaries and Gravitational Waves","Most stars are born in pairs, and a binary is the only setting where a stellar mass can be measured directly. Visual, spectroscopic, and eclipsing binaries each expose a different combination of the orbital elements, and together they calibrate the mass-luminosity relation. When one star swells to fill its Roche lobe, gas streams through the inner Lagrange point onto its companion. Conservative transfer widens or shrinks the orbit depending on the mass ratio, and the sign of that response explains the Algol paradox.\n",{"path":6752,"title":6753,"module":6749,"summary":6754},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Faccreting-compact-objects","Accreting Compact Objects","Gas falling onto a compact object converts gravitational binding energy into radiation with an efficiency set by the depth of the potential well, up to tens of percent of the rest mass for a neutron star or black hole. Angular momentum forces the flow into a disk, and viscous dissipation gives a temperature profile that falls as radius to the minus three-quarters, producing a multicolor blackbody spectrum. Radiation pressure caps the steady luminosity at the Eddington limit. Unstable nuclear burning of the accreted fuel powers classical novae on white dwarfs and Type I X-ray bursts on neutron stars.\n",{"path":6756,"title":6757,"module":6749,"summary":6758},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fgravitational-waves-from-inspiraling-binaries","Gravitational Waves from Inspiraling Binaries","A time-varying mass quadrupole radiates gravitational waves, ripples in spacetime that stretch and squeeze a ring of free masses along two polarizations. The radiated power drains a binary's orbital energy, shrinking the orbit and sweeping the wave frequency upward in a chirp whose rate fixes the chirp mass. Laser interferometers with kilometre arms measure the resulting strain of order ten to the minus twenty-one. The first detection, GW150914, matched a template for two merging black holes near thirty solar masses each.\n",{"path":6760,"title":6761,"module":6749,"summary":6762},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fmultimessenger-astronomy-and-gamma-ray-bursts","Multimessenger Astronomy and Gamma-Ray Bursts","Gamma-ray bursts split into two populations: long bursts from the collapse of massive stars and short bursts from merging compact objects. The compactness problem forces the emitting plasma to move at ultra-relativistic speed, beaming the radiation into a narrow jet. The neutron-star merger GW170817 tied a gravitational chirp to a short gamma-ray burst, a radioactive kilonova, and a broadband afterglow, confirming that mergers forge r-process elements. A merger with a measured redshift is a standard siren that reads the Hubble constant from gravitational data alone.\n",{"path":6764,"title":6765,"module":6766,"summary":6767},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fthe-milky-way","The Milky Way Galaxy","Galaxies and Dark Matter","The Galaxy resolves into a thin disk of gas and young stars, a central bar and bulge, and a diffuse old halo studded with globular clusters. Star counts and the reddening of distant light map these components, while the differential rotation of the disk — encoded in the Oort constants and the flat rotation curve — measures the enclosed mass and reveals more than the stars can account for. Spiral arms are density waves, not material structures, and the innermost stellar orbits around Sgr A* weigh a four-million-solar-mass black hole.\n",{"path":6769,"title":6770,"module":6766,"summary":6771},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-morphology-and-classification","Galaxy Morphology and Classification","Galaxies sort along the Hubble tuning fork from smooth ellipticals through lenticulars to grand-design and barred spirals, with irregulars off the end. The light of a spheroid follows the de Vaucouleurs quarter-power law while a disk fades exponentially, and the general Sérsic profile interpolates between them. Virial scaling relations — Tully–Fisher for disks, Faber–Jackson and the fundamental plane for spheroids — tie luminosity to internal motions, and the Schechter function fixes the abundance of galaxies as a function of luminosity.\n",{"path":6773,"title":6774,"module":6766,"summary":6775},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-rotation-curves-and-dark-matter","Galaxy Rotation Curves and Dark Matter","The rotation curves of disk galaxies stay flat far beyond the light, demanding an extended halo whose density falls as the inverse square of radius. Decomposing the curve into disk, bulge, and halo, and fitting isothermal or NFW profiles, quantifies the missing mass. Gravitational lensing weighs the same mass without dynamics, the mass-to-light ratio climbs from stars to clusters, and the Bullet Cluster separates the collisionless dark matter from the colliding gas — evidence that MOND strains to match.\n",{"path":6777,"title":6778,"module":6766,"summary":6779},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Factive-galactic-nuclei-and-supermassive-black-holes","Active Galactic Nuclei","A small fraction of galaxies pour out enormous luminosity from a region smaller than the solar system. Accretion onto a supermassive black hole, limited by the Eddington balance of radiation pressure and gravity, powers the Seyferts, quasars, radio galaxies, and blazars — one engine seen from different angles through an obscuring torus. Relativistic jets produce apparent superluminal motion, reverberation mapping and stellar dynamics weigh the central mass, and the M–sigma relation ties that mass to the host bulge.\n",{"path":6781,"title":6782,"module":6766,"summary":6783},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-clusters-and-large-scale-structure","Galaxy Clusters and Large-Scale Structure","Galaxies gather into groups and rich clusters bound by a common dark halo and filled with hot X-ray gas. Three independent probes — the virial theorem, the hydrostatic X-ray temperature, and gravitational lensing — agree on a mass that dwarfs the stars. On the largest scales galaxies trace a cosmic web of filaments, walls, and voids, quantified by the two-point correlation function, whose baryon acoustic oscillation bump provides a standard ruler for cosmology.\n",{"path":6785,"title":6786,"module":6787,"summary":6788},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-expanding-universe-and-hubbles-law","The Expanding Universe and Hubble's Law","Cosmic Expansion and Dynamics","The universe is homogeneous and isotropic on large scales, so its expansion is captured by a single function of time, the scale factor. Comoving coordinates stay fixed while proper distances grow in proportion to the scale factor, producing Hubble's law and a cosmological redshift that measures stretched space rather than a Doppler shift. A Newtonian energy argument reproduces the dynamics, and the same finite, expanding cosmos resolves Olbers' paradox.\n",{"path":6790,"title":6791,"module":6787,"summary":6792},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-frw-metric-and-cosmological-redshift","The FRW Metric and Cosmological Redshift","The geometry of a homogeneous, isotropic universe is fixed by symmetry to the Robertson-Walker metric, with the entire freedom reduced to a scale factor and a single curvature constant selecting an open, flat, or closed space. From the metric the null geodesic of light gives comoving distance, the exact cosmological redshift, and the distinction between the proper distance we cannot measure and the redshift we can.\n",{"path":6794,"title":3874,"module":6787,"summary":6795},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-friedmann-equations-and-cosmic-dynamics","The scale factor obeys the Friedmann equation, the acceleration equation, and the fluid equation, only two of which are independent. An equation of state fixes how each component behaves under expansion, so radiation dilutes as the inverse fourth power of the scale factor, matter as the inverse cube, and vacuum energy not at all. The critical density defines the density parameters, and the deceleration parameter encodes whether gravity or dark energy is winning.\n",{"path":6797,"title":6798,"module":6787,"summary":6799},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fcosmological-models-and-distances","Cosmological Models and Distances","Integrating the Friedmann equation for particular mixtures gives the benchmark models, from the matter-only Einstein-de Sitter universe to the concordance Lambda-CDM, each with its own scale-factor history and age. Because the redshift is the only direct observable, several distance measures diverge at high redshift, and the angular-diameter distance even turns over so that the most distant objects look larger. The horizon and lookback time set what is causally and observationally reachable.\n",{"path":6801,"title":6802,"module":6787,"summary":6803},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fdark-energy-and-the-accelerating-universe","Dark Energy and the Accelerating Universe","In 1998 two teams found that distant Type Ia supernovae are fainter than a decelerating universe predicts, revealing that the expansion is accelerating and that a component with negative pressure dominates the energy budget. The simplest candidate is the cosmological constant, or vacuum energy, with an equation of state near minus one. It works observationally but leaves two deep puzzles: why the vacuum energy is a hundred and twenty orders of magnitude smaller than expected, and why it is comparable to the matter density just now.\n",{"path":6805,"title":6806,"module":6807,"summary":6808},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fthe-thermal-history-of-the-universe","The Thermal History of the Universe","The Hot Big Bang","Running the expansion backward compresses and heats the universe, so its past is a sequence of thermal epochs set by temperature. Temperature scales as the inverse scale factor; species stay in equilibrium while their interaction rate exceeds the expansion rate and freeze out when it drops below. The effective degrees of freedom count the relativistic species and step down through mass thresholds, and neutrino decoupling just before electron-positron annihilation leaves a relic neutrino background slightly cooler than the photons.\n",{"path":6810,"title":6811,"module":6807,"summary":6812},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fbig-bang-nucleosynthesis","Big Bang Nucleosynthesis","In the first three minutes the weak interactions freeze out the neutron-to-proton ratio, and once deuterium survives photodissociation a fast reaction network converts nearly all free neutrons into helium-4. The primordial abundances of deuterium, helium-3, helium-4, and lithium-7 depend on a single free parameter, the baryon-to-photon ratio, so measuring them fixes the baryon density. The predictions match observation across nine decades of abundance, with a persistent discrepancy in lithium-7.\n",{"path":6814,"title":6815,"module":6807,"summary":6816},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Frecombination-and-the-cosmic-microwave-background","Recombination and the Cosmic Microwave Background","As the universe cooled through a few thousand kelvin the free electrons bound to protons, and the Saha equation tracks the falling ionization fraction. Once the plasma neutralized, photons stopped scattering and streamed freely from a spherical surface of last scattering at redshift about 1100. Those photons are the cosmic microwave background, an almost perfect blackbody at 2.725 kelvin with a dipole from our motion through it.\n",{"path":6818,"title":6819,"module":6807,"summary":6820},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcmb-anisotropies-and-cosmological-parameters","CMB Anisotropies and Cosmological Parameters","The cosmic microwave background carries temperature fluctuations at the ten-parts-per-million level, imprinted by sound waves in the photon-baryon plasma before recombination. Decomposed into spherical harmonics, the fluctuations form an angular power spectrum whose acoustic peaks encode the geometry and contents of the universe: the first peak fixes spatial flatness, the odd-even peak ratio the baryon density, and the third peak the dark-matter density. Polarization adds an independent channel, and the Planck measurements pin the concordance parameters.\n",{"path":6822,"title":6823,"module":6807,"summary":6824},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcosmic-inflation","Cosmic Inflation","The hot Big Bang leaves three initial-condition puzzles unexplained: why causally disconnected patches share a temperature, why the geometry is so nearly flat, and why no magnetic monopoles are seen. A brief epoch of accelerated expansion driven by a slowly rolling scalar field solves all three by stretching a small causal patch across the observable universe. The same accelerated expansion freezes quantum fluctuations into a near-scale-invariant spectrum of density perturbations, seeding all later structure.\n",{"path":6826,"title":6827,"module":6807,"summary":6828},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fstructure-formation-and-the-growth-of-perturbations","Structure Formation and the Growth of Perturbations","The near-uniform early universe grew its galaxies and clusters by gravitational instability acting on the tiny inflationary perturbations. In an expanding background the growth is slowed to a power law rather than the exponential of a static medium; perturbations stall during radiation domination and grow with the scale factor once matter dominates. The transfer function turns the primordial spectrum into the processed matter power spectrum, and cold dark matter builds structure from the bottom up.\n",{"path":6830,"title":6831,"module":6807,"summary":6832},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fdark-matter-dark-energy-and-open-questions","Dark Matter, Dark Energy, and Open Questions","Five independent lines of evidence converge on a universe whose energy budget is dominated by dark energy and dark matter, with ordinary baryons a small remainder. The candidate particles for dark matter range from WIMPs to axions to sterile neutrinos, each with its own detection strategy. The concordance model fits the data with six parameters but leaves the nature of dark energy, the Hubble tension, small-scale structure, and the matter-antimatter asymmetry unexplained.\n",{"path":6834,"title":6835,"module":6,"summary":6},"\u002Fastrophysics-cosmology","Astrophysics & Cosmology",{"path":6837,"title":6838,"module":6,"summary":6},"\u002Fcolophon","Colophon",{"path":6840,"title":6841,"module":6,"summary":6},"\u002F","Study Notes",[6843,6854,6888,6915,6937,6956],{"module":1231,"moduleNumber":1228,"slug":6844,"lessons":6845},"foundations",[6846,6848,6850,6852],{"title":5828,"path":5827,"lessonNumber":1228,"topics":6847,"summary":5829},[1231],{"title":5832,"path":5831,"lessonNumber":1208,"topics":6849,"summary":5833},[1231],{"title":18,"path":17,"lessonNumber":1213,"topics":6851,"summary":5835},[1231],{"title":5,"path":1233,"lessonNumber":1229,"topics":6853,"summary":1249},[1231],{"module":5839,"moduleNumber":1208,"slug":685,"lessons":6855},[6856,6858,6860,6862,6864,6867,6870,6873,6876,6879,6882,6885],{"title":5838,"path":684,"lessonNumber":1228,"topics":6857,"summary":5840},[5839],{"title":5843,"path":5842,"lessonNumber":1208,"topics":6859,"summary":5844},[5839],{"title":5847,"path":5846,"lessonNumber":1213,"topics":6861,"summary":5848},[5839],{"title":5851,"path":5850,"lessonNumber":1229,"topics":6863,"summary":5852},[5839],{"title":5855,"path":5854,"lessonNumber":6865,"topics":6866,"summary":5856},5,[5839],{"title":5859,"path":5858,"lessonNumber":6868,"topics":6869,"summary":5860},6,[5839],{"title":5863,"path":5862,"lessonNumber":6871,"topics":6872,"summary":5864},7,[5839],{"title":5867,"path":5866,"lessonNumber":6874,"topics":6875,"summary":5868},8,[5839],{"title":5870,"path":1058,"lessonNumber":6877,"topics":6878,"summary":5871},9,[5839],{"title":5874,"path":5873,"lessonNumber":6880,"topics":6881,"summary":5875},10,[5839],{"title":5878,"path":5877,"lessonNumber":6883,"topics":6884,"summary":5879},11,[5839],{"title":5882,"path":5881,"lessonNumber":6886,"topics":6887,"summary":5883},12,[5839],{"module":5886,"moduleNumber":1213,"slug":6889,"lessons":6890},"logic-and-planning",[6891,6893,6895,6897,6899,6901,6903,6905,6907,6909,6911,6913],{"title":5885,"path":1063,"lessonNumber":1228,"topics":6892,"summary":5887},[5540],{"title":5890,"path":5889,"lessonNumber":1208,"topics":6894,"summary":5891},[5540],{"title":5893,"path":1077,"lessonNumber":1213,"topics":6896,"summary":5894},[5540],{"title":5897,"path":5896,"lessonNumber":1229,"topics":6898,"summary":5898},[5540],{"title":5901,"path":5900,"lessonNumber":6865,"topics":6900,"summary":5902},[5540],{"title":5905,"path":5904,"lessonNumber":6868,"topics":6902,"summary":5906},[5540],{"title":5908,"path":688,"lessonNumber":6871,"topics":6904,"summary":5909},[5540],{"title":5912,"path":5911,"lessonNumber":6874,"topics":6906,"summary":5913},[5540],{"title":5916,"path":5915,"lessonNumber":6877,"topics":6908,"summary":5917},[5540],{"title":5920,"path":5919,"lessonNumber":6880,"topics":6910,"summary":5921},[5540],{"title":5924,"path":5923,"lessonNumber":6883,"topics":6912,"summary":5925},[5540],{"title":5928,"path":5927,"lessonNumber":6886,"topics":6914,"summary":5929},[5540],{"module":5933,"moduleNumber":1229,"slug":964,"lessons":6916},[6917,6919,6921,6923,6925,6927,6929,6931,6933,6935],{"title":5932,"path":5931,"lessonNumber":1228,"topics":6918,"summary":5934},[5933],{"title":5937,"path":5936,"lessonNumber":1208,"topics":6920,"summary":5938},[5933],{"title":5940,"path":1068,"lessonNumber":1213,"topics":6922,"summary":5941},[5933],{"title":5944,"path":5943,"lessonNumber":1229,"topics":6924,"summary":5945},[5933],{"title":5948,"path":5947,"lessonNumber":6865,"topics":6926,"summary":5949},[5933],{"title":5952,"path":5951,"lessonNumber":6868,"topics":6928,"summary":5953},[5933],{"title":5955,"path":963,"lessonNumber":6871,"topics":6930,"summary":5956},[5933],{"title":5559,"path":5958,"lessonNumber":6874,"topics":6932,"summary":5959},[5933],{"title":5962,"path":5961,"lessonNumber":6877,"topics":6934,"summary":5963},[5933],{"title":5966,"path":5965,"lessonNumber":6880,"topics":6936,"summary":5967},[5933],{"module":5971,"moduleNumber":6865,"slug":6938,"lessons":6939},"learning",[6940,6942,6944,6946,6948,6950,6952,6954],{"title":5970,"path":5969,"lessonNumber":1228,"topics":6941,"summary":5972},[5971],{"title":5975,"path":5974,"lessonNumber":1208,"topics":6943,"summary":5976},[5971],{"title":5979,"path":5978,"lessonNumber":1213,"topics":6945,"summary":5980},[5971],{"title":5983,"path":5982,"lessonNumber":1229,"topics":6947,"summary":5984},[5971],{"title":4981,"path":1020,"lessonNumber":6865,"topics":6949,"summary":5986},[5971],{"title":5989,"path":5988,"lessonNumber":6868,"topics":6951,"summary":5990},[5971],{"title":5993,"path":5992,"lessonNumber":6871,"topics":6953,"summary":5994},[5971],{"title":5997,"path":5996,"lessonNumber":6874,"topics":6955,"summary":5998},[5971],{"module":6002,"moduleNumber":6868,"slug":6957,"lessons":6958},"frontiers",[6959,6961,6963,6965,6967,6969,6971,6973],{"title":6001,"path":6000,"lessonNumber":1228,"topics":6960,"summary":6003},[6002],{"title":6006,"path":6005,"lessonNumber":1208,"topics":6962,"summary":6007},[6002],{"title":6010,"path":6009,"lessonNumber":1213,"topics":6964,"summary":6011},[6002],{"title":6014,"path":6013,"lessonNumber":1229,"topics":6966,"summary":6015},[6002],{"title":6018,"path":6017,"lessonNumber":6865,"topics":6968,"summary":6019},[6002],{"title":6022,"path":6021,"lessonNumber":6868,"topics":6970,"summary":6023},[6002],{"title":6026,"path":6025,"lessonNumber":6871,"topics":6972,"summary":6027},[6002],{"title":6030,"path":6029,"lessonNumber":6874,"topics":6974,"summary":6031},[6002],"\u003Csvg style=\"width:100%;max-width:428.391px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 321.293 153.352\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-48.431 61.157h204.86V-58.345h-204.86Z\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-99.297 -51.151)\">\u003Cpath d=\"M56.038 1.406L54.288 1.406L54.288 1.109Q54.987 1.109 55.175 0.629L56.976-4.196Q57.030-4.305 57.144-4.305L57.214-4.305Q57.327-4.305 57.382-4.196L59.272 0.847Q59.351 1.015 59.554 1.062Q59.757 1.109 60.069 1.109L60.069 1.406L57.847 1.406L57.847 1.109Q58.487 1.109 58.487 0.894Q58.487 0.875 58.485 0.865Q58.483 0.855 58.479 0.847L58.015-0.387L55.870-0.387L55.487 0.629Q55.483 0.644 55.478 0.674Q55.472 0.703 55.472 0.726Q55.472 0.867 55.562 0.951Q55.651 1.035 55.784 1.072Q55.917 1.109 56.038 1.109L56.038 1.406M56.944-3.250L55.976-0.684L57.901-0.684L56.944-3.250M60.597 2.015Q60.597 1.734 60.808 1.523Q61.019 1.312 61.304 1.222Q61.147 1.097 61.069 0.908Q60.991 0.718 60.991 0.519Q60.991 0.164 61.222-0.129Q60.854-0.469 60.854-0.938Q60.854-1.289 61.058-1.559Q61.261-1.828 61.581-1.975Q61.901-2.121 62.245-2.121Q62.765-2.121 63.136-1.840Q63.499-2.211 64.046-2.211Q64.226-2.211 64.353-2.084Q64.479-1.957 64.479-1.778Q64.479-1.672 64.401-1.594Q64.323-1.516 64.214-1.516Q64.104-1.516 64.028-1.592Q63.952-1.668 63.952-1.778Q63.952-1.879 63.991-1.930Q63.999-1.938 64.003-1.944Q64.007-1.949 64.007-1.953Q63.632-1.953 63.312-1.699Q63.632-1.360 63.632-0.938Q63.632-0.668 63.515-0.451Q63.397-0.235 63.192-0.076Q62.987 0.082 62.745 0.164Q62.503 0.246 62.245 0.246Q62.026 0.246 61.813 0.187Q61.601 0.129 61.405 0.008Q61.312 0.148 61.312 0.328Q61.312 0.535 61.448 0.687Q61.585 0.840 61.792 0.840L62.487 0.840Q62.976 0.840 63.388 0.924Q63.800 1.008 64.079 1.265Q64.358 1.523 64.358 2.015Q64.358 2.379 64.038 2.611Q63.718 2.843 63.276 2.945Q62.835 3.047 62.479 3.047Q62.124 3.047 61.681 2.945Q61.237 2.843 60.917 2.611Q60.597 2.379 60.597 2.015M61.101 2.015Q61.101 2.211 61.245 2.359Q61.390 2.508 61.603 2.597Q61.815 2.687 62.056 2.734Q62.296 2.781 62.479 2.781Q62.722 2.781 63.052 2.703Q63.382 2.625 63.618 2.451Q63.854 2.277 63.854 2.015Q63.854 1.609 63.444 1.500Q63.034 1.390 62.472 1.390L61.792 1.390Q61.522 1.390 61.312 1.568Q61.101 1.746 61.101 2.015M62.245-0.020Q62.968-0.020 62.968-0.938Q62.968-1.860 62.245-1.860Q61.519-1.860 61.519-0.938Q61.519-0.020 62.245-0.020M64.843-0.348Q64.843-0.828 65.075-1.244Q65.308-1.660 65.718-1.910Q66.128-2.160 66.604-2.160Q67.335-2.160 67.733-1.719Q68.132-1.278 68.132-0.547Q68.132-0.442 68.038-0.418L65.589-0.418L65.589-0.348Q65.589 0.062 65.710 0.418Q65.831 0.773 66.103 0.990Q66.374 1.207 66.804 1.207Q67.167 1.207 67.464 0.978Q67.761 0.750 67.862 0.398Q67.870 0.351 67.956 0.336L68.038 0.336Q68.132 0.363 68.132 0.445Q68.132 0.453 68.124 0.484Q68.061 0.711 67.923 0.894Q67.784 1.078 67.593 1.211Q67.401 1.343 67.183 1.414Q66.964 1.484 66.726 1.484Q66.354 1.484 66.017 1.347Q65.679 1.211 65.411 0.959Q65.144 0.707 64.993 0.367Q64.843 0.027 64.843-0.348M65.597-0.657L67.558-0.657Q67.558-0.961 67.456-1.252Q67.354-1.543 67.138-1.725Q66.921-1.907 66.604-1.907Q66.304-1.907 66.073-1.719Q65.843-1.532 65.720-1.240Q65.597-0.949 65.597-0.657M70.550 1.406L68.694 1.406L68.694 1.109Q68.968 1.109 69.136 1.062Q69.304 1.015 69.304 0.847L69.304-1.289Q69.304-1.504 69.241-1.600Q69.179-1.696 69.060-1.717Q68.940-1.739 68.694-1.739L68.694-2.035L69.886-2.121L69.886-1.387Q69.999-1.602 70.192-1.770Q70.386-1.938 70.624-2.030Q70.862-2.121 71.116-2.121Q72.284-2.121 72.284-1.043L72.284 0.847Q72.284 1.015 72.454 1.062Q72.624 1.109 72.894 1.109L72.894 1.406L71.038 1.406L71.038 1.109Q71.311 1.109 71.479 1.062Q71.647 1.015 71.647 0.847L71.647-1.028Q71.647-1.410 71.526-1.639Q71.405-1.867 71.054-1.867Q70.741-1.867 70.487-1.705Q70.233-1.543 70.087-1.274Q69.940-1.004 69.940-0.707L69.940 0.847Q69.940 1.015 70.110 1.062Q70.280 1.109 70.550 1.109\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-99.297 -51.151)\">\u003Cpath d=\"M73.743 0.445L73.743-1.746L73.040-1.746L73.040-2Q73.396-2 73.638-2.233Q73.880-2.465 73.991-2.813Q74.103-3.160 74.103-3.516L74.384-3.516L74.384-2.043L75.560-2.043L75.560-1.746L74.384-1.746L74.384 0.429Q74.384 0.750 74.503 0.978Q74.622 1.207 74.903 1.207Q75.083 1.207 75.200 1.084Q75.317 0.961 75.370 0.781Q75.423 0.601 75.423 0.429L75.423-0.043L75.704-0.043L75.704 0.445Q75.704 0.699 75.599 0.939Q75.493 1.179 75.296 1.332Q75.099 1.484 74.841 1.484Q74.525 1.484 74.273 1.361Q74.021 1.238 73.882 1.004Q73.743 0.769 73.743 0.445\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M183.846 61.157h58.977V-58.345h-58.977Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr9\" font-size=\"9\">\u003Cg transform=\"translate(133.18 3.075)\">\u003Cpath d=\"M59.633 1.406L54.324 1.406L54.324 1.090Q55.243 1.090 55.243 0.795L55.243-4.131Q55.243-4.426 54.324-4.426L54.324-4.742L59.514-4.742L59.769-2.681L59.479-2.681Q59.409-3.274 59.294-3.606Q59.180-3.938 58.971-4.114Q58.763-4.289 58.418-4.357Q58.073-4.426 57.462-4.426L56.548-4.426Q56.297-4.426 56.192-4.377Q56.086-4.329 56.086-4.131L56.086-1.943L56.772-1.943Q57.251-1.943 57.473-2.017Q57.695-2.092 57.787-2.307Q57.879-2.523 57.879-2.993L58.165-2.993L58.165-0.576L57.879-0.576Q57.879-1.046 57.787-1.261Q57.695-1.477 57.473-1.552Q57.251-1.626 56.772-1.626L56.086-1.626L56.086 0.795Q56.086 0.989 56.192 1.039Q56.297 1.090 56.548 1.090L57.528 1.090Q58.165 1.090 58.554 0.993Q58.943 0.896 59.163 0.674Q59.382 0.452 59.503 0.074Q59.624-0.303 59.734-0.954L60.020-0.954L59.633 1.406M62.678 1.406L60.591 1.406L60.591 1.090Q60.898 1.090 61.090 1.037Q61.281 0.984 61.281 0.795L61.281-1.653Q61.281-1.894 61.210-2.002Q61.140-2.110 61.006-2.134Q60.872-2.158 60.591-2.158L60.591-2.474L61.931-2.571L61.931-1.736Q62.129-2.118 62.483-2.345Q62.836-2.571 63.263-2.571Q64.541-2.571 64.541-1.358L64.541 0.795Q64.541 0.984 64.733 1.037Q64.924 1.090 65.231 1.090L65.231 1.406L63.144 1.406L63.144 1.090Q63.456 1.090 63.647 1.037Q63.838 0.984 63.838 0.795L63.838-1.323Q63.838-1.582 63.794-1.804Q63.750-2.026 63.605-2.169Q63.460-2.312 63.201-2.312Q62.858-2.312 62.577-2.123Q62.296-1.934 62.140-1.622Q61.984-1.310 61.984-0.963L61.984 0.795Q61.984 0.984 62.177 1.037Q62.371 1.090 62.678 1.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(133.18 3.075)\">\u003Cpath d=\"M67.407 1.388L66.076-1.859Q65.988-2.057 65.823-2.107Q65.658-2.158 65.355-2.158L65.355-2.474L67.280-2.474L67.280-2.158Q66.788-2.158 66.788-1.943Q66.788-1.921 66.805-1.859L67.821 0.615L68.730-1.609Q68.765-1.692 68.765-1.789Q68.765-1.960 68.642-2.059Q68.519-2.158 68.352-2.158L68.352-2.474L69.864-2.474L69.864-2.158Q69.578-2.158 69.365-2.015Q69.152-1.872 69.047-1.609L67.812 1.388Q67.768 1.507 67.640 1.507L67.579 1.507Q67.451 1.507 67.407 1.388M72.347 1.406L70.361 1.406L70.361 1.090Q70.668 1.090 70.859 1.037Q71.050 0.984 71.050 0.795L71.050-1.653Q71.050-1.899 70.985-2.004Q70.919-2.110 70.793-2.134Q70.668-2.158 70.396-2.158L70.396-2.474L71.727-2.571L71.727 0.795Q71.727 0.989 71.892 1.039Q72.057 1.090 72.347 1.090L72.347 1.406M70.747-4.118Q70.747-4.324 70.897-4.474Q71.046-4.623 71.248-4.623Q71.380-4.623 71.497-4.553Q71.613-4.483 71.683-4.366Q71.754-4.250 71.754-4.118Q71.754-3.916 71.604-3.766Q71.455-3.617 71.248-3.617Q71.046-3.617 70.897-3.766Q70.747-3.916 70.747-4.118M75.102 1.406L72.870 1.406L72.870 1.090Q73.182 1.090 73.373 1.037Q73.564 0.984 73.564 0.795L73.564-1.653Q73.564-1.894 73.494-2.002Q73.424-2.110 73.290-2.134Q73.155-2.158 72.870-2.158L72.870-2.474L74.184-2.571L74.184-1.710Q74.346-2.101 74.614-2.336Q74.883-2.571 75.274-2.571Q75.546-2.571 75.761-2.408Q75.977-2.246 75.977-1.987Q75.977-1.811 75.858-1.692Q75.739-1.573 75.564-1.573Q75.383-1.573 75.265-1.692Q75.146-1.811 75.146-1.987Q75.146-2.202 75.300-2.312L75.282-2.312Q74.904-2.312 74.672-2.050Q74.439-1.789 74.340-1.402Q74.241-1.015 74.241-0.655L74.241 0.795Q74.241 0.984 74.498 1.037Q74.755 1.090 75.102 1.090L75.102 1.406M76.495-0.501Q76.495-1.068 76.768-1.556Q77.040-2.044 77.510-2.336Q77.981-2.628 78.548-2.628Q78.969-2.628 79.345-2.459Q79.721-2.290 79.998-1.998Q80.275-1.705 80.433-1.310Q80.591-0.914 80.591-0.501Q80.591 0.048 80.312 0.510Q80.033 0.971 79.565 1.239Q79.097 1.507 78.548 1.507Q77.994 1.507 77.524 1.239Q77.053 0.971 76.774 0.510Q76.495 0.048 76.495-0.501M78.548 1.217Q79.044 1.217 79.321 0.956Q79.598 0.694 79.690 0.290Q79.782-0.115 79.782-0.611Q79.782-1.086 79.684-1.475Q79.585-1.864 79.312-2.114Q79.040-2.365 78.548-2.365Q77.836-2.365 77.572-1.870Q77.308-1.376 77.308-0.611Q77.308 0.189 77.563 0.703Q77.818 1.217 78.548 1.217M83.241 1.406L81.154 1.406L81.154 1.090Q81.461 1.090 81.652 1.037Q81.843 0.984 81.843 0.795L81.843-1.653Q81.843-1.894 81.773-2.002Q81.703-2.110 81.569-2.134Q81.435-2.158 81.154-2.158L81.154-2.474L82.494-2.571L82.494-1.736Q82.692-2.118 83.045-2.345Q83.399-2.571 83.825-2.571Q85.104-2.571 85.104-1.358L85.104 0.795Q85.104 0.984 85.295 1.037Q85.487 1.090 85.794 1.090L85.794 1.406L83.707 1.406L83.707 1.090Q84.019 1.090 84.210 1.037Q84.401 0.984 84.401 0.795L84.401-1.323Q84.401-1.582 84.357-1.804Q84.313-2.026 84.168-2.169Q84.023-2.312 83.764-2.312Q83.421-2.312 83.140-2.123Q82.859-1.934 82.703-1.622Q82.547-1.310 82.547-0.963L82.547 0.795Q82.547 0.984 82.740 1.037Q82.933 1.090 83.241 1.090L83.241 1.406M88.378 1.406L86.291 1.406L86.291 1.090Q86.598 1.090 86.790 1.037Q86.981 0.984 86.981 0.795L86.981-1.653Q86.981-1.894 86.910-2.002Q86.840-2.110 86.706-2.134Q86.572-2.158 86.291-2.158L86.291-2.474L87.631-2.571L87.631-1.736Q87.829-2.114 88.189-2.343Q88.550-2.571 88.971-2.571Q90.017-2.571 90.202-1.762Q90.404-2.132 90.762-2.351Q91.120-2.571 91.538-2.571Q92.162-2.571 92.487-2.277Q92.812-1.982 92.812-1.358L92.812 0.795Q92.812 0.984 93.006 1.037Q93.199 1.090 93.507 1.090L93.507 1.406L91.419 1.406L91.419 1.090Q91.727 1.090 91.920 1.037Q92.113 0.984 92.113 0.795L92.113-1.323Q92.113-1.754 91.986-2.033Q91.859-2.312 91.472-2.312Q91.129-2.312 90.846-2.123Q90.562-1.934 90.406-1.622Q90.250-1.310 90.250-0.963L90.250 0.795Q90.250 0.984 90.441 1.037Q90.633 1.090 90.940 1.090L90.940 1.406L88.853 1.406L88.853 1.090Q89.165 1.090 89.356 1.037Q89.547 0.984 89.547 0.795L89.547-1.323Q89.547-1.582 89.503-1.804Q89.459-2.026 89.314-2.169Q89.169-2.312 88.910-2.312Q88.374-2.312 88.029-1.905Q87.684-1.499 87.684-0.963L87.684 0.795Q87.684 0.984 87.877 1.037Q88.071 1.090 88.378 1.090L88.378 1.406M96.007 1.507Q95.449 1.507 94.977 1.224Q94.504 0.940 94.229 0.463Q93.955-0.013 93.955-0.567Q93.955-0.963 94.098-1.338Q94.240-1.714 94.498-2.002Q94.755-2.290 95.113-2.459Q95.471-2.628 95.875-2.628Q96.420-2.628 96.791-2.391Q97.163-2.154 97.350-1.736Q97.536-1.319 97.536-0.782Q97.536-0.730 97.512-0.692Q97.488-0.655 97.440-0.655L94.768-0.655L94.768-0.576Q94.768 0.171 95.080 0.694Q95.392 1.217 96.091 1.217Q96.495 1.217 96.816 0.960Q97.136 0.703 97.259 0.299Q97.277 0.219 97.361 0.219L97.440 0.219Q97.479 0.219 97.508 0.250Q97.536 0.281 97.536 0.325L97.536 0.360Q97.431 0.703 97.209 0.962Q96.987 1.221 96.673 1.364Q96.359 1.507 96.007 1.507M94.777-0.906L96.890-0.906Q96.890-1.174 96.838-1.420Q96.785-1.666 96.664-1.888Q96.543-2.110 96.345-2.237Q96.148-2.365 95.875-2.365Q95.532-2.365 95.280-2.140Q95.027-1.916 94.902-1.578Q94.777-1.240 94.777-0.906M100.195 1.406L98.108 1.406L98.108 1.090Q98.415 1.090 98.606 1.037Q98.798 0.984 98.798 0.795L98.798-1.653Q98.798-1.894 98.727-2.002Q98.657-2.110 98.523-2.134Q98.389-2.158 98.108-2.158L98.108-2.474L99.448-2.571L99.448-1.736Q99.646-2.118 99.999-2.345Q100.353-2.571 100.779-2.571Q102.058-2.571 102.058-1.358L102.058 0.795Q102.058 0.984 102.249 1.037Q102.441 1.090 102.748 1.090L102.748 1.406L100.661 1.406L100.661 1.090Q100.973 1.090 101.164 1.037Q101.355 0.984 101.355 0.795L101.355-1.323Q101.355-1.582 101.311-1.804Q101.267-2.026 101.122-2.169Q100.977-2.312 100.718-2.312Q100.375-2.312 100.094-2.123Q99.813-1.934 99.657-1.622Q99.501-1.310 99.501-0.963L99.501 0.795Q99.501 0.984 99.694 1.037Q99.887 1.090 100.195 1.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(133.18 3.075)\">\u003Cpath d=\"M103.649 0.334L103.649-2.158L102.884-2.158L102.884-2.417Q103.289-2.417 103.555-2.683Q103.820-2.949 103.941-3.349Q104.062-3.749 104.062-4.131L104.352-4.131L104.352-2.474L105.640-2.474L105.640-2.158L104.352-2.158L104.352 0.299Q104.352 0.668 104.477 0.942Q104.603 1.217 104.928 1.217Q105.227 1.217 105.365 0.923Q105.504 0.628 105.504 0.299L105.504-0.224L105.789-0.224L105.789 0.334Q105.789 0.611 105.679 0.883Q105.569 1.156 105.356 1.331Q105.143 1.507 104.862 1.507Q104.502 1.507 104.229 1.369Q103.957 1.230 103.803 0.967Q103.649 0.703 103.649 0.334\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(43.185 -65.56)\">\u003Cpath d=\"M54.488 1.468L54.488-0.105Q54.488-0.132 54.513-0.158Q54.539-0.183 54.566-0.183L54.679-0.183Q54.707-0.183 54.730-0.156Q54.754-0.129 54.754-0.105Q54.754 0.240 54.886 0.504Q55.018 0.767 55.247 0.936Q55.476 1.105 55.778 1.186Q56.081 1.266 56.422 1.266Q56.689 1.266 56.925 1.138Q57.161 1.010 57.306 0.787Q57.451 0.565 57.451 0.299Q57.451 0.076 57.345-0.120Q57.239-0.317 57.058-0.452Q56.877-0.587 56.651-0.638L55.623-0.870Q55.312-0.942 55.052-1.128Q54.792-1.315 54.640-1.586Q54.488-1.858 54.488-2.173Q54.488-2.559 54.701-2.866Q54.915-3.174 55.262-3.345Q55.609-3.516 55.988-3.516Q56.217-3.516 56.446-3.463Q56.675-3.410 56.874-3.302Q57.072-3.195 57.226-3.031L57.520-3.471Q57.543-3.516 57.584-3.516L57.632-3.516Q57.663-3.516 57.685-3.490Q57.707-3.465 57.707-3.437L57.707-1.862Q57.707-1.841 57.684-1.814Q57.660-1.786 57.632-1.786L57.520-1.786Q57.458-1.786 57.444-1.862Q57.403-2.275 57.222-2.595Q57.041-2.914 56.730-3.089Q56.419-3.263 55.988-3.263Q55.739-3.263 55.499-3.152Q55.260-3.041 55.110-2.843Q54.959-2.644 54.959-2.381Q54.959-2.169 55.067-1.988Q55.175-1.807 55.351-1.687Q55.527-1.568 55.735-1.527L56.764-1.298Q57.082-1.226 57.349-1.021Q57.615-0.816 57.767-0.522Q57.919-0.228 57.919 0.104Q57.919 0.497 57.714 0.832Q57.509 1.167 57.164 1.356Q56.819 1.546 56.422 1.546Q56.002 1.546 55.623 1.433Q55.243 1.321 54.973 1.071L54.679 1.505Q54.652 1.546 54.614 1.546L54.566 1.546Q54.539 1.546 54.513 1.521Q54.488 1.495 54.488 1.468M58.688-0.129Q58.688-0.450 58.813-0.739Q58.938-1.028 59.164-1.251Q59.389-1.475 59.685-1.595Q59.980-1.715 60.298-1.715Q60.626-1.715 60.888-1.615Q61.149-1.516 61.325-1.334Q61.501-1.151 61.595-0.893Q61.689-0.635 61.689-0.303Q61.689-0.211 61.607-0.190L59.352-0.190L59.352-0.129Q59.352 0.459 59.635 0.842Q59.919 1.225 60.486 1.225Q60.808 1.225 61.076 1.032Q61.344 0.839 61.433 0.524Q61.440 0.483 61.515 0.469L61.607 0.469Q61.689 0.493 61.689 0.565Q61.689 0.572 61.683 0.599Q61.570 0.996 61.199 1.235Q60.828 1.474 60.404 1.474Q59.967 1.474 59.567 1.266Q59.167 1.057 58.928 0.690Q58.688 0.323 58.688-0.129M59.358-0.399L61.173-0.399Q61.173-0.676 61.076-0.928Q60.978-1.181 60.780-1.337Q60.582-1.492 60.298-1.492Q60.021-1.492 59.808-1.334Q59.594-1.175 59.476-0.920Q59.358-0.665 59.358-0.399M63.959 1.406L62.325 1.406L62.325 1.126Q62.554 1.126 62.703 1.092Q62.852 1.057 62.852 0.917L62.852-0.932Q62.852-1.202 62.744-1.263Q62.636-1.325 62.325-1.325L62.325-1.605L63.385-1.680L63.385-1.031Q63.556-1.339 63.860-1.510Q64.164-1.680 64.509-1.680Q65.015-1.680 65.299-1.457Q65.582-1.233 65.582-0.737L65.582 0.917Q65.582 1.054 65.731 1.090Q65.880 1.126 66.105 1.126L66.105 1.406L64.475 1.406L64.475 1.126Q64.704 1.126 64.853 1.092Q65.001 1.057 65.001 0.917L65.001-0.723Q65.001-1.058 64.882-1.258Q64.762-1.458 64.448-1.458Q64.178-1.458 63.944-1.322Q63.709-1.185 63.571-0.951Q63.433-0.717 63.433-0.443L63.433 0.917Q63.433 1.054 63.583 1.090Q63.733 1.126 63.959 1.126L63.959 1.406M66.693 1.399L66.693 0.336Q66.693 0.312 66.721 0.285Q66.748 0.258 66.772 0.258L66.881 0.258Q66.946 0.258 66.960 0.316Q67.056 0.750 67.302 1.001Q67.548 1.252 67.961 1.252Q68.303 1.252 68.556 1.119Q68.809 0.986 68.809 0.678Q68.809 0.521 68.715 0.406Q68.621 0.292 68.483 0.223Q68.344 0.155 68.177 0.117L67.596 0.018Q67.240-0.050 66.967-0.271Q66.693-0.491 66.693-0.833Q66.693-1.082 66.804-1.257Q66.916-1.431 67.102-1.530Q67.288-1.629 67.503-1.672Q67.719-1.715 67.961-1.715Q68.375-1.715 68.655-1.533L68.871-1.708Q68.881-1.711 68.888-1.713Q68.895-1.715 68.905-1.715L68.956-1.715Q68.983-1.715 69.007-1.691Q69.031-1.667 69.031-1.639L69.031-0.792Q69.031-0.771 69.007-0.744Q68.983-0.717 68.956-0.717L68.843-0.717Q68.816-0.717 68.790-0.742Q68.765-0.768 68.765-0.792Q68.765-1.028 68.659-1.192Q68.553-1.356 68.370-1.438Q68.187-1.520 67.955-1.520Q67.626-1.520 67.370-1.417Q67.114-1.315 67.114-1.038Q67.114-0.843 67.297-0.734Q67.479-0.624 67.708-0.583L68.283-0.477Q68.529-0.429 68.742-0.301Q68.956-0.173 69.093 0.030Q69.229 0.234 69.229 0.483Q69.229 0.996 68.864 1.235Q68.498 1.474 67.961 1.474Q67.466 1.474 67.134 1.180L66.868 1.454Q66.847 1.474 66.820 1.474L66.772 1.474Q66.748 1.474 66.721 1.447Q66.693 1.420 66.693 1.399M69.817-0.077Q69.817-0.419 69.952-0.718Q70.087-1.017 70.327-1.241Q70.566-1.465 70.884-1.590Q71.202-1.715 71.533-1.715Q71.978-1.715 72.377-1.499Q72.777-1.284 73.011-0.906Q73.246-0.529 73.246-0.077Q73.246 0.264 73.104 0.548Q72.962 0.832 72.718 1.039Q72.473 1.245 72.164 1.360Q71.854 1.474 71.533 1.474Q71.103 1.474 70.701 1.273Q70.299 1.071 70.058 0.719Q69.817 0.367 69.817-0.077M71.533 1.225Q72.135 1.225 72.359 0.847Q72.582 0.469 72.582-0.163Q72.582-0.775 72.348-1.134Q72.114-1.492 71.533-1.492Q70.480-1.492 70.480-0.163Q70.480 0.469 70.706 0.847Q70.932 1.225 71.533 1.225M75.590 1.406L73.854 1.406L73.854 1.126Q74.083 1.126 74.232 1.092Q74.380 1.057 74.380 0.917L74.380-0.932Q74.380-1.202 74.273-1.263Q74.165-1.325 73.854-1.325L73.854-1.605L74.883-1.680L74.883-0.973Q75.013-1.281 75.255-1.480Q75.498-1.680 75.816-1.680Q76.035-1.680 76.206-1.556Q76.376-1.431 76.376-1.219Q76.376-1.082 76.277-0.983Q76.178-0.884 76.045-0.884Q75.908-0.884 75.809-0.983Q75.710-1.082 75.710-1.219Q75.710-1.359 75.809-1.458Q75.519-1.458 75.319-1.262Q75.119-1.065 75.026-0.771Q74.934-0.477 74.934-0.197L74.934 0.917Q74.934 1.126 75.590 1.126L75.590 1.406M76.961 1.399L76.961 0.336Q76.961 0.312 76.988 0.285Q77.016 0.258 77.040 0.258L77.149 0.258Q77.214 0.258 77.228 0.316Q77.323 0.750 77.569 1.001Q77.815 1.252 78.229 1.252Q78.571 1.252 78.824 1.119Q79.077 0.986 79.077 0.678Q79.077 0.521 78.983 0.406Q78.889 0.292 78.750 0.223Q78.612 0.155 78.444 0.117L77.863 0.018Q77.508-0.050 77.234-0.271Q76.961-0.491 76.961-0.833Q76.961-1.082 77.072-1.257Q77.183-1.431 77.369-1.530Q77.556-1.629 77.771-1.672Q77.986-1.715 78.229-1.715Q78.643-1.715 78.923-1.533L79.138-1.708Q79.148-1.711 79.155-1.713Q79.162-1.715 79.172-1.715L79.224-1.715Q79.251-1.715 79.275-1.691Q79.299-1.667 79.299-1.639L79.299-0.792Q79.299-0.771 79.275-0.744Q79.251-0.717 79.224-0.717L79.111-0.717Q79.083-0.717 79.058-0.742Q79.032-0.768 79.032-0.792Q79.032-1.028 78.926-1.192Q78.820-1.356 78.637-1.438Q78.455-1.520 78.222-1.520Q77.894-1.520 77.638-1.417Q77.381-1.315 77.381-1.038Q77.381-0.843 77.564-0.734Q77.747-0.624 77.976-0.583L78.550-0.477Q78.796-0.429 79.010-0.301Q79.224-0.173 79.360 0.030Q79.497 0.234 79.497 0.483Q79.497 0.996 79.131 1.235Q78.766 1.474 78.229 1.474Q77.733 1.474 77.402 1.180L77.135 1.454Q77.115 1.474 77.087 1.474L77.040 1.474Q77.016 1.474 76.988 1.447Q76.961 1.420 76.961 1.399\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(34.631 70.343)\">\u003Cpath d=\"M55.903 1.406L54.313 1.406L54.313 1.126Q54.956 1.126 55.113 0.726L56.757-3.489Q56.791-3.584 56.904-3.584L56.986-3.584Q57.096-3.584 57.137-3.489L58.856 0.917Q58.924 1.057 59.114 1.092Q59.304 1.126 59.577 1.126L59.577 1.406L57.578 1.406L57.578 1.126Q58.142 1.126 58.142 0.951Q58.142 0.934 58.140 0.927Q58.138 0.921 58.135 0.917L57.714-0.149L55.756-0.149L55.414 0.726Q55.400 0.726 55.400 0.804Q55.400 0.965 55.563 1.045Q55.725 1.126 55.903 1.126L55.903 1.406M56.737-2.668L55.869-0.429L57.612-0.429L56.737-2.668M60.213-0.105Q60.213-0.433 60.348-0.734Q60.483-1.034 60.719-1.255Q60.955-1.475 61.259-1.595Q61.563-1.715 61.888-1.715Q62.394-1.715 62.742-1.612Q63.091-1.510 63.091-1.134Q63.091-0.987 62.993-0.886Q62.896-0.785 62.749-0.785Q62.595-0.785 62.496-0.884Q62.397-0.983 62.397-1.134Q62.397-1.322 62.537-1.414Q62.335-1.465 61.895-1.465Q61.539-1.465 61.310-1.269Q61.081-1.072 60.980-0.763Q60.879-0.453 60.879-0.105Q60.879 0.244 61.006 0.550Q61.132 0.856 61.387 1.040Q61.642 1.225 61.997 1.225Q62.219 1.225 62.404 1.141Q62.588 1.057 62.723 0.902Q62.858 0.746 62.916 0.538Q62.930 0.483 62.985 0.483L63.098 0.483Q63.128 0.483 63.151 0.507Q63.173 0.531 63.173 0.565L63.173 0.586Q63.087 0.873 62.899 1.071Q62.711 1.269 62.447 1.372Q62.182 1.474 61.888 1.474Q61.457 1.474 61.069 1.268Q60.681 1.061 60.447 0.698Q60.213 0.336 60.213-0.105M64.287 0.565L64.287-1.332L63.648-1.332L63.648-1.554Q63.966-1.554 64.183-1.764Q64.400-1.974 64.501-2.284Q64.602-2.593 64.602-2.901L64.868-2.901L64.868-1.612L65.945-1.612L65.945-1.332L64.868-1.332L64.868 0.552Q64.868 0.828 64.972 1.027Q65.077 1.225 65.336 1.225Q65.494 1.225 65.600 1.121Q65.706 1.016 65.755 0.863Q65.805 0.709 65.805 0.552L65.805 0.138L66.071 0.138L66.071 0.565Q66.071 0.791 65.972 1.001Q65.873 1.211 65.688 1.343Q65.504 1.474 65.275 1.474Q64.837 1.474 64.562 1.237Q64.287 0.999 64.287 0.565M67.456 0.572L67.456-0.932Q67.456-1.202 67.348-1.263Q67.240-1.325 66.929-1.325L66.929-1.605L68.037-1.680L68.037 0.552L68.037 0.572Q68.037 0.852 68.088 0.996Q68.139 1.139 68.281 1.196Q68.423 1.252 68.710 1.252Q68.963 1.252 69.168 1.112Q69.373 0.972 69.489 0.746Q69.605 0.521 69.605 0.271L69.605-0.932Q69.605-1.202 69.498-1.263Q69.390-1.325 69.079-1.325L69.079-1.605L70.186-1.680L70.186 0.733Q70.186 0.924 70.239 1.006Q70.292 1.088 70.393 1.107Q70.494 1.126 70.709 1.126L70.709 1.406L69.633 1.474L69.633 0.910Q69.523 1.092 69.378 1.215Q69.233 1.338 69.047 1.406Q68.860 1.474 68.659 1.474Q67.456 1.474 67.456 0.572M71.355 0.678Q71.355 0.346 71.579 0.119Q71.803-0.108 72.147-0.236Q72.490-0.365 72.863-0.417Q73.235-0.470 73.540-0.470L73.540-0.723Q73.540-0.928 73.432-1.108Q73.324-1.287 73.143-1.390Q72.962-1.492 72.753-1.492Q72.347-1.492 72.111-1.400Q72.200-1.363 72.246-1.279Q72.292-1.195 72.292-1.093Q72.292-0.997 72.246-0.918Q72.200-0.840 72.119-0.795Q72.039-0.751 71.950-0.751Q71.800-0.751 71.699-0.848Q71.598-0.946 71.598-1.093Q71.598-1.715 72.753-1.715Q72.965-1.715 73.215-1.651Q73.464-1.588 73.666-1.469Q73.868-1.349 73.994-1.164Q74.121-0.980 74.121-0.737L74.121 0.839Q74.121 0.955 74.182 1.051Q74.244 1.146 74.356 1.146Q74.466 1.146 74.531 1.052Q74.596 0.958 74.596 0.839L74.596 0.391L74.862 0.391L74.862 0.839Q74.862 1.109 74.635 1.274Q74.408 1.440 74.127 1.440Q73.919 1.440 73.782 1.286Q73.645 1.133 73.622 0.917Q73.475 1.184 73.193 1.329Q72.911 1.474 72.586 1.474Q72.309 1.474 72.025 1.399Q71.742 1.324 71.549 1.145Q71.355 0.965 71.355 0.678M71.971 0.678Q71.971 0.852 72.072 0.982Q72.172 1.112 72.328 1.182Q72.483 1.252 72.647 1.252Q72.866 1.252 73.075 1.155Q73.283 1.057 73.411 0.876Q73.540 0.695 73.540 0.469L73.540-0.259Q73.215-0.259 72.849-0.168Q72.483-0.077 72.227 0.135Q71.971 0.346 71.971 0.678M75.806 0.565L75.806-1.332L75.166-1.332L75.166-1.554Q75.484-1.554 75.701-1.764Q75.918-1.974 76.019-2.284Q76.120-2.593 76.120-2.901L76.387-2.901L76.387-1.612L77.463-1.612L77.463-1.332L76.387-1.332L76.387 0.552Q76.387 0.828 76.491 1.027Q76.595 1.225 76.855 1.225Q77.012 1.225 77.118 1.121Q77.224 1.016 77.274 0.863Q77.323 0.709 77.323 0.552L77.323 0.138L77.590 0.138L77.590 0.565Q77.590 0.791 77.491 1.001Q77.392 1.211 77.207 1.343Q77.022 1.474 76.793 1.474Q76.356 1.474 76.081 1.237Q75.806 0.999 75.806 0.565M78.359-0.077Q78.359-0.419 78.494-0.718Q78.629-1.017 78.868-1.241Q79.107-1.465 79.425-1.590Q79.743-1.715 80.075-1.715Q80.519-1.715 80.919-1.499Q81.319-1.284 81.553-0.906Q81.787-0.529 81.787-0.077Q81.787 0.264 81.645 0.548Q81.503 0.832 81.259 1.039Q81.015 1.245 80.705 1.360Q80.396 1.474 80.075 1.474Q79.644 1.474 79.242 1.273Q78.841 1.071 78.600 0.719Q78.359 0.367 78.359-0.077M80.075 1.225Q80.676 1.225 80.900 0.847Q81.124 0.469 81.124-0.163Q81.124-0.775 80.890-1.134Q80.656-1.492 80.075-1.492Q79.022-1.492 79.022-0.163Q79.022 0.469 79.248 0.847Q79.473 1.225 80.075 1.225M84.132 1.406L82.395 1.406L82.395 1.126Q82.624 1.126 82.773 1.092Q82.922 1.057 82.922 0.917L82.922-0.932Q82.922-1.202 82.814-1.263Q82.707-1.325 82.395-1.325L82.395-1.605L83.424-1.680L83.424-0.973Q83.554-1.281 83.797-1.480Q84.040-1.680 84.357-1.680Q84.576-1.680 84.747-1.556Q84.918-1.431 84.918-1.219Q84.918-1.082 84.819-0.983Q84.720-0.884 84.586-0.884Q84.450-0.884 84.351-0.983Q84.251-1.082 84.251-1.219Q84.251-1.359 84.351-1.458Q84.060-1.458 83.860-1.262Q83.660-1.065 83.568-0.771Q83.476-0.477 83.476-0.197L83.476 0.917Q83.476 1.126 84.132 1.126L84.132 1.406M85.502 1.399L85.502 0.336Q85.502 0.312 85.530 0.285Q85.557 0.258 85.581 0.258L85.690 0.258Q85.755 0.258 85.769 0.316Q85.865 0.750 86.111 1.001Q86.357 1.252 86.770 1.252Q87.112 1.252 87.365 1.119Q87.618 0.986 87.618 0.678Q87.618 0.521 87.524 0.406Q87.430 0.292 87.292 0.223Q87.153 0.155 86.986 0.117L86.405 0.018Q86.049-0.050 85.776-0.271Q85.502-0.491 85.502-0.833Q85.502-1.082 85.614-1.257Q85.725-1.431 85.911-1.530Q86.097-1.629 86.312-1.672Q86.528-1.715 86.770-1.715Q87.184-1.715 87.464-1.533L87.680-1.708Q87.690-1.711 87.697-1.713Q87.704-1.715 87.714-1.715L87.765-1.715Q87.792-1.715 87.816-1.691Q87.840-1.667 87.840-1.639L87.840-0.792Q87.840-0.771 87.816-0.744Q87.792-0.717 87.765-0.717L87.652-0.717Q87.625-0.717 87.599-0.742Q87.574-0.768 87.574-0.792Q87.574-1.028 87.468-1.192Q87.362-1.356 87.179-1.438Q86.996-1.520 86.764-1.520Q86.436-1.520 86.179-1.417Q85.923-1.315 85.923-1.038Q85.923-0.843 86.106-0.734Q86.289-0.624 86.518-0.583L87.092-0.477Q87.338-0.429 87.551-0.301Q87.765-0.173 87.902 0.030Q88.039 0.234 88.039 0.483Q88.039 0.996 87.673 1.235Q87.307 1.474 86.770 1.474Q86.275 1.474 85.943 1.180L85.677 1.454Q85.656 1.474 85.629 1.474L85.581 1.474Q85.557 1.474 85.530 1.447Q85.502 1.420 85.502 1.399\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M48.309-15.666h73.977v-28.453H48.309Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M55.823-8.125L54.753-10.981Q54.687-11.160 54.556-11.203Q54.425-11.246 54.167-11.246L54.167-11.543L55.847-11.543L55.847-11.246Q55.397-11.246 55.397-11.047Q55.401-11.031 55.403-11.014Q55.405-10.996 55.405-10.981L56.198-8.887L56.909-10.797Q56.874-10.891 56.874-10.936Q56.874-10.981 56.839-10.981Q56.772-11.160 56.642-11.203Q56.511-11.246 56.257-11.246L56.257-11.543L57.847-11.543L57.847-11.246Q57.397-11.246 57.397-11.047Q57.401-11.028 57.403-11.010Q57.405-10.992 57.405-10.981L58.237-8.766L58.991-10.766Q59.015-10.824 59.015-10.895Q59.015-11.055 58.878-11.151Q58.741-11.246 58.573-11.246L58.573-11.543L59.960-11.543L59.960-11.246Q59.726-11.246 59.548-11.119Q59.370-10.992 59.288-10.766L58.304-8.125Q58.249-8.016 58.136-8.016L58.077-8.016Q57.964-8.016 57.921-8.125L57.062-10.399L56.206-8.125Q56.167-8.016 56.046-8.016L55.991-8.016Q55.878-8.016 55.823-8.125M62.304-8.094L60.448-8.094L60.448-8.391Q60.722-8.391 60.890-8.438Q61.058-8.485 61.058-8.653L61.058-12.813Q61.058-13.028 60.995-13.123Q60.933-13.219 60.813-13.240Q60.694-13.262 60.448-13.262L60.448-13.559L61.671-13.645L61.671-10.942Q61.796-11.153 61.983-11.303Q62.171-11.453 62.397-11.537Q62.624-11.621 62.870-11.621Q64.038-11.621 64.038-10.543L64.038-8.653Q64.038-8.485 64.208-8.438Q64.378-8.391 64.647-8.391L64.647-8.094L62.792-8.094L62.792-8.391Q63.065-8.391 63.233-8.438Q63.401-8.485 63.401-8.653L63.401-10.528Q63.401-10.910 63.280-11.139Q63.159-11.367 62.808-11.367Q62.495-11.367 62.241-11.205Q61.987-11.043 61.841-10.774Q61.694-10.504 61.694-10.207L61.694-8.653Q61.694-8.485 61.864-8.438Q62.034-8.391 62.304-8.391L62.304-8.094M65.190-8.926Q65.190-9.410 65.593-9.705Q65.995-10 66.546-10.119Q67.097-10.239 67.589-10.239L67.589-10.528Q67.589-10.754 67.474-10.961Q67.358-11.168 67.161-11.287Q66.964-11.406 66.733-11.406Q66.308-11.406 66.022-11.301Q66.093-11.274 66.140-11.219Q66.186-11.164 66.212-11.094Q66.237-11.024 66.237-10.949Q66.237-10.844 66.186-10.752Q66.136-10.660 66.044-10.610Q65.952-10.559 65.847-10.559Q65.741-10.559 65.649-10.610Q65.558-10.660 65.507-10.752Q65.456-10.844 65.456-10.949Q65.456-11.367 65.845-11.514Q66.233-11.660 66.733-11.660Q67.065-11.660 67.419-11.530Q67.772-11.399 68.001-11.145Q68.229-10.891 68.229-10.543L68.229-8.742Q68.229-8.610 68.302-8.500Q68.374-8.391 68.503-8.391Q68.628-8.391 68.696-8.496Q68.765-8.602 68.765-8.742L68.765-9.254L69.046-9.254L69.046-8.742Q69.046-8.539 68.929-8.381Q68.811-8.223 68.630-8.139Q68.448-8.055 68.245-8.055Q68.015-8.055 67.862-8.227Q67.710-8.399 67.679-8.629Q67.519-8.348 67.210-8.182Q66.901-8.016 66.550-8.016Q66.038-8.016 65.614-8.239Q65.190-8.461 65.190-8.926M65.878-8.926Q65.878-8.641 66.104-8.455Q66.331-8.270 66.624-8.270Q66.870-8.270 67.095-8.387Q67.319-8.504 67.454-8.707Q67.589-8.910 67.589-9.164L67.589-9.996Q67.323-9.996 67.038-9.942Q66.753-9.887 66.481-9.758Q66.210-9.629 66.044-9.422Q65.878-9.215 65.878-8.926M69.964-9.055L69.964-11.246L69.261-11.246L69.261-11.500Q69.616-11.500 69.858-11.733Q70.101-11.965 70.212-12.313Q70.323-12.660 70.323-13.016L70.604-13.016L70.604-11.543L71.780-11.543L71.780-11.246L70.604-11.246L70.604-9.071Q70.604-8.750 70.724-8.522Q70.843-8.293 71.124-8.293Q71.304-8.293 71.421-8.416Q71.538-8.539 71.591-8.719Q71.644-8.899 71.644-9.071L71.644-9.543L71.925-9.543L71.925-9.055Q71.925-8.801 71.819-8.561Q71.714-8.321 71.517-8.168Q71.319-8.016 71.061-8.016Q70.745-8.016 70.493-8.139Q70.241-8.262 70.103-8.496Q69.964-8.731 69.964-9.055\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M76.112-9.055L76.112-11.246L75.409-11.246L75.409-11.500Q75.765-11.500 76.007-11.733Q76.249-11.965 76.360-12.313Q76.472-12.660 76.472-13.016L76.753-13.016L76.753-11.543L77.929-11.543L77.929-11.246L76.753-11.246L76.753-9.071Q76.753-8.750 76.872-8.522Q76.991-8.293 77.272-8.293Q77.452-8.293 77.569-8.416Q77.686-8.539 77.739-8.719Q77.792-8.899 77.792-9.071L77.792-9.543L78.073-9.543L78.073-9.055Q78.073-8.801 77.968-8.561Q77.862-8.321 77.665-8.168Q77.468-8.016 77.210-8.016Q76.894-8.016 76.642-8.139Q76.390-8.262 76.251-8.496Q76.112-8.731 76.112-9.055M80.722-8.094L78.866-8.094L78.866-8.391Q79.140-8.391 79.308-8.438Q79.476-8.485 79.476-8.653L79.476-12.813Q79.476-13.028 79.413-13.123Q79.351-13.219 79.231-13.240Q79.112-13.262 78.866-13.262L78.866-13.559L80.089-13.645L80.089-10.942Q80.214-11.153 80.401-11.303Q80.589-11.453 80.815-11.537Q81.042-11.621 81.288-11.621Q82.456-11.621 82.456-10.543L82.456-8.653Q82.456-8.485 82.626-8.438Q82.796-8.391 83.065-8.391L83.065-8.094L81.210-8.094L81.210-8.391Q81.483-8.391 81.651-8.438Q81.819-8.485 81.819-8.653L81.819-10.528Q81.819-10.910 81.698-11.139Q81.577-11.367 81.226-11.367Q80.913-11.367 80.659-11.205Q80.405-11.043 80.259-10.774Q80.112-10.504 80.112-10.207L80.112-8.653Q80.112-8.485 80.282-8.438Q80.452-8.391 80.722-8.391L80.722-8.094M83.511-9.848Q83.511-10.328 83.743-10.744Q83.976-11.160 84.386-11.410Q84.796-11.660 85.272-11.660Q86.003-11.660 86.401-11.219Q86.800-10.778 86.800-10.047Q86.800-9.942 86.706-9.918L84.257-9.918L84.257-9.848Q84.257-9.438 84.378-9.082Q84.499-8.727 84.770-8.510Q85.042-8.293 85.472-8.293Q85.835-8.293 86.132-8.522Q86.429-8.750 86.530-9.102Q86.538-9.149 86.624-9.164L86.706-9.164Q86.800-9.137 86.800-9.055Q86.800-9.047 86.792-9.016Q86.729-8.789 86.591-8.606Q86.452-8.422 86.261-8.289Q86.069-8.156 85.851-8.086Q85.632-8.016 85.394-8.016Q85.022-8.016 84.685-8.153Q84.347-8.289 84.079-8.541Q83.811-8.793 83.661-9.133Q83.511-9.473 83.511-9.848M84.265-10.156L86.226-10.156Q86.226-10.461 86.124-10.752Q86.022-11.043 85.806-11.225Q85.589-11.406 85.272-11.406Q84.972-11.406 84.741-11.219Q84.511-11.031 84.388-10.740Q84.265-10.449 84.265-10.156\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M91.712-8.125L90.642-10.981Q90.576-11.160 90.445-11.203Q90.314-11.246 90.056-11.246L90.056-11.543L91.736-11.543L91.736-11.246Q91.286-11.246 91.286-11.047Q91.290-11.031 91.292-11.014Q91.294-10.996 91.294-10.981L92.087-8.887L92.798-10.797Q92.763-10.891 92.763-10.936Q92.763-10.981 92.728-10.981Q92.661-11.160 92.531-11.203Q92.400-11.246 92.146-11.246L92.146-11.543L93.736-11.543L93.736-11.246Q93.286-11.246 93.286-11.047Q93.290-11.028 93.292-11.010Q93.294-10.992 93.294-10.981L94.126-8.766L94.880-10.766Q94.904-10.824 94.904-10.895Q94.904-11.055 94.767-11.151Q94.630-11.246 94.462-11.246L94.462-11.543L95.849-11.543L95.849-11.246Q95.615-11.246 95.437-11.119Q95.259-10.992 95.177-10.766L94.193-8.125Q94.138-8.016 94.025-8.016L93.966-8.016Q93.853-8.016 93.810-8.125L92.951-10.399L92.095-8.125Q92.056-8.016 91.935-8.016L91.880-8.016Q91.767-8.016 91.712-8.125\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M96.029-9.789Q96.029-10.293 96.285-10.725Q96.541-11.156 96.977-11.408Q97.412-11.660 97.912-11.660Q98.299-11.660 98.641-11.516Q98.982-11.371 99.244-11.110Q99.506-10.848 99.648-10.512Q99.791-10.176 99.791-9.789Q99.791-9.297 99.527-8.887Q99.264-8.477 98.834-8.246Q98.404-8.016 97.912-8.016Q97.420-8.016 96.986-8.248Q96.553-8.481 96.291-8.889Q96.029-9.297 96.029-9.789M97.912-8.293Q98.369-8.293 98.621-8.516Q98.873-8.739 98.961-9.090Q99.049-9.442 99.049-9.887Q99.049-10.317 98.955-10.655Q98.861-10.992 98.607-11.199Q98.353-11.406 97.912-11.406Q97.264-11.406 97.020-10.990Q96.775-10.574 96.775-9.887Q96.775-9.442 96.863-9.090Q96.951-8.739 97.203-8.516Q97.455-8.293 97.912-8.293M102.283-8.094L100.303-8.094L100.303-8.391Q100.572-8.391 100.740-8.436Q100.908-8.481 100.908-8.653L100.908-10.789Q100.908-11.004 100.846-11.100Q100.783-11.196 100.666-11.217Q100.549-11.239 100.303-11.239L100.303-11.535L101.471-11.621L101.471-10.836Q101.549-11.047 101.701-11.233Q101.853-11.418 102.053-11.520Q102.252-11.621 102.478-11.621Q102.725-11.621 102.916-11.477Q103.107-11.332 103.107-11.102Q103.107-10.946 103.002-10.836Q102.896-10.727 102.740-10.727Q102.584-10.727 102.475-10.836Q102.365-10.946 102.365-11.102Q102.365-11.262 102.471-11.367Q102.146-11.367 101.932-11.139Q101.717-10.910 101.621-10.571Q101.525-10.231 101.525-9.926L101.525-8.653Q101.525-8.485 101.752-8.438Q101.978-8.391 102.283-8.391L102.283-8.094M105.502-8.094L103.670-8.094L103.670-8.391Q103.943-8.391 104.111-8.438Q104.279-8.485 104.279-8.653L104.279-12.813Q104.279-13.028 104.217-13.123Q104.154-13.219 104.035-13.240Q103.916-13.262 103.670-13.262L103.670-13.559L104.893-13.645L104.893-8.653Q104.893-8.485 105.061-8.438Q105.228-8.391 105.502-8.391L105.502-8.094M107.764-8.016Q107.283-8.016 106.875-8.260Q106.467-8.504 106.228-8.918Q105.990-9.332 105.990-9.821Q105.990-10.313 106.248-10.729Q106.506-11.145 106.937-11.383Q107.369-11.621 107.861-11.621Q108.482-11.621 108.932-11.184L108.932-12.813Q108.932-13.028 108.869-13.123Q108.807-13.219 108.689-13.240Q108.572-13.262 108.326-13.262L108.326-13.559L109.549-13.645L109.549-8.836Q109.549-8.625 109.611-8.530Q109.674-8.434 109.791-8.412Q109.908-8.391 110.158-8.391L110.158-8.094L108.908-8.016L108.908-8.500Q108.443-8.016 107.764-8.016M107.830-8.270Q108.170-8.270 108.463-8.461Q108.756-8.653 108.908-8.949L108.908-10.781Q108.760-11.055 108.498-11.211Q108.236-11.367 107.924-11.367Q107.299-11.367 107.016-10.920Q106.732-10.473 106.732-9.813Q106.732-9.168 106.984-8.719Q107.236-8.270 107.830-8.270\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M64.813 1.406L63.035 1.406L63.035 1.109Q63.309 1.109 63.477 1.062Q63.645 1.015 63.645 0.847L63.645-1.289Q63.645-1.504 63.588-1.600Q63.531-1.696 63.418-1.717Q63.305-1.739 63.059-1.739L63.059-2.035L64.258-2.121L64.258 0.847Q64.258 1.015 64.404 1.062Q64.551 1.109 64.813 1.109L64.813 1.406M63.371-3.516Q63.371-3.707 63.506-3.838Q63.641-3.969 63.836-3.969Q63.957-3.969 64.061-3.907Q64.164-3.844 64.227-3.740Q64.289-3.637 64.289-3.516Q64.289-3.321 64.158-3.186Q64.028-3.051 63.836-3.051Q63.637-3.051 63.504-3.184Q63.371-3.317 63.371-3.516M65.356 1.398L65.356 0.176Q65.356 0.148 65.387 0.117Q65.418 0.086 65.442 0.086L65.547 0.086Q65.617 0.086 65.633 0.148Q65.695 0.468 65.834 0.709Q65.973 0.949 66.205 1.090Q66.438 1.230 66.746 1.230Q66.985 1.230 67.194 1.170Q67.403 1.109 67.539 0.961Q67.676 0.812 67.676 0.566Q67.676 0.312 67.465 0.146Q67.254-0.020 66.985-0.074L66.363-0.188Q65.957-0.266 65.656-0.522Q65.356-0.778 65.356-1.153Q65.356-1.520 65.557-1.742Q65.758-1.965 66.082-2.063Q66.406-2.160 66.746-2.160Q67.211-2.160 67.508-1.953L67.731-2.137Q67.754-2.160 67.785-2.160L67.836-2.160Q67.867-2.160 67.895-2.133Q67.922-2.106 67.922-2.074L67.922-1.090Q67.922-1.059 67.897-1.030Q67.871-1 67.836-1L67.731-1Q67.695-1 67.668-1.028Q67.641-1.055 67.641-1.090Q67.641-1.489 67.389-1.709Q67.137-1.930 66.738-1.930Q66.383-1.930 66.100-1.807Q65.817-1.684 65.817-1.379Q65.817-1.160 66.018-1.028Q66.219-0.895 66.465-0.852L67.090-0.739Q67.520-0.649 67.828-0.352Q68.137-0.055 68.137 0.359Q68.137 0.929 67.738 1.207Q67.340 1.484 66.746 1.484Q66.195 1.484 65.844 1.148L65.547 1.461Q65.524 1.484 65.488 1.484L65.442 1.484Q65.418 1.484 65.387 1.453Q65.356 1.422 65.356 1.398\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M73.414 1.406L71.582 1.406L71.582 1.109Q71.856 1.109 72.024 1.062Q72.192 1.015 72.192 0.847L72.192-3.313Q72.192-3.528 72.129-3.623Q72.067-3.719 71.948-3.740Q71.828-3.762 71.582-3.762L71.582-4.059L72.805-4.145L72.805 0.847Q72.805 1.015 72.973 1.062Q73.141 1.109 73.414 1.109L73.414 1.406M75.719 1.406L73.942 1.406L73.942 1.109Q74.215 1.109 74.383 1.062Q74.551 1.015 74.551 0.847L74.551-1.289Q74.551-1.504 74.494-1.600Q74.438-1.696 74.325-1.717Q74.211-1.739 73.965-1.739L73.965-2.035L75.164-2.121L75.164 0.847Q75.164 1.015 75.311 1.062Q75.457 1.109 75.719 1.109L75.719 1.406M74.278-3.516Q74.278-3.707 74.412-3.838Q74.547-3.969 74.742-3.969Q74.864-3.969 74.967-3.907Q75.071-3.844 75.133-3.740Q75.196-3.637 75.196-3.516Q75.196-3.321 75.065-3.186Q74.934-3.051 74.742-3.051Q74.543-3.051 74.410-3.184Q74.278-3.317 74.278-3.516M78.043 1.406L76.246 1.406L76.246 1.109Q76.516 1.109 76.684 1.064Q76.852 1.019 76.852 0.847L76.852-3.313Q76.852-3.528 76.789-3.623Q76.727-3.719 76.610-3.740Q76.492-3.762 76.246-3.762L76.246-4.059L77.469-4.145L77.469-0.379L78.567-1.266Q78.774-1.446 78.774-1.594Q78.774-1.660 78.721-1.703Q78.668-1.746 78.598-1.746L78.598-2.043L80.133-2.043L80.133-1.746Q79.602-1.746 79.004-1.266L78.395-0.770L79.469 0.629Q79.606 0.804 79.713 0.912Q79.821 1.019 79.955 1.064Q80.090 1.109 80.317 1.109L80.317 1.406L78.692 1.406L78.692 1.109Q78.934 1.109 78.934 0.957Q78.934 0.879 78.891 0.808Q78.848 0.738 78.766 0.629L77.965-0.418L77.438 0.008L77.438 0.847Q77.438 1.015 77.606 1.062Q77.774 1.109 78.043 1.109\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M80.473-0.348Q80.473-0.828 80.706-1.244Q80.938-1.660 81.348-1.910Q81.758-2.160 82.235-2.160Q82.965-2.160 83.364-1.719Q83.762-1.278 83.762-0.547Q83.762-0.442 83.669-0.418L81.219-0.418L81.219-0.348Q81.219 0.062 81.340 0.418Q81.462 0.773 81.733 0.990Q82.005 1.207 82.434 1.207Q82.797 1.207 83.094 0.978Q83.391 0.750 83.493 0.398Q83.501 0.351 83.587 0.336L83.669 0.336Q83.762 0.363 83.762 0.445Q83.762 0.453 83.755 0.484Q83.692 0.711 83.553 0.894Q83.415 1.078 83.223 1.211Q83.032 1.343 82.813 1.414Q82.594 1.484 82.356 1.484Q81.985 1.484 81.647 1.347Q81.309 1.211 81.042 0.959Q80.774 0.707 80.624 0.367Q80.473 0.027 80.473-0.348M81.227-0.657L83.188-0.657Q83.188-0.961 83.087-1.252Q82.985-1.543 82.768-1.725Q82.551-1.907 82.235-1.907Q81.934-1.907 81.704-1.719Q81.473-1.532 81.350-1.240Q81.227-0.949 81.227-0.657\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M89.014 1.406L87.159 1.406L87.159 1.109Q87.432 1.109 87.600 1.062Q87.768 1.015 87.768 0.847L87.768-1.289Q87.768-1.504 87.705-1.600Q87.643-1.696 87.524-1.717Q87.405-1.739 87.159-1.739L87.159-2.035L88.350-2.121L88.350-1.387Q88.463-1.602 88.657-1.770Q88.850-1.938 89.088-2.030Q89.326-2.121 89.580-2.121Q90.748-2.121 90.748-1.043L90.748 0.847Q90.748 1.015 90.918 1.062Q91.088 1.109 91.358 1.109L91.358 1.406L89.502 1.406L89.502 1.109Q89.776 1.109 89.944 1.062Q90.112 1.015 90.112 0.847L90.112-1.028Q90.112-1.410 89.991-1.639Q89.869-1.867 89.518-1.867Q89.205-1.867 88.951-1.705Q88.698-1.543 88.551-1.274Q88.405-1.004 88.405-0.707L88.405 0.847Q88.405 1.015 88.575 1.062Q88.744 1.109 89.014 1.109L89.014 1.406M91.803-0.289Q91.803-0.793 92.059-1.225Q92.315-1.657 92.750-1.908Q93.186-2.160 93.686-2.160Q94.073-2.160 94.414-2.016Q94.756-1.871 95.018-1.610Q95.280-1.348 95.422-1.012Q95.565-0.676 95.565-0.289Q95.565 0.203 95.301 0.613Q95.037 1.023 94.608 1.254Q94.178 1.484 93.686 1.484Q93.194 1.484 92.760 1.252Q92.326 1.019 92.065 0.611Q91.803 0.203 91.803-0.289M93.686 1.207Q94.143 1.207 94.395 0.984Q94.647 0.761 94.735 0.410Q94.823 0.058 94.823-0.387Q94.823-0.817 94.729-1.155Q94.635-1.492 94.381-1.699Q94.127-1.907 93.686-1.907Q93.037-1.907 92.793-1.490Q92.549-1.074 92.549-0.387Q92.549 0.058 92.637 0.410Q92.725 0.761 92.977 0.984Q93.229 1.207 93.686 1.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.079 -23.77)\">\u003Cpath d=\"M97.406 1.375L96.336-1.481Q96.269-1.660 96.139-1.703Q96.008-1.746 95.750-1.746L95.750-2.043L97.430-2.043L97.430-1.746Q96.980-1.746 96.980-1.547Q96.984-1.532 96.986-1.514Q96.988-1.496 96.988-1.481L97.781 0.613L98.492-1.297Q98.457-1.391 98.457-1.436Q98.457-1.481 98.422-1.481Q98.355-1.660 98.225-1.703Q98.094-1.746 97.840-1.746L97.840-2.043L99.430-2.043L99.430-1.746Q98.980-1.746 98.980-1.547Q98.984-1.528 98.986-1.510Q98.988-1.492 98.988-1.481L99.820 0.734L100.574-1.266Q100.598-1.324 100.598-1.395Q100.598-1.555 100.461-1.651Q100.324-1.746 100.156-1.746L100.156-2.043L101.543-2.043L101.543-1.746Q101.309-1.746 101.131-1.619Q100.953-1.492 100.871-1.266L99.887 1.375Q99.832 1.484 99.719 1.484L99.660 1.484Q99.547 1.484 99.504 1.375L98.644-0.899L97.789 1.375Q97.750 1.484 97.629 1.484L97.574 1.484Q97.461 1.484 97.406 1.375\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M51.055 32.704c0-7.071-26.07-12.804-58.23-12.804s-58.228 5.733-58.228 12.804 26.07 12.804 58.229 12.804 58.229-5.732 58.229-12.804Zm-58.23 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-99.014 33.729)\">\u003Cpath d=\"M54.313-0.105Q54.313-0.433 54.448-0.734Q54.583-1.034 54.819-1.255Q55.055-1.475 55.359-1.595Q55.664-1.715 55.988-1.715Q56.494-1.715 56.843-1.612Q57.191-1.510 57.191-1.134Q57.191-0.987 57.094-0.886Q56.997-0.785 56.850-0.785Q56.696-0.785 56.597-0.884Q56.498-0.983 56.498-1.134Q56.498-1.322 56.638-1.414Q56.436-1.465 55.995-1.465Q55.640-1.465 55.411-1.269Q55.182-1.072 55.081-0.763Q54.980-0.453 54.980-0.105Q54.980 0.244 55.106 0.550Q55.233 0.856 55.488 1.040Q55.742 1.225 56.098 1.225Q56.320 1.225 56.504 1.141Q56.689 1.057 56.824 0.902Q56.959 0.746 57.017 0.538Q57.031 0.483 57.085 0.483L57.198 0.483Q57.229 0.483 57.251 0.507Q57.273 0.531 57.273 0.565L57.273 0.586Q57.188 0.873 57 1.071Q56.812 1.269 56.547 1.372Q56.282 1.474 55.988 1.474Q55.558 1.474 55.170 1.268Q54.782 1.061 54.548 0.698Q54.313 0.336 54.313-0.105M57.820-0.077Q57.820-0.419 57.955-0.718Q58.090-1.017 58.330-1.241Q58.569-1.465 58.887-1.590Q59.205-1.715 59.536-1.715Q59.980-1.715 60.380-1.499Q60.780-1.284 61.014-0.906Q61.249-0.529 61.249-0.077Q61.249 0.264 61.107 0.548Q60.965 0.832 60.720 1.039Q60.476 1.245 60.167 1.360Q59.857 1.474 59.536 1.474Q59.105 1.474 58.704 1.273Q58.302 1.071 58.061 0.719Q57.820 0.367 57.820-0.077M59.536 1.225Q60.138 1.225 60.362 0.847Q60.585 0.469 60.585-0.163Q60.585-0.775 60.351-1.134Q60.117-1.492 59.536-1.492Q58.483-1.492 58.483-0.163Q58.483 0.469 58.709 0.847Q58.935 1.225 59.536 1.225M63.525 1.406L61.891 1.406L61.891 1.126Q62.120 1.126 62.269 1.092Q62.417 1.057 62.417 0.917L62.417-0.932Q62.417-1.202 62.310-1.263Q62.202-1.325 61.891-1.325L61.891-1.605L62.951-1.680L62.951-1.031Q63.122-1.339 63.426-1.510Q63.730-1.680 64.075-1.680Q64.581-1.680 64.865-1.457Q65.148-1.233 65.148-0.737L65.148 0.917Q65.148 1.054 65.297 1.090Q65.446 1.126 65.671 1.126L65.671 1.406L64.041 1.406L64.041 1.126Q64.270 1.126 64.419 1.092Q64.567 1.057 64.567 0.917L64.567-0.723Q64.567-1.058 64.448-1.258Q64.328-1.458 64.014-1.458Q63.744-1.458 63.509-1.322Q63.275-1.185 63.137-0.951Q62.999-0.717 62.999-0.443L62.999 0.917Q62.999 1.054 63.149 1.090Q63.299 1.126 63.525 1.126L63.525 1.406M66.259-0.105Q66.259-0.443 66.399-0.734Q66.540-1.024 66.784-1.238Q67.028-1.451 67.332-1.566Q67.637-1.680 67.961-1.680Q68.231-1.680 68.495-1.581Q68.758-1.482 68.949-1.304L68.949-2.702Q68.949-2.972 68.842-3.034Q68.734-3.095 68.423-3.095L68.423-3.376L69.499-3.451L69.499 0.733Q69.499 0.921 69.554 1.004Q69.609 1.088 69.710 1.107Q69.811 1.126 70.026 1.126L70.026 1.406L68.918 1.474L68.918 1.057Q68.501 1.474 67.876 1.474Q67.445 1.474 67.073 1.262Q66.700 1.051 66.480 0.690Q66.259 0.329 66.259-0.105M67.934 1.252Q68.143 1.252 68.329 1.180Q68.515 1.109 68.669 0.972Q68.823 0.835 68.918 0.657L68.918-0.952Q68.833-1.099 68.688-1.219Q68.542-1.339 68.373-1.398Q68.204-1.458 68.023-1.458Q67.462-1.458 67.194-1.069Q66.926-0.679 66.926-0.098Q66.926 0.473 67.160 0.863Q67.394 1.252 67.934 1.252M72.292 1.406L70.740 1.406L70.740 1.126Q70.966 1.126 71.114 1.092Q71.263 1.057 71.263 0.917L71.263-0.932Q71.263-1.120 71.215-1.204Q71.167-1.287 71.070-1.306Q70.973-1.325 70.761-1.325L70.761-1.605L71.817-1.680L71.817 0.917Q71.817 1.057 71.948 1.092Q72.080 1.126 72.292 1.126L72.292 1.406M71.020-2.901Q71.020-3.072 71.144-3.191Q71.267-3.311 71.437-3.311Q71.605-3.311 71.728-3.191Q71.851-3.072 71.851-2.901Q71.851-2.726 71.728-2.603Q71.605-2.480 71.437-2.480Q71.267-2.480 71.144-2.603Q71.020-2.726 71.020-2.901M73.464 0.565L73.464-1.332L72.825-1.332L72.825-1.554Q73.143-1.554 73.360-1.764Q73.577-1.974 73.678-2.284Q73.779-2.593 73.779-2.901L74.045-2.901L74.045-1.612L75.122-1.612L75.122-1.332L74.045-1.332L74.045 0.552Q74.045 0.828 74.150 1.027Q74.254 1.225 74.514 1.225Q74.671 1.225 74.777 1.121Q74.883 1.016 74.932 0.863Q74.982 0.709 74.982 0.552L74.982 0.138L75.249 0.138L75.249 0.565Q75.249 0.791 75.149 1.001Q75.050 1.211 74.866 1.343Q74.681 1.474 74.452 1.474Q74.015 1.474 73.739 1.237Q73.464 0.999 73.464 0.565M77.675 1.406L76.124 1.406L76.124 1.126Q76.349 1.126 76.498 1.092Q76.646 1.057 76.646 0.917L76.646-0.932Q76.646-1.120 76.599-1.204Q76.551-1.287 76.453-1.306Q76.356-1.325 76.144-1.325L76.144-1.605L77.200-1.680L77.200 0.917Q77.200 1.057 77.332 1.092Q77.463 1.126 77.675 1.126L77.675 1.406M76.404-2.901Q76.404-3.072 76.527-3.191Q76.650-3.311 76.821-3.311Q76.988-3.311 77.111-3.191Q77.234-3.072 77.234-2.901Q77.234-2.726 77.111-2.603Q76.988-2.480 76.821-2.480Q76.650-2.480 76.527-2.603Q76.404-2.726 76.404-2.901M78.280-0.077Q78.280-0.419 78.415-0.718Q78.550-1.017 78.790-1.241Q79.029-1.465 79.347-1.590Q79.665-1.715 79.996-1.715Q80.440-1.715 80.840-1.499Q81.240-1.284 81.474-0.906Q81.708-0.529 81.708-0.077Q81.708 0.264 81.567 0.548Q81.425 0.832 81.180 1.039Q80.936 1.245 80.627 1.360Q80.317 1.474 79.996 1.474Q79.565 1.474 79.164 1.273Q78.762 1.071 78.521 0.719Q78.280 0.367 78.280-0.077M79.996 1.225Q80.598 1.225 80.822 0.847Q81.045 0.469 81.045-0.163Q81.045-0.775 80.811-1.134Q80.577-1.492 79.996-1.492Q78.943-1.492 78.943-0.163Q78.943 0.469 79.169 0.847Q79.395 1.225 79.996 1.225M83.985 1.406L82.351 1.406L82.351 1.126Q82.580 1.126 82.729 1.092Q82.877 1.057 82.877 0.917L82.877-0.932Q82.877-1.202 82.770-1.263Q82.662-1.325 82.351-1.325L82.351-1.605L83.411-1.680L83.411-1.031Q83.582-1.339 83.886-1.510Q84.190-1.680 84.535-1.680Q85.041-1.680 85.325-1.457Q85.608-1.233 85.608-0.737L85.608 0.917Q85.608 1.054 85.757 1.090Q85.906 1.126 86.131 1.126L86.131 1.406L84.501 1.406L84.501 1.126Q84.730 1.126 84.879 1.092Q85.027 1.057 85.027 0.917L85.027-0.723Q85.027-1.058 84.908-1.258Q84.788-1.458 84.474-1.458Q84.204-1.458 83.969-1.322Q83.735-1.185 83.597-0.951Q83.458-0.717 83.458-0.443L83.458 0.917Q83.458 1.054 83.609 1.090Q83.759 1.126 83.985 1.126L83.985 1.406M88.603 0.152L86.545 0.152L86.545-0.351L88.603-0.351L88.603 0.152M89.464 0.678Q89.464 0.346 89.688 0.119Q89.912-0.108 90.255-0.236Q90.599-0.365 90.971-0.417Q91.344-0.470 91.648-0.470L91.648-0.723Q91.648-0.928 91.540-1.108Q91.433-1.287 91.251-1.390Q91.070-1.492 90.862-1.492Q90.455-1.492 90.219-1.400Q90.308-1.363 90.354-1.279Q90.400-1.195 90.400-1.093Q90.400-0.997 90.354-0.918Q90.308-0.840 90.228-0.795Q90.147-0.751 90.059-0.751Q89.908-0.751 89.807-0.848Q89.707-0.946 89.707-1.093Q89.707-1.715 90.862-1.715Q91.074-1.715 91.323-1.651Q91.573-1.588 91.774-1.469Q91.976-1.349 92.103-1.164Q92.229-0.980 92.229-0.737L92.229 0.839Q92.229 0.955 92.291 1.051Q92.352 1.146 92.465 1.146Q92.574 1.146 92.639 1.052Q92.704 0.958 92.704 0.839L92.704 0.391L92.971 0.391L92.971 0.839Q92.971 1.109 92.743 1.274Q92.516 1.440 92.236 1.440Q92.027 1.440 91.891 1.286Q91.754 1.133 91.730 0.917Q91.583 1.184 91.301 1.329Q91.019 1.474 90.694 1.474Q90.417 1.474 90.134 1.399Q89.850 1.324 89.657 1.145Q89.464 0.965 89.464 0.678M90.079 0.678Q90.079 0.852 90.180 0.982Q90.281 1.112 90.436 1.182Q90.592 1.252 90.756 1.252Q90.975 1.252 91.183 1.155Q91.392 1.057 91.520 0.876Q91.648 0.695 91.648 0.469L91.648-0.259Q91.323-0.259 90.957-0.168Q90.592-0.077 90.335 0.135Q90.079 0.346 90.079 0.678M93.388-0.105Q93.388-0.433 93.523-0.734Q93.658-1.034 93.894-1.255Q94.129-1.475 94.434-1.595Q94.738-1.715 95.062-1.715Q95.568-1.715 95.917-1.612Q96.266-1.510 96.266-1.134Q96.266-0.987 96.168-0.886Q96.071-0.785 95.924-0.785Q95.770-0.785 95.671-0.884Q95.572-0.983 95.572-1.134Q95.572-1.322 95.712-1.414Q95.510-1.465 95.069-1.465Q94.714-1.465 94.485-1.269Q94.256-1.072 94.155-0.763Q94.054-0.453 94.054-0.105Q94.054 0.244 94.181 0.550Q94.307 0.856 94.562 1.040Q94.816 1.225 95.172 1.225Q95.394 1.225 95.579 1.141Q95.763 1.057 95.898 0.902Q96.033 0.746 96.091 0.538Q96.105 0.483 96.160 0.483L96.272 0.483Q96.303 0.483 96.325 0.507Q96.348 0.531 96.348 0.565L96.348 0.586Q96.262 0.873 96.074 1.071Q95.886 1.269 95.621 1.372Q95.356 1.474 95.062 1.474Q94.632 1.474 94.244 1.268Q93.856 1.061 93.622 0.698Q93.388 0.336 93.388-0.105M97.462 0.565L97.462-1.332L96.823-1.332L96.823-1.554Q97.141-1.554 97.358-1.764Q97.575-1.974 97.676-2.284Q97.776-2.593 97.776-2.901L98.043-2.901L98.043-1.612L99.120-1.612L99.120-1.332L98.043-1.332L98.043 0.552Q98.043 0.828 98.147 1.027Q98.251 1.225 98.511 1.225Q98.668 1.225 98.774 1.121Q98.880 1.016 98.930 0.863Q98.979 0.709 98.979 0.552L98.979 0.138L99.246 0.138L99.246 0.565Q99.246 0.791 99.147 1.001Q99.048 1.211 98.863 1.343Q98.679 1.474 98.450 1.474Q98.012 1.474 97.737 1.237Q97.462 0.999 97.462 0.565M101.673 1.406L100.121 1.406L100.121 1.126Q100.347 1.126 100.495 1.092Q100.644 1.057 100.644 0.917L100.644-0.932Q100.644-1.120 100.596-1.204Q100.548-1.287 100.451-1.306Q100.353-1.325 100.142-1.325L100.142-1.605L101.198-1.680L101.198 0.917Q101.198 1.057 101.329 1.092Q101.461 1.126 101.673 1.126L101.673 1.406M100.401-2.901Q100.401-3.072 100.524-3.191Q100.647-3.311 100.818-3.311Q100.986-3.311 101.109-3.191Q101.232-3.072 101.232-2.901Q101.232-2.726 101.109-2.603Q100.986-2.480 100.818-2.480Q100.647-2.480 100.524-2.603Q100.401-2.726 100.401-2.901M102.278-0.077Q102.278-0.419 102.413-0.718Q102.548-1.017 102.787-1.241Q103.026-1.465 103.344-1.590Q103.662-1.715 103.994-1.715Q104.438-1.715 104.838-1.499Q105.238-1.284 105.472-0.906Q105.706-0.529 105.706-0.077Q105.706 0.264 105.564 0.548Q105.422 0.832 105.178 1.039Q104.934 1.245 104.624 1.360Q104.315 1.474 103.994 1.474Q103.563 1.474 103.161 1.273Q102.760 1.071 102.519 0.719Q102.278 0.367 102.278-0.077M103.994 1.225Q104.595 1.225 104.819 0.847Q105.043 0.469 105.043-0.163Q105.043-0.775 104.809-1.134Q104.575-1.492 103.994-1.492Q102.941-1.492 102.941-0.163Q102.941 0.469 103.166 0.847Q103.392 1.225 103.994 1.225M107.982 1.406L106.349 1.406L106.349 1.126Q106.578 1.126 106.726 1.092Q106.875 1.057 106.875 0.917L106.875-0.932Q106.875-1.202 106.767-1.263Q106.660-1.325 106.349-1.325L106.349-1.605L107.408-1.680L107.408-1.031Q107.579-1.339 107.883-1.510Q108.187-1.680 108.533-1.680Q109.039-1.680 109.322-1.457Q109.606-1.233 109.606-0.737L109.606 0.917Q109.606 1.054 109.755 1.090Q109.903 1.126 110.129 1.126L110.129 1.406L108.499 1.406L108.499 1.126Q108.728 1.126 108.876 1.092Q109.025 1.057 109.025 0.917L109.025-0.723Q109.025-1.058 108.905-1.258Q108.786-1.458 108.471-1.458Q108.201-1.458 107.967-1.322Q107.733-1.185 107.594-0.951Q107.456-0.717 107.456-0.443L107.456 0.917Q107.456 1.054 107.606 1.090Q107.757 1.126 107.982 1.126\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-99.014 33.729)\">\u003Cpath d=\"M115.216 1.406L113.480 1.406L113.480 1.126Q113.709 1.126 113.858 1.092Q114.006 1.057 114.006 0.917L114.006-0.932Q114.006-1.202 113.899-1.263Q113.791-1.325 113.480-1.325L113.480-1.605L114.509-1.680L114.509-0.973Q114.639-1.281 114.881-1.480Q115.124-1.680 115.442-1.680Q115.661-1.680 115.832-1.556Q116.003-1.431 116.003-1.219Q116.003-1.082 115.903-0.983Q115.804-0.884 115.671-0.884Q115.534-0.884 115.435-0.983Q115.336-1.082 115.336-1.219Q115.336-1.359 115.435-1.458Q115.145-1.458 114.945-1.262Q114.745-1.065 114.652-0.771Q114.560-0.477 114.560-0.197L114.560 0.917Q114.560 1.126 115.216 1.126L115.216 1.406M117.161 0.572L117.161-0.932Q117.161-1.202 117.054-1.263Q116.946-1.325 116.635-1.325L116.635-1.605L117.742-1.680L117.742 0.552L117.742 0.572Q117.742 0.852 117.794 0.996Q117.845 1.139 117.987 1.196Q118.129 1.252 118.416 1.252Q118.669 1.252 118.874 1.112Q119.079 0.972 119.195 0.746Q119.311 0.521 119.311 0.271L119.311-0.932Q119.311-1.202 119.204-1.263Q119.096-1.325 118.785-1.325L118.785-1.605L119.892-1.680L119.892 0.733Q119.892 0.924 119.945 1.006Q119.998 1.088 120.099 1.107Q120.200 1.126 120.415 1.126L120.415 1.406L119.339 1.474L119.339 0.910Q119.229 1.092 119.084 1.215Q118.939 1.338 118.752 1.406Q118.566 1.474 118.364 1.474Q117.161 1.474 117.161 0.572M122.671 1.406L121.068 1.406L121.068 1.126Q121.294 1.126 121.442 1.092Q121.591 1.057 121.591 0.917L121.591-2.702Q121.591-2.972 121.483-3.034Q121.376-3.095 121.068-3.095L121.068-3.376L122.145-3.451L122.145 0.917Q122.145 1.054 122.295 1.090Q122.445 1.126 122.671 1.126L122.671 1.406M123.225-0.129Q123.225-0.450 123.350-0.739Q123.474-1.028 123.700-1.251Q123.925-1.475 124.221-1.595Q124.517-1.715 124.835-1.715Q125.163-1.715 125.424-1.615Q125.686-1.516 125.862-1.334Q126.038-1.151 126.132-0.893Q126.226-0.635 126.226-0.303Q126.226-0.211 126.144-0.190L123.888-0.190L123.888-0.129Q123.888 0.459 124.172 0.842Q124.455 1.225 125.023 1.225Q125.344 1.225 125.612 1.032Q125.881 0.839 125.969 0.524Q125.976 0.483 126.051 0.469L126.144 0.469Q126.226 0.493 126.226 0.565Q126.226 0.572 126.219 0.599Q126.106 0.996 125.735 1.235Q125.364 1.474 124.941 1.474Q124.503 1.474 124.103 1.266Q123.703 1.057 123.464 0.690Q123.225 0.323 123.225-0.129M123.895-0.399L125.710-0.399Q125.710-0.676 125.612-0.928Q125.515-1.181 125.317-1.337Q125.118-1.492 124.835-1.492Q124.558-1.492 124.344-1.334Q124.131-1.175 124.013-0.920Q123.895-0.665 123.895-0.399M126.814 1.399L126.814 0.336Q126.814 0.312 126.841 0.285Q126.868 0.258 126.892 0.258L127.002 0.258Q127.067 0.258 127.080 0.316Q127.176 0.750 127.422 1.001Q127.668 1.252 128.082 1.252Q128.423 1.252 128.676 1.119Q128.929 0.986 128.929 0.678Q128.929 0.521 128.835 0.406Q128.741 0.292 128.603 0.223Q128.464 0.155 128.297 0.117L127.716 0.018Q127.360-0.050 127.087-0.271Q126.814-0.491 126.814-0.833Q126.814-1.082 126.925-1.257Q127.036-1.431 127.222-1.530Q127.408-1.629 127.624-1.672Q127.839-1.715 128.082-1.715Q128.495-1.715 128.776-1.533L128.991-1.708Q129.001-1.711 129.008-1.713Q129.015-1.715 129.025-1.715L129.076-1.715Q129.104-1.715 129.128-1.691Q129.152-1.667 129.152-1.639L129.152-0.792Q129.152-0.771 129.128-0.744Q129.104-0.717 129.076-0.717L128.964-0.717Q128.936-0.717 128.911-0.742Q128.885-0.768 128.885-0.792Q128.885-1.028 128.779-1.192Q128.673-1.356 128.490-1.438Q128.307-1.520 128.075-1.520Q127.747-1.520 127.490-1.417Q127.234-1.315 127.234-1.038Q127.234-0.843 127.417-0.734Q127.600-0.624 127.829-0.583L128.403-0.477Q128.649-0.429 128.863-0.301Q129.076-0.173 129.213 0.030Q129.350 0.234 129.350 0.483Q129.350 0.996 128.984 1.235Q128.618 1.474 128.082 1.474Q127.586 1.474 127.255 1.180L126.988 1.454Q126.967 1.474 126.940 1.474L126.892 1.474Q126.868 1.474 126.841 1.447Q126.814 1.420 126.814 1.399\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M48.309 46.93h73.977V18.479H48.309Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M57.740-8.125L56.670-10.981Q56.603-11.160 56.473-11.203Q56.342-11.246 56.084-11.246L56.084-11.543L57.764-11.543L57.764-11.246Q57.314-11.246 57.314-11.047Q57.318-11.031 57.320-11.014Q57.322-10.996 57.322-10.981L58.115-8.887L58.826-10.797Q58.791-10.891 58.791-10.936Q58.791-10.981 58.756-10.981Q58.689-11.160 58.559-11.203Q58.428-11.246 58.174-11.246L58.174-11.543L59.764-11.543L59.764-11.246Q59.314-11.246 59.314-11.047Q59.318-11.028 59.320-11.010Q59.322-10.992 59.322-10.981L60.154-8.766L60.908-10.766Q60.932-10.824 60.932-10.895Q60.932-11.055 60.795-11.151Q60.658-11.246 60.490-11.246L60.490-11.543L61.877-11.543L61.877-11.246Q61.643-11.246 61.465-11.119Q61.287-10.992 61.205-10.766L60.221-8.125Q60.166-8.016 60.053-8.016L59.994-8.016Q59.881-8.016 59.838-8.125L58.978-10.399L58.123-8.125Q58.084-8.016 57.963-8.016L57.908-8.016Q57.795-8.016 57.740-8.125M64.221-8.094L62.365-8.094L62.365-8.391Q62.639-8.391 62.807-8.438Q62.975-8.485 62.975-8.653L62.975-12.813Q62.975-13.028 62.912-13.123Q62.850-13.219 62.730-13.240Q62.611-13.262 62.365-13.262L62.365-13.559L63.588-13.645L63.588-10.942Q63.713-11.153 63.900-11.303Q64.088-11.453 64.314-11.537Q64.541-11.621 64.787-11.621Q65.955-11.621 65.955-10.543L65.955-8.653Q65.955-8.485 66.125-8.438Q66.295-8.391 66.564-8.391L66.564-8.094L64.709-8.094L64.709-8.391Q64.982-8.391 65.150-8.438Q65.318-8.485 65.318-8.653L65.318-10.528Q65.318-10.910 65.197-11.139Q65.076-11.367 64.725-11.367Q64.412-11.367 64.158-11.205Q63.904-11.043 63.758-10.774Q63.611-10.504 63.611-10.207L63.611-8.653Q63.611-8.485 63.781-8.438Q63.951-8.391 64.221-8.391L64.221-8.094M67.107-8.926Q67.107-9.410 67.510-9.705Q67.912-10 68.463-10.119Q69.014-10.239 69.506-10.239L69.506-10.528Q69.506-10.754 69.391-10.961Q69.275-11.168 69.078-11.287Q68.881-11.406 68.650-11.406Q68.225-11.406 67.939-11.301Q68.010-11.274 68.057-11.219Q68.103-11.164 68.129-11.094Q68.154-11.024 68.154-10.949Q68.154-10.844 68.103-10.752Q68.053-10.660 67.961-10.610Q67.869-10.559 67.764-10.559Q67.658-10.559 67.566-10.610Q67.475-10.660 67.424-10.752Q67.373-10.844 67.373-10.949Q67.373-11.367 67.762-11.514Q68.150-11.660 68.650-11.660Q68.982-11.660 69.336-11.530Q69.689-11.399 69.918-11.145Q70.146-10.891 70.146-10.543L70.146-8.742Q70.146-8.610 70.219-8.500Q70.291-8.391 70.420-8.391Q70.545-8.391 70.613-8.496Q70.682-8.602 70.682-8.742L70.682-9.254L70.963-9.254L70.963-8.742Q70.963-8.539 70.846-8.381Q70.728-8.223 70.547-8.139Q70.365-8.055 70.162-8.055Q69.932-8.055 69.779-8.227Q69.627-8.399 69.596-8.629Q69.436-8.348 69.127-8.182Q68.818-8.016 68.467-8.016Q67.955-8.016 67.531-8.239Q67.107-8.461 67.107-8.926M67.795-8.926Q67.795-8.641 68.021-8.455Q68.248-8.270 68.541-8.270Q68.787-8.270 69.012-8.387Q69.236-8.504 69.371-8.707Q69.506-8.910 69.506-9.164L69.506-9.996Q69.240-9.996 68.955-9.942Q68.670-9.887 68.398-9.758Q68.127-9.629 67.961-9.422Q67.795-9.215 67.795-8.926M71.881-9.055L71.881-11.246L71.178-11.246L71.178-11.500Q71.533-11.500 71.775-11.733Q72.018-11.965 72.129-12.313Q72.240-12.660 72.240-13.016L72.521-13.016L72.521-11.543L73.697-11.543L73.697-11.246L72.521-11.246L72.521-9.071Q72.521-8.750 72.641-8.522Q72.760-8.293 73.041-8.293Q73.221-8.293 73.338-8.416Q73.455-8.539 73.508-8.719Q73.561-8.899 73.561-9.071L73.561-9.543L73.842-9.543L73.842-9.055Q73.842-8.801 73.736-8.561Q73.631-8.321 73.434-8.168Q73.236-8.016 72.978-8.016Q72.662-8.016 72.410-8.139Q72.158-8.262 72.020-8.496Q71.881-8.731 71.881-9.055\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M77.502-8.926Q77.502-9.410 77.904-9.705Q78.307-10 78.857-10.119Q79.408-10.239 79.900-10.239L79.900-10.528Q79.900-10.754 79.785-10.961Q79.670-11.168 79.473-11.287Q79.275-11.406 79.045-11.406Q78.619-11.406 78.334-11.301Q78.404-11.274 78.451-11.219Q78.498-11.164 78.523-11.094Q78.549-11.024 78.549-10.949Q78.549-10.844 78.498-10.752Q78.447-10.660 78.355-10.610Q78.264-10.559 78.158-10.559Q78.053-10.559 77.961-10.610Q77.869-10.660 77.818-10.752Q77.768-10.844 77.768-10.949Q77.768-11.367 78.156-11.514Q78.545-11.660 79.045-11.660Q79.377-11.660 79.730-11.530Q80.084-11.399 80.312-11.145Q80.541-10.891 80.541-10.543L80.541-8.742Q80.541-8.610 80.613-8.500Q80.686-8.391 80.814-8.391Q80.939-8.391 81.008-8.496Q81.076-8.602 81.076-8.742L81.076-9.254L81.357-9.254L81.357-8.742Q81.357-8.539 81.240-8.381Q81.123-8.223 80.941-8.139Q80.760-8.055 80.557-8.055Q80.326-8.055 80.174-8.227Q80.021-8.399 79.990-8.629Q79.830-8.348 79.521-8.182Q79.213-8.016 78.861-8.016Q78.350-8.016 77.926-8.239Q77.502-8.461 77.502-8.926M78.189-8.926Q78.189-8.641 78.416-8.455Q78.643-8.270 78.936-8.270Q79.182-8.270 79.406-8.387Q79.631-8.504 79.766-8.707Q79.900-8.910 79.900-9.164L79.900-9.996Q79.635-9.996 79.350-9.942Q79.064-9.887 78.793-9.758Q78.521-9.629 78.355-9.422Q78.189-9.215 78.189-8.926M81.693-9.821Q81.693-10.317 81.943-10.742Q82.193-11.168 82.613-11.414Q83.033-11.660 83.533-11.660Q84.072-11.660 84.463-11.535Q84.853-11.410 84.853-10.996Q84.853-10.891 84.803-10.799Q84.752-10.707 84.660-10.656Q84.568-10.606 84.459-10.606Q84.353-10.606 84.262-10.656Q84.170-10.707 84.119-10.799Q84.068-10.891 84.068-10.996Q84.068-11.219 84.236-11.324Q84.014-11.383 83.541-11.383Q83.244-11.383 83.029-11.244Q82.814-11.106 82.684-10.875Q82.553-10.645 82.494-10.375Q82.436-10.106 82.436-9.821Q82.436-9.426 82.568-9.076Q82.701-8.727 82.973-8.510Q83.244-8.293 83.643-8.293Q84.018-8.293 84.293-8.510Q84.568-8.727 84.670-9.086Q84.686-9.149 84.748-9.149L84.853-9.149Q84.889-9.149 84.914-9.121Q84.939-9.094 84.939-9.055L84.939-9.031Q84.807-8.551 84.422-8.283Q84.037-8.016 83.533-8.016Q83.170-8.016 82.836-8.153Q82.502-8.289 82.242-8.539Q81.982-8.789 81.838-9.125Q81.693-9.461 81.693-9.821M86.053-9.055L86.053-11.246L85.350-11.246L85.350-11.500Q85.705-11.500 85.947-11.733Q86.189-11.965 86.301-12.313Q86.412-12.660 86.412-13.016L86.693-13.016L86.693-11.543L87.869-11.543L87.869-11.246L86.693-11.246L86.693-9.071Q86.693-8.750 86.812-8.522Q86.932-8.293 87.213-8.293Q87.393-8.293 87.510-8.416Q87.627-8.539 87.680-8.719Q87.732-8.899 87.732-9.071L87.732-9.543L88.014-9.543L88.014-9.055Q88.014-8.801 87.908-8.561Q87.803-8.321 87.605-8.168Q87.408-8.016 87.150-8.016Q86.834-8.016 86.582-8.139Q86.330-8.262 86.191-8.496Q86.053-8.731 86.053-9.055M90.592-8.094L88.814-8.094L88.814-8.391Q89.088-8.391 89.256-8.438Q89.424-8.485 89.424-8.653L89.424-10.789Q89.424-11.004 89.367-11.100Q89.311-11.196 89.197-11.217Q89.084-11.239 88.838-11.239L88.838-11.535L90.037-11.621L90.037-8.653Q90.037-8.485 90.184-8.438Q90.330-8.391 90.592-8.391L90.592-8.094M89.150-13.016Q89.150-13.207 89.285-13.338Q89.420-13.469 89.615-13.469Q89.736-13.469 89.840-13.406Q89.943-13.344 90.006-13.240Q90.068-13.137 90.068-13.016Q90.068-12.821 89.937-12.686Q89.807-12.551 89.615-12.551Q89.416-12.551 89.283-12.684Q89.150-12.817 89.150-13.016M91.092-9.789Q91.092-10.293 91.348-10.725Q91.603-11.156 92.039-11.408Q92.475-11.660 92.975-11.660Q93.361-11.660 93.703-11.516Q94.045-11.371 94.307-11.110Q94.568-10.848 94.711-10.512Q94.853-10.176 94.853-9.789Q94.853-9.297 94.590-8.887Q94.326-8.477 93.896-8.246Q93.467-8.016 92.975-8.016Q92.482-8.016 92.049-8.248Q91.615-8.481 91.353-8.889Q91.092-9.297 91.092-9.789M92.975-8.293Q93.432-8.293 93.684-8.516Q93.936-8.739 94.023-9.090Q94.111-9.442 94.111-9.887Q94.111-10.317 94.018-10.655Q93.924-10.992 93.670-11.199Q93.416-11.406 92.975-11.406Q92.326-11.406 92.082-10.990Q91.838-10.574 91.838-9.887Q91.838-9.442 91.926-9.090Q92.014-8.739 92.266-8.516Q92.518-8.293 92.975-8.293M97.268-8.094L95.412-8.094L95.412-8.391Q95.686-8.391 95.853-8.438Q96.021-8.485 96.021-8.653L96.021-10.789Q96.021-11.004 95.959-11.100Q95.896-11.196 95.777-11.217Q95.658-11.239 95.412-11.239L95.412-11.535L96.603-11.621L96.603-10.887Q96.717-11.102 96.910-11.270Q97.103-11.438 97.342-11.530Q97.580-11.621 97.834-11.621Q99.002-11.621 99.002-10.543L99.002-8.653Q99.002-8.485 99.172-8.438Q99.342-8.391 99.611-8.391L99.611-8.094L97.756-8.094L97.756-8.391Q98.029-8.391 98.197-8.438Q98.365-8.485 98.365-8.653L98.365-10.528Q98.365-10.910 98.244-11.139Q98.123-11.367 97.771-11.367Q97.459-11.367 97.205-11.205Q96.951-11.043 96.805-10.774Q96.658-10.504 96.658-10.207L96.658-8.653Q96.658-8.485 96.828-8.438Q96.998-8.391 97.268-8.391\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M105.428-8.094L102.963-8.094L102.963-8.391Q103.295-8.391 103.553-8.438Q103.811-8.485 103.811-8.653L103.811-12.996Q103.811-13.262 102.963-13.262L102.963-13.559L105.428-13.559L105.428-13.262Q104.576-13.262 104.576-12.996L104.576-8.653Q104.576-8.391 105.428-8.391\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M54.280 1.398L54.280 0.176Q54.280 0.148 54.312 0.117Q54.343 0.086 54.366 0.086L54.472 0.086Q54.542 0.086 54.558 0.148Q54.620 0.468 54.759 0.709Q54.897 0.949 55.130 1.090Q55.362 1.230 55.671 1.230Q55.909 1.230 56.118 1.170Q56.327 1.109 56.464 0.961Q56.601 0.812 56.601 0.566Q56.601 0.312 56.390 0.146Q56.179-0.020 55.909-0.074L55.288-0.188Q54.882-0.266 54.581-0.522Q54.280-0.778 54.280-1.153Q54.280-1.520 54.481-1.742Q54.683-1.965 55.007-2.063Q55.331-2.160 55.671-2.160Q56.136-2.160 56.433-1.953L56.655-2.137Q56.679-2.160 56.710-2.160L56.761-2.160Q56.792-2.160 56.819-2.133Q56.847-2.106 56.847-2.074L56.847-1.090Q56.847-1.059 56.821-1.030Q56.796-1 56.761-1L56.655-1Q56.620-1 56.593-1.028Q56.565-1.055 56.565-1.090Q56.565-1.489 56.313-1.709Q56.062-1.930 55.663-1.930Q55.308-1.930 55.024-1.807Q54.741-1.684 54.741-1.379Q54.741-1.160 54.942-1.028Q55.144-0.895 55.390-0.852L56.015-0.739Q56.444-0.649 56.753-0.352Q57.062-0.055 57.062 0.359Q57.062 0.929 56.663 1.207Q56.265 1.484 55.671 1.484Q55.120 1.484 54.769 1.148L54.472 1.461Q54.448 1.484 54.413 1.484L54.366 1.484Q54.343 1.484 54.312 1.453Q54.280 1.422 54.280 1.398M59.519 1.406L57.663 1.406L57.663 1.109Q57.937 1.109 58.104 1.062Q58.272 1.015 58.272 0.847L58.272-3.313Q58.272-3.528 58.210-3.623Q58.147-3.719 58.028-3.740Q57.909-3.762 57.663-3.762L57.663-4.059L58.886-4.145L58.886-1.442Q59.011-1.653 59.198-1.803Q59.386-1.953 59.612-2.037Q59.839-2.121 60.085-2.121Q61.253-2.121 61.253-1.043L61.253 0.847Q61.253 1.015 61.423 1.062Q61.593 1.109 61.862 1.109L61.862 1.406L60.007 1.406L60.007 1.109Q60.280 1.109 60.448 1.062Q60.616 1.015 60.616 0.847L60.616-1.028Q60.616-1.410 60.495-1.639Q60.374-1.867 60.022-1.867Q59.710-1.867 59.456-1.705Q59.202-1.543 59.056-1.274Q58.909-1.004 58.909-0.707L58.909 0.847Q58.909 1.015 59.079 1.062Q59.249 1.109 59.519 1.109L59.519 1.406M62.308-0.289Q62.308-0.793 62.563-1.225Q62.819-1.657 63.255-1.908Q63.690-2.160 64.190-2.160Q64.577-2.160 64.919-2.016Q65.261-1.871 65.522-1.610Q65.784-1.348 65.927-1.012Q66.069-0.676 66.069-0.289Q66.069 0.203 65.806 0.613Q65.542 1.023 65.112 1.254Q64.683 1.484 64.190 1.484Q63.698 1.484 63.265 1.252Q62.831 1.019 62.569 0.611Q62.308 0.203 62.308-0.289M64.190 1.207Q64.647 1.207 64.899 0.984Q65.151 0.761 65.239 0.410Q65.327 0.058 65.327-0.387Q65.327-0.817 65.233-1.155Q65.140-1.492 64.886-1.699Q64.632-1.907 64.190-1.907Q63.542-1.907 63.298-1.490Q63.054-1.074 63.054-0.387Q63.054 0.058 63.142 0.410Q63.229 0.761 63.481 0.984Q63.733 1.207 64.190 1.207M67.237 0.453L67.237-1.289Q67.237-1.504 67.175-1.600Q67.112-1.696 66.993-1.717Q66.874-1.739 66.628-1.739L66.628-2.035L67.874-2.121L67.874 0.429L67.874 0.453Q67.874 0.765 67.929 0.927Q67.983 1.090 68.134 1.160Q68.284 1.230 68.604 1.230Q69.034 1.230 69.308 0.892Q69.581 0.554 69.581 0.109L69.581-1.289Q69.581-1.504 69.519-1.600Q69.456-1.696 69.337-1.717Q69.218-1.739 68.972-1.739L68.972-2.035L70.218-2.121L70.218 0.664Q70.218 0.875 70.280 0.970Q70.343 1.066 70.462 1.088Q70.581 1.109 70.827 1.109L70.827 1.406L69.604 1.484L69.604 0.863Q69.436 1.152 69.155 1.318Q68.874 1.484 68.554 1.484Q67.237 1.484 67.237 0.453M73.186 1.406L71.354 1.406L71.354 1.109Q71.628 1.109 71.796 1.062Q71.964 1.015 71.964 0.847L71.964-3.313Q71.964-3.528 71.901-3.623Q71.839-3.719 71.720-3.740Q71.601-3.762 71.354-3.762L71.354-4.059L72.577-4.145L72.577 0.847Q72.577 1.015 72.745 1.062Q72.913 1.109 73.186 1.109L73.186 1.406M75.448 1.484Q74.968 1.484 74.560 1.240Q74.151 0.996 73.913 0.582Q73.675 0.168 73.675-0.321Q73.675-0.813 73.933-1.229Q74.190-1.645 74.622-1.883Q75.054-2.121 75.546-2.121Q76.167-2.121 76.616-1.684L76.616-3.313Q76.616-3.528 76.554-3.623Q76.491-3.719 76.374-3.740Q76.257-3.762 76.011-3.762L76.011-4.059L77.233-4.145L77.233 0.664Q77.233 0.875 77.296 0.970Q77.358 1.066 77.476 1.088Q77.593 1.109 77.843 1.109L77.843 1.406L76.593 1.484L76.593 1Q76.128 1.484 75.448 1.484M75.515 1.230Q75.854 1.230 76.147 1.039Q76.440 0.847 76.593 0.551L76.593-1.282Q76.444-1.555 76.183-1.711Q75.921-1.867 75.608-1.867Q74.983-1.867 74.700-1.420Q74.417-0.973 74.417-0.313Q74.417 0.332 74.669 0.781Q74.921 1.230 75.515 1.230\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M83.018 1.484Q82.537 1.484 82.129 1.240Q81.721 0.996 81.483 0.582Q81.244 0.168 81.244-0.321Q81.244-0.813 81.502-1.229Q81.760-1.645 82.192-1.883Q82.623-2.121 83.115-2.121Q83.736-2.121 84.186-1.684L84.186-3.313Q84.186-3.528 84.123-3.623Q84.061-3.719 83.943-3.740Q83.826-3.762 83.580-3.762L83.580-4.059L84.803-4.145L84.803 0.664Q84.803 0.875 84.865 0.970Q84.928 1.066 85.045 1.088Q85.162 1.109 85.412 1.109L85.412 1.406L84.162 1.484L84.162 1Q83.697 1.484 83.018 1.484M83.084 1.230Q83.424 1.230 83.717 1.039Q84.010 0.847 84.162 0.551L84.162-1.282Q84.014-1.555 83.752-1.711Q83.490-1.867 83.178-1.867Q82.553-1.867 82.270-1.420Q81.986-0.973 81.986-0.313Q81.986 0.332 82.238 0.781Q82.490 1.230 83.084 1.230M85.920-0.289Q85.920-0.793 86.176-1.225Q86.432-1.657 86.867-1.908Q87.303-2.160 87.803-2.160Q88.190-2.160 88.531-2.016Q88.873-1.871 89.135-1.610Q89.397-1.348 89.539-1.012Q89.682-0.676 89.682-0.289Q89.682 0.203 89.418 0.613Q89.154 1.023 88.725 1.254Q88.295 1.484 87.803 1.484Q87.311 1.484 86.877 1.252Q86.443 1.019 86.182 0.611Q85.920 0.203 85.920-0.289M87.803 1.207Q88.260 1.207 88.512 0.984Q88.764 0.761 88.852 0.410Q88.940 0.058 88.940-0.387Q88.940-0.817 88.846-1.155Q88.752-1.492 88.498-1.699Q88.244-1.907 87.803-1.907Q87.154-1.907 86.910-1.490Q86.666-1.074 86.666-0.387Q86.666 0.058 86.754 0.410Q86.842 0.761 87.094 0.984Q87.346 1.207 87.803 1.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M94.937 1.406L93.082 1.406L93.082 1.109Q93.355 1.109 93.523 1.062Q93.691 1.015 93.691 0.847L93.691-1.289Q93.691-1.504 93.628-1.600Q93.566-1.696 93.447-1.717Q93.328-1.739 93.082-1.739L93.082-2.035L94.273-2.121L94.273-1.387Q94.386-1.602 94.580-1.770Q94.773-1.938 95.011-2.030Q95.249-2.121 95.503-2.121Q96.671-2.121 96.671-1.043L96.671 0.847Q96.671 1.015 96.841 1.062Q97.011 1.109 97.281 1.109L97.281 1.406L95.425 1.406L95.425 1.109Q95.699 1.109 95.867 1.062Q96.035 1.015 96.035 0.847L96.035-1.028Q96.035-1.410 95.914-1.639Q95.792-1.867 95.441-1.867Q95.128-1.867 94.874-1.705Q94.621-1.543 94.474-1.274Q94.328-1.004 94.328-0.707L94.328 0.847Q94.328 1.015 94.498 1.062Q94.667 1.109 94.937 1.109L94.937 1.406M97.726-0.289Q97.726-0.793 97.982-1.225Q98.238-1.657 98.673-1.908Q99.109-2.160 99.609-2.160Q99.996-2.160 100.337-2.016Q100.679-1.871 100.941-1.610Q101.203-1.348 101.345-1.012Q101.488-0.676 101.488-0.289Q101.488 0.203 101.224 0.613Q100.960 1.023 100.531 1.254Q100.101 1.484 99.609 1.484Q99.117 1.484 98.683 1.252Q98.249 1.019 97.988 0.611Q97.726 0.203 97.726-0.289M99.609 1.207Q100.066 1.207 100.318 0.984Q100.570 0.761 100.658 0.410Q100.746 0.058 100.746-0.387Q100.746-0.817 100.652-1.155Q100.558-1.492 100.304-1.699Q100.050-1.907 99.609-1.907Q98.960-1.907 98.716-1.490Q98.472-1.074 98.472-0.387Q98.472 0.058 98.560 0.410Q98.648 0.761 98.900 0.984Q99.152 1.207 99.609 1.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(4.476 38.826)\">\u003Cpath d=\"M103.329 1.375L102.259-1.481Q102.192-1.660 102.062-1.703Q101.931-1.746 101.673-1.746L101.673-2.043L103.353-2.043L103.353-1.746Q102.903-1.746 102.903-1.547Q102.907-1.532 102.909-1.514Q102.911-1.496 102.911-1.481L103.704 0.613L104.415-1.297Q104.380-1.391 104.380-1.436Q104.380-1.481 104.345-1.481Q104.278-1.660 104.148-1.703Q104.017-1.746 103.763-1.746L103.763-2.043L105.353-2.043L105.353-1.746Q104.903-1.746 104.903-1.547Q104.907-1.528 104.909-1.510Q104.911-1.492 104.911-1.481L105.743 0.734L106.497-1.266Q106.521-1.324 106.521-1.395Q106.521-1.555 106.384-1.651Q106.247-1.746 106.079-1.746L106.079-2.043L107.466-2.043L107.466-1.746Q107.232-1.746 107.054-1.619Q106.876-1.492 106.794-1.266L105.810 1.375Q105.755 1.484 105.642 1.484L105.583 1.484Q105.470 1.484 105.427 1.375L104.567-0.899L103.712 1.375Q103.673 1.484 103.552 1.484L103.497 1.484Q103.384 1.484 103.329 1.375\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M183.646-47.164H85.297v.246\"\u002F>\u003Cpath stroke=\"none\" d=\"m85.297-44.319 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M85.297-15.466v31.144\"\u002F>\u003Cpath stroke=\"none\" d=\"m85.297 18.278 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M51.255 32.704h-.546\"\u002F>\u003Cpath stroke=\"none\" d=\"m48.109 32.704 4.16 2.08-1.56-2.08 1.56-2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M85.297 47.13v14.227h98.349v2.6\"\u002F>\u003Cpath stroke=\"none\" d=\"m183.646 61.357-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">A simple reflex agent. The current percept is abstracted into a description of the world now; a matching condition-action rule selects the action. There is no memory of past percepts.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:454.163px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 340.622 164.734\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-51.864 72.538h227.622V-58.344H-51.864Z\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-110.678 60.753)\">\u003Cpath d=\"M63.986 7.097L62.236 7.097L62.236 6.800Q62.935 6.800 63.123 6.320L64.924 1.495Q64.978 1.386 65.092 1.386L65.162 1.386Q65.275 1.386 65.330 1.495L67.220 6.538Q67.299 6.706 67.502 6.753Q67.705 6.800 68.017 6.800L68.017 7.097L65.795 7.097L65.795 6.800Q66.435 6.800 66.435 6.585Q66.435 6.566 66.433 6.556Q66.431 6.546 66.427 6.538L65.963 5.304L63.818 5.304L63.435 6.320Q63.431 6.335 63.426 6.365Q63.420 6.394 63.420 6.417Q63.420 6.558 63.510 6.642Q63.599 6.726 63.732 6.763Q63.865 6.800 63.986 6.800L63.986 7.097M64.892 2.441L63.924 5.007L65.849 5.007L64.892 2.441M68.545 7.706Q68.545 7.425 68.756 7.214Q68.967 7.003 69.252 6.913Q69.095 6.788 69.017 6.599Q68.939 6.410 68.939 6.210Q68.939 5.855 69.170 5.562Q68.802 5.222 68.802 4.753Q68.802 4.402 69.006 4.132Q69.209 3.863 69.529 3.716Q69.849 3.570 70.193 3.570Q70.713 3.570 71.084 3.851Q71.447 3.480 71.994 3.480Q72.174 3.480 72.301 3.607Q72.427 3.734 72.427 3.913Q72.427 4.019 72.349 4.097Q72.271 4.175 72.162 4.175Q72.052 4.175 71.976 4.099Q71.900 4.023 71.900 3.913Q71.900 3.812 71.939 3.761Q71.947 3.753 71.951 3.747Q71.955 3.742 71.955 3.738Q71.580 3.738 71.260 3.992Q71.580 4.331 71.580 4.753Q71.580 5.023 71.463 5.240Q71.345 5.456 71.140 5.615Q70.935 5.773 70.693 5.855Q70.451 5.937 70.193 5.937Q69.974 5.937 69.761 5.878Q69.549 5.820 69.353 5.699Q69.260 5.839 69.260 6.019Q69.260 6.226 69.396 6.378Q69.533 6.531 69.740 6.531L70.435 6.531Q70.924 6.531 71.336 6.615Q71.748 6.699 72.027 6.956Q72.306 7.214 72.306 7.706Q72.306 8.070 71.986 8.302Q71.666 8.535 71.224 8.636Q70.783 8.738 70.427 8.738Q70.072 8.738 69.629 8.636Q69.185 8.535 68.865 8.302Q68.545 8.070 68.545 7.706M69.049 7.706Q69.049 7.902 69.193 8.050Q69.338 8.199 69.551 8.288Q69.763 8.378 70.004 8.425Q70.244 8.472 70.427 8.472Q70.670 8.472 71 8.394Q71.330 8.316 71.566 8.142Q71.802 7.968 71.802 7.706Q71.802 7.300 71.392 7.191Q70.982 7.081 70.420 7.081L69.740 7.081Q69.470 7.081 69.260 7.259Q69.049 7.437 69.049 7.706M70.193 5.671Q70.916 5.671 70.916 4.753Q70.916 3.831 70.193 3.831Q69.467 3.831 69.467 4.753Q69.467 5.671 70.193 5.671M72.791 5.343Q72.791 4.863 73.023 4.447Q73.256 4.031 73.666 3.781Q74.076 3.531 74.552 3.531Q75.283 3.531 75.681 3.972Q76.080 4.413 76.080 5.144Q76.080 5.249 75.986 5.273L73.537 5.273L73.537 5.343Q73.537 5.753 73.658 6.109Q73.779 6.464 74.051 6.681Q74.322 6.898 74.752 6.898Q75.115 6.898 75.412 6.669Q75.709 6.441 75.810 6.089Q75.818 6.042 75.904 6.027L75.986 6.027Q76.080 6.054 76.080 6.136Q76.080 6.144 76.072 6.175Q76.010 6.402 75.871 6.585Q75.732 6.769 75.541 6.902Q75.349 7.035 75.131 7.105Q74.912 7.175 74.674 7.175Q74.302 7.175 73.965 7.038Q73.627 6.902 73.359 6.650Q73.092 6.398 72.941 6.058Q72.791 5.718 72.791 5.343M73.545 5.035L75.506 5.035Q75.506 4.730 75.404 4.439Q75.302 4.148 75.086 3.966Q74.869 3.785 74.552 3.785Q74.252 3.785 74.021 3.972Q73.791 4.160 73.668 4.451Q73.545 4.742 73.545 5.035M78.498 7.097L76.642 7.097L76.642 6.800Q76.916 6.800 77.084 6.753Q77.252 6.706 77.252 6.538L77.252 4.402Q77.252 4.187 77.189 4.091Q77.127 3.995 77.008 3.974Q76.888 3.952 76.642 3.952L76.642 3.656L77.834 3.570L77.834 4.304Q77.947 4.089 78.140 3.921Q78.334 3.753 78.572 3.661Q78.810 3.570 79.064 3.570Q80.232 3.570 80.232 4.648L80.232 6.538Q80.232 6.706 80.402 6.753Q80.572 6.800 80.842 6.800L80.842 7.097L78.986 7.097L78.986 6.800Q79.260 6.800 79.427 6.753Q79.595 6.706 79.595 6.538L79.595 4.663Q79.595 4.281 79.474 4.052Q79.353 3.824 79.002 3.824Q78.689 3.824 78.435 3.986Q78.181 4.148 78.035 4.417Q77.888 4.687 77.888 4.984L77.888 6.538Q77.888 6.706 78.058 6.753Q78.228 6.800 78.498 6.800\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-110.678 60.753)\">\u003Cpath d=\"M81.691 6.136L81.691 3.945L80.988 3.945L80.988 3.691Q81.344 3.691 81.586 3.458Q81.828 3.226 81.939 2.878Q82.051 2.531 82.051 2.175L82.332 2.175L82.332 3.648L83.508 3.648L83.508 3.945L82.332 3.945L82.332 6.120Q82.332 6.441 82.451 6.669Q82.570 6.898 82.851 6.898Q83.031 6.898 83.148 6.775Q83.266 6.652 83.318 6.472Q83.371 6.292 83.371 6.120L83.371 5.648L83.652 5.648L83.652 6.136Q83.652 6.390 83.547 6.630Q83.441 6.870 83.244 7.023Q83.047 7.175 82.789 7.175Q82.473 7.175 82.221 7.052Q81.969 6.929 81.830 6.695Q81.691 6.460 81.691 6.136\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M203.175 72.538h58.977V-58.344h-58.977Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr9\" font-size=\"9\">\u003Cg transform=\"translate(144.56 3.075)\">\u003Cpath d=\"M67.581 7.097L62.272 7.097L62.272 6.781Q63.191 6.781 63.191 6.486L63.191 1.560Q63.191 1.265 62.272 1.265L62.272 0.949L67.462 0.949L67.717 3.010L67.427 3.010Q67.357 2.417 67.242 2.085Q67.128 1.753 66.919 1.577Q66.711 1.402 66.366 1.334Q66.021 1.265 65.410 1.265L64.496 1.265Q64.245 1.265 64.140 1.314Q64.034 1.362 64.034 1.560L64.034 3.748L64.720 3.748Q65.199 3.748 65.421 3.674Q65.643 3.599 65.735 3.384Q65.827 3.168 65.827 2.698L66.113 2.698L66.113 5.115L65.827 5.115Q65.827 4.645 65.735 4.430Q65.643 4.214 65.421 4.139Q65.199 4.065 64.720 4.065L64.034 4.065L64.034 6.486Q64.034 6.680 64.140 6.730Q64.245 6.781 64.496 6.781L65.476 6.781Q66.113 6.781 66.502 6.684Q66.891 6.587 67.111 6.365Q67.330 6.143 67.451 5.765Q67.572 5.388 67.682 4.737L67.968 4.737L67.581 7.097M70.626 7.097L68.539 7.097L68.539 6.781Q68.846 6.781 69.038 6.728Q69.229 6.675 69.229 6.486L69.229 4.038Q69.229 3.797 69.158 3.689Q69.088 3.581 68.954 3.557Q68.820 3.533 68.539 3.533L68.539 3.217L69.879 3.120L69.879 3.955Q70.077 3.573 70.431 3.346Q70.784 3.120 71.211 3.120Q72.489 3.120 72.489 4.333L72.489 6.486Q72.489 6.675 72.681 6.728Q72.872 6.781 73.179 6.781L73.179 7.097L71.092 7.097L71.092 6.781Q71.404 6.781 71.595 6.728Q71.786 6.675 71.786 6.486L71.786 4.368Q71.786 4.109 71.742 3.887Q71.698 3.665 71.553 3.522Q71.408 3.379 71.149 3.379Q70.806 3.379 70.525 3.568Q70.244 3.757 70.088 4.069Q69.932 4.381 69.932 4.728L69.932 6.486Q69.932 6.675 70.125 6.728Q70.319 6.781 70.626 6.781\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(144.56 3.075)\">\u003Cpath d=\"M75.355 7.079L74.024 3.832Q73.936 3.634 73.771 3.584Q73.606 3.533 73.303 3.533L73.303 3.217L75.228 3.217L75.228 3.533Q74.736 3.533 74.736 3.748Q74.736 3.770 74.753 3.832L75.769 6.306L76.678 4.082Q76.713 3.999 76.713 3.902Q76.713 3.731 76.590 3.632Q76.467 3.533 76.300 3.533L76.300 3.217L77.812 3.217L77.812 3.533Q77.526 3.533 77.313 3.676Q77.100 3.819 76.995 4.082L75.760 7.079Q75.716 7.198 75.588 7.198L75.527 7.198Q75.399 7.198 75.355 7.079M80.295 7.097L78.309 7.097L78.309 6.781Q78.616 6.781 78.807 6.728Q78.998 6.675 78.998 6.486L78.998 4.038Q78.998 3.792 78.933 3.687Q78.867 3.581 78.741 3.557Q78.616 3.533 78.344 3.533L78.344 3.217L79.675 3.120L79.675 6.486Q79.675 6.680 79.840 6.730Q80.005 6.781 80.295 6.781L80.295 7.097M78.695 1.573Q78.695 1.367 78.845 1.217Q78.994 1.068 79.196 1.068Q79.328 1.068 79.445 1.138Q79.561 1.208 79.631 1.325Q79.702 1.441 79.702 1.573Q79.702 1.775 79.552 1.925Q79.403 2.074 79.196 2.074Q78.994 2.074 78.845 1.925Q78.695 1.775 78.695 1.573M83.050 7.097L80.818 7.097L80.818 6.781Q81.130 6.781 81.321 6.728Q81.512 6.675 81.512 6.486L81.512 4.038Q81.512 3.797 81.442 3.689Q81.372 3.581 81.238 3.557Q81.103 3.533 80.818 3.533L80.818 3.217L82.132 3.120L82.132 3.981Q82.294 3.590 82.562 3.355Q82.831 3.120 83.222 3.120Q83.494 3.120 83.709 3.283Q83.925 3.445 83.925 3.704Q83.925 3.880 83.806 3.999Q83.687 4.118 83.512 4.118Q83.331 4.118 83.213 3.999Q83.094 3.880 83.094 3.704Q83.094 3.489 83.248 3.379L83.230 3.379Q82.852 3.379 82.620 3.641Q82.387 3.902 82.288 4.289Q82.189 4.676 82.189 5.036L82.189 6.486Q82.189 6.675 82.446 6.728Q82.703 6.781 83.050 6.781L83.050 7.097M84.443 5.190Q84.443 4.623 84.716 4.135Q84.988 3.647 85.458 3.355Q85.929 3.063 86.496 3.063Q86.917 3.063 87.293 3.232Q87.669 3.401 87.946 3.693Q88.223 3.986 88.381 4.381Q88.539 4.777 88.539 5.190Q88.539 5.739 88.260 6.201Q87.981 6.662 87.513 6.930Q87.045 7.198 86.496 7.198Q85.942 7.198 85.472 6.930Q85.001 6.662 84.722 6.201Q84.443 5.739 84.443 5.190M86.496 6.908Q86.992 6.908 87.269 6.647Q87.546 6.385 87.638 5.981Q87.730 5.576 87.730 5.080Q87.730 4.605 87.632 4.216Q87.533 3.827 87.260 3.577Q86.988 3.326 86.496 3.326Q85.784 3.326 85.520 3.821Q85.256 4.315 85.256 5.080Q85.256 5.880 85.511 6.394Q85.766 6.908 86.496 6.908M91.189 7.097L89.102 7.097L89.102 6.781Q89.409 6.781 89.600 6.728Q89.791 6.675 89.791 6.486L89.791 4.038Q89.791 3.797 89.721 3.689Q89.651 3.581 89.517 3.557Q89.383 3.533 89.102 3.533L89.102 3.217L90.442 3.120L90.442 3.955Q90.640 3.573 90.993 3.346Q91.347 3.120 91.773 3.120Q93.052 3.120 93.052 4.333L93.052 6.486Q93.052 6.675 93.243 6.728Q93.435 6.781 93.742 6.781L93.742 7.097L91.655 7.097L91.655 6.781Q91.967 6.781 92.158 6.728Q92.349 6.675 92.349 6.486L92.349 4.368Q92.349 4.109 92.305 3.887Q92.261 3.665 92.116 3.522Q91.971 3.379 91.712 3.379Q91.369 3.379 91.088 3.568Q90.807 3.757 90.651 4.069Q90.495 4.381 90.495 4.728L90.495 6.486Q90.495 6.675 90.688 6.728Q90.881 6.781 91.189 6.781L91.189 7.097M96.326 7.097L94.239 7.097L94.239 6.781Q94.546 6.781 94.738 6.728Q94.929 6.675 94.929 6.486L94.929 4.038Q94.929 3.797 94.858 3.689Q94.788 3.581 94.654 3.557Q94.520 3.533 94.239 3.533L94.239 3.217L95.579 3.120L95.579 3.955Q95.777 3.577 96.137 3.348Q96.498 3.120 96.919 3.120Q97.965 3.120 98.150 3.929Q98.352 3.559 98.710 3.340Q99.068 3.120 99.486 3.120Q100.110 3.120 100.435 3.414Q100.760 3.709 100.760 4.333L100.760 6.486Q100.760 6.675 100.954 6.728Q101.147 6.781 101.455 6.781L101.455 7.097L99.367 7.097L99.367 6.781Q99.675 6.781 99.868 6.728Q100.061 6.675 100.061 6.486L100.061 4.368Q100.061 3.937 99.934 3.658Q99.807 3.379 99.420 3.379Q99.077 3.379 98.794 3.568Q98.510 3.757 98.354 4.069Q98.198 4.381 98.198 4.728L98.198 6.486Q98.198 6.675 98.389 6.728Q98.581 6.781 98.888 6.781L98.888 7.097L96.801 7.097L96.801 6.781Q97.113 6.781 97.304 6.728Q97.495 6.675 97.495 6.486L97.495 4.368Q97.495 4.109 97.451 3.887Q97.407 3.665 97.262 3.522Q97.117 3.379 96.858 3.379Q96.322 3.379 95.977 3.786Q95.632 4.192 95.632 4.728L95.632 6.486Q95.632 6.675 95.825 6.728Q96.019 6.781 96.326 6.781L96.326 7.097M103.955 7.198Q103.397 7.198 102.925 6.915Q102.452 6.631 102.177 6.154Q101.903 5.678 101.903 5.124Q101.903 4.728 102.046 4.353Q102.188 3.977 102.446 3.689Q102.703 3.401 103.061 3.232Q103.419 3.063 103.823 3.063Q104.368 3.063 104.739 3.300Q105.111 3.537 105.298 3.955Q105.484 4.372 105.484 4.909Q105.484 4.961 105.460 4.999Q105.436 5.036 105.388 5.036L102.716 5.036L102.716 5.115Q102.716 5.862 103.028 6.385Q103.340 6.908 104.039 6.908Q104.443 6.908 104.764 6.651Q105.084 6.394 105.207 5.990Q105.225 5.910 105.309 5.910L105.388 5.910Q105.427 5.910 105.456 5.941Q105.484 5.972 105.484 6.016L105.484 6.051Q105.379 6.394 105.157 6.653Q104.935 6.912 104.621 7.055Q104.307 7.198 103.955 7.198M102.725 4.785L104.838 4.785Q104.838 4.517 104.786 4.271Q104.733 4.025 104.612 3.803Q104.491 3.581 104.293 3.454Q104.096 3.326 103.823 3.326Q103.480 3.326 103.228 3.551Q102.975 3.775 102.850 4.113Q102.725 4.451 102.725 4.785M108.143 7.097L106.056 7.097L106.056 6.781Q106.363 6.781 106.554 6.728Q106.746 6.675 106.746 6.486L106.746 4.038Q106.746 3.797 106.675 3.689Q106.605 3.581 106.471 3.557Q106.337 3.533 106.056 3.533L106.056 3.217L107.396 3.120L107.396 3.955Q107.594 3.573 107.947 3.346Q108.301 3.120 108.727 3.120Q110.006 3.120 110.006 4.333L110.006 6.486Q110.006 6.675 110.197 6.728Q110.389 6.781 110.696 6.781L110.696 7.097L108.609 7.097L108.609 6.781Q108.921 6.781 109.112 6.728Q109.303 6.675 109.303 6.486L109.303 4.368Q109.303 4.109 109.259 3.887Q109.215 3.665 109.070 3.522Q108.925 3.379 108.666 3.379Q108.323 3.379 108.042 3.568Q107.761 3.757 107.605 4.069Q107.449 4.381 107.449 4.728L107.449 6.486Q107.449 6.675 107.642 6.728Q107.835 6.781 108.143 6.781\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(144.56 3.075)\">\u003Cpath d=\"M111.597 6.025L111.597 3.533L110.832 3.533L110.832 3.274Q111.237 3.274 111.503 3.008Q111.768 2.742 111.889 2.342Q112.010 1.942 112.010 1.560L112.300 1.560L112.300 3.217L113.588 3.217L113.588 3.533L112.300 3.533L112.300 5.990Q112.300 6.359 112.425 6.633Q112.551 6.908 112.876 6.908Q113.175 6.908 113.313 6.614Q113.452 6.319 113.452 5.990L113.452 5.467L113.737 5.467L113.737 6.025Q113.737 6.302 113.627 6.574Q113.517 6.847 113.304 7.022Q113.091 7.198 112.810 7.198Q112.450 7.198 112.177 7.060Q111.905 6.921 111.751 6.658Q111.597 6.394 111.597 6.025\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(54.566 -71.25)\">\u003Cpath d=\"M62.436 7.159L62.436 5.586Q62.436 5.559 62.461 5.533Q62.487 5.508 62.514 5.508L62.627 5.508Q62.655 5.508 62.678 5.535Q62.702 5.562 62.702 5.586Q62.702 5.931 62.834 6.195Q62.966 6.458 63.195 6.627Q63.424 6.796 63.726 6.877Q64.029 6.957 64.370 6.957Q64.637 6.957 64.873 6.829Q65.109 6.701 65.254 6.478Q65.399 6.256 65.399 5.990Q65.399 5.767 65.293 5.571Q65.187 5.374 65.006 5.239Q64.825 5.104 64.599 5.053L63.571 4.821Q63.260 4.749 63 4.563Q62.740 4.376 62.588 4.105Q62.436 3.833 62.436 3.518Q62.436 3.132 62.649 2.825Q62.863 2.517 63.210 2.346Q63.557 2.175 63.936 2.175Q64.165 2.175 64.394 2.228Q64.623 2.281 64.822 2.389Q65.020 2.496 65.174 2.660L65.468 2.220Q65.491 2.175 65.532 2.175L65.580 2.175Q65.611 2.175 65.633 2.201Q65.655 2.226 65.655 2.254L65.655 3.829Q65.655 3.850 65.632 3.877Q65.608 3.905 65.580 3.905L65.468 3.905Q65.406 3.905 65.392 3.829Q65.351 3.416 65.170 3.096Q64.989 2.777 64.678 2.602Q64.367 2.428 63.936 2.428Q63.687 2.428 63.447 2.539Q63.208 2.650 63.058 2.848Q62.907 3.047 62.907 3.310Q62.907 3.522 63.015 3.703Q63.123 3.884 63.299 4.004Q63.475 4.123 63.683 4.164L64.712 4.393Q65.030 4.465 65.297 4.670Q65.563 4.875 65.715 5.169Q65.867 5.463 65.867 5.795Q65.867 6.188 65.662 6.523Q65.457 6.858 65.112 7.047Q64.767 7.237 64.370 7.237Q63.950 7.237 63.571 7.124Q63.191 7.012 62.921 6.762L62.627 7.196Q62.600 7.237 62.562 7.237L62.514 7.237Q62.487 7.237 62.461 7.212Q62.436 7.186 62.436 7.159M66.636 5.562Q66.636 5.241 66.761 4.952Q66.886 4.663 67.112 4.440Q67.337 4.216 67.633 4.096Q67.928 3.976 68.246 3.976Q68.574 3.976 68.836 4.076Q69.097 4.175 69.273 4.357Q69.449 4.540 69.543 4.798Q69.637 5.056 69.637 5.388Q69.637 5.480 69.555 5.501L67.300 5.501L67.300 5.562Q67.300 6.150 67.583 6.533Q67.867 6.916 68.434 6.916Q68.756 6.916 69.024 6.723Q69.292 6.530 69.381 6.215Q69.388 6.174 69.463 6.160L69.555 6.160Q69.637 6.184 69.637 6.256Q69.637 6.263 69.631 6.290Q69.518 6.687 69.147 6.926Q68.776 7.165 68.352 7.165Q67.915 7.165 67.515 6.957Q67.115 6.748 66.876 6.381Q66.636 6.014 66.636 5.562M67.306 5.292L69.121 5.292Q69.121 5.015 69.024 4.763Q68.926 4.510 68.728 4.354Q68.530 4.199 68.246 4.199Q67.969 4.199 67.756 4.357Q67.542 4.516 67.424 4.771Q67.306 5.026 67.306 5.292M71.907 7.097L70.273 7.097L70.273 6.817Q70.502 6.817 70.651 6.783Q70.800 6.748 70.800 6.608L70.800 4.759Q70.800 4.489 70.692 4.428Q70.584 4.366 70.273 4.366L70.273 4.086L71.333 4.011L71.333 4.660Q71.504 4.352 71.808 4.181Q72.112 4.011 72.457 4.011Q72.963 4.011 73.247 4.234Q73.530 4.458 73.530 4.954L73.530 6.608Q73.530 6.745 73.679 6.781Q73.828 6.817 74.053 6.817L74.053 7.097L72.423 7.097L72.423 6.817Q72.652 6.817 72.801 6.783Q72.949 6.748 72.949 6.608L72.949 4.968Q72.949 4.633 72.830 4.433Q72.710 4.233 72.396 4.233Q72.126 4.233 71.892 4.369Q71.657 4.506 71.519 4.740Q71.381 4.974 71.381 5.248L71.381 6.608Q71.381 6.745 71.531 6.781Q71.681 6.817 71.907 6.817L71.907 7.097M74.641 7.090L74.641 6.027Q74.641 6.003 74.669 5.976Q74.696 5.949 74.720 5.949L74.829 5.949Q74.894 5.949 74.908 6.007Q75.004 6.441 75.250 6.692Q75.496 6.943 75.909 6.943Q76.251 6.943 76.504 6.810Q76.757 6.677 76.757 6.369Q76.757 6.212 76.663 6.097Q76.569 5.983 76.431 5.914Q76.292 5.846 76.125 5.808L75.544 5.709Q75.188 5.641 74.915 5.420Q74.641 5.200 74.641 4.858Q74.641 4.609 74.752 4.434Q74.864 4.260 75.050 4.161Q75.236 4.062 75.451 4.019Q75.667 3.976 75.909 3.976Q76.323 3.976 76.603 4.158L76.819 3.983Q76.829 3.980 76.836 3.978Q76.843 3.976 76.853 3.976L76.904 3.976Q76.931 3.976 76.955 4Q76.979 4.024 76.979 4.052L76.979 4.899Q76.979 4.920 76.955 4.947Q76.931 4.974 76.904 4.974L76.791 4.974Q76.764 4.974 76.738 4.949Q76.713 4.923 76.713 4.899Q76.713 4.663 76.607 4.499Q76.501 4.335 76.318 4.253Q76.135 4.171 75.903 4.171Q75.574 4.171 75.318 4.274Q75.062 4.376 75.062 4.653Q75.062 4.848 75.245 4.957Q75.427 5.067 75.656 5.108L76.231 5.214Q76.477 5.262 76.690 5.390Q76.904 5.518 77.041 5.721Q77.177 5.925 77.177 6.174Q77.177 6.687 76.812 6.926Q76.446 7.165 75.909 7.165Q75.414 7.165 75.082 6.871L74.816 7.145Q74.795 7.165 74.768 7.165L74.720 7.165Q74.696 7.165 74.669 7.138Q74.641 7.111 74.641 7.090M77.765 5.614Q77.765 5.272 77.900 4.973Q78.035 4.674 78.275 4.450Q78.514 4.226 78.832 4.101Q79.150 3.976 79.481 3.976Q79.926 3.976 80.325 4.192Q80.725 4.407 80.959 4.785Q81.194 5.162 81.194 5.614Q81.194 5.955 81.052 6.239Q80.910 6.523 80.666 6.730Q80.421 6.936 80.112 7.051Q79.802 7.165 79.481 7.165Q79.051 7.165 78.649 6.964Q78.247 6.762 78.006 6.410Q77.765 6.058 77.765 5.614M79.481 6.916Q80.083 6.916 80.307 6.538Q80.530 6.160 80.530 5.528Q80.530 4.916 80.296 4.557Q80.062 4.199 79.481 4.199Q78.428 4.199 78.428 5.528Q78.428 6.160 78.654 6.538Q78.880 6.916 79.481 6.916M83.538 7.097L81.802 7.097L81.802 6.817Q82.031 6.817 82.180 6.783Q82.328 6.748 82.328 6.608L82.328 4.759Q82.328 4.489 82.221 4.428Q82.113 4.366 81.802 4.366L81.802 4.086L82.831 4.011L82.831 4.718Q82.961 4.410 83.203 4.211Q83.446 4.011 83.764 4.011Q83.983 4.011 84.154 4.135Q84.324 4.260 84.324 4.472Q84.324 4.609 84.225 4.708Q84.126 4.807 83.993 4.807Q83.856 4.807 83.757 4.708Q83.658 4.609 83.658 4.472Q83.658 4.332 83.757 4.233Q83.467 4.233 83.267 4.429Q83.067 4.626 82.974 4.920Q82.882 5.214 82.882 5.494L82.882 6.608Q82.882 6.817 83.538 6.817L83.538 7.097M84.909 7.090L84.909 6.027Q84.909 6.003 84.936 5.976Q84.964 5.949 84.988 5.949L85.097 5.949Q85.162 5.949 85.176 6.007Q85.271 6.441 85.517 6.692Q85.763 6.943 86.177 6.943Q86.519 6.943 86.772 6.810Q87.025 6.677 87.025 6.369Q87.025 6.212 86.931 6.097Q86.837 5.983 86.698 5.914Q86.560 5.846 86.392 5.808L85.811 5.709Q85.456 5.641 85.182 5.420Q84.909 5.200 84.909 4.858Q84.909 4.609 85.020 4.434Q85.131 4.260 85.317 4.161Q85.504 4.062 85.719 4.019Q85.934 3.976 86.177 3.976Q86.591 3.976 86.871 4.158L87.086 3.983Q87.096 3.980 87.103 3.978Q87.110 3.976 87.120 3.976L87.172 3.976Q87.199 3.976 87.223 4Q87.247 4.024 87.247 4.052L87.247 4.899Q87.247 4.920 87.223 4.947Q87.199 4.974 87.172 4.974L87.059 4.974Q87.031 4.974 87.006 4.949Q86.980 4.923 86.980 4.899Q86.980 4.663 86.874 4.499Q86.768 4.335 86.585 4.253Q86.403 4.171 86.170 4.171Q85.842 4.171 85.586 4.274Q85.329 4.376 85.329 4.653Q85.329 4.848 85.512 4.957Q85.695 5.067 85.924 5.108L86.498 5.214Q86.744 5.262 86.958 5.390Q87.172 5.518 87.308 5.721Q87.445 5.925 87.445 6.174Q87.445 6.687 87.079 6.926Q86.714 7.165 86.177 7.165Q85.681 7.165 85.350 6.871L85.083 7.145Q85.063 7.165 85.035 7.165L84.988 7.165Q84.964 7.165 84.936 7.138Q84.909 7.111 84.909 7.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.012 76.034)\">\u003Cpath d=\"M63.851 7.097L62.261 7.097L62.261 6.817Q62.904 6.817 63.061 6.417L64.705 2.202Q64.739 2.107 64.852 2.107L64.934 2.107Q65.044 2.107 65.085 2.202L66.804 6.608Q66.872 6.748 67.062 6.783Q67.252 6.817 67.525 6.817L67.525 7.097L65.526 7.097L65.526 6.817Q66.090 6.817 66.090 6.642Q66.090 6.625 66.088 6.618Q66.086 6.612 66.083 6.608L65.662 5.542L63.704 5.542L63.362 6.417Q63.348 6.417 63.348 6.495Q63.348 6.656 63.511 6.736Q63.673 6.817 63.851 6.817L63.851 7.097M64.685 3.023L63.817 5.262L65.560 5.262L64.685 3.023M68.161 5.586Q68.161 5.258 68.296 4.957Q68.431 4.657 68.667 4.436Q68.903 4.216 69.207 4.096Q69.511 3.976 69.836 3.976Q70.342 3.976 70.690 4.079Q71.039 4.181 71.039 4.557Q71.039 4.704 70.941 4.805Q70.844 4.906 70.697 4.906Q70.543 4.906 70.444 4.807Q70.345 4.708 70.345 4.557Q70.345 4.369 70.485 4.277Q70.283 4.226 69.843 4.226Q69.487 4.226 69.258 4.422Q69.029 4.619 68.928 4.928Q68.827 5.238 68.827 5.586Q68.827 5.935 68.954 6.241Q69.080 6.547 69.335 6.731Q69.590 6.916 69.945 6.916Q70.167 6.916 70.352 6.832Q70.536 6.748 70.671 6.593Q70.806 6.437 70.864 6.229Q70.878 6.174 70.933 6.174L71.046 6.174Q71.076 6.174 71.099 6.198Q71.121 6.222 71.121 6.256L71.121 6.277Q71.035 6.564 70.847 6.762Q70.659 6.960 70.395 7.063Q70.130 7.165 69.836 7.165Q69.405 7.165 69.017 6.959Q68.629 6.752 68.395 6.389Q68.161 6.027 68.161 5.586M72.235 6.256L72.235 4.359L71.596 4.359L71.596 4.137Q71.914 4.137 72.131 3.927Q72.348 3.717 72.449 3.407Q72.550 3.098 72.550 2.790L72.816 2.790L72.816 4.079L73.893 4.079L73.893 4.359L72.816 4.359L72.816 6.243Q72.816 6.519 72.920 6.718Q73.025 6.916 73.284 6.916Q73.442 6.916 73.548 6.812Q73.654 6.707 73.703 6.554Q73.753 6.400 73.753 6.243L73.753 5.829L74.019 5.829L74.019 6.256Q74.019 6.482 73.920 6.692Q73.821 6.902 73.636 7.034Q73.452 7.165 73.223 7.165Q72.785 7.165 72.510 6.928Q72.235 6.690 72.235 6.256M75.404 6.263L75.404 4.759Q75.404 4.489 75.296 4.428Q75.188 4.366 74.877 4.366L74.877 4.086L75.985 4.011L75.985 6.243L75.985 6.263Q75.985 6.543 76.036 6.687Q76.087 6.830 76.229 6.887Q76.371 6.943 76.658 6.943Q76.911 6.943 77.116 6.803Q77.321 6.663 77.437 6.437Q77.553 6.212 77.553 5.962L77.553 4.759Q77.553 4.489 77.446 4.428Q77.338 4.366 77.027 4.366L77.027 4.086L78.135 4.011L78.135 6.424Q78.135 6.615 78.187 6.697Q78.240 6.779 78.341 6.798Q78.442 6.817 78.657 6.817L78.657 7.097L77.581 7.165L77.581 6.601Q77.471 6.783 77.326 6.906Q77.181 7.029 76.995 7.097Q76.808 7.165 76.607 7.165Q75.404 7.165 75.404 6.263M79.303 6.369Q79.303 6.037 79.527 5.810Q79.751 5.583 80.095 5.455Q80.438 5.326 80.811 5.274Q81.183 5.221 81.488 5.221L81.488 4.968Q81.488 4.763 81.380 4.583Q81.272 4.404 81.091 4.301Q80.910 4.199 80.701 4.199Q80.295 4.199 80.059 4.291Q80.148 4.328 80.194 4.412Q80.240 4.496 80.240 4.598Q80.240 4.694 80.194 4.773Q80.148 4.851 80.067 4.896Q79.987 4.940 79.898 4.940Q79.748 4.940 79.647 4.843Q79.546 4.745 79.546 4.598Q79.546 3.976 80.701 3.976Q80.913 3.976 81.163 4.040Q81.412 4.103 81.614 4.222Q81.816 4.342 81.942 4.527Q82.069 4.711 82.069 4.954L82.069 6.530Q82.069 6.646 82.130 6.742Q82.192 6.837 82.304 6.837Q82.414 6.837 82.479 6.743Q82.544 6.649 82.544 6.530L82.544 6.082L82.810 6.082L82.810 6.530Q82.810 6.800 82.583 6.965Q82.356 7.131 82.075 7.131Q81.867 7.131 81.730 6.977Q81.593 6.824 81.570 6.608Q81.423 6.875 81.141 7.020Q80.859 7.165 80.534 7.165Q80.257 7.165 79.973 7.090Q79.690 7.015 79.497 6.836Q79.303 6.656 79.303 6.369M79.919 6.369Q79.919 6.543 80.020 6.673Q80.120 6.803 80.276 6.873Q80.431 6.943 80.595 6.943Q80.814 6.943 81.023 6.846Q81.231 6.748 81.359 6.567Q81.488 6.386 81.488 6.160L81.488 5.432Q81.163 5.432 80.797 5.523Q80.431 5.614 80.175 5.826Q79.919 6.037 79.919 6.369M83.754 6.256L83.754 4.359L83.114 4.359L83.114 4.137Q83.432 4.137 83.649 3.927Q83.866 3.717 83.967 3.407Q84.068 3.098 84.068 2.790L84.335 2.790L84.335 4.079L85.411 4.079L85.411 4.359L84.335 4.359L84.335 6.243Q84.335 6.519 84.439 6.718Q84.543 6.916 84.803 6.916Q84.960 6.916 85.066 6.812Q85.172 6.707 85.222 6.554Q85.271 6.400 85.271 6.243L85.271 5.829L85.538 5.829L85.538 6.256Q85.538 6.482 85.439 6.692Q85.340 6.902 85.155 7.034Q84.970 7.165 84.741 7.165Q84.304 7.165 84.029 6.928Q83.754 6.690 83.754 6.256M86.307 5.614Q86.307 5.272 86.442 4.973Q86.577 4.674 86.816 4.450Q87.055 4.226 87.373 4.101Q87.691 3.976 88.023 3.976Q88.467 3.976 88.867 4.192Q89.267 4.407 89.501 4.785Q89.735 5.162 89.735 5.614Q89.735 5.955 89.593 6.239Q89.451 6.523 89.207 6.730Q88.963 6.936 88.653 7.051Q88.344 7.165 88.023 7.165Q87.592 7.165 87.190 6.964Q86.789 6.762 86.548 6.410Q86.307 6.058 86.307 5.614M88.023 6.916Q88.624 6.916 88.848 6.538Q89.072 6.160 89.072 5.528Q89.072 4.916 88.838 4.557Q88.604 4.199 88.023 4.199Q86.970 4.199 86.970 5.528Q86.970 6.160 87.196 6.538Q87.421 6.916 88.023 6.916M92.080 7.097L90.343 7.097L90.343 6.817Q90.572 6.817 90.721 6.783Q90.870 6.748 90.870 6.608L90.870 4.759Q90.870 4.489 90.762 4.428Q90.655 4.366 90.343 4.366L90.343 4.086L91.372 4.011L91.372 4.718Q91.502 4.410 91.745 4.211Q91.988 4.011 92.305 4.011Q92.524 4.011 92.695 4.135Q92.866 4.260 92.866 4.472Q92.866 4.609 92.767 4.708Q92.668 4.807 92.534 4.807Q92.398 4.807 92.299 4.708Q92.199 4.609 92.199 4.472Q92.199 4.332 92.299 4.233Q92.008 4.233 91.808 4.429Q91.608 4.626 91.516 4.920Q91.424 5.214 91.424 5.494L91.424 6.608Q91.424 6.817 92.080 6.817L92.080 7.097M93.450 7.090L93.450 6.027Q93.450 6.003 93.478 5.976Q93.505 5.949 93.529 5.949L93.638 5.949Q93.703 5.949 93.717 6.007Q93.813 6.441 94.059 6.692Q94.305 6.943 94.718 6.943Q95.060 6.943 95.313 6.810Q95.566 6.677 95.566 6.369Q95.566 6.212 95.472 6.097Q95.378 5.983 95.240 5.914Q95.101 5.846 94.934 5.808L94.353 5.709Q93.997 5.641 93.724 5.420Q93.450 5.200 93.450 4.858Q93.450 4.609 93.562 4.434Q93.673 4.260 93.859 4.161Q94.045 4.062 94.260 4.019Q94.476 3.976 94.718 3.976Q95.132 3.976 95.412 4.158L95.628 3.983Q95.638 3.980 95.645 3.978Q95.652 3.976 95.662 3.976L95.713 3.976Q95.740 3.976 95.764 4Q95.788 4.024 95.788 4.052L95.788 4.899Q95.788 4.920 95.764 4.947Q95.740 4.974 95.713 4.974L95.600 4.974Q95.573 4.974 95.547 4.949Q95.522 4.923 95.522 4.899Q95.522 4.663 95.416 4.499Q95.310 4.335 95.127 4.253Q94.944 4.171 94.712 4.171Q94.384 4.171 94.127 4.274Q93.871 4.376 93.871 4.653Q93.871 4.848 94.054 4.957Q94.237 5.067 94.466 5.108L95.040 5.214Q95.286 5.262 95.499 5.390Q95.713 5.518 95.850 5.721Q95.987 5.925 95.987 6.174Q95.987 6.687 95.621 6.926Q95.255 7.165 94.718 7.165Q94.223 7.165 93.891 6.871L93.625 7.145Q93.604 7.165 93.577 7.165L93.529 7.165Q93.505 7.165 93.478 7.138Q93.450 7.111 93.450 7.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M67.637-12.82h68.287v-28.453H67.637Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M63.771-2.434L62.701-5.290Q62.635-5.469 62.504-5.512Q62.373-5.555 62.115-5.555L62.115-5.852L63.795-5.852L63.795-5.555Q63.345-5.555 63.345-5.356Q63.349-5.341 63.351-5.323Q63.353-5.305 63.353-5.290L64.146-3.196L64.857-5.106Q64.822-5.200 64.822-5.245Q64.822-5.290 64.787-5.290Q64.720-5.469 64.590-5.512Q64.459-5.555 64.205-5.555L64.205-5.852L65.795-5.852L65.795-5.555Q65.345-5.555 65.345-5.356Q65.349-5.337 65.351-5.319Q65.353-5.301 65.353-5.290L66.185-3.075L66.939-5.075Q66.963-5.133 66.963-5.204Q66.963-5.364 66.826-5.460Q66.689-5.555 66.521-5.555L66.521-5.852L67.908-5.852L67.908-5.555Q67.674-5.555 67.496-5.428Q67.318-5.301 67.236-5.075L66.252-2.434Q66.197-2.325 66.084-2.325L66.025-2.325Q65.912-2.325 65.869-2.434L65.010-4.708L64.154-2.434Q64.115-2.325 63.994-2.325L63.939-2.325Q63.826-2.325 63.771-2.434M70.252-2.403L68.396-2.403L68.396-2.700Q68.670-2.700 68.838-2.747Q69.006-2.794 69.006-2.962L69.006-7.122Q69.006-7.337 68.943-7.432Q68.881-7.528 68.761-7.549Q68.642-7.571 68.396-7.571L68.396-7.868L69.619-7.954L69.619-5.251Q69.744-5.462 69.931-5.612Q70.119-5.762 70.345-5.846Q70.572-5.930 70.818-5.930Q71.986-5.930 71.986-4.852L71.986-2.962Q71.986-2.794 72.156-2.747Q72.326-2.700 72.595-2.700L72.595-2.403L70.740-2.403L70.740-2.700Q71.013-2.700 71.181-2.747Q71.349-2.794 71.349-2.962L71.349-4.837Q71.349-5.219 71.228-5.448Q71.107-5.676 70.756-5.676Q70.443-5.676 70.189-5.514Q69.935-5.352 69.789-5.083Q69.642-4.813 69.642-4.516L69.642-2.962Q69.642-2.794 69.812-2.747Q69.982-2.700 70.252-2.700L70.252-2.403M73.138-3.235Q73.138-3.719 73.541-4.014Q73.943-4.309 74.494-4.428Q75.045-4.548 75.537-4.548L75.537-4.837Q75.537-5.063 75.422-5.270Q75.306-5.477 75.109-5.596Q74.912-5.716 74.681-5.716Q74.256-5.716 73.970-5.610Q74.041-5.583 74.088-5.528Q74.135-5.473 74.160-5.403Q74.185-5.333 74.185-5.258Q74.185-5.153 74.135-5.061Q74.084-4.969 73.992-4.919Q73.900-4.868 73.795-4.868Q73.689-4.868 73.597-4.919Q73.506-4.969 73.455-5.061Q73.404-5.153 73.404-5.258Q73.404-5.676 73.793-5.823Q74.181-5.969 74.681-5.969Q75.013-5.969 75.367-5.839Q75.720-5.708 75.949-5.454Q76.177-5.200 76.177-4.852L76.177-3.051Q76.177-2.919 76.250-2.809Q76.322-2.700 76.451-2.700Q76.576-2.700 76.644-2.805Q76.713-2.911 76.713-3.051L76.713-3.563L76.994-3.563L76.994-3.051Q76.994-2.848 76.877-2.690Q76.760-2.532 76.578-2.448Q76.396-2.364 76.193-2.364Q75.963-2.364 75.810-2.536Q75.658-2.708 75.627-2.938Q75.467-2.657 75.158-2.491Q74.849-2.325 74.498-2.325Q73.986-2.325 73.562-2.548Q73.138-2.770 73.138-3.235M73.826-3.235Q73.826-2.950 74.052-2.764Q74.279-2.579 74.572-2.579Q74.818-2.579 75.043-2.696Q75.267-2.813 75.402-3.016Q75.537-3.219 75.537-3.473L75.537-4.305Q75.271-4.305 74.986-4.251Q74.701-4.196 74.429-4.067Q74.158-3.938 73.992-3.731Q73.826-3.524 73.826-3.235M77.912-3.364L77.912-5.555L77.209-5.555L77.209-5.809Q77.564-5.809 77.806-6.042Q78.049-6.274 78.160-6.622Q78.271-6.969 78.271-7.325L78.552-7.325L78.552-5.852L79.728-5.852L79.728-5.555L78.552-5.555L78.552-3.380Q78.552-3.059 78.672-2.831Q78.791-2.602 79.072-2.602Q79.252-2.602 79.369-2.725Q79.486-2.848 79.539-3.028Q79.592-3.208 79.592-3.380L79.592-3.852L79.873-3.852L79.873-3.364Q79.873-3.110 79.767-2.870Q79.662-2.630 79.465-2.477Q79.267-2.325 79.010-2.325Q78.693-2.325 78.441-2.448Q78.189-2.571 78.051-2.805Q77.912-3.040 77.912-3.364\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M84.060-3.364L84.060-5.555L83.357-5.555L83.357-5.809Q83.713-5.809 83.955-6.042Q84.197-6.274 84.308-6.622Q84.420-6.969 84.420-7.325L84.701-7.325L84.701-5.852L85.877-5.852L85.877-5.555L84.701-5.555L84.701-3.380Q84.701-3.059 84.820-2.831Q84.939-2.602 85.220-2.602Q85.400-2.602 85.517-2.725Q85.635-2.848 85.687-3.028Q85.740-3.208 85.740-3.380L85.740-3.852L86.021-3.852L86.021-3.364Q86.021-3.110 85.916-2.870Q85.810-2.630 85.613-2.477Q85.416-2.325 85.158-2.325Q84.842-2.325 84.590-2.448Q84.338-2.571 84.199-2.805Q84.060-3.040 84.060-3.364M88.670-2.403L86.814-2.403L86.814-2.700Q87.088-2.700 87.256-2.747Q87.424-2.794 87.424-2.962L87.424-7.122Q87.424-7.337 87.361-7.432Q87.299-7.528 87.179-7.549Q87.060-7.571 86.814-7.571L86.814-7.868L88.037-7.954L88.037-5.251Q88.162-5.462 88.349-5.612Q88.537-5.762 88.763-5.846Q88.990-5.930 89.236-5.930Q90.404-5.930 90.404-4.852L90.404-2.962Q90.404-2.794 90.574-2.747Q90.744-2.700 91.013-2.700L91.013-2.403L89.158-2.403L89.158-2.700Q89.431-2.700 89.599-2.747Q89.767-2.794 89.767-2.962L89.767-4.837Q89.767-5.219 89.646-5.448Q89.525-5.676 89.174-5.676Q88.861-5.676 88.607-5.514Q88.353-5.352 88.207-5.083Q88.060-4.813 88.060-4.516L88.060-2.962Q88.060-2.794 88.230-2.747Q88.400-2.700 88.670-2.700L88.670-2.403M91.459-4.157Q91.459-4.637 91.691-5.053Q91.924-5.469 92.334-5.719Q92.744-5.969 93.220-5.969Q93.951-5.969 94.349-5.528Q94.748-5.087 94.748-4.356Q94.748-4.251 94.654-4.227L92.205-4.227L92.205-4.157Q92.205-3.747 92.326-3.391Q92.447-3.036 92.718-2.819Q92.990-2.602 93.420-2.602Q93.783-2.602 94.080-2.831Q94.377-3.059 94.478-3.411Q94.486-3.458 94.572-3.473L94.654-3.473Q94.748-3.446 94.748-3.364Q94.748-3.356 94.740-3.325Q94.677-3.098 94.539-2.915Q94.400-2.731 94.209-2.598Q94.017-2.465 93.799-2.395Q93.580-2.325 93.342-2.325Q92.970-2.325 92.633-2.462Q92.295-2.598 92.027-2.850Q91.760-3.102 91.609-3.442Q91.459-3.782 91.459-4.157M92.213-4.466L94.174-4.466Q94.174-4.770 94.072-5.061Q93.970-5.352 93.754-5.534Q93.537-5.716 93.220-5.716Q92.920-5.716 92.689-5.528Q92.459-5.341 92.336-5.049Q92.213-4.758 92.213-4.466\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M99.660-2.434L98.590-5.290Q98.523-5.469 98.393-5.512Q98.262-5.555 98.004-5.555L98.004-5.852L99.684-5.852L99.684-5.555Q99.234-5.555 99.234-5.356Q99.238-5.341 99.240-5.323Q99.242-5.305 99.242-5.290L100.035-3.196L100.746-5.106Q100.711-5.200 100.711-5.245Q100.711-5.290 100.676-5.290Q100.609-5.469 100.479-5.512Q100.348-5.555 100.094-5.555L100.094-5.852L101.684-5.852L101.684-5.555Q101.234-5.555 101.234-5.356Q101.238-5.337 101.240-5.319Q101.242-5.301 101.242-5.290L102.074-3.075L102.828-5.075Q102.852-5.133 102.852-5.204Q102.852-5.364 102.715-5.460Q102.578-5.555 102.410-5.555L102.410-5.852L103.797-5.852L103.797-5.555Q103.563-5.555 103.385-5.428Q103.207-5.301 103.125-5.075L102.141-2.434Q102.086-2.325 101.973-2.325L101.914-2.325Q101.801-2.325 101.758-2.434L100.898-4.708L100.043-2.434Q100.004-2.325 99.883-2.325L99.828-2.325Q99.715-2.325 99.660-2.434\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M103.977-4.098Q103.977-4.602 104.233-5.034Q104.489-5.466 104.925-5.717Q105.360-5.969 105.860-5.969Q106.247-5.969 106.589-5.825Q106.930-5.680 107.192-5.419Q107.454-5.157 107.596-4.821Q107.739-4.485 107.739-4.098Q107.739-3.606 107.475-3.196Q107.212-2.786 106.782-2.555Q106.352-2.325 105.860-2.325Q105.368-2.325 104.934-2.557Q104.501-2.790 104.239-3.198Q103.977-3.606 103.977-4.098M105.860-2.602Q106.317-2.602 106.569-2.825Q106.821-3.048 106.909-3.399Q106.997-3.751 106.997-4.196Q106.997-4.626 106.903-4.964Q106.809-5.301 106.555-5.508Q106.302-5.716 105.860-5.716Q105.212-5.716 104.968-5.299Q104.723-4.883 104.723-4.196Q104.723-3.751 104.811-3.399Q104.899-3.048 105.151-2.825Q105.403-2.602 105.860-2.602M110.231-2.403L108.251-2.403L108.251-2.700Q108.520-2.700 108.688-2.745Q108.856-2.790 108.856-2.962L108.856-5.098Q108.856-5.313 108.794-5.409Q108.731-5.505 108.614-5.526Q108.497-5.548 108.251-5.548L108.251-5.844L109.419-5.930L109.419-5.145Q109.497-5.356 109.649-5.542Q109.802-5.727 110.001-5.829Q110.200-5.930 110.427-5.930Q110.673-5.930 110.864-5.786Q111.055-5.641 111.055-5.411Q111.055-5.255 110.950-5.145Q110.844-5.036 110.688-5.036Q110.532-5.036 110.423-5.145Q110.313-5.255 110.313-5.411Q110.313-5.571 110.419-5.676Q110.094-5.676 109.880-5.448Q109.665-5.219 109.569-4.880Q109.473-4.540 109.473-4.235L109.473-2.962Q109.473-2.794 109.700-2.747Q109.927-2.700 110.231-2.700L110.231-2.403M113.450-2.403L111.618-2.403L111.618-2.700Q111.891-2.700 112.059-2.747Q112.227-2.794 112.227-2.962L112.227-7.122Q112.227-7.337 112.165-7.432Q112.102-7.528 111.983-7.549Q111.864-7.571 111.618-7.571L111.618-7.868L112.841-7.954L112.841-2.962Q112.841-2.794 113.009-2.747Q113.177-2.700 113.450-2.700L113.450-2.403M115.712-2.325Q115.231-2.325 114.823-2.569Q114.415-2.813 114.177-3.227Q113.938-3.641 113.938-4.130Q113.938-4.622 114.196-5.038Q114.454-5.454 114.885-5.692Q115.317-5.930 115.809-5.930Q116.430-5.930 116.880-5.493L116.880-7.122Q116.880-7.337 116.817-7.432Q116.755-7.528 116.637-7.549Q116.520-7.571 116.274-7.571L116.274-7.868L117.497-7.954L117.497-3.145Q117.497-2.934 117.559-2.839Q117.622-2.743 117.739-2.721Q117.856-2.700 118.106-2.700L118.106-2.403L116.856-2.325L116.856-2.809Q116.391-2.325 115.712-2.325M115.778-2.579Q116.118-2.579 116.411-2.770Q116.704-2.962 116.856-3.258L116.856-5.091Q116.708-5.364 116.446-5.520Q116.184-5.676 115.872-5.676Q115.247-5.676 114.964-5.229Q114.680-4.782 114.680-4.122Q114.680-3.477 114.932-3.028Q115.184-2.579 115.778-2.579\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M72.761 7.097L70.983 7.097L70.983 6.800Q71.257 6.800 71.425 6.753Q71.593 6.706 71.593 6.538L71.593 4.402Q71.593 4.187 71.536 4.091Q71.479 3.995 71.366 3.974Q71.253 3.952 71.007 3.952L71.007 3.656L72.206 3.570L72.206 6.538Q72.206 6.706 72.352 6.753Q72.499 6.800 72.761 6.800L72.761 7.097M71.319 2.175Q71.319 1.984 71.454 1.853Q71.589 1.722 71.784 1.722Q71.905 1.722 72.009 1.785Q72.112 1.847 72.175 1.951Q72.237 2.054 72.237 2.175Q72.237 2.370 72.106 2.505Q71.975 2.640 71.784 2.640Q71.585 2.640 71.452 2.507Q71.319 2.374 71.319 2.175M73.304 7.089L73.304 5.867Q73.304 5.839 73.335 5.808Q73.366 5.777 73.390 5.777L73.495 5.777Q73.565 5.777 73.581 5.839Q73.643 6.160 73.782 6.400Q73.921 6.640 74.153 6.781Q74.386 6.921 74.694 6.921Q74.933 6.921 75.142 6.861Q75.350 6.800 75.487 6.652Q75.624 6.503 75.624 6.257Q75.624 6.003 75.413 5.837Q75.202 5.671 74.933 5.617L74.311 5.503Q73.905 5.425 73.604 5.169Q73.304 4.913 73.304 4.538Q73.304 4.171 73.505 3.949Q73.706 3.726 74.030 3.628Q74.354 3.531 74.694 3.531Q75.159 3.531 75.456 3.738L75.679 3.554Q75.702 3.531 75.733 3.531L75.784 3.531Q75.815 3.531 75.843 3.558Q75.870 3.585 75.870 3.617L75.870 4.601Q75.870 4.632 75.845 4.661Q75.819 4.691 75.784 4.691L75.679 4.691Q75.643 4.691 75.616 4.663Q75.589 4.636 75.589 4.601Q75.589 4.202 75.337 3.982Q75.085 3.761 74.686 3.761Q74.331 3.761 74.048 3.884Q73.765 4.007 73.765 4.312Q73.765 4.531 73.966 4.663Q74.167 4.796 74.413 4.839L75.038 4.952Q75.468 5.042 75.776 5.339Q76.085 5.636 76.085 6.050Q76.085 6.620 75.686 6.898Q75.288 7.175 74.694 7.175Q74.143 7.175 73.792 6.839L73.495 7.152Q73.472 7.175 73.436 7.175L73.390 7.175Q73.366 7.175 73.335 7.144Q73.304 7.113 73.304 7.089\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M81.362 7.097L79.530 7.097L79.530 6.800Q79.804 6.800 79.972 6.753Q80.140 6.706 80.140 6.538L80.140 2.378Q80.140 2.163 80.077 2.068Q80.015 1.972 79.896 1.951Q79.776 1.929 79.530 1.929L79.530 1.632L80.753 1.546L80.753 6.538Q80.753 6.706 80.921 6.753Q81.089 6.800 81.362 6.800L81.362 7.097M83.667 7.097L81.890 7.097L81.890 6.800Q82.163 6.800 82.331 6.753Q82.499 6.706 82.499 6.538L82.499 4.402Q82.499 4.187 82.442 4.091Q82.386 3.995 82.272 3.974Q82.159 3.952 81.913 3.952L81.913 3.656L83.112 3.570L83.112 6.538Q83.112 6.706 83.259 6.753Q83.405 6.800 83.667 6.800L83.667 7.097M82.226 2.175Q82.226 1.984 82.360 1.853Q82.495 1.722 82.690 1.722Q82.812 1.722 82.915 1.785Q83.019 1.847 83.081 1.951Q83.144 2.054 83.144 2.175Q83.144 2.370 83.013 2.505Q82.882 2.640 82.690 2.640Q82.491 2.640 82.358 2.507Q82.226 2.374 82.226 2.175M85.991 7.097L84.194 7.097L84.194 6.800Q84.464 6.800 84.632 6.755Q84.800 6.710 84.800 6.538L84.800 2.378Q84.800 2.163 84.737 2.068Q84.675 1.972 84.558 1.951Q84.440 1.929 84.194 1.929L84.194 1.632L85.417 1.546L85.417 5.312L86.515 4.425Q86.722 4.245 86.722 4.097Q86.722 4.031 86.669 3.988Q86.616 3.945 86.546 3.945L86.546 3.648L88.081 3.648L88.081 3.945Q87.550 3.945 86.952 4.425L86.343 4.921L87.417 6.320Q87.554 6.495 87.661 6.603Q87.769 6.710 87.903 6.755Q88.038 6.800 88.265 6.800L88.265 7.097L86.640 7.097L86.640 6.800Q86.882 6.800 86.882 6.648Q86.882 6.570 86.839 6.499Q86.796 6.429 86.714 6.320L85.913 5.273L85.386 5.699L85.386 6.538Q85.386 6.706 85.554 6.753Q85.722 6.800 85.991 6.800\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M88.421 5.343Q88.421 4.863 88.654 4.447Q88.886 4.031 89.296 3.781Q89.706 3.531 90.183 3.531Q90.913 3.531 91.312 3.972Q91.710 4.413 91.710 5.144Q91.710 5.249 91.617 5.273L89.167 5.273L89.167 5.343Q89.167 5.753 89.288 6.109Q89.410 6.464 89.681 6.681Q89.953 6.898 90.382 6.898Q90.746 6.898 91.042 6.669Q91.339 6.441 91.441 6.089Q91.449 6.042 91.535 6.027L91.617 6.027Q91.710 6.054 91.710 6.136Q91.710 6.144 91.703 6.175Q91.640 6.402 91.501 6.585Q91.363 6.769 91.171 6.902Q90.980 7.035 90.761 7.105Q90.542 7.175 90.304 7.175Q89.933 7.175 89.595 7.038Q89.257 6.902 88.990 6.650Q88.722 6.398 88.572 6.058Q88.421 5.718 88.421 5.343M89.175 5.035L91.136 5.035Q91.136 4.730 91.035 4.439Q90.933 4.148 90.716 3.966Q90.499 3.785 90.183 3.785Q89.882 3.785 89.652 3.972Q89.421 4.160 89.298 4.451Q89.175 4.742 89.175 5.035\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M96.962 7.097L95.106 7.097L95.106 6.800Q95.380 6.800 95.548 6.753Q95.716 6.706 95.716 6.538L95.716 4.402Q95.716 4.187 95.653 4.091Q95.591 3.995 95.472 3.974Q95.353 3.952 95.106 3.952L95.106 3.656L96.298 3.570L96.298 4.304Q96.411 4.089 96.605 3.921Q96.798 3.753 97.036 3.661Q97.274 3.570 97.528 3.570Q98.696 3.570 98.696 4.648L98.696 6.538Q98.696 6.706 98.866 6.753Q99.036 6.800 99.306 6.800L99.306 7.097L97.450 7.097L97.450 6.800Q97.724 6.800 97.892 6.753Q98.060 6.706 98.060 6.538L98.060 4.663Q98.060 4.281 97.939 4.052Q97.817 3.824 97.466 3.824Q97.153 3.824 96.899 3.986Q96.646 4.148 96.499 4.417Q96.353 4.687 96.353 4.984L96.353 6.538Q96.353 6.706 96.523 6.753Q96.692 6.800 96.962 6.800L96.962 7.097M99.751 5.402Q99.751 4.898 100.007 4.466Q100.263 4.035 100.698 3.783Q101.134 3.531 101.634 3.531Q102.021 3.531 102.362 3.675Q102.704 3.820 102.966 4.081Q103.228 4.343 103.370 4.679Q103.513 5.015 103.513 5.402Q103.513 5.894 103.249 6.304Q102.985 6.714 102.556 6.945Q102.126 7.175 101.634 7.175Q101.142 7.175 100.708 6.943Q100.274 6.710 100.013 6.302Q99.751 5.894 99.751 5.402M101.634 6.898Q102.091 6.898 102.343 6.675Q102.595 6.452 102.683 6.101Q102.771 5.749 102.771 5.304Q102.771 4.874 102.677 4.536Q102.583 4.199 102.329 3.992Q102.075 3.785 101.634 3.785Q100.985 3.785 100.741 4.201Q100.497 4.617 100.497 5.304Q100.497 5.749 100.585 6.101Q100.673 6.452 100.925 6.675Q101.177 6.898 101.634 6.898\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(11.615 -26.615)\">\u003Cpath d=\"M105.354 7.066L104.284 4.210Q104.218 4.031 104.087 3.988Q103.956 3.945 103.698 3.945L103.698 3.648L105.378 3.648L105.378 3.945Q104.928 3.945 104.928 4.144Q104.932 4.160 104.934 4.177Q104.936 4.195 104.936 4.210L105.729 6.304L106.440 4.394Q106.405 4.300 106.405 4.255Q106.405 4.210 106.370 4.210Q106.303 4.031 106.173 3.988Q106.042 3.945 105.788 3.945L105.788 3.648L107.378 3.648L107.378 3.945Q106.928 3.945 106.928 4.144Q106.932 4.163 106.934 4.181Q106.936 4.199 106.936 4.210L107.768 6.425L108.522 4.425Q108.546 4.367 108.546 4.296Q108.546 4.136 108.409 4.040Q108.272 3.945 108.104 3.945L108.104 3.648L109.491 3.648L109.491 3.945Q109.257 3.945 109.079 4.072Q108.901 4.199 108.819 4.425L107.835 7.066Q107.780 7.175 107.667 7.175L107.608 7.175Q107.495 7.175 107.452 7.066L106.593 4.792L105.737 7.066Q105.698 7.175 105.577 7.175L105.522 7.175Q105.409 7.175 105.354 7.066\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M52.724-12.82c0-6.286-26.443-11.381-59.064-11.381s-59.063 5.095-59.063 11.381S-38.96-1.439-6.34-1.439s59.064-5.095 59.064-11.38Zm-59.064 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M63.943 7.097L62.309 7.097L62.309 6.817Q62.538 6.817 62.687 6.783Q62.836 6.748 62.836 6.608L62.836 2.989Q62.836 2.719 62.728 2.657Q62.620 2.596 62.309 2.596L62.309 2.315L63.389 2.240L63.389 4.626Q63.495 4.441 63.673 4.299Q63.851 4.158 64.059 4.084Q64.268 4.011 64.493 4.011Q64.999 4.011 65.283 4.234Q65.567 4.458 65.567 4.954L65.567 6.608Q65.567 6.745 65.715 6.781Q65.864 6.817 66.090 6.817L66.090 7.097L64.459 7.097L64.459 6.817Q64.688 6.817 64.837 6.783Q64.986 6.748 64.986 6.608L64.986 4.968Q64.986 4.633 64.866 4.433Q64.746 4.233 64.432 4.233Q64.162 4.233 63.928 4.369Q63.694 4.506 63.555 4.740Q63.417 4.974 63.417 5.248L63.417 6.608Q63.417 6.745 63.567 6.781Q63.718 6.817 63.943 6.817L63.943 7.097M66.636 5.614Q66.636 5.272 66.771 4.973Q66.906 4.674 67.146 4.450Q67.385 4.226 67.703 4.101Q68.021 3.976 68.352 3.976Q68.797 3.976 69.197 4.192Q69.596 4.407 69.831 4.785Q70.065 5.162 70.065 5.614Q70.065 5.955 69.923 6.239Q69.781 6.523 69.537 6.730Q69.292 6.936 68.983 7.051Q68.674 7.165 68.352 7.165Q67.922 7.165 67.520 6.964Q67.118 6.762 66.877 6.410Q66.636 6.058 66.636 5.614M68.352 6.916Q68.954 6.916 69.178 6.538Q69.402 6.160 69.402 5.528Q69.402 4.916 69.167 4.557Q68.933 4.199 68.352 4.199Q67.300 4.199 67.300 5.528Q67.300 6.160 67.525 6.538Q67.751 6.916 68.352 6.916\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M71.836 7.070L70.855 4.571Q70.794 4.428 70.676 4.393Q70.558 4.359 70.342 4.359L70.342 4.079L71.822 4.079L71.822 4.359Q71.443 4.359 71.443 4.520Q71.443 4.530 71.457 4.571L72.171 6.403L72.844 4.698Q72.814 4.626 72.814 4.598Q72.814 4.571 72.786 4.571Q72.725 4.424 72.607 4.392Q72.489 4.359 72.277 4.359L72.277 4.079L73.675 4.079L73.675 4.359Q73.299 4.359 73.299 4.520Q73.299 4.551 73.306 4.571L74.061 6.509L74.748 4.759Q74.769 4.708 74.769 4.653Q74.769 4.513 74.656 4.436Q74.543 4.359 74.403 4.359L74.403 4.079L75.623 4.079L75.623 4.359Q75.418 4.359 75.263 4.465Q75.107 4.571 75.035 4.759L74.130 7.070Q74.095 7.165 73.983 7.165L73.914 7.165Q73.805 7.165 73.767 7.070L72.985 5.067L72.198 7.070Q72.164 7.165 72.051 7.165L71.983 7.165Q71.874 7.165 71.836 7.070\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M79.378 6.256L79.378 4.359L78.739 4.359L78.739 4.137Q79.057 4.137 79.274 3.927Q79.491 3.717 79.591 3.407Q79.692 3.098 79.692 2.790L79.959 2.790L79.959 4.079L81.036 4.079L81.036 4.359L79.959 4.359L79.959 6.243Q79.959 6.519 80.063 6.718Q80.167 6.916 80.427 6.916Q80.584 6.916 80.690 6.812Q80.796 6.707 80.846 6.554Q80.895 6.400 80.895 6.243L80.895 5.829L81.162 5.829L81.162 6.256Q81.162 6.482 81.063 6.692Q80.964 6.902 80.779 7.034Q80.595 7.165 80.366 7.165Q79.928 7.165 79.653 6.928Q79.378 6.690 79.378 6.256M83.654 7.097L82.020 7.097L82.020 6.817Q82.249 6.817 82.398 6.783Q82.546 6.748 82.546 6.608L82.546 2.989Q82.546 2.719 82.439 2.657Q82.331 2.596 82.020 2.596L82.020 2.315L83.100 2.240L83.100 4.626Q83.206 4.441 83.384 4.299Q83.561 4.158 83.770 4.084Q83.978 4.011 84.204 4.011Q84.710 4.011 84.994 4.234Q85.277 4.458 85.277 4.954L85.277 6.608Q85.277 6.745 85.426 6.781Q85.575 6.817 85.800 6.817L85.800 7.097L84.170 7.097L84.170 6.817Q84.399 6.817 84.547 6.783Q84.696 6.748 84.696 6.608L84.696 4.968Q84.696 4.633 84.577 4.433Q84.457 4.233 84.142 4.233Q83.872 4.233 83.638 4.369Q83.404 4.506 83.266 4.740Q83.127 4.974 83.127 5.248L83.127 6.608Q83.127 6.745 83.278 6.781Q83.428 6.817 83.654 6.817L83.654 7.097M86.347 5.562Q86.347 5.241 86.472 4.952Q86.597 4.663 86.822 4.440Q87.048 4.216 87.343 4.096Q87.639 3.976 87.957 3.976Q88.285 3.976 88.547 4.076Q88.808 4.175 88.984 4.357Q89.160 4.540 89.254 4.798Q89.348 5.056 89.348 5.388Q89.348 5.480 89.266 5.501L87.010 5.501L87.010 5.562Q87.010 6.150 87.294 6.533Q87.578 6.916 88.145 6.916Q88.466 6.916 88.735 6.723Q89.003 6.530 89.092 6.215Q89.099 6.174 89.174 6.160L89.266 6.160Q89.348 6.184 89.348 6.256Q89.348 6.263 89.341 6.290Q89.228 6.687 88.858 6.926Q88.487 7.165 88.063 7.165Q87.625 7.165 87.225 6.957Q86.826 6.748 86.586 6.381Q86.347 6.014 86.347 5.562M87.017 5.292L88.832 5.292Q88.832 5.015 88.735 4.763Q88.637 4.510 88.439 4.354Q88.241 4.199 87.957 4.199Q87.680 4.199 87.466 4.357Q87.253 4.516 87.135 4.771Q87.017 5.026 87.017 5.292\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M94.031 7.070L93.050 4.571Q92.989 4.428 92.871 4.393Q92.753 4.359 92.537 4.359L92.537 4.079L94.017 4.079L94.017 4.359Q93.638 4.359 93.638 4.520Q93.638 4.530 93.652 4.571L94.366 6.403L95.039 4.698Q95.009 4.626 95.009 4.598Q95.009 4.571 94.981 4.571Q94.920 4.424 94.802 4.392Q94.684 4.359 94.472 4.359L94.472 4.079L95.870 4.079L95.870 4.359Q95.494 4.359 95.494 4.520Q95.494 4.551 95.501 4.571L96.256 6.509L96.943 4.759Q96.964 4.708 96.964 4.653Q96.964 4.513 96.851 4.436Q96.738 4.359 96.598 4.359L96.598 4.079L97.818 4.079L97.818 4.359Q97.613 4.359 97.458 4.465Q97.302 4.571 97.230 4.759L96.325 7.070Q96.290 7.165 96.178 7.165L96.109 7.165Q96 7.165 95.962 7.070L95.180 5.067L94.393 7.070Q94.359 7.165 94.246 7.165L94.178 7.165Q94.069 7.165 94.031 7.070\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M98.095 5.614Q98.095 5.272 98.230 4.973Q98.365 4.674 98.605 4.450Q98.844 4.226 99.162 4.101Q99.480 3.976 99.811 3.976Q100.256 3.976 100.655 4.192Q101.055 4.407 101.290 4.785Q101.524 5.162 101.524 5.614Q101.524 5.955 101.382 6.239Q101.240 6.523 100.996 6.730Q100.751 6.936 100.442 7.051Q100.133 7.165 99.811 7.165Q99.381 7.165 98.979 6.964Q98.577 6.762 98.336 6.410Q98.095 6.058 98.095 5.614M99.811 6.916Q100.413 6.916 100.637 6.538Q100.861 6.160 100.861 5.528Q100.861 4.916 100.626 4.557Q100.392 4.199 99.811 4.199Q98.759 4.199 98.759 5.528Q98.759 6.160 98.984 6.538Q99.210 6.916 99.811 6.916M103.868 7.097L102.132 7.097L102.132 6.817Q102.361 6.817 102.510 6.783Q102.658 6.748 102.658 6.608L102.658 4.759Q102.658 4.489 102.551 4.428Q102.443 4.366 102.132 4.366L102.132 4.086L103.161 4.011L103.161 4.718Q103.291 4.410 103.533 4.211Q103.776 4.011 104.094 4.011Q104.313 4.011 104.484 4.135Q104.655 4.260 104.655 4.472Q104.655 4.609 104.555 4.708Q104.456 4.807 104.323 4.807Q104.186 4.807 104.087 4.708Q103.988 4.609 103.988 4.472Q103.988 4.332 104.087 4.233Q103.797 4.233 103.597 4.429Q103.397 4.626 103.304 4.920Q103.212 5.214 103.212 5.494L103.212 6.608Q103.212 6.817 103.868 6.817L103.868 7.097M106.907 7.097L105.304 7.097L105.304 6.817Q105.530 6.817 105.678 6.783Q105.827 6.748 105.827 6.608L105.827 2.989Q105.827 2.719 105.719 2.657Q105.612 2.596 105.304 2.596L105.304 2.315L106.381 2.240L106.381 6.608Q106.381 6.745 106.531 6.781Q106.681 6.817 106.907 6.817L106.907 7.097M107.502 5.586Q107.502 5.248 107.642 4.957Q107.782 4.667 108.026 4.453Q108.271 4.240 108.575 4.125Q108.879 4.011 109.204 4.011Q109.474 4.011 109.737 4.110Q110 4.209 110.192 4.387L110.192 2.989Q110.192 2.719 110.084 2.657Q109.976 2.596 109.665 2.596L109.665 2.315L110.742 2.240L110.742 6.424Q110.742 6.612 110.797 6.695Q110.851 6.779 110.952 6.798Q111.053 6.817 111.268 6.817L111.268 7.097L110.161 7.165L110.161 6.748Q109.744 7.165 109.118 7.165Q108.688 7.165 108.315 6.953Q107.943 6.742 107.722 6.381Q107.502 6.020 107.502 5.586M109.176 6.943Q109.385 6.943 109.571 6.871Q109.758 6.800 109.911 6.663Q110.065 6.526 110.161 6.348L110.161 4.739Q110.075 4.592 109.930 4.472Q109.785 4.352 109.616 4.293Q109.447 4.233 109.265 4.233Q108.705 4.233 108.437 4.622Q108.168 5.012 108.168 5.593Q108.168 6.164 108.402 6.554Q108.636 6.943 109.176 6.943\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M114.581 5.562Q114.581 5.241 114.706 4.952Q114.831 4.663 115.057 4.440Q115.282 4.216 115.578 4.096Q115.873 3.976 116.191 3.976Q116.519 3.976 116.781 4.076Q117.042 4.175 117.218 4.357Q117.394 4.540 117.488 4.798Q117.582 5.056 117.582 5.388Q117.582 5.480 117.500 5.501L115.245 5.501L115.245 5.562Q115.245 6.150 115.528 6.533Q115.812 6.916 116.379 6.916Q116.701 6.916 116.969 6.723Q117.237 6.530 117.326 6.215Q117.333 6.174 117.408 6.160L117.500 6.160Q117.582 6.184 117.582 6.256Q117.582 6.263 117.576 6.290Q117.463 6.687 117.092 6.926Q116.721 7.165 116.297 7.165Q115.860 7.165 115.460 6.957Q115.060 6.748 114.821 6.381Q114.581 6.014 114.581 5.562M115.251 5.292L117.066 5.292Q117.066 5.015 116.969 4.763Q116.871 4.510 116.673 4.354Q116.475 4.199 116.191 4.199Q115.914 4.199 115.701 4.357Q115.487 4.516 115.369 4.771Q115.251 5.026 115.251 5.292M119.760 7.070L118.632 4.571Q118.560 4.424 118.430 4.392Q118.300 4.359 118.071 4.359L118.071 4.079L119.585 4.079L119.585 4.359Q119.233 4.359 119.233 4.506Q119.233 4.551 119.244 4.571L120.108 6.489L120.888 4.759Q120.922 4.691 120.922 4.612Q120.922 4.499 120.838 4.429Q120.754 4.359 120.635 4.359L120.635 4.079L121.831 4.079L121.831 4.359Q121.612 4.359 121.441 4.462Q121.270 4.564 121.182 4.759L120.146 7.070Q120.098 7.165 119.992 7.165L119.913 7.165Q119.808 7.165 119.760 7.070\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M122.123 5.614Q122.123 5.272 122.258 4.973Q122.393 4.674 122.633 4.450Q122.872 4.226 123.190 4.101Q123.508 3.976 123.839 3.976Q124.284 3.976 124.683 4.192Q125.083 4.407 125.318 4.785Q125.552 5.162 125.552 5.614Q125.552 5.955 125.410 6.239Q125.268 6.523 125.024 6.730Q124.779 6.936 124.470 7.051Q124.161 7.165 123.839 7.165Q123.409 7.165 123.007 6.964Q122.605 6.762 122.364 6.410Q122.123 6.058 122.123 5.614M123.839 6.916Q124.441 6.916 124.665 6.538Q124.889 6.160 124.889 5.528Q124.889 4.916 124.654 4.557Q124.420 4.199 123.839 4.199Q122.787 4.199 122.787 5.528Q122.787 6.160 123.012 6.538Q123.238 6.916 123.839 6.916M127.814 7.097L126.211 7.097L126.211 6.817Q126.437 6.817 126.586 6.783Q126.734 6.748 126.734 6.608L126.734 2.989Q126.734 2.719 126.627 2.657Q126.519 2.596 126.211 2.596L126.211 2.315L127.288 2.240L127.288 6.608Q127.288 6.745 127.438 6.781Q127.589 6.817 127.814 6.817L127.814 7.097M129.998 7.070L128.871 4.571Q128.799 4.424 128.669 4.392Q128.539 4.359 128.310 4.359L128.310 4.079L129.824 4.079L129.824 4.359Q129.472 4.359 129.472 4.506Q129.472 4.551 129.482 4.571L130.347 6.489L131.126 4.759Q131.161 4.691 131.161 4.612Q131.161 4.499 131.077 4.429Q130.993 4.359 130.873 4.359L130.873 4.079L132.070 4.079L132.070 4.359Q131.851 4.359 131.680 4.462Q131.509 4.564 131.420 4.759L130.385 7.070Q130.337 7.165 130.231 7.165L130.152 7.165Q130.046 7.165 129.998 7.070\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.718 -17.486)\">\u003Cpath d=\"M132.359 5.562Q132.359 5.241 132.484 4.952Q132.609 4.663 132.835 4.440Q133.060 4.216 133.356 4.096Q133.651 3.976 133.969 3.976Q134.297 3.976 134.559 4.076Q134.820 4.175 134.996 4.357Q135.172 4.540 135.266 4.798Q135.360 5.056 135.360 5.388Q135.360 5.480 135.278 5.501L133.023 5.501L133.023 5.562Q133.023 6.150 133.306 6.533Q133.590 6.916 134.157 6.916Q134.479 6.916 134.747 6.723Q135.015 6.530 135.104 6.215Q135.111 6.174 135.186 6.160L135.278 6.160Q135.360 6.184 135.360 6.256Q135.360 6.263 135.354 6.290Q135.241 6.687 134.870 6.926Q134.499 7.165 134.075 7.165Q133.638 7.165 133.238 6.957Q132.838 6.748 132.599 6.381Q132.359 6.014 132.359 5.562M133.029 5.292L134.844 5.292Q134.844 5.015 134.747 4.763Q134.649 4.510 134.451 4.354Q134.253 4.199 133.969 4.199Q133.692 4.199 133.479 4.357Q133.265 4.516 133.147 4.771Q133.029 5.026 133.029 5.292M135.948 7.090L135.948 6.027Q135.948 6.003 135.976 5.976Q136.003 5.949 136.027 5.949L136.136 5.949Q136.201 5.949 136.215 6.007Q136.311 6.441 136.557 6.692Q136.803 6.943 137.216 6.943Q137.558 6.943 137.811 6.810Q138.064 6.677 138.064 6.369Q138.064 6.212 137.970 6.097Q137.876 5.983 137.738 5.914Q137.599 5.846 137.432 5.808L136.851 5.709Q136.495 5.641 136.222 5.420Q135.948 5.200 135.948 4.858Q135.948 4.609 136.059 4.434Q136.170 4.260 136.357 4.161Q136.543 4.062 136.758 4.019Q136.974 3.976 137.216 3.976Q137.630 3.976 137.910 4.158L138.126 3.983Q138.136 3.980 138.143 3.978Q138.149 3.976 138.160 3.976L138.211 3.976Q138.238 3.976 138.262 4Q138.286 4.024 138.286 4.052L138.286 4.899Q138.286 4.920 138.262 4.947Q138.238 4.974 138.211 4.974L138.098 4.974Q138.071 4.974 138.045 4.949Q138.020 4.923 138.020 4.899Q138.020 4.663 137.914 4.499Q137.808 4.335 137.625 4.253Q137.442 4.171 137.210 4.171Q136.881 4.171 136.625 4.274Q136.369 4.376 136.369 4.653Q136.369 4.848 136.552 4.957Q136.734 5.067 136.963 5.108L137.538 5.214Q137.784 5.262 137.997 5.390Q138.211 5.518 138.348 5.721Q138.484 5.925 138.484 6.174Q138.484 6.687 138.119 6.926Q137.753 7.165 137.216 7.165Q136.721 7.165 136.389 6.871L136.123 7.145Q136.102 7.165 136.075 7.165L136.027 7.165Q136.003 7.165 135.976 7.138Q135.948 7.111 135.948 7.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M47.009 17.056c0-6.286-23.885-11.382-53.349-11.382s-53.348 5.096-53.348 11.382 23.885 11.38 53.348 11.38c29.464 0 53.349-5.095 53.349-11.38Zm-53.349 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-102.676 11.709)\">\u003Cpath d=\"M63.649 7.070L62.668 4.571Q62.607 4.428 62.489 4.393Q62.371 4.359 62.155 4.359L62.155 4.079L63.635 4.079L63.635 4.359Q63.256 4.359 63.256 4.520Q63.256 4.530 63.270 4.571L63.984 6.403L64.657 4.698Q64.627 4.626 64.627 4.598Q64.627 4.571 64.599 4.571Q64.538 4.424 64.420 4.392Q64.302 4.359 64.090 4.359L64.090 4.079L65.488 4.079L65.488 4.359Q65.112 4.359 65.112 4.520Q65.112 4.551 65.119 4.571L65.874 6.509L66.561 4.759Q66.582 4.708 66.582 4.653Q66.582 4.513 66.469 4.436Q66.356 4.359 66.216 4.359L66.216 4.079L67.436 4.079L67.436 4.359Q67.231 4.359 67.076 4.465Q66.920 4.571 66.848 4.759L65.943 7.070Q65.908 7.165 65.796 7.165L65.727 7.165Q65.618 7.165 65.580 7.070L64.798 5.067L64.011 7.070Q63.977 7.165 63.864 7.165L63.796 7.165Q63.687 7.165 63.649 7.070M69.648 7.097L68.014 7.097L68.014 6.817Q68.243 6.817 68.392 6.783Q68.540 6.748 68.540 6.608L68.540 2.989Q68.540 2.719 68.433 2.657Q68.325 2.596 68.014 2.596L68.014 2.315L69.094 2.240L69.094 4.626Q69.200 4.441 69.378 4.299Q69.555 4.158 69.764 4.084Q69.972 4.011 70.198 4.011Q70.704 4.011 70.988 4.234Q71.271 4.458 71.271 4.954L71.271 6.608Q71.271 6.745 71.420 6.781Q71.569 6.817 71.794 6.817L71.794 7.097L70.164 7.097L70.164 6.817Q70.393 6.817 70.541 6.783Q70.690 6.748 70.690 6.608L70.690 4.968Q70.690 4.633 70.571 4.433Q70.451 4.233 70.136 4.233Q69.866 4.233 69.632 4.369Q69.398 4.506 69.260 4.740Q69.121 4.974 69.121 5.248L69.121 6.608Q69.121 6.745 69.272 6.781Q69.422 6.817 69.648 6.817L69.648 7.097M72.440 6.369Q72.440 6.037 72.664 5.810Q72.888 5.583 73.231 5.455Q73.575 5.326 73.947 5.274Q74.320 5.221 74.624 5.221L74.624 4.968Q74.624 4.763 74.517 4.583Q74.409 4.404 74.228 4.301Q74.047 4.199 73.838 4.199Q73.431 4.199 73.196 4.291Q73.284 4.328 73.331 4.412Q73.377 4.496 73.377 4.598Q73.377 4.694 73.331 4.773Q73.284 4.851 73.204 4.896Q73.124 4.940 73.035 4.940Q72.885 4.940 72.784 4.843Q72.683 4.745 72.683 4.598Q72.683 3.976 73.838 3.976Q74.050 3.976 74.300 4.040Q74.549 4.103 74.751 4.222Q74.952 4.342 75.079 4.527Q75.205 4.711 75.205 4.954L75.205 6.530Q75.205 6.646 75.267 6.742Q75.328 6.837 75.441 6.837Q75.551 6.837 75.615 6.743Q75.680 6.649 75.680 6.530L75.680 6.082L75.947 6.082L75.947 6.530Q75.947 6.800 75.720 6.965Q75.492 7.131 75.212 7.131Q75.004 7.131 74.867 6.977Q74.730 6.824 74.706 6.608Q74.559 6.875 74.277 7.020Q73.995 7.165 73.671 7.165Q73.394 7.165 73.110 7.090Q72.826 7.015 72.633 6.836Q72.440 6.656 72.440 6.369M73.055 6.369Q73.055 6.543 73.156 6.673Q73.257 6.803 73.413 6.873Q73.568 6.943 73.732 6.943Q73.951 6.943 74.159 6.846Q74.368 6.748 74.496 6.567Q74.624 6.386 74.624 6.160L74.624 5.432Q74.300 5.432 73.934 5.523Q73.568 5.614 73.312 5.826Q73.055 6.037 73.055 6.369M76.890 6.256L76.890 4.359L76.251 4.359L76.251 4.137Q76.569 4.137 76.786 3.927Q77.003 3.717 77.104 3.407Q77.205 3.098 77.205 2.790L77.471 2.790L77.471 4.079L78.548 4.079L78.548 4.359L77.471 4.359L77.471 6.243Q77.471 6.519 77.576 6.718Q77.680 6.916 77.940 6.916Q78.097 6.916 78.203 6.812Q78.309 6.707 78.358 6.554Q78.408 6.400 78.408 6.243L78.408 5.829L78.675 5.829L78.675 6.256Q78.675 6.482 78.575 6.692Q78.476 6.902 78.292 7.034Q78.107 7.165 77.878 7.165Q77.441 7.165 77.166 6.928Q76.890 6.690 76.890 6.256\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-102.676 11.709)\">\u003Cpath d=\"M83.874 7.097L82.240 7.097L82.240 6.817Q82.469 6.817 82.618 6.783Q82.767 6.748 82.767 6.608L82.767 4.759Q82.767 4.489 82.659 4.428Q82.551 4.366 82.240 4.366L82.240 4.086L83.300 4.011L83.300 4.660Q83.471 4.352 83.775 4.181Q84.079 4.011 84.424 4.011Q84.824 4.011 85.101 4.151Q85.378 4.291 85.463 4.639Q85.631 4.346 85.930 4.178Q86.229 4.011 86.574 4.011Q87.080 4.011 87.364 4.234Q87.648 4.458 87.648 4.954L87.648 6.608Q87.648 6.745 87.796 6.781Q87.945 6.817 88.170 6.817L88.170 7.097L86.540 7.097L86.540 6.817Q86.766 6.817 86.916 6.781Q87.066 6.745 87.066 6.608L87.066 4.968Q87.066 4.633 86.947 4.433Q86.827 4.233 86.513 4.233Q86.243 4.233 86.009 4.369Q85.774 4.506 85.636 4.740Q85.498 4.974 85.498 5.248L85.498 6.608Q85.498 6.745 85.646 6.781Q85.795 6.817 86.021 6.817L86.021 7.097L84.390 7.097L84.390 6.817Q84.619 6.817 84.768 6.783Q84.917 6.748 84.917 6.608L84.917 4.968Q84.917 4.633 84.797 4.433Q84.677 4.233 84.363 4.233Q84.093 4.233 83.859 4.369Q83.625 4.506 83.486 4.740Q83.348 4.974 83.348 5.248L83.348 6.608Q83.348 6.745 83.498 6.781Q83.649 6.817 83.874 6.817\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-102.676 11.709)\">\u003Cpath d=\"M88.881 8.232Q89.011 8.300 89.148 8.300Q89.319 8.300 89.469 8.211Q89.620 8.122 89.731 7.977Q89.842 7.832 89.920 7.664L90.184 7.097L89.015 4.571Q88.940 4.424 88.810 4.392Q88.680 4.359 88.447 4.359L88.447 4.079L89.968 4.079L89.968 4.359Q89.620 4.359 89.620 4.506Q89.623 4.527 89.625 4.544Q89.627 4.561 89.627 4.571L90.484 6.430L91.257 4.759Q91.291 4.691 91.291 4.612Q91.291 4.499 91.207 4.429Q91.124 4.359 91.011 4.359L91.011 4.079L92.207 4.079L92.207 4.359Q91.988 4.359 91.816 4.463Q91.643 4.568 91.551 4.759L90.214 7.664Q90.044 8.034 89.774 8.280Q89.503 8.526 89.148 8.526Q88.878 8.526 88.659 8.360Q88.440 8.194 88.440 7.931Q88.440 7.794 88.533 7.705Q88.625 7.617 88.765 7.617Q88.902 7.617 88.991 7.705Q89.080 7.794 89.080 7.931Q89.080 8.034 89.027 8.112Q88.974 8.191 88.881 8.232\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-102.676 11.709)\">\u003Cpath d=\"M95.501 6.369Q95.501 6.037 95.724 5.810Q95.948 5.583 96.292 5.455Q96.635 5.326 97.008 5.274Q97.380 5.221 97.685 5.221L97.685 4.968Q97.685 4.763 97.577 4.583Q97.469 4.404 97.288 4.301Q97.107 4.199 96.899 4.199Q96.492 4.199 96.256 4.291Q96.345 4.328 96.391 4.412Q96.437 4.496 96.437 4.598Q96.437 4.694 96.391 4.773Q96.345 4.851 96.264 4.896Q96.184 4.940 96.095 4.940Q95.945 4.940 95.844 4.843Q95.743 4.745 95.743 4.598Q95.743 3.976 96.899 3.976Q97.110 3.976 97.360 4.040Q97.609 4.103 97.811 4.222Q98.013 4.342 98.139 4.527Q98.266 4.711 98.266 4.954L98.266 6.530Q98.266 6.646 98.327 6.742Q98.389 6.837 98.502 6.837Q98.611 6.837 98.676 6.743Q98.741 6.649 98.741 6.530L98.741 6.082L99.007 6.082L99.007 6.530Q99.007 6.800 98.780 6.965Q98.553 7.131 98.273 7.131Q98.064 7.131 97.927 6.977Q97.791 6.824 97.767 6.608Q97.620 6.875 97.338 7.020Q97.056 7.165 96.731 7.165Q96.454 7.165 96.170 7.090Q95.887 7.015 95.694 6.836Q95.501 6.656 95.501 6.369M96.116 6.369Q96.116 6.543 96.217 6.673Q96.317 6.803 96.473 6.873Q96.628 6.943 96.793 6.943Q97.011 6.943 97.220 6.846Q97.428 6.748 97.556 6.567Q97.685 6.386 97.685 6.160L97.685 5.432Q97.360 5.432 96.994 5.523Q96.628 5.614 96.372 5.826Q96.116 6.037 96.116 6.369M99.424 5.586Q99.424 5.258 99.559 4.957Q99.694 4.657 99.930 4.436Q100.166 4.216 100.470 4.096Q100.774 3.976 101.099 3.976Q101.605 3.976 101.954 4.079Q102.302 4.181 102.302 4.557Q102.302 4.704 102.205 4.805Q102.107 4.906 101.961 4.906Q101.807 4.906 101.708 4.807Q101.608 4.708 101.608 4.557Q101.608 4.369 101.749 4.277Q101.547 4.226 101.106 4.226Q100.751 4.226 100.522 4.422Q100.293 4.619 100.192 4.928Q100.091 5.238 100.091 5.586Q100.091 5.935 100.217 6.241Q100.344 6.547 100.598 6.731Q100.853 6.916 101.209 6.916Q101.431 6.916 101.615 6.832Q101.800 6.748 101.935 6.593Q102.070 6.437 102.128 6.229Q102.142 6.174 102.196 6.174L102.309 6.174Q102.340 6.174 102.362 6.198Q102.384 6.222 102.384 6.256L102.384 6.277Q102.299 6.564 102.111 6.762Q101.923 6.960 101.658 7.063Q101.393 7.165 101.099 7.165Q100.669 7.165 100.281 6.959Q99.893 6.752 99.659 6.389Q99.424 6.027 99.424 5.586M103.499 6.256L103.499 4.359L102.859 4.359L102.859 4.137Q103.177 4.137 103.394 3.927Q103.611 3.717 103.712 3.407Q103.813 3.098 103.813 2.790L104.080 2.790L104.080 4.079L105.156 4.079L105.156 4.359L104.080 4.359L104.080 6.243Q104.080 6.519 104.184 6.718Q104.288 6.916 104.548 6.916Q104.705 6.916 104.811 6.812Q104.917 6.707 104.967 6.554Q105.016 6.400 105.016 6.243L105.016 5.829L105.283 5.829L105.283 6.256Q105.283 6.482 105.184 6.692Q105.085 6.902 104.900 7.034Q104.715 7.165 104.486 7.165Q104.049 7.165 103.774 6.928Q103.499 6.690 103.499 6.256M107.710 7.097L106.158 7.097L106.158 6.817Q106.383 6.817 106.532 6.783Q106.681 6.748 106.681 6.608L106.681 4.759Q106.681 4.571 106.633 4.487Q106.585 4.404 106.488 4.385Q106.390 4.366 106.178 4.366L106.178 4.086L107.234 4.011L107.234 6.608Q107.234 6.748 107.366 6.783Q107.498 6.817 107.710 6.817L107.710 7.097M106.438 2.790Q106.438 2.619 106.561 2.500Q106.684 2.380 106.855 2.380Q107.023 2.380 107.146 2.500Q107.269 2.619 107.269 2.790Q107.269 2.965 107.146 3.088Q107.023 3.211 106.855 3.211Q106.684 3.211 106.561 3.088Q106.438 2.965 106.438 2.790M108.315 5.614Q108.315 5.272 108.450 4.973Q108.585 4.674 108.824 4.450Q109.063 4.226 109.381 4.101Q109.699 3.976 110.030 3.976Q110.475 3.976 110.875 4.192Q111.274 4.407 111.509 4.785Q111.743 5.162 111.743 5.614Q111.743 5.955 111.601 6.239Q111.459 6.523 111.215 6.730Q110.970 6.936 110.661 7.051Q110.352 7.165 110.030 7.165Q109.600 7.165 109.198 6.964Q108.796 6.762 108.555 6.410Q108.315 6.058 108.315 5.614M110.030 6.916Q110.632 6.916 110.856 6.538Q111.080 6.160 111.080 5.528Q111.080 4.916 110.846 4.557Q110.611 4.199 110.030 4.199Q108.978 4.199 108.978 5.528Q108.978 6.160 109.203 6.538Q109.429 6.916 110.030 6.916M114.019 7.097L112.385 7.097L112.385 6.817Q112.614 6.817 112.763 6.783Q112.912 6.748 112.912 6.608L112.912 4.759Q112.912 4.489 112.804 4.428Q112.696 4.366 112.385 4.366L112.385 4.086L113.445 4.011L113.445 4.660Q113.616 4.352 113.920 4.181Q114.224 4.011 114.569 4.011Q115.075 4.011 115.359 4.234Q115.643 4.458 115.643 4.954L115.643 6.608Q115.643 6.745 115.791 6.781Q115.940 6.817 116.166 6.817L116.166 7.097L114.535 7.097L114.535 6.817Q114.764 6.817 114.913 6.783Q115.062 6.748 115.062 6.608L115.062 4.968Q115.062 4.633 114.942 4.433Q114.822 4.233 114.508 4.233Q114.238 4.233 114.004 4.369Q113.770 4.506 113.631 4.740Q113.493 4.974 113.493 5.248L113.493 6.608Q113.493 6.745 113.643 6.781Q113.794 6.817 114.019 6.817L114.019 7.097M116.753 7.090L116.753 6.027Q116.753 6.003 116.781 5.976Q116.808 5.949 116.832 5.949L116.941 5.949Q117.006 5.949 117.020 6.007Q117.116 6.441 117.362 6.692Q117.608 6.943 118.022 6.943Q118.363 6.943 118.616 6.810Q118.869 6.677 118.869 6.369Q118.869 6.212 118.775 6.097Q118.681 5.983 118.543 5.914Q118.404 5.846 118.237 5.808L117.656 5.709Q117.300 5.641 117.027 5.420Q116.753 5.200 116.753 4.858Q116.753 4.609 116.865 4.434Q116.976 4.260 117.162 4.161Q117.348 4.062 117.564 4.019Q117.779 3.976 118.022 3.976Q118.435 3.976 118.715 4.158L118.931 3.983Q118.941 3.980 118.948 3.978Q118.955 3.976 118.965 3.976L119.016 3.976Q119.044 3.976 119.067 4Q119.091 4.024 119.091 4.052L119.091 4.899Q119.091 4.920 119.067 4.947Q119.044 4.974 119.016 4.974L118.903 4.974Q118.876 4.974 118.850 4.949Q118.825 4.923 118.825 4.899Q118.825 4.663 118.719 4.499Q118.613 4.335 118.430 4.253Q118.247 4.171 118.015 4.171Q117.687 4.171 117.430 4.274Q117.174 4.376 117.174 4.653Q117.174 4.848 117.357 4.957Q117.540 5.067 117.769 5.108L118.343 5.214Q118.589 5.262 118.803 5.390Q119.016 5.518 119.153 5.721Q119.290 5.925 119.290 6.174Q119.290 6.687 118.924 6.926Q118.558 7.165 118.022 7.165Q117.526 7.165 117.194 6.871L116.928 7.145Q116.907 7.165 116.880 7.165L116.832 7.165Q116.808 7.165 116.781 7.138Q116.753 7.111 116.753 7.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-102.676 11.709)\">\u003Cpath d=\"M122.638 5.586Q122.638 5.248 122.779 4.957Q122.919 4.667 123.163 4.453Q123.407 4.240 123.712 4.125Q124.016 4.011 124.341 4.011Q124.611 4.011 124.874 4.110Q125.137 4.209 125.328 4.387L125.328 2.989Q125.328 2.719 125.221 2.657Q125.113 2.596 124.802 2.596L124.802 2.315L125.879 2.240L125.879 6.424Q125.879 6.612 125.933 6.695Q125.988 6.779 126.089 6.798Q126.190 6.817 126.405 6.817L126.405 7.097L125.298 7.165L125.298 6.748Q124.881 7.165 124.255 7.165Q123.824 7.165 123.452 6.953Q123.079 6.742 122.859 6.381Q122.638 6.020 122.638 5.586M124.313 6.943Q124.522 6.943 124.708 6.871Q124.894 6.800 125.048 6.663Q125.202 6.526 125.298 6.348L125.298 4.739Q125.212 4.592 125.067 4.472Q124.922 4.352 124.752 4.293Q124.583 4.233 124.402 4.233Q123.842 4.233 123.573 4.622Q123.305 5.012 123.305 5.593Q123.305 6.164 123.539 6.554Q123.773 6.943 124.313 6.943M127.013 5.614Q127.013 5.272 127.148 4.973Q127.283 4.674 127.523 4.450Q127.762 4.226 128.080 4.101Q128.398 3.976 128.729 3.976Q129.174 3.976 129.574 4.192Q129.973 4.407 130.208 4.785Q130.442 5.162 130.442 5.614Q130.442 5.955 130.300 6.239Q130.158 6.523 129.914 6.730Q129.669 6.936 129.360 7.051Q129.051 7.165 128.729 7.165Q128.299 7.165 127.897 6.964Q127.495 6.762 127.254 6.410Q127.013 6.058 127.013 5.614M128.729 6.916Q129.331 6.916 129.555 6.538Q129.779 6.160 129.779 5.528Q129.779 4.916 129.544 4.557Q129.310 4.199 128.729 4.199Q127.677 4.199 127.677 5.528Q127.677 6.160 127.902 6.538Q128.128 6.916 128.729 6.916\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M51.89 46.93c0-6.285-26.07-11.38-58.23-11.38s-58.229 5.095-58.229 11.38 26.07 11.382 58.23 11.382S51.89 53.216 51.89 46.93Zm-58.23 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-106.128 42.264)\">\u003Cpath d=\"M62.261 5.586Q62.261 5.258 62.396 4.957Q62.531 4.657 62.767 4.436Q63.003 4.216 63.307 4.096Q63.612 3.976 63.936 3.976Q64.442 3.976 64.791 4.079Q65.139 4.181 65.139 4.557Q65.139 4.704 65.042 4.805Q64.945 4.906 64.798 4.906Q64.644 4.906 64.545 4.807Q64.446 4.708 64.446 4.557Q64.446 4.369 64.586 4.277Q64.384 4.226 63.943 4.226Q63.588 4.226 63.359 4.422Q63.130 4.619 63.029 4.928Q62.928 5.238 62.928 5.586Q62.928 5.935 63.054 6.241Q63.181 6.547 63.436 6.731Q63.690 6.916 64.046 6.916Q64.268 6.916 64.452 6.832Q64.637 6.748 64.772 6.593Q64.907 6.437 64.965 6.229Q64.979 6.174 65.033 6.174L65.146 6.174Q65.177 6.174 65.199 6.198Q65.221 6.222 65.221 6.256L65.221 6.277Q65.136 6.564 64.948 6.762Q64.760 6.960 64.495 7.063Q64.230 7.165 63.936 7.165Q63.506 7.165 63.118 6.959Q62.730 6.752 62.496 6.389Q62.261 6.027 62.261 5.586M65.768 5.614Q65.768 5.272 65.903 4.973Q66.038 4.674 66.278 4.450Q66.517 4.226 66.835 4.101Q67.153 3.976 67.484 3.976Q67.928 3.976 68.328 4.192Q68.728 4.407 68.962 4.785Q69.197 5.162 69.197 5.614Q69.197 5.955 69.055 6.239Q68.913 6.523 68.668 6.730Q68.424 6.936 68.115 7.051Q67.805 7.165 67.484 7.165Q67.053 7.165 66.652 6.964Q66.250 6.762 66.009 6.410Q65.768 6.058 65.768 5.614M67.484 6.916Q68.086 6.916 68.310 6.538Q68.533 6.160 68.533 5.528Q68.533 4.916 68.299 4.557Q68.065 4.199 67.484 4.199Q66.431 4.199 66.431 5.528Q66.431 6.160 66.657 6.538Q66.883 6.916 67.484 6.916M71.473 7.097L69.839 7.097L69.839 6.817Q70.068 6.817 70.217 6.783Q70.365 6.748 70.365 6.608L70.365 4.759Q70.365 4.489 70.258 4.428Q70.150 4.366 69.839 4.366L69.839 4.086L70.899 4.011L70.899 4.660Q71.070 4.352 71.374 4.181Q71.678 4.011 72.023 4.011Q72.529 4.011 72.813 4.234Q73.096 4.458 73.096 4.954L73.096 6.608Q73.096 6.745 73.245 6.781Q73.394 6.817 73.619 6.817L73.619 7.097L71.989 7.097L71.989 6.817Q72.218 6.817 72.367 6.783Q72.515 6.748 72.515 6.608L72.515 4.968Q72.515 4.633 72.396 4.433Q72.276 4.233 71.962 4.233Q71.692 4.233 71.457 4.369Q71.223 4.506 71.085 4.740Q70.947 4.974 70.947 5.248L70.947 6.608Q70.947 6.745 71.097 6.781Q71.247 6.817 71.473 6.817L71.473 7.097M74.207 5.586Q74.207 5.248 74.347 4.957Q74.488 4.667 74.732 4.453Q74.976 4.240 75.280 4.125Q75.585 4.011 75.909 4.011Q76.179 4.011 76.443 4.110Q76.706 4.209 76.897 4.387L76.897 2.989Q76.897 2.719 76.790 2.657Q76.682 2.596 76.371 2.596L76.371 2.315L77.447 2.240L77.447 6.424Q77.447 6.612 77.502 6.695Q77.557 6.779 77.658 6.798Q77.759 6.817 77.974 6.817L77.974 7.097L76.866 7.165L76.866 6.748Q76.449 7.165 75.824 7.165Q75.393 7.165 75.021 6.953Q74.648 6.742 74.428 6.381Q74.207 6.020 74.207 5.586M75.882 6.943Q76.091 6.943 76.277 6.871Q76.463 6.800 76.617 6.663Q76.771 6.526 76.866 6.348L76.866 4.739Q76.781 4.592 76.636 4.472Q76.490 4.352 76.321 4.293Q76.152 4.233 75.971 4.233Q75.410 4.233 75.142 4.622Q74.874 5.012 74.874 5.593Q74.874 6.164 75.108 6.554Q75.342 6.943 75.882 6.943M80.240 7.097L78.688 7.097L78.688 6.817Q78.914 6.817 79.062 6.783Q79.211 6.748 79.211 6.608L79.211 4.759Q79.211 4.571 79.163 4.487Q79.115 4.404 79.018 4.385Q78.921 4.366 78.709 4.366L78.709 4.086L79.765 4.011L79.765 6.608Q79.765 6.748 79.896 6.783Q80.028 6.817 80.240 6.817L80.240 7.097M78.968 2.790Q78.968 2.619 79.092 2.500Q79.215 2.380 79.385 2.380Q79.553 2.380 79.676 2.500Q79.799 2.619 79.799 2.790Q79.799 2.965 79.676 3.088Q79.553 3.211 79.385 3.211Q79.215 3.211 79.092 3.088Q78.968 2.965 78.968 2.790M81.412 6.256L81.412 4.359L80.773 4.359L80.773 4.137Q81.091 4.137 81.308 3.927Q81.525 3.717 81.626 3.407Q81.727 3.098 81.727 2.790L81.993 2.790L81.993 4.079L83.070 4.079L83.070 4.359L81.993 4.359L81.993 6.243Q81.993 6.519 82.098 6.718Q82.202 6.916 82.462 6.916Q82.619 6.916 82.725 6.812Q82.831 6.707 82.880 6.554Q82.930 6.400 82.930 6.243L82.930 5.829L83.197 5.829L83.197 6.256Q83.197 6.482 83.097 6.692Q82.998 6.902 82.814 7.034Q82.629 7.165 82.400 7.165Q81.963 7.165 81.687 6.928Q81.412 6.690 81.412 6.256M85.623 7.097L84.072 7.097L84.072 6.817Q84.297 6.817 84.446 6.783Q84.594 6.748 84.594 6.608L84.594 4.759Q84.594 4.571 84.547 4.487Q84.499 4.404 84.401 4.385Q84.304 4.366 84.092 4.366L84.092 4.086L85.148 4.011L85.148 6.608Q85.148 6.748 85.280 6.783Q85.411 6.817 85.623 6.817L85.623 7.097M84.352 2.790Q84.352 2.619 84.475 2.500Q84.598 2.380 84.769 2.380Q84.936 2.380 85.059 2.500Q85.182 2.619 85.182 2.790Q85.182 2.965 85.059 3.088Q84.936 3.211 84.769 3.211Q84.598 3.211 84.475 3.088Q84.352 2.965 84.352 2.790M86.228 5.614Q86.228 5.272 86.363 4.973Q86.498 4.674 86.738 4.450Q86.977 4.226 87.295 4.101Q87.613 3.976 87.944 3.976Q88.388 3.976 88.788 4.192Q89.188 4.407 89.422 4.785Q89.656 5.162 89.656 5.614Q89.656 5.955 89.515 6.239Q89.373 6.523 89.128 6.730Q88.884 6.936 88.575 7.051Q88.265 7.165 87.944 7.165Q87.513 7.165 87.112 6.964Q86.710 6.762 86.469 6.410Q86.228 6.058 86.228 5.614M87.944 6.916Q88.546 6.916 88.770 6.538Q88.993 6.160 88.993 5.528Q88.993 4.916 88.759 4.557Q88.525 4.199 87.944 4.199Q86.891 4.199 86.891 5.528Q86.891 6.160 87.117 6.538Q87.343 6.916 87.944 6.916M91.933 7.097L90.299 7.097L90.299 6.817Q90.528 6.817 90.677 6.783Q90.825 6.748 90.825 6.608L90.825 4.759Q90.825 4.489 90.718 4.428Q90.610 4.366 90.299 4.366L90.299 4.086L91.359 4.011L91.359 4.660Q91.530 4.352 91.834 4.181Q92.138 4.011 92.483 4.011Q92.989 4.011 93.273 4.234Q93.556 4.458 93.556 4.954L93.556 6.608Q93.556 6.745 93.705 6.781Q93.854 6.817 94.079 6.817L94.079 7.097L92.449 7.097L92.449 6.817Q92.678 6.817 92.827 6.783Q92.975 6.748 92.975 6.608L92.975 4.968Q92.975 4.633 92.856 4.433Q92.736 4.233 92.422 4.233Q92.152 4.233 91.917 4.369Q91.683 4.506 91.545 4.740Q91.406 4.974 91.406 5.248L91.406 6.608Q91.406 6.745 91.557 6.781Q91.707 6.817 91.933 6.817L91.933 7.097M96.551 5.843L94.493 5.843L94.493 5.340L96.551 5.340L96.551 5.843M97.412 6.369Q97.412 6.037 97.636 5.810Q97.860 5.583 98.203 5.455Q98.547 5.326 98.919 5.274Q99.292 5.221 99.596 5.221L99.596 4.968Q99.596 4.763 99.488 4.583Q99.381 4.404 99.199 4.301Q99.018 4.199 98.810 4.199Q98.403 4.199 98.167 4.291Q98.256 4.328 98.302 4.412Q98.348 4.496 98.348 4.598Q98.348 4.694 98.302 4.773Q98.256 4.851 98.176 4.896Q98.095 4.940 98.007 4.940Q97.856 4.940 97.755 4.843Q97.655 4.745 97.655 4.598Q97.655 3.976 98.810 3.976Q99.022 3.976 99.271 4.040Q99.521 4.103 99.722 4.222Q99.924 4.342 100.051 4.527Q100.177 4.711 100.177 4.954L100.177 6.530Q100.177 6.646 100.239 6.742Q100.300 6.837 100.413 6.837Q100.522 6.837 100.587 6.743Q100.652 6.649 100.652 6.530L100.652 6.082L100.919 6.082L100.919 6.530Q100.919 6.800 100.691 6.965Q100.464 7.131 100.184 7.131Q99.975 7.131 99.839 6.977Q99.702 6.824 99.678 6.608Q99.531 6.875 99.249 7.020Q98.967 7.165 98.642 7.165Q98.365 7.165 98.082 7.090Q97.798 7.015 97.605 6.836Q97.412 6.656 97.412 6.369M98.027 6.369Q98.027 6.543 98.128 6.673Q98.229 6.803 98.384 6.873Q98.540 6.943 98.704 6.943Q98.923 6.943 99.131 6.846Q99.340 6.748 99.468 6.567Q99.596 6.386 99.596 6.160L99.596 5.432Q99.271 5.432 98.905 5.523Q98.540 5.614 98.283 5.826Q98.027 6.037 98.027 6.369M101.336 5.586Q101.336 5.258 101.471 4.957Q101.606 4.657 101.842 4.436Q102.077 4.216 102.382 4.096Q102.686 3.976 103.010 3.976Q103.516 3.976 103.865 4.079Q104.214 4.181 104.214 4.557Q104.214 4.704 104.116 4.805Q104.019 4.906 103.872 4.906Q103.718 4.906 103.619 4.807Q103.520 4.708 103.520 4.557Q103.520 4.369 103.660 4.277Q103.458 4.226 103.017 4.226Q102.662 4.226 102.433 4.422Q102.204 4.619 102.103 4.928Q102.002 5.238 102.002 5.586Q102.002 5.935 102.129 6.241Q102.255 6.547 102.510 6.731Q102.764 6.916 103.120 6.916Q103.342 6.916 103.527 6.832Q103.711 6.748 103.846 6.593Q103.981 6.437 104.039 6.229Q104.053 6.174 104.108 6.174L104.220 6.174Q104.251 6.174 104.273 6.198Q104.296 6.222 104.296 6.256L104.296 6.277Q104.210 6.564 104.022 6.762Q103.834 6.960 103.569 7.063Q103.304 7.165 103.010 7.165Q102.580 7.165 102.192 6.959Q101.804 6.752 101.570 6.389Q101.336 6.027 101.336 5.586M105.410 6.256L105.410 4.359L104.771 4.359L104.771 4.137Q105.089 4.137 105.306 3.927Q105.523 3.717 105.624 3.407Q105.724 3.098 105.724 2.790L105.991 2.790L105.991 4.079L107.068 4.079L107.068 4.359L105.991 4.359L105.991 6.243Q105.991 6.519 106.095 6.718Q106.199 6.916 106.459 6.916Q106.616 6.916 106.722 6.812Q106.828 6.707 106.878 6.554Q106.927 6.400 106.927 6.243L106.927 5.829L107.194 5.829L107.194 6.256Q107.194 6.482 107.095 6.692Q106.996 6.902 106.811 7.034Q106.627 7.165 106.398 7.165Q105.960 7.165 105.685 6.928Q105.410 6.690 105.410 6.256M109.621 7.097L108.069 7.097L108.069 6.817Q108.295 6.817 108.443 6.783Q108.592 6.748 108.592 6.608L108.592 4.759Q108.592 4.571 108.544 4.487Q108.496 4.404 108.399 4.385Q108.301 4.366 108.090 4.366L108.090 4.086L109.146 4.011L109.146 6.608Q109.146 6.748 109.277 6.783Q109.409 6.817 109.621 6.817L109.621 7.097M108.349 2.790Q108.349 2.619 108.472 2.500Q108.595 2.380 108.766 2.380Q108.934 2.380 109.057 2.500Q109.180 2.619 109.180 2.790Q109.180 2.965 109.057 3.088Q108.934 3.211 108.766 3.211Q108.595 3.211 108.472 3.088Q108.349 2.965 108.349 2.790M110.226 5.614Q110.226 5.272 110.361 4.973Q110.496 4.674 110.735 4.450Q110.974 4.226 111.292 4.101Q111.610 3.976 111.942 3.976Q112.386 3.976 112.786 4.192Q113.186 4.407 113.420 4.785Q113.654 5.162 113.654 5.614Q113.654 5.955 113.512 6.239Q113.370 6.523 113.126 6.730Q112.882 6.936 112.572 7.051Q112.263 7.165 111.942 7.165Q111.511 7.165 111.109 6.964Q110.708 6.762 110.467 6.410Q110.226 6.058 110.226 5.614M111.942 6.916Q112.543 6.916 112.767 6.538Q112.991 6.160 112.991 5.528Q112.991 4.916 112.757 4.557Q112.523 4.199 111.942 4.199Q110.889 4.199 110.889 5.528Q110.889 6.160 111.114 6.538Q111.340 6.916 111.942 6.916M115.930 7.097L114.297 7.097L114.297 6.817Q114.526 6.817 114.674 6.783Q114.823 6.748 114.823 6.608L114.823 4.759Q114.823 4.489 114.715 4.428Q114.608 4.366 114.297 4.366L114.297 4.086L115.356 4.011L115.356 4.660Q115.527 4.352 115.831 4.181Q116.135 4.011 116.481 4.011Q116.987 4.011 117.270 4.234Q117.554 4.458 117.554 4.954L117.554 6.608Q117.554 6.745 117.703 6.781Q117.851 6.817 118.077 6.817L118.077 7.097L116.447 7.097L116.447 6.817Q116.676 6.817 116.824 6.783Q116.973 6.748 116.973 6.608L116.973 4.968Q116.973 4.633 116.853 4.433Q116.734 4.233 116.419 4.233Q116.149 4.233 115.915 4.369Q115.681 4.506 115.542 4.740Q115.404 4.974 115.404 5.248L115.404 6.608Q115.404 6.745 115.554 6.781Q115.705 6.817 115.930 6.817\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-106.128 42.264)\">\u003Cpath d=\"M123.164 7.097L121.428 7.097L121.428 6.817Q121.657 6.817 121.806 6.783Q121.954 6.748 121.954 6.608L121.954 4.759Q121.954 4.489 121.847 4.428Q121.739 4.366 121.428 4.366L121.428 4.086L122.457 4.011L122.457 4.718Q122.587 4.410 122.829 4.211Q123.072 4.011 123.390 4.011Q123.609 4.011 123.780 4.135Q123.951 4.260 123.951 4.472Q123.951 4.609 123.851 4.708Q123.752 4.807 123.619 4.807Q123.482 4.807 123.383 4.708Q123.284 4.609 123.284 4.472Q123.284 4.332 123.383 4.233Q123.093 4.233 122.893 4.429Q122.693 4.626 122.600 4.920Q122.508 5.214 122.508 5.494L122.508 6.608Q122.508 6.817 123.164 6.817L123.164 7.097M125.109 6.263L125.109 4.759Q125.109 4.489 125.002 4.428Q124.894 4.366 124.583 4.366L124.583 4.086L125.690 4.011L125.690 6.243L125.690 6.263Q125.690 6.543 125.742 6.687Q125.793 6.830 125.935 6.887Q126.077 6.943 126.364 6.943Q126.617 6.943 126.822 6.803Q127.027 6.663 127.143 6.437Q127.259 6.212 127.259 5.962L127.259 4.759Q127.259 4.489 127.152 4.428Q127.044 4.366 126.733 4.366L126.733 4.086L127.840 4.011L127.840 6.424Q127.840 6.615 127.893 6.697Q127.946 6.779 128.047 6.798Q128.148 6.817 128.363 6.817L128.363 7.097L127.287 7.165L127.287 6.601Q127.177 6.783 127.032 6.906Q126.887 7.029 126.700 7.097Q126.514 7.165 126.312 7.165Q125.109 7.165 125.109 6.263M130.619 7.097L129.016 7.097L129.016 6.817Q129.242 6.817 129.390 6.783Q129.539 6.748 129.539 6.608L129.539 2.989Q129.539 2.719 129.431 2.657Q129.324 2.596 129.016 2.596L129.016 2.315L130.093 2.240L130.093 6.608Q130.093 6.745 130.243 6.781Q130.393 6.817 130.619 6.817L130.619 7.097M131.173 5.562Q131.173 5.241 131.298 4.952Q131.422 4.663 131.648 4.440Q131.873 4.216 132.169 4.096Q132.465 3.976 132.783 3.976Q133.111 3.976 133.372 4.076Q133.634 4.175 133.810 4.357Q133.986 4.540 134.080 4.798Q134.174 5.056 134.174 5.388Q134.174 5.480 134.092 5.501L131.836 5.501L131.836 5.562Q131.836 6.150 132.120 6.533Q132.403 6.916 132.971 6.916Q133.292 6.916 133.560 6.723Q133.829 6.530 133.917 6.215Q133.924 6.174 133.999 6.160L134.092 6.160Q134.174 6.184 134.174 6.256Q134.174 6.263 134.167 6.290Q134.054 6.687 133.683 6.926Q133.312 7.165 132.889 7.165Q132.451 7.165 132.051 6.957Q131.651 6.748 131.412 6.381Q131.173 6.014 131.173 5.562M131.843 5.292L133.658 5.292Q133.658 5.015 133.560 4.763Q133.463 4.510 133.265 4.354Q133.066 4.199 132.783 4.199Q132.506 4.199 132.292 4.357Q132.079 4.516 131.961 4.771Q131.843 5.026 131.843 5.292M134.762 7.090L134.762 6.027Q134.762 6.003 134.789 5.976Q134.816 5.949 134.840 5.949L134.950 5.949Q135.015 5.949 135.028 6.007Q135.124 6.441 135.370 6.692Q135.616 6.943 136.030 6.943Q136.371 6.943 136.624 6.810Q136.877 6.677 136.877 6.369Q136.877 6.212 136.783 6.097Q136.689 5.983 136.551 5.914Q136.412 5.846 136.245 5.808L135.664 5.709Q135.308 5.641 135.035 5.420Q134.762 5.200 134.762 4.858Q134.762 4.609 134.873 4.434Q134.984 4.260 135.170 4.161Q135.356 4.062 135.572 4.019Q135.787 3.976 136.030 3.976Q136.443 3.976 136.724 4.158L136.939 3.983Q136.949 3.980 136.956 3.978Q136.963 3.976 136.973 3.976L137.024 3.976Q137.052 3.976 137.076 4Q137.100 4.024 137.100 4.052L137.100 4.899Q137.100 4.920 137.076 4.947Q137.052 4.974 137.024 4.974L136.912 4.974Q136.884 4.974 136.859 4.949Q136.833 4.923 136.833 4.899Q136.833 4.663 136.727 4.499Q136.621 4.335 136.438 4.253Q136.255 4.171 136.023 4.171Q135.695 4.171 135.438 4.274Q135.182 4.376 135.182 4.653Q135.182 4.848 135.365 4.957Q135.548 5.067 135.777 5.108L136.351 5.214Q136.597 5.262 136.811 5.390Q137.024 5.518 137.161 5.721Q137.298 5.925 137.298 6.174Q137.298 6.687 136.932 6.926Q136.566 7.165 136.030 7.165Q135.534 7.165 135.203 6.871L134.936 7.145Q134.915 7.165 134.888 7.165L134.840 7.165Q134.816 7.165 134.789 7.138Q134.762 7.111 134.762 7.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M67.637 61.157h68.287V32.704H67.637Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M65.688-2.434L64.618-5.290Q64.552-5.469 64.421-5.512Q64.290-5.555 64.032-5.555L64.032-5.852L65.712-5.852L65.712-5.555Q65.262-5.555 65.262-5.356Q65.266-5.341 65.268-5.323Q65.270-5.305 65.270-5.290L66.063-3.196L66.774-5.106Q66.739-5.200 66.739-5.245Q66.739-5.290 66.704-5.290Q66.637-5.469 66.507-5.512Q66.376-5.555 66.122-5.555L66.122-5.852L67.712-5.852L67.712-5.555Q67.262-5.555 67.262-5.356Q67.266-5.337 67.268-5.319Q67.270-5.301 67.270-5.290L68.102-3.075L68.856-5.075Q68.880-5.133 68.880-5.204Q68.880-5.364 68.743-5.460Q68.606-5.555 68.438-5.555L68.438-5.852L69.825-5.852L69.825-5.555Q69.591-5.555 69.413-5.428Q69.235-5.301 69.153-5.075L68.169-2.434Q68.114-2.325 68.001-2.325L67.942-2.325Q67.829-2.325 67.786-2.434L66.927-4.708L66.071-2.434Q66.032-2.325 65.911-2.325L65.856-2.325Q65.743-2.325 65.688-2.434M72.169-2.403L70.313-2.403L70.313-2.700Q70.587-2.700 70.755-2.747Q70.923-2.794 70.923-2.962L70.923-7.122Q70.923-7.337 70.860-7.432Q70.798-7.528 70.678-7.549Q70.559-7.571 70.313-7.571L70.313-7.868L71.536-7.954L71.536-5.251Q71.661-5.462 71.848-5.612Q72.036-5.762 72.262-5.846Q72.489-5.930 72.735-5.930Q73.903-5.930 73.903-4.852L73.903-2.962Q73.903-2.794 74.073-2.747Q74.243-2.700 74.512-2.700L74.512-2.403L72.657-2.403L72.657-2.700Q72.930-2.700 73.098-2.747Q73.266-2.794 73.266-2.962L73.266-4.837Q73.266-5.219 73.145-5.448Q73.024-5.676 72.673-5.676Q72.360-5.676 72.106-5.514Q71.852-5.352 71.706-5.083Q71.559-4.813 71.559-4.516L71.559-2.962Q71.559-2.794 71.729-2.747Q71.899-2.700 72.169-2.700L72.169-2.403M75.055-3.235Q75.055-3.719 75.458-4.014Q75.860-4.309 76.411-4.428Q76.962-4.548 77.454-4.548L77.454-4.837Q77.454-5.063 77.339-5.270Q77.223-5.477 77.026-5.596Q76.829-5.716 76.598-5.716Q76.173-5.716 75.887-5.610Q75.958-5.583 76.005-5.528Q76.052-5.473 76.077-5.403Q76.102-5.333 76.102-5.258Q76.102-5.153 76.052-5.061Q76.001-4.969 75.909-4.919Q75.817-4.868 75.712-4.868Q75.606-4.868 75.514-4.919Q75.423-4.969 75.372-5.061Q75.321-5.153 75.321-5.258Q75.321-5.676 75.710-5.823Q76.098-5.969 76.598-5.969Q76.930-5.969 77.284-5.839Q77.637-5.708 77.866-5.454Q78.094-5.200 78.094-4.852L78.094-3.051Q78.094-2.919 78.167-2.809Q78.239-2.700 78.368-2.700Q78.493-2.700 78.561-2.805Q78.630-2.911 78.630-3.051L78.630-3.563L78.911-3.563L78.911-3.051Q78.911-2.848 78.794-2.690Q78.677-2.532 78.495-2.448Q78.313-2.364 78.110-2.364Q77.880-2.364 77.727-2.536Q77.575-2.708 77.544-2.938Q77.384-2.657 77.075-2.491Q76.766-2.325 76.415-2.325Q75.903-2.325 75.479-2.548Q75.055-2.770 75.055-3.235M75.743-3.235Q75.743-2.950 75.969-2.764Q76.196-2.579 76.489-2.579Q76.735-2.579 76.960-2.696Q77.184-2.813 77.319-3.016Q77.454-3.219 77.454-3.473L77.454-4.305Q77.188-4.305 76.903-4.251Q76.618-4.196 76.346-4.067Q76.075-3.938 75.909-3.731Q75.743-3.524 75.743-3.235M79.829-3.364L79.829-5.555L79.126-5.555L79.126-5.809Q79.481-5.809 79.723-6.042Q79.966-6.274 80.077-6.622Q80.188-6.969 80.188-7.325L80.469-7.325L80.469-5.852L81.645-5.852L81.645-5.555L80.469-5.555L80.469-3.380Q80.469-3.059 80.589-2.831Q80.708-2.602 80.989-2.602Q81.169-2.602 81.286-2.725Q81.403-2.848 81.456-3.028Q81.509-3.208 81.509-3.380L81.509-3.852L81.790-3.852L81.790-3.364Q81.790-3.110 81.684-2.870Q81.579-2.630 81.382-2.477Q81.184-2.325 80.927-2.325Q80.610-2.325 80.358-2.448Q80.106-2.571 79.968-2.805Q79.829-3.040 79.829-3.364\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M85.450-3.235Q85.450-3.719 85.852-4.014Q86.255-4.309 86.805-4.428Q87.356-4.548 87.848-4.548L87.848-4.837Q87.848-5.063 87.733-5.270Q87.618-5.477 87.421-5.596Q87.223-5.716 86.993-5.716Q86.567-5.716 86.282-5.610Q86.352-5.583 86.399-5.528Q86.446-5.473 86.471-5.403Q86.497-5.333 86.497-5.258Q86.497-5.153 86.446-5.061Q86.395-4.969 86.303-4.919Q86.212-4.868 86.106-4.868Q86.001-4.868 85.909-4.919Q85.817-4.969 85.766-5.061Q85.716-5.153 85.716-5.258Q85.716-5.676 86.104-5.823Q86.493-5.969 86.993-5.969Q87.325-5.969 87.678-5.839Q88.032-5.708 88.260-5.454Q88.489-5.200 88.489-4.852L88.489-3.051Q88.489-2.919 88.561-2.809Q88.634-2.700 88.762-2.700Q88.887-2.700 88.956-2.805Q89.024-2.911 89.024-3.051L89.024-3.563L89.305-3.563L89.305-3.051Q89.305-2.848 89.188-2.690Q89.071-2.532 88.889-2.448Q88.708-2.364 88.505-2.364Q88.274-2.364 88.122-2.536Q87.969-2.708 87.938-2.938Q87.778-2.657 87.469-2.491Q87.161-2.325 86.809-2.325Q86.298-2.325 85.874-2.548Q85.450-2.770 85.450-3.235M86.137-3.235Q86.137-2.950 86.364-2.764Q86.591-2.579 86.884-2.579Q87.130-2.579 87.354-2.696Q87.579-2.813 87.714-3.016Q87.848-3.219 87.848-3.473L87.848-4.305Q87.583-4.305 87.298-4.251Q87.012-4.196 86.741-4.067Q86.469-3.938 86.303-3.731Q86.137-3.524 86.137-3.235M89.641-4.130Q89.641-4.626 89.891-5.051Q90.141-5.477 90.561-5.723Q90.981-5.969 91.481-5.969Q92.020-5.969 92.411-5.844Q92.802-5.719 92.802-5.305Q92.802-5.200 92.751-5.108Q92.700-5.016 92.608-4.966Q92.516-4.915 92.407-4.915Q92.302-4.915 92.210-4.966Q92.118-5.016 92.067-5.108Q92.016-5.200 92.016-5.305Q92.016-5.528 92.184-5.633Q91.962-5.692 91.489-5.692Q91.192-5.692 90.977-5.553Q90.762-5.415 90.632-5.184Q90.501-4.954 90.442-4.684Q90.384-4.415 90.384-4.130Q90.384-3.735 90.516-3.385Q90.649-3.036 90.921-2.819Q91.192-2.602 91.591-2.602Q91.966-2.602 92.241-2.819Q92.516-3.036 92.618-3.395Q92.634-3.458 92.696-3.458L92.802-3.458Q92.837-3.458 92.862-3.430Q92.887-3.403 92.887-3.364L92.887-3.340Q92.755-2.860 92.370-2.592Q91.985-2.325 91.481-2.325Q91.118-2.325 90.784-2.462Q90.450-2.598 90.190-2.848Q89.930-3.098 89.786-3.434Q89.641-3.770 89.641-4.130M94.001-3.364L94.001-5.555L93.298-5.555L93.298-5.809Q93.653-5.809 93.895-6.042Q94.137-6.274 94.249-6.622Q94.360-6.969 94.360-7.325L94.641-7.325L94.641-5.852L95.817-5.852L95.817-5.555L94.641-5.555L94.641-3.380Q94.641-3.059 94.760-2.831Q94.880-2.602 95.161-2.602Q95.341-2.602 95.458-2.725Q95.575-2.848 95.628-3.028Q95.680-3.208 95.680-3.380L95.680-3.852L95.962-3.852L95.962-3.364Q95.962-3.110 95.856-2.870Q95.751-2.630 95.553-2.477Q95.356-2.325 95.098-2.325Q94.782-2.325 94.530-2.448Q94.278-2.571 94.139-2.805Q94.001-3.040 94.001-3.364M98.540-2.403L96.762-2.403L96.762-2.700Q97.036-2.700 97.204-2.747Q97.372-2.794 97.372-2.962L97.372-5.098Q97.372-5.313 97.315-5.409Q97.259-5.505 97.145-5.526Q97.032-5.548 96.786-5.548L96.786-5.844L97.985-5.930L97.985-2.962Q97.985-2.794 98.132-2.747Q98.278-2.700 98.540-2.700L98.540-2.403M97.098-7.325Q97.098-7.516 97.233-7.647Q97.368-7.778 97.563-7.778Q97.684-7.778 97.788-7.716Q97.891-7.653 97.954-7.549Q98.016-7.446 98.016-7.325Q98.016-7.130 97.885-6.995Q97.755-6.860 97.563-6.860Q97.364-6.860 97.231-6.993Q97.098-7.126 97.098-7.325M99.040-4.098Q99.040-4.602 99.296-5.034Q99.552-5.466 99.987-5.717Q100.423-5.969 100.923-5.969Q101.309-5.969 101.651-5.825Q101.993-5.680 102.255-5.419Q102.516-5.157 102.659-4.821Q102.802-4.485 102.802-4.098Q102.802-3.606 102.538-3.196Q102.274-2.786 101.844-2.555Q101.415-2.325 100.923-2.325Q100.430-2.325 99.997-2.557Q99.563-2.790 99.302-3.198Q99.040-3.606 99.040-4.098M100.923-2.602Q101.380-2.602 101.632-2.825Q101.884-3.048 101.971-3.399Q102.059-3.751 102.059-4.196Q102.059-4.626 101.966-4.964Q101.872-5.301 101.618-5.508Q101.364-5.716 100.923-5.716Q100.274-5.716 100.030-5.299Q99.786-4.883 99.786-4.196Q99.786-3.751 99.874-3.399Q99.962-3.048 100.214-2.825Q100.466-2.602 100.923-2.602M105.216-2.403L103.360-2.403L103.360-2.700Q103.634-2.700 103.802-2.747Q103.969-2.794 103.969-2.962L103.969-5.098Q103.969-5.313 103.907-5.409Q103.844-5.505 103.725-5.526Q103.606-5.548 103.360-5.548L103.360-5.844L104.552-5.930L104.552-5.196Q104.665-5.411 104.858-5.579Q105.052-5.747 105.290-5.839Q105.528-5.930 105.782-5.930Q106.950-5.930 106.950-4.852L106.950-2.962Q106.950-2.794 107.120-2.747Q107.290-2.700 107.559-2.700L107.559-2.403L105.704-2.403L105.704-2.700Q105.977-2.700 106.145-2.747Q106.313-2.794 106.313-2.962L106.313-4.837Q106.313-5.219 106.192-5.448Q106.071-5.676 105.719-5.676Q105.407-5.676 105.153-5.514Q104.899-5.352 104.753-5.083Q104.606-4.813 104.606-4.516L104.606-2.962Q104.606-2.794 104.776-2.747Q104.946-2.700 105.216-2.700\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M113.376-2.403L110.911-2.403L110.911-2.700Q111.243-2.700 111.501-2.747Q111.759-2.794 111.759-2.962L111.759-7.305Q111.759-7.571 110.911-7.571L110.911-7.868L113.376-7.868L113.376-7.571Q112.524-7.571 112.524-7.305L112.524-2.962Q112.524-2.700 113.376-2.700\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M62.228 7.089L62.228 5.867Q62.228 5.839 62.260 5.808Q62.291 5.777 62.314 5.777L62.420 5.777Q62.490 5.777 62.506 5.839Q62.568 6.160 62.707 6.400Q62.845 6.640 63.078 6.781Q63.310 6.921 63.619 6.921Q63.857 6.921 64.066 6.861Q64.275 6.800 64.412 6.652Q64.549 6.503 64.549 6.257Q64.549 6.003 64.338 5.837Q64.127 5.671 63.857 5.617L63.236 5.503Q62.830 5.425 62.529 5.169Q62.228 4.913 62.228 4.538Q62.228 4.171 62.429 3.949Q62.631 3.726 62.955 3.628Q63.279 3.531 63.619 3.531Q64.084 3.531 64.381 3.738L64.603 3.554Q64.627 3.531 64.658 3.531L64.709 3.531Q64.740 3.531 64.767 3.558Q64.795 3.585 64.795 3.617L64.795 4.601Q64.795 4.632 64.769 4.661Q64.744 4.691 64.709 4.691L64.603 4.691Q64.568 4.691 64.541 4.663Q64.513 4.636 64.513 4.601Q64.513 4.202 64.261 3.982Q64.010 3.761 63.611 3.761Q63.256 3.761 62.972 3.884Q62.689 4.007 62.689 4.312Q62.689 4.531 62.890 4.663Q63.092 4.796 63.338 4.839L63.963 4.952Q64.392 5.042 64.701 5.339Q65.010 5.636 65.010 6.050Q65.010 6.620 64.611 6.898Q64.213 7.175 63.619 7.175Q63.068 7.175 62.717 6.839L62.420 7.152Q62.396 7.175 62.361 7.175L62.314 7.175Q62.291 7.175 62.260 7.144Q62.228 7.113 62.228 7.089M67.467 7.097L65.611 7.097L65.611 6.800Q65.885 6.800 66.052 6.753Q66.220 6.706 66.220 6.538L66.220 2.378Q66.220 2.163 66.158 2.068Q66.095 1.972 65.976 1.951Q65.857 1.929 65.611 1.929L65.611 1.632L66.834 1.546L66.834 4.249Q66.959 4.038 67.146 3.888Q67.334 3.738 67.560 3.654Q67.787 3.570 68.033 3.570Q69.201 3.570 69.201 4.648L69.201 6.538Q69.201 6.706 69.371 6.753Q69.541 6.800 69.810 6.800L69.810 7.097L67.955 7.097L67.955 6.800Q68.228 6.800 68.396 6.753Q68.564 6.706 68.564 6.538L68.564 4.663Q68.564 4.281 68.443 4.052Q68.322 3.824 67.970 3.824Q67.658 3.824 67.404 3.986Q67.150 4.148 67.004 4.417Q66.857 4.687 66.857 4.984L66.857 6.538Q66.857 6.706 67.027 6.753Q67.197 6.800 67.467 6.800L67.467 7.097M70.256 5.402Q70.256 4.898 70.511 4.466Q70.767 4.035 71.203 3.783Q71.638 3.531 72.138 3.531Q72.525 3.531 72.867 3.675Q73.209 3.820 73.470 4.081Q73.732 4.343 73.875 4.679Q74.017 5.015 74.017 5.402Q74.017 5.894 73.754 6.304Q73.490 6.714 73.060 6.945Q72.631 7.175 72.138 7.175Q71.646 7.175 71.213 6.943Q70.779 6.710 70.517 6.302Q70.256 5.894 70.256 5.402M72.138 6.898Q72.595 6.898 72.847 6.675Q73.099 6.452 73.187 6.101Q73.275 5.749 73.275 5.304Q73.275 4.874 73.181 4.536Q73.088 4.199 72.834 3.992Q72.580 3.785 72.138 3.785Q71.490 3.785 71.246 4.201Q71.002 4.617 71.002 5.304Q71.002 5.749 71.090 6.101Q71.177 6.452 71.429 6.675Q71.681 6.898 72.138 6.898M75.185 6.144L75.185 4.402Q75.185 4.187 75.123 4.091Q75.060 3.995 74.941 3.974Q74.822 3.952 74.576 3.952L74.576 3.656L75.822 3.570L75.822 6.120L75.822 6.144Q75.822 6.456 75.877 6.618Q75.931 6.781 76.082 6.851Q76.232 6.921 76.552 6.921Q76.982 6.921 77.256 6.583Q77.529 6.245 77.529 5.800L77.529 4.402Q77.529 4.187 77.467 4.091Q77.404 3.995 77.285 3.974Q77.166 3.952 76.920 3.952L76.920 3.656L78.166 3.570L78.166 6.355Q78.166 6.566 78.228 6.661Q78.291 6.757 78.410 6.779Q78.529 6.800 78.775 6.800L78.775 7.097L77.552 7.175L77.552 6.554Q77.385 6.843 77.103 7.009Q76.822 7.175 76.502 7.175Q75.185 7.175 75.185 6.144M81.135 7.097L79.302 7.097L79.302 6.800Q79.576 6.800 79.744 6.753Q79.912 6.706 79.912 6.538L79.912 2.378Q79.912 2.163 79.849 2.068Q79.787 1.972 79.668 1.951Q79.549 1.929 79.302 1.929L79.302 1.632L80.525 1.546L80.525 6.538Q80.525 6.706 80.693 6.753Q80.861 6.800 81.135 6.800L81.135 7.097M83.396 7.175Q82.916 7.175 82.508 6.931Q82.099 6.687 81.861 6.273Q81.623 5.859 81.623 5.370Q81.623 4.878 81.881 4.462Q82.138 4.046 82.570 3.808Q83.002 3.570 83.494 3.570Q84.115 3.570 84.564 4.007L84.564 2.378Q84.564 2.163 84.502 2.068Q84.439 1.972 84.322 1.951Q84.205 1.929 83.959 1.929L83.959 1.632L85.181 1.546L85.181 6.355Q85.181 6.566 85.244 6.661Q85.306 6.757 85.424 6.779Q85.541 6.800 85.791 6.800L85.791 7.097L84.541 7.175L84.541 6.691Q84.076 7.175 83.396 7.175M83.463 6.921Q83.802 6.921 84.095 6.730Q84.388 6.538 84.541 6.242L84.541 4.410Q84.392 4.136 84.131 3.980Q83.869 3.824 83.556 3.824Q82.931 3.824 82.648 4.271Q82.365 4.718 82.365 5.378Q82.365 6.023 82.617 6.472Q82.869 6.921 83.463 6.921\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M90.966 7.175Q90.485 7.175 90.077 6.931Q89.669 6.687 89.431 6.273Q89.192 5.859 89.192 5.370Q89.192 4.878 89.450 4.462Q89.708 4.046 90.140 3.808Q90.571 3.570 91.063 3.570Q91.684 3.570 92.134 4.007L92.134 2.378Q92.134 2.163 92.071 2.068Q92.009 1.972 91.891 1.951Q91.774 1.929 91.528 1.929L91.528 1.632L92.751 1.546L92.751 6.355Q92.751 6.566 92.813 6.661Q92.876 6.757 92.993 6.779Q93.110 6.800 93.360 6.800L93.360 7.097L92.110 7.175L92.110 6.691Q91.645 7.175 90.966 7.175M91.032 6.921Q91.372 6.921 91.665 6.730Q91.958 6.538 92.110 6.242L92.110 4.410Q91.962 4.136 91.700 3.980Q91.438 3.824 91.126 3.824Q90.501 3.824 90.218 4.271Q89.934 4.718 89.934 5.378Q89.934 6.023 90.186 6.472Q90.438 6.921 91.032 6.921M93.868 5.402Q93.868 4.898 94.124 4.466Q94.380 4.035 94.815 3.783Q95.251 3.531 95.751 3.531Q96.138 3.531 96.479 3.675Q96.821 3.820 97.083 4.081Q97.345 4.343 97.487 4.679Q97.630 5.015 97.630 5.402Q97.630 5.894 97.366 6.304Q97.102 6.714 96.673 6.945Q96.243 7.175 95.751 7.175Q95.259 7.175 94.825 6.943Q94.391 6.710 94.130 6.302Q93.868 5.894 93.868 5.402M95.751 6.898Q96.208 6.898 96.460 6.675Q96.712 6.452 96.800 6.101Q96.888 5.749 96.888 5.304Q96.888 4.874 96.794 4.536Q96.700 4.199 96.446 3.992Q96.192 3.785 95.751 3.785Q95.102 3.785 94.858 4.201Q94.614 4.617 94.614 5.304Q94.614 5.749 94.702 6.101Q94.790 6.452 95.042 6.675Q95.294 6.898 95.751 6.898\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M102.885 7.097L101.029 7.097L101.029 6.800Q101.303 6.800 101.471 6.753Q101.639 6.706 101.639 6.538L101.639 4.402Q101.639 4.187 101.576 4.091Q101.514 3.995 101.395 3.974Q101.276 3.952 101.029 3.952L101.029 3.656L102.221 3.570L102.221 4.304Q102.334 4.089 102.528 3.921Q102.721 3.753 102.959 3.661Q103.197 3.570 103.451 3.570Q104.619 3.570 104.619 4.648L104.619 6.538Q104.619 6.706 104.789 6.753Q104.959 6.800 105.229 6.800L105.229 7.097L103.373 7.097L103.373 6.800Q103.647 6.800 103.815 6.753Q103.983 6.706 103.983 6.538L103.983 4.663Q103.983 4.281 103.862 4.052Q103.740 3.824 103.389 3.824Q103.076 3.824 102.822 3.986Q102.569 4.148 102.422 4.417Q102.276 4.687 102.276 4.984L102.276 6.538Q102.276 6.706 102.446 6.753Q102.615 6.800 102.885 6.800L102.885 7.097M105.674 5.402Q105.674 4.898 105.930 4.466Q106.186 4.035 106.621 3.783Q107.057 3.531 107.557 3.531Q107.944 3.531 108.285 3.675Q108.627 3.820 108.889 4.081Q109.151 4.343 109.293 4.679Q109.436 5.015 109.436 5.402Q109.436 5.894 109.172 6.304Q108.908 6.714 108.479 6.945Q108.049 7.175 107.557 7.175Q107.065 7.175 106.631 6.943Q106.197 6.710 105.936 6.302Q105.674 5.894 105.674 5.402M107.557 6.898Q108.014 6.898 108.266 6.675Q108.518 6.452 108.606 6.101Q108.694 5.749 108.694 5.304Q108.694 4.874 108.600 4.536Q108.506 4.199 108.252 3.992Q107.998 3.785 107.557 3.785Q106.908 3.785 106.664 4.201Q106.420 4.617 106.420 5.304Q106.420 5.749 106.508 6.101Q106.596 6.452 106.848 6.675Q107.100 6.898 107.557 6.898\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(13.011 47.361)\">\u003Cpath d=\"M111.277 7.066L110.207 4.210Q110.141 4.031 110.010 3.988Q109.879 3.945 109.621 3.945L109.621 3.648L111.301 3.648L111.301 3.945Q110.851 3.945 110.851 4.144Q110.855 4.160 110.857 4.177Q110.859 4.195 110.859 4.210L111.652 6.304L112.363 4.394Q112.328 4.300 112.328 4.255Q112.328 4.210 112.293 4.210Q112.226 4.031 112.096 3.988Q111.965 3.945 111.711 3.945L111.711 3.648L113.301 3.648L113.301 3.945Q112.851 3.945 112.851 4.144Q112.855 4.163 112.857 4.181Q112.859 4.199 112.859 4.210L113.691 6.425L114.445 4.425Q114.469 4.367 114.469 4.296Q114.469 4.136 114.332 4.040Q114.195 3.945 114.027 3.945L114.027 3.648L115.414 3.648L115.414 3.945Q115.180 3.945 115.002 4.072Q114.824 4.199 114.742 4.425L113.758 7.066Q113.703 7.175 113.590 7.175L113.531 7.175Q113.418 7.175 113.375 7.066L112.516 4.792L111.660 7.066Q111.621 7.175 111.500 7.175L111.445 7.175Q111.332 7.175 111.277 7.066\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M202.975-47.164H101.78v3.091\"\u002F>\u003Cpath stroke=\"none\" d=\"m101.78-41.473 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m52.924-12.82 12.657-12.406\"\u002F>\u003Cpath stroke=\"none\" d=\"m67.437-27.046-4.426 1.426 2.57.394.342 2.577\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M47.209 17.056h14.226v-44.102h3.402\"\u002F>\u003Cpath stroke=\"none\" d=\"m67.437-27.046-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M101.78-12.62v42.524\"\u002F>\u003Cpath stroke=\"none\" d=\"m101.78 32.504 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M52.09 46.93h12.747\"\u002F>\u003Cpath stroke=\"none\" d=\"m67.437 46.93-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M101.78 61.357v14.226h101.195v-.245\"\u002F>\u003Cpath stroke=\"none\" d=\"m202.975 72.738-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">A model-based reflex agent. It combines the current percept with the previous internal state, using its model of how the world evolves and what its actions do, to update its best estimate of the world now, then applies condition-action rules as before.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:461.751px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 346.313 176.115\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-51.864 83.92h233.313V-58.345H-51.864Z\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-113.523 66.443)\">\u003Cpath d=\"M66.831 12.787L65.081 12.787L65.081 12.490Q65.780 12.490 65.968 12.010L67.769 7.185Q67.823 7.076 67.937 7.076L68.007 7.076Q68.120 7.076 68.175 7.185L70.065 12.228Q70.144 12.396 70.347 12.443Q70.550 12.490 70.862 12.490L70.862 12.787L68.640 12.787L68.640 12.490Q69.280 12.490 69.280 12.275Q69.280 12.256 69.278 12.246Q69.276 12.236 69.272 12.228L68.808 10.994L66.663 10.994L66.280 12.010Q66.276 12.025 66.271 12.055Q66.265 12.084 66.265 12.107Q66.265 12.248 66.355 12.332Q66.444 12.416 66.577 12.453Q66.710 12.490 66.831 12.490L66.831 12.787M67.737 8.131L66.769 10.697L68.694 10.697L67.737 8.131M71.390 13.396Q71.390 13.115 71.601 12.904Q71.812 12.693 72.097 12.603Q71.940 12.478 71.862 12.289Q71.784 12.100 71.784 11.900Q71.784 11.545 72.015 11.252Q71.647 10.912 71.647 10.443Q71.647 10.092 71.851 9.822Q72.054 9.553 72.374 9.406Q72.694 9.260 73.038 9.260Q73.558 9.260 73.929 9.541Q74.292 9.170 74.839 9.170Q75.019 9.170 75.146 9.297Q75.272 9.424 75.272 9.603Q75.272 9.709 75.194 9.787Q75.116 9.865 75.007 9.865Q74.897 9.865 74.821 9.789Q74.745 9.713 74.745 9.603Q74.745 9.502 74.784 9.451Q74.792 9.443 74.796 9.437Q74.800 9.432 74.800 9.428Q74.425 9.428 74.105 9.682Q74.425 10.021 74.425 10.443Q74.425 10.713 74.308 10.930Q74.190 11.146 73.985 11.305Q73.780 11.463 73.538 11.545Q73.296 11.627 73.038 11.627Q72.819 11.627 72.606 11.568Q72.394 11.510 72.198 11.389Q72.105 11.529 72.105 11.709Q72.105 11.916 72.241 12.068Q72.378 12.221 72.585 12.221L73.280 12.221Q73.769 12.221 74.181 12.305Q74.593 12.389 74.872 12.646Q75.151 12.904 75.151 13.396Q75.151 13.760 74.831 13.992Q74.511 14.225 74.069 14.326Q73.628 14.428 73.272 14.428Q72.917 14.428 72.474 14.326Q72.030 14.225 71.710 13.992Q71.390 13.760 71.390 13.396M71.894 13.396Q71.894 13.592 72.038 13.740Q72.183 13.889 72.396 13.978Q72.608 14.068 72.849 14.115Q73.089 14.162 73.272 14.162Q73.515 14.162 73.845 14.084Q74.175 14.006 74.411 13.832Q74.647 13.658 74.647 13.396Q74.647 12.990 74.237 12.881Q73.827 12.771 73.265 12.771L72.585 12.771Q72.315 12.771 72.105 12.949Q71.894 13.127 71.894 13.396M73.038 11.361Q73.761 11.361 73.761 10.443Q73.761 9.521 73.038 9.521Q72.312 9.521 72.312 10.443Q72.312 11.361 73.038 11.361M75.636 11.033Q75.636 10.553 75.868 10.137Q76.101 9.721 76.511 9.471Q76.921 9.221 77.397 9.221Q78.128 9.221 78.526 9.662Q78.925 10.103 78.925 10.834Q78.925 10.939 78.831 10.963L76.382 10.963L76.382 11.033Q76.382 11.443 76.503 11.799Q76.624 12.154 76.896 12.371Q77.167 12.588 77.597 12.588Q77.960 12.588 78.257 12.359Q78.554 12.131 78.655 11.779Q78.663 11.732 78.749 11.717L78.831 11.717Q78.925 11.744 78.925 11.826Q78.925 11.834 78.917 11.865Q78.855 12.092 78.716 12.275Q78.577 12.459 78.386 12.592Q78.194 12.725 77.976 12.795Q77.757 12.865 77.519 12.865Q77.147 12.865 76.810 12.728Q76.472 12.592 76.204 12.340Q75.937 12.088 75.786 11.748Q75.636 11.408 75.636 11.033M76.390 10.725L78.351 10.725Q78.351 10.420 78.249 10.129Q78.147 9.838 77.931 9.656Q77.714 9.475 77.397 9.475Q77.097 9.475 76.866 9.662Q76.636 9.850 76.513 10.141Q76.390 10.432 76.390 10.725M81.343 12.787L79.487 12.787L79.487 12.490Q79.761 12.490 79.929 12.443Q80.097 12.396 80.097 12.228L80.097 10.092Q80.097 9.877 80.034 9.781Q79.972 9.685 79.853 9.664Q79.733 9.642 79.487 9.642L79.487 9.346L80.679 9.260L80.679 9.994Q80.792 9.779 80.985 9.611Q81.179 9.443 81.417 9.351Q81.655 9.260 81.909 9.260Q83.077 9.260 83.077 10.338L83.077 12.228Q83.077 12.396 83.247 12.443Q83.417 12.490 83.687 12.490L83.687 12.787L81.831 12.787L81.831 12.490Q82.105 12.490 82.272 12.443Q82.440 12.396 82.440 12.228L82.440 10.353Q82.440 9.971 82.319 9.742Q82.198 9.514 81.847 9.514Q81.534 9.514 81.280 9.676Q81.026 9.838 80.880 10.107Q80.733 10.377 80.733 10.674L80.733 12.228Q80.733 12.396 80.903 12.443Q81.073 12.490 81.343 12.490\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-113.523 66.443)\">\u003Cpath d=\"M84.536 11.826L84.536 9.635L83.833 9.635L83.833 9.381Q84.189 9.381 84.431 9.148Q84.673 8.916 84.784 8.568Q84.896 8.221 84.896 7.865L85.177 7.865L85.177 9.338L86.353 9.338L86.353 9.635L85.177 9.635L85.177 11.810Q85.177 12.131 85.296 12.359Q85.415 12.588 85.696 12.588Q85.876 12.588 85.993 12.465Q86.111 12.342 86.163 12.162Q86.216 11.982 86.216 11.810L86.216 11.338L86.497 11.338L86.497 11.826Q86.497 12.080 86.392 12.320Q86.286 12.560 86.089 12.713Q85.892 12.865 85.634 12.865Q85.318 12.865 85.066 12.742Q84.814 12.619 84.675 12.385Q84.536 12.150 84.536 11.826\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M208.866 83.92h58.977V-58.345h-58.977Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr9\" font-size=\"9\">\u003Cg transform=\"translate(147.406 3.075)\">\u003Cpath d=\"M70.426 12.787L65.117 12.787L65.117 12.471Q66.036 12.471 66.036 12.176L66.036 7.250Q66.036 6.955 65.117 6.955L65.117 6.639L70.307 6.639L70.562 8.700L70.272 8.700Q70.202 8.107 70.087 7.775Q69.973 7.443 69.764 7.267Q69.556 7.092 69.211 7.024Q68.866 6.955 68.255 6.955L67.341 6.955Q67.090 6.955 66.985 7.004Q66.879 7.052 66.879 7.250L66.879 9.438L67.565 9.438Q68.044 9.438 68.266 9.364Q68.488 9.289 68.580 9.074Q68.672 8.858 68.672 8.388L68.958 8.388L68.958 10.805L68.672 10.805Q68.672 10.335 68.580 10.120Q68.488 9.904 68.266 9.829Q68.044 9.755 67.565 9.755L66.879 9.755L66.879 12.176Q66.879 12.370 66.985 12.420Q67.090 12.471 67.341 12.471L68.321 12.471Q68.958 12.471 69.347 12.374Q69.736 12.277 69.956 12.055Q70.175 11.833 70.296 11.455Q70.417 11.078 70.527 10.427L70.813 10.427L70.426 12.787M73.471 12.787L71.384 12.787L71.384 12.471Q71.691 12.471 71.883 12.418Q72.074 12.365 72.074 12.176L72.074 9.728Q72.074 9.487 72.003 9.379Q71.933 9.271 71.799 9.247Q71.665 9.223 71.384 9.223L71.384 8.907L72.724 8.810L72.724 9.645Q72.922 9.263 73.276 9.036Q73.629 8.810 74.056 8.810Q75.334 8.810 75.334 10.023L75.334 12.176Q75.334 12.365 75.526 12.418Q75.717 12.471 76.024 12.471L76.024 12.787L73.937 12.787L73.937 12.471Q74.249 12.471 74.440 12.418Q74.631 12.365 74.631 12.176L74.631 10.058Q74.631 9.799 74.587 9.577Q74.543 9.355 74.398 9.212Q74.253 9.069 73.994 9.069Q73.651 9.069 73.370 9.258Q73.089 9.447 72.933 9.759Q72.777 10.071 72.777 10.418L72.777 12.176Q72.777 12.365 72.970 12.418Q73.164 12.471 73.471 12.471\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(147.406 3.075)\">\u003Cpath d=\"M78.201 12.769L76.870 9.522Q76.782 9.324 76.617 9.274Q76.452 9.223 76.149 9.223L76.149 8.907L78.074 8.907L78.074 9.223Q77.582 9.223 77.582 9.438Q77.582 9.460 77.599 9.522L78.615 11.996L79.524 9.772Q79.559 9.689 79.559 9.592Q79.559 9.421 79.436 9.322Q79.313 9.223 79.146 9.223L79.146 8.907L80.658 8.907L80.658 9.223Q80.372 9.223 80.159 9.366Q79.946 9.509 79.841 9.772L78.606 12.769Q78.562 12.888 78.434 12.888L78.373 12.888Q78.245 12.888 78.201 12.769M83.141 12.787L81.155 12.787L81.155 12.471Q81.462 12.471 81.653 12.418Q81.844 12.365 81.844 12.176L81.844 9.728Q81.844 9.482 81.779 9.377Q81.713 9.271 81.587 9.247Q81.462 9.223 81.190 9.223L81.190 8.907L82.521 8.810L82.521 12.176Q82.521 12.370 82.686 12.420Q82.851 12.471 83.141 12.471L83.141 12.787M81.541 7.263Q81.541 7.057 81.691 6.907Q81.840 6.758 82.042 6.758Q82.174 6.758 82.291 6.828Q82.407 6.898 82.477 7.015Q82.548 7.131 82.548 7.263Q82.548 7.465 82.398 7.615Q82.249 7.764 82.042 7.764Q81.840 7.764 81.691 7.615Q81.541 7.465 81.541 7.263M85.896 12.787L83.664 12.787L83.664 12.471Q83.976 12.471 84.167 12.418Q84.358 12.365 84.358 12.176L84.358 9.728Q84.358 9.487 84.288 9.379Q84.218 9.271 84.084 9.247Q83.949 9.223 83.664 9.223L83.664 8.907L84.978 8.810L84.978 9.671Q85.140 9.280 85.408 9.045Q85.677 8.810 86.068 8.810Q86.340 8.810 86.555 8.973Q86.771 9.135 86.771 9.394Q86.771 9.570 86.652 9.689Q86.533 9.808 86.358 9.808Q86.177 9.808 86.059 9.689Q85.940 9.570 85.940 9.394Q85.940 9.179 86.094 9.069L86.076 9.069Q85.698 9.069 85.466 9.331Q85.233 9.592 85.134 9.979Q85.035 10.366 85.035 10.726L85.035 12.176Q85.035 12.365 85.292 12.418Q85.549 12.471 85.896 12.471L85.896 12.787M87.289 10.880Q87.289 10.313 87.562 9.825Q87.834 9.337 88.304 9.045Q88.775 8.753 89.342 8.753Q89.763 8.753 90.139 8.922Q90.515 9.091 90.792 9.383Q91.069 9.676 91.227 10.071Q91.385 10.467 91.385 10.880Q91.385 11.429 91.106 11.891Q90.827 12.352 90.359 12.620Q89.891 12.888 89.342 12.888Q88.788 12.888 88.318 12.620Q87.847 12.352 87.568 11.891Q87.289 11.429 87.289 10.880M89.342 12.598Q89.838 12.598 90.115 12.337Q90.392 12.075 90.484 11.671Q90.576 11.266 90.576 10.770Q90.576 10.295 90.478 9.906Q90.379 9.517 90.106 9.267Q89.834 9.016 89.342 9.016Q88.630 9.016 88.366 9.511Q88.102 10.005 88.102 10.770Q88.102 11.570 88.357 12.084Q88.612 12.598 89.342 12.598M94.035 12.787L91.948 12.787L91.948 12.471Q92.255 12.471 92.446 12.418Q92.637 12.365 92.637 12.176L92.637 9.728Q92.637 9.487 92.567 9.379Q92.497 9.271 92.363 9.247Q92.229 9.223 91.948 9.223L91.948 8.907L93.288 8.810L93.288 9.645Q93.486 9.263 93.839 9.036Q94.193 8.810 94.619 8.810Q95.898 8.810 95.898 10.023L95.898 12.176Q95.898 12.365 96.089 12.418Q96.281 12.471 96.588 12.471L96.588 12.787L94.501 12.787L94.501 12.471Q94.813 12.471 95.004 12.418Q95.195 12.365 95.195 12.176L95.195 10.058Q95.195 9.799 95.151 9.577Q95.107 9.355 94.962 9.212Q94.817 9.069 94.558 9.069Q94.215 9.069 93.934 9.258Q93.653 9.447 93.497 9.759Q93.341 10.071 93.341 10.418L93.341 12.176Q93.341 12.365 93.534 12.418Q93.727 12.471 94.035 12.471L94.035 12.787M99.172 12.787L97.085 12.787L97.085 12.471Q97.392 12.471 97.584 12.418Q97.775 12.365 97.775 12.176L97.775 9.728Q97.775 9.487 97.704 9.379Q97.634 9.271 97.500 9.247Q97.366 9.223 97.085 9.223L97.085 8.907L98.425 8.810L98.425 9.645Q98.623 9.267 98.983 9.038Q99.344 8.810 99.765 8.810Q100.811 8.810 100.996 9.619Q101.198 9.249 101.556 9.030Q101.914 8.810 102.332 8.810Q102.956 8.810 103.281 9.104Q103.606 9.399 103.606 10.023L103.606 12.176Q103.606 12.365 103.800 12.418Q103.993 12.471 104.301 12.471L104.301 12.787L102.213 12.787L102.213 12.471Q102.521 12.471 102.714 12.418Q102.907 12.365 102.907 12.176L102.907 10.058Q102.907 9.627 102.780 9.348Q102.653 9.069 102.266 9.069Q101.923 9.069 101.640 9.258Q101.356 9.447 101.200 9.759Q101.044 10.071 101.044 10.418L101.044 12.176Q101.044 12.365 101.235 12.418Q101.427 12.471 101.734 12.471L101.734 12.787L99.647 12.787L99.647 12.471Q99.959 12.471 100.150 12.418Q100.341 12.365 100.341 12.176L100.341 10.058Q100.341 9.799 100.297 9.577Q100.253 9.355 100.108 9.212Q99.963 9.069 99.704 9.069Q99.168 9.069 98.823 9.476Q98.478 9.882 98.478 10.418L98.478 12.176Q98.478 12.365 98.671 12.418Q98.865 12.471 99.172 12.471L99.172 12.787M106.801 12.888Q106.243 12.888 105.771 12.605Q105.298 12.321 105.023 11.844Q104.749 11.368 104.749 10.814Q104.749 10.418 104.892 10.043Q105.034 9.667 105.292 9.379Q105.549 9.091 105.907 8.922Q106.265 8.753 106.669 8.753Q107.214 8.753 107.585 8.990Q107.957 9.227 108.144 9.645Q108.330 10.062 108.330 10.599Q108.330 10.651 108.306 10.689Q108.282 10.726 108.234 10.726L105.562 10.726L105.562 10.805Q105.562 11.552 105.874 12.075Q106.186 12.598 106.885 12.598Q107.289 12.598 107.610 12.341Q107.930 12.084 108.053 11.680Q108.071 11.600 108.155 11.600L108.234 11.600Q108.273 11.600 108.302 11.631Q108.330 11.662 108.330 11.706L108.330 11.741Q108.225 12.084 108.003 12.343Q107.781 12.602 107.467 12.745Q107.153 12.888 106.801 12.888M105.571 10.475L107.684 10.475Q107.684 10.207 107.632 9.961Q107.579 9.715 107.458 9.493Q107.337 9.271 107.139 9.144Q106.942 9.016 106.669 9.016Q106.326 9.016 106.074 9.241Q105.821 9.465 105.696 9.803Q105.571 10.141 105.571 10.475M110.989 12.787L108.902 12.787L108.902 12.471Q109.209 12.471 109.400 12.418Q109.592 12.365 109.592 12.176L109.592 9.728Q109.592 9.487 109.521 9.379Q109.451 9.271 109.317 9.247Q109.183 9.223 108.902 9.223L108.902 8.907L110.242 8.810L110.242 9.645Q110.440 9.263 110.793 9.036Q111.147 8.810 111.573 8.810Q112.852 8.810 112.852 10.023L112.852 12.176Q112.852 12.365 113.043 12.418Q113.235 12.471 113.542 12.471L113.542 12.787L111.455 12.787L111.455 12.471Q111.767 12.471 111.958 12.418Q112.149 12.365 112.149 12.176L112.149 10.058Q112.149 9.799 112.105 9.577Q112.061 9.355 111.916 9.212Q111.771 9.069 111.512 9.069Q111.169 9.069 110.888 9.258Q110.607 9.447 110.451 9.759Q110.295 10.071 110.295 10.418L110.295 12.176Q110.295 12.365 110.488 12.418Q110.681 12.471 110.989 12.471\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(147.406 3.075)\">\u003Cpath d=\"M114.443 11.715L114.443 9.223L113.678 9.223L113.678 8.964Q114.083 8.964 114.349 8.698Q114.614 8.432 114.735 8.032Q114.856 7.632 114.856 7.250L115.146 7.250L115.146 8.907L116.434 8.907L116.434 9.223L115.146 9.223L115.146 11.680Q115.146 12.049 115.271 12.323Q115.397 12.598 115.722 12.598Q116.021 12.598 116.159 12.304Q116.298 12.009 116.298 11.680L116.298 11.157L116.583 11.157L116.583 11.715Q116.583 11.992 116.473 12.264Q116.363 12.537 116.150 12.712Q115.937 12.888 115.656 12.888Q115.296 12.888 115.023 12.750Q114.751 12.611 114.597 12.348Q114.443 12.084 114.443 11.715\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(57.412 -76.941)\">\u003Cpath d=\"M65.281 12.849L65.281 11.276Q65.281 11.249 65.306 11.223Q65.332 11.198 65.359 11.198L65.472 11.198Q65.500 11.198 65.523 11.225Q65.547 11.252 65.547 11.276Q65.547 11.621 65.679 11.885Q65.811 12.148 66.040 12.317Q66.269 12.486 66.571 12.567Q66.874 12.647 67.215 12.647Q67.482 12.647 67.718 12.519Q67.954 12.391 68.099 12.168Q68.244 11.946 68.244 11.680Q68.244 11.457 68.138 11.261Q68.032 11.064 67.851 10.929Q67.670 10.794 67.444 10.743L66.416 10.511Q66.105 10.439 65.845 10.253Q65.585 10.066 65.433 9.795Q65.281 9.523 65.281 9.208Q65.281 8.822 65.494 8.515Q65.708 8.207 66.055 8.036Q66.402 7.865 66.781 7.865Q67.010 7.865 67.239 7.918Q67.468 7.971 67.667 8.079Q67.865 8.186 68.019 8.350L68.313 7.910Q68.336 7.865 68.377 7.865L68.425 7.865Q68.456 7.865 68.478 7.891Q68.500 7.916 68.500 7.944L68.500 9.519Q68.500 9.540 68.477 9.567Q68.453 9.595 68.425 9.595L68.313 9.595Q68.251 9.595 68.237 9.519Q68.196 9.106 68.015 8.786Q67.834 8.467 67.523 8.292Q67.212 8.118 66.781 8.118Q66.532 8.118 66.292 8.229Q66.053 8.340 65.903 8.538Q65.752 8.737 65.752 9Q65.752 9.212 65.860 9.393Q65.968 9.574 66.144 9.694Q66.320 9.813 66.528 9.854L67.557 10.083Q67.875 10.155 68.142 10.360Q68.408 10.565 68.560 10.859Q68.712 11.153 68.712 11.485Q68.712 11.878 68.507 12.213Q68.302 12.548 67.957 12.737Q67.612 12.927 67.215 12.927Q66.795 12.927 66.416 12.814Q66.036 12.702 65.766 12.452L65.472 12.886Q65.445 12.927 65.407 12.927L65.359 12.927Q65.332 12.927 65.306 12.902Q65.281 12.876 65.281 12.849M69.481 11.252Q69.481 10.931 69.606 10.642Q69.731 10.353 69.957 10.130Q70.182 9.906 70.478 9.786Q70.773 9.666 71.091 9.666Q71.419 9.666 71.681 9.766Q71.942 9.865 72.118 10.047Q72.294 10.230 72.388 10.488Q72.482 10.746 72.482 11.078Q72.482 11.170 72.400 11.191L70.145 11.191L70.145 11.252Q70.145 11.840 70.428 12.223Q70.712 12.606 71.279 12.606Q71.601 12.606 71.869 12.413Q72.137 12.220 72.226 11.905Q72.233 11.864 72.308 11.850L72.400 11.850Q72.482 11.874 72.482 11.946Q72.482 11.953 72.476 11.980Q72.363 12.377 71.992 12.616Q71.621 12.855 71.197 12.855Q70.760 12.855 70.360 12.647Q69.960 12.438 69.721 12.071Q69.481 11.704 69.481 11.252M70.151 10.982L71.966 10.982Q71.966 10.705 71.869 10.453Q71.771 10.200 71.573 10.044Q71.375 9.889 71.091 9.889Q70.814 9.889 70.601 10.047Q70.387 10.206 70.269 10.461Q70.151 10.716 70.151 10.982M74.752 12.787L73.118 12.787L73.118 12.507Q73.347 12.507 73.496 12.473Q73.645 12.438 73.645 12.298L73.645 10.449Q73.645 10.179 73.537 10.118Q73.429 10.056 73.118 10.056L73.118 9.776L74.178 9.701L74.178 10.350Q74.349 10.042 74.653 9.871Q74.957 9.701 75.302 9.701Q75.808 9.701 76.092 9.924Q76.375 10.148 76.375 10.644L76.375 12.298Q76.375 12.435 76.524 12.471Q76.673 12.507 76.898 12.507L76.898 12.787L75.268 12.787L75.268 12.507Q75.497 12.507 75.646 12.473Q75.794 12.438 75.794 12.298L75.794 10.658Q75.794 10.323 75.675 10.123Q75.555 9.923 75.241 9.923Q74.971 9.923 74.737 10.059Q74.502 10.196 74.364 10.430Q74.226 10.664 74.226 10.938L74.226 12.298Q74.226 12.435 74.376 12.471Q74.526 12.507 74.752 12.507L74.752 12.787M77.486 12.780L77.486 11.717Q77.486 11.693 77.514 11.666Q77.541 11.639 77.565 11.639L77.674 11.639Q77.739 11.639 77.753 11.697Q77.849 12.131 78.095 12.382Q78.341 12.633 78.754 12.633Q79.096 12.633 79.349 12.500Q79.602 12.367 79.602 12.059Q79.602 11.902 79.508 11.787Q79.414 11.673 79.276 11.604Q79.137 11.536 78.970 11.498L78.389 11.399Q78.033 11.331 77.760 11.110Q77.486 10.890 77.486 10.548Q77.486 10.299 77.597 10.124Q77.709 9.950 77.895 9.851Q78.081 9.752 78.296 9.709Q78.512 9.666 78.754 9.666Q79.168 9.666 79.448 9.848L79.664 9.673Q79.674 9.670 79.681 9.668Q79.688 9.666 79.698 9.666L79.749 9.666Q79.776 9.666 79.800 9.690Q79.824 9.714 79.824 9.742L79.824 10.589Q79.824 10.610 79.800 10.637Q79.776 10.664 79.749 10.664L79.636 10.664Q79.609 10.664 79.583 10.639Q79.558 10.613 79.558 10.589Q79.558 10.353 79.452 10.189Q79.346 10.025 79.163 9.943Q78.980 9.861 78.748 9.861Q78.419 9.861 78.163 9.964Q77.907 10.066 77.907 10.343Q77.907 10.538 78.090 10.647Q78.272 10.757 78.501 10.798L79.076 10.904Q79.322 10.952 79.535 11.080Q79.749 11.208 79.886 11.411Q80.022 11.615 80.022 11.864Q80.022 12.377 79.657 12.616Q79.291 12.855 78.754 12.855Q78.259 12.855 77.927 12.561L77.661 12.835Q77.640 12.855 77.613 12.855L77.565 12.855Q77.541 12.855 77.514 12.828Q77.486 12.801 77.486 12.780M80.610 11.304Q80.610 10.962 80.745 10.663Q80.880 10.364 81.120 10.140Q81.359 9.916 81.677 9.791Q81.995 9.666 82.326 9.666Q82.771 9.666 83.170 9.882Q83.570 10.097 83.804 10.475Q84.039 10.852 84.039 11.304Q84.039 11.645 83.897 11.929Q83.755 12.213 83.511 12.420Q83.266 12.626 82.957 12.741Q82.647 12.855 82.326 12.855Q81.896 12.855 81.494 12.654Q81.092 12.452 80.851 12.100Q80.610 11.748 80.610 11.304M82.326 12.606Q82.928 12.606 83.152 12.228Q83.375 11.850 83.375 11.218Q83.375 10.606 83.141 10.247Q82.907 9.889 82.326 9.889Q81.273 9.889 81.273 11.218Q81.273 11.850 81.499 12.228Q81.725 12.606 82.326 12.606M86.383 12.787L84.647 12.787L84.647 12.507Q84.876 12.507 85.025 12.473Q85.173 12.438 85.173 12.298L85.173 10.449Q85.173 10.179 85.066 10.118Q84.958 10.056 84.647 10.056L84.647 9.776L85.676 9.701L85.676 10.408Q85.806 10.100 86.048 9.901Q86.291 9.701 86.609 9.701Q86.828 9.701 86.999 9.825Q87.169 9.950 87.169 10.162Q87.169 10.299 87.070 10.398Q86.971 10.497 86.838 10.497Q86.701 10.497 86.602 10.398Q86.503 10.299 86.503 10.162Q86.503 10.022 86.602 9.923Q86.312 9.923 86.112 10.119Q85.912 10.316 85.819 10.610Q85.727 10.904 85.727 11.184L85.727 12.298Q85.727 12.507 86.383 12.507L86.383 12.787M87.754 12.780L87.754 11.717Q87.754 11.693 87.781 11.666Q87.809 11.639 87.833 11.639L87.942 11.639Q88.007 11.639 88.021 11.697Q88.116 12.131 88.362 12.382Q88.608 12.633 89.022 12.633Q89.364 12.633 89.617 12.500Q89.870 12.367 89.870 12.059Q89.870 11.902 89.776 11.787Q89.682 11.673 89.543 11.604Q89.405 11.536 89.237 11.498L88.656 11.399Q88.301 11.331 88.027 11.110Q87.754 10.890 87.754 10.548Q87.754 10.299 87.865 10.124Q87.976 9.950 88.162 9.851Q88.349 9.752 88.564 9.709Q88.779 9.666 89.022 9.666Q89.436 9.666 89.716 9.848L89.931 9.673Q89.941 9.670 89.948 9.668Q89.955 9.666 89.965 9.666L90.017 9.666Q90.044 9.666 90.068 9.690Q90.092 9.714 90.092 9.742L90.092 10.589Q90.092 10.610 90.068 10.637Q90.044 10.664 90.017 10.664L89.904 10.664Q89.876 10.664 89.851 10.639Q89.825 10.613 89.825 10.589Q89.825 10.353 89.719 10.189Q89.613 10.025 89.430 9.943Q89.248 9.861 89.015 9.861Q88.687 9.861 88.431 9.964Q88.174 10.066 88.174 10.343Q88.174 10.538 88.357 10.647Q88.540 10.757 88.769 10.798L89.343 10.904Q89.589 10.952 89.803 11.080Q90.017 11.208 90.153 11.411Q90.290 11.615 90.290 11.864Q90.290 12.377 89.924 12.616Q89.559 12.855 89.022 12.855Q88.526 12.855 88.195 12.561L87.928 12.835Q87.908 12.855 87.880 12.855L87.833 12.855Q87.809 12.855 87.781 12.828Q87.754 12.801 87.754 12.780\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(48.858 81.724)\">\u003Cpath d=\"M66.696 12.787L65.106 12.787L65.106 12.507Q65.749 12.507 65.906 12.107L67.550 7.892Q67.584 7.797 67.697 7.797L67.779 7.797Q67.889 7.797 67.930 7.892L69.649 12.298Q69.717 12.438 69.907 12.473Q70.097 12.507 70.370 12.507L70.370 12.787L68.371 12.787L68.371 12.507Q68.935 12.507 68.935 12.332Q68.935 12.315 68.933 12.308Q68.931 12.302 68.928 12.298L68.507 11.232L66.549 11.232L66.207 12.107Q66.193 12.107 66.193 12.185Q66.193 12.346 66.356 12.426Q66.518 12.507 66.696 12.507L66.696 12.787M67.530 8.713L66.662 10.952L68.405 10.952L67.530 8.713M71.006 11.276Q71.006 10.948 71.141 10.647Q71.276 10.347 71.512 10.126Q71.748 9.906 72.052 9.786Q72.356 9.666 72.681 9.666Q73.187 9.666 73.535 9.769Q73.884 9.871 73.884 10.247Q73.884 10.394 73.786 10.495Q73.689 10.596 73.542 10.596Q73.388 10.596 73.289 10.497Q73.190 10.398 73.190 10.247Q73.190 10.059 73.330 9.967Q73.128 9.916 72.688 9.916Q72.332 9.916 72.103 10.112Q71.874 10.309 71.773 10.618Q71.672 10.928 71.672 11.276Q71.672 11.625 71.799 11.931Q71.925 12.237 72.180 12.421Q72.435 12.606 72.790 12.606Q73.012 12.606 73.197 12.522Q73.381 12.438 73.516 12.283Q73.651 12.127 73.709 11.919Q73.723 11.864 73.778 11.864L73.891 11.864Q73.921 11.864 73.944 11.888Q73.966 11.912 73.966 11.946L73.966 11.967Q73.880 12.254 73.692 12.452Q73.504 12.650 73.240 12.753Q72.975 12.855 72.681 12.855Q72.250 12.855 71.862 12.649Q71.474 12.442 71.240 12.079Q71.006 11.717 71.006 11.276M75.080 11.946L75.080 10.049L74.441 10.049L74.441 9.827Q74.759 9.827 74.976 9.617Q75.193 9.407 75.294 9.097Q75.395 8.788 75.395 8.480L75.661 8.480L75.661 9.769L76.738 9.769L76.738 10.049L75.661 10.049L75.661 11.933Q75.661 12.209 75.765 12.408Q75.870 12.606 76.129 12.606Q76.287 12.606 76.393 12.502Q76.499 12.397 76.548 12.244Q76.598 12.090 76.598 11.933L76.598 11.519L76.864 11.519L76.864 11.946Q76.864 12.172 76.765 12.382Q76.666 12.592 76.481 12.724Q76.297 12.855 76.068 12.855Q75.630 12.855 75.355 12.618Q75.080 12.380 75.080 11.946M78.249 11.953L78.249 10.449Q78.249 10.179 78.141 10.118Q78.033 10.056 77.722 10.056L77.722 9.776L78.830 9.701L78.830 11.933L78.830 11.953Q78.830 12.233 78.881 12.377Q78.932 12.520 79.074 12.577Q79.216 12.633 79.503 12.633Q79.756 12.633 79.961 12.493Q80.166 12.353 80.282 12.127Q80.398 11.902 80.398 11.652L80.398 10.449Q80.398 10.179 80.291 10.118Q80.183 10.056 79.872 10.056L79.872 9.776L80.980 9.701L80.980 12.114Q80.980 12.305 81.032 12.387Q81.085 12.469 81.186 12.488Q81.287 12.507 81.502 12.507L81.502 12.787L80.426 12.855L80.426 12.291Q80.316 12.473 80.171 12.596Q80.026 12.719 79.840 12.787Q79.653 12.855 79.452 12.855Q78.249 12.855 78.249 11.953M82.148 12.059Q82.148 11.727 82.372 11.500Q82.596 11.273 82.940 11.145Q83.283 11.016 83.656 10.964Q84.028 10.911 84.333 10.911L84.333 10.658Q84.333 10.453 84.225 10.273Q84.117 10.094 83.936 9.991Q83.755 9.889 83.546 9.889Q83.140 9.889 82.904 9.981Q82.993 10.018 83.039 10.102Q83.085 10.186 83.085 10.288Q83.085 10.384 83.039 10.463Q82.993 10.541 82.912 10.586Q82.832 10.630 82.743 10.630Q82.593 10.630 82.492 10.533Q82.391 10.435 82.391 10.288Q82.391 9.666 83.546 9.666Q83.758 9.666 84.008 9.730Q84.257 9.793 84.459 9.912Q84.661 10.032 84.787 10.217Q84.914 10.401 84.914 10.644L84.914 12.220Q84.914 12.336 84.975 12.432Q85.037 12.527 85.149 12.527Q85.259 12.527 85.324 12.433Q85.389 12.339 85.389 12.220L85.389 11.772L85.655 11.772L85.655 12.220Q85.655 12.490 85.428 12.655Q85.201 12.821 84.920 12.821Q84.712 12.821 84.575 12.667Q84.438 12.514 84.415 12.298Q84.268 12.565 83.986 12.710Q83.704 12.855 83.379 12.855Q83.102 12.855 82.818 12.780Q82.535 12.705 82.342 12.526Q82.148 12.346 82.148 12.059M82.764 12.059Q82.764 12.233 82.865 12.363Q82.965 12.493 83.121 12.563Q83.276 12.633 83.440 12.633Q83.659 12.633 83.868 12.536Q84.076 12.438 84.204 12.257Q84.333 12.076 84.333 11.850L84.333 11.122Q84.008 11.122 83.642 11.213Q83.276 11.304 83.020 11.516Q82.764 11.727 82.764 12.059M86.599 11.946L86.599 10.049L85.959 10.049L85.959 9.827Q86.277 9.827 86.494 9.617Q86.711 9.407 86.812 9.097Q86.913 8.788 86.913 8.480L87.180 8.480L87.180 9.769L88.256 9.769L88.256 10.049L87.180 10.049L87.180 11.933Q87.180 12.209 87.284 12.408Q87.388 12.606 87.648 12.606Q87.805 12.606 87.911 12.502Q88.017 12.397 88.067 12.244Q88.116 12.090 88.116 11.933L88.116 11.519L88.383 11.519L88.383 11.946Q88.383 12.172 88.284 12.382Q88.185 12.592 88 12.724Q87.815 12.855 87.586 12.855Q87.149 12.855 86.874 12.618Q86.599 12.380 86.599 11.946M89.152 11.304Q89.152 10.962 89.287 10.663Q89.422 10.364 89.661 10.140Q89.900 9.916 90.218 9.791Q90.536 9.666 90.868 9.666Q91.312 9.666 91.712 9.882Q92.112 10.097 92.346 10.475Q92.580 10.852 92.580 11.304Q92.580 11.645 92.438 11.929Q92.296 12.213 92.052 12.420Q91.808 12.626 91.498 12.741Q91.189 12.855 90.868 12.855Q90.437 12.855 90.035 12.654Q89.634 12.452 89.393 12.100Q89.152 11.748 89.152 11.304M90.868 12.606Q91.469 12.606 91.693 12.228Q91.917 11.850 91.917 11.218Q91.917 10.606 91.683 10.247Q91.449 9.889 90.868 9.889Q89.815 9.889 89.815 11.218Q89.815 11.850 90.041 12.228Q90.266 12.606 90.868 12.606M94.925 12.787L93.188 12.787L93.188 12.507Q93.417 12.507 93.566 12.473Q93.715 12.438 93.715 12.298L93.715 10.449Q93.715 10.179 93.607 10.118Q93.500 10.056 93.188 10.056L93.188 9.776L94.217 9.701L94.217 10.408Q94.347 10.100 94.590 9.901Q94.833 9.701 95.150 9.701Q95.369 9.701 95.540 9.825Q95.711 9.950 95.711 10.162Q95.711 10.299 95.612 10.398Q95.513 10.497 95.379 10.497Q95.243 10.497 95.144 10.398Q95.044 10.299 95.044 10.162Q95.044 10.022 95.144 9.923Q94.853 9.923 94.653 10.119Q94.453 10.316 94.361 10.610Q94.269 10.904 94.269 11.184L94.269 12.298Q94.269 12.507 94.925 12.507L94.925 12.787M96.295 12.780L96.295 11.717Q96.295 11.693 96.323 11.666Q96.350 11.639 96.374 11.639L96.483 11.639Q96.548 11.639 96.562 11.697Q96.658 12.131 96.904 12.382Q97.150 12.633 97.563 12.633Q97.905 12.633 98.158 12.500Q98.411 12.367 98.411 12.059Q98.411 11.902 98.317 11.787Q98.223 11.673 98.085 11.604Q97.946 11.536 97.779 11.498L97.198 11.399Q96.842 11.331 96.569 11.110Q96.295 10.890 96.295 10.548Q96.295 10.299 96.407 10.124Q96.518 9.950 96.704 9.851Q96.890 9.752 97.105 9.709Q97.321 9.666 97.563 9.666Q97.977 9.666 98.257 9.848L98.473 9.673Q98.483 9.670 98.490 9.668Q98.497 9.666 98.507 9.666L98.558 9.666Q98.585 9.666 98.609 9.690Q98.633 9.714 98.633 9.742L98.633 10.589Q98.633 10.610 98.609 10.637Q98.585 10.664 98.558 10.664L98.445 10.664Q98.418 10.664 98.392 10.639Q98.367 10.613 98.367 10.589Q98.367 10.353 98.261 10.189Q98.155 10.025 97.972 9.943Q97.789 9.861 97.557 9.861Q97.229 9.861 96.972 9.964Q96.716 10.066 96.716 10.343Q96.716 10.538 96.899 10.647Q97.082 10.757 97.311 10.798L97.885 10.904Q98.131 10.952 98.344 11.080Q98.558 11.208 98.695 11.411Q98.832 11.615 98.832 11.864Q98.832 12.377 98.466 12.616Q98.100 12.855 97.563 12.855Q97.068 12.855 96.736 12.561L96.470 12.835Q96.449 12.855 96.422 12.855L96.374 12.855Q96.350 12.855 96.323 12.828Q96.295 12.801 96.295 12.780\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M70.483-18.51h73.977v-28.454H70.483Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M66.616 3.256L65.546 0.400Q65.480 0.221 65.349 0.178Q65.218 0.135 64.960 0.135L64.960-0.162L66.640-0.162L66.640 0.135Q66.190 0.135 66.190 0.334Q66.194 0.349 66.196 0.367Q66.198 0.385 66.198 0.400L66.991 2.494L67.702 0.584Q67.667 0.490 67.667 0.445Q67.667 0.400 67.632 0.400Q67.565 0.221 67.435 0.178Q67.304 0.135 67.050 0.135L67.050-0.162L68.640-0.162L68.640 0.135Q68.190 0.135 68.190 0.334Q68.194 0.353 68.196 0.371Q68.198 0.389 68.198 0.400L69.030 2.615L69.784 0.615Q69.808 0.557 69.808 0.486Q69.808 0.326 69.671 0.230Q69.534 0.135 69.366 0.135L69.366-0.162L70.753-0.162L70.753 0.135Q70.519 0.135 70.341 0.262Q70.163 0.389 70.081 0.615L69.097 3.256Q69.042 3.365 68.929 3.365L68.870 3.365Q68.757 3.365 68.714 3.256L67.855 0.982L66.999 3.256Q66.960 3.365 66.839 3.365L66.784 3.365Q66.671 3.365 66.616 3.256M73.097 3.287L71.241 3.287L71.241 2.990Q71.515 2.990 71.683 2.943Q71.851 2.896 71.851 2.728L71.851-1.432Q71.851-1.647 71.788-1.742Q71.726-1.838 71.606-1.859Q71.487-1.881 71.241-1.881L71.241-2.178L72.464-2.264L72.464 0.439Q72.589 0.228 72.776 0.078Q72.964-0.072 73.190-0.156Q73.417-0.240 73.663-0.240Q74.831-0.240 74.831 0.838L74.831 2.728Q74.831 2.896 75.001 2.943Q75.171 2.990 75.440 2.990L75.440 3.287L73.585 3.287L73.585 2.990Q73.858 2.990 74.026 2.943Q74.194 2.896 74.194 2.728L74.194 0.853Q74.194 0.471 74.073 0.242Q73.952 0.014 73.601 0.014Q73.288 0.014 73.034 0.176Q72.780 0.338 72.634 0.607Q72.487 0.877 72.487 1.174L72.487 2.728Q72.487 2.896 72.657 2.943Q72.827 2.990 73.097 2.990L73.097 3.287M75.983 2.455Q75.983 1.971 76.386 1.676Q76.788 1.381 77.339 1.262Q77.890 1.142 78.382 1.142L78.382 0.853Q78.382 0.627 78.267 0.420Q78.151 0.213 77.954 0.094Q77.757-0.026 77.526-0.026Q77.101-0.026 76.815 0.080Q76.886 0.107 76.933 0.162Q76.980 0.217 77.005 0.287Q77.030 0.357 77.030 0.432Q77.030 0.537 76.980 0.629Q76.929 0.721 76.837 0.771Q76.745 0.822 76.640 0.822Q76.534 0.822 76.442 0.771Q76.351 0.721 76.300 0.629Q76.249 0.537 76.249 0.432Q76.249 0.014 76.638-0.133Q77.026-0.279 77.526-0.279Q77.858-0.279 78.212-0.149Q78.565-0.018 78.794 0.236Q79.022 0.490 79.022 0.838L79.022 2.639Q79.022 2.771 79.095 2.881Q79.167 2.990 79.296 2.990Q79.421 2.990 79.489 2.885Q79.558 2.779 79.558 2.639L79.558 2.127L79.839 2.127L79.839 2.639Q79.839 2.842 79.722 3Q79.605 3.158 79.423 3.242Q79.241 3.326 79.038 3.326Q78.808 3.326 78.655 3.154Q78.503 2.982 78.472 2.752Q78.312 3.033 78.003 3.199Q77.694 3.365 77.343 3.365Q76.831 3.365 76.407 3.142Q75.983 2.920 75.983 2.455M76.671 2.455Q76.671 2.740 76.897 2.926Q77.124 3.111 77.417 3.111Q77.663 3.111 77.888 2.994Q78.112 2.877 78.247 2.674Q78.382 2.471 78.382 2.217L78.382 1.385Q78.116 1.385 77.831 1.439Q77.546 1.494 77.274 1.623Q77.003 1.752 76.837 1.959Q76.671 2.166 76.671 2.455M80.757 2.326L80.757 0.135L80.054 0.135L80.054-0.119Q80.409-0.119 80.651-0.352Q80.894-0.584 81.005-0.932Q81.116-1.279 81.116-1.635L81.397-1.635L81.397-0.162L82.573-0.162L82.573 0.135L81.397 0.135L81.397 2.310Q81.397 2.631 81.517 2.859Q81.636 3.088 81.917 3.088Q82.097 3.088 82.214 2.965Q82.331 2.842 82.384 2.662Q82.437 2.482 82.437 2.310L82.437 1.838L82.718 1.838L82.718 2.326Q82.718 2.580 82.612 2.820Q82.507 3.060 82.310 3.213Q82.112 3.365 81.855 3.365Q81.538 3.365 81.286 3.242Q81.034 3.119 80.896 2.885Q80.757 2.650 80.757 2.326\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M86.906 2.326L86.906 0.135L86.203 0.135L86.203-0.119Q86.559-0.119 86.801-0.352Q87.043-0.584 87.154-0.932Q87.266-1.279 87.266-1.635L87.547-1.635L87.547-0.162L88.723-0.162L88.723 0.135L87.547 0.135L87.547 2.310Q87.547 2.631 87.666 2.859Q87.785 3.088 88.066 3.088Q88.246 3.088 88.363 2.965Q88.481 2.842 88.533 2.662Q88.586 2.482 88.586 2.310L88.586 1.838L88.867 1.838L88.867 2.326Q88.867 2.580 88.762 2.820Q88.656 3.060 88.459 3.213Q88.262 3.365 88.004 3.365Q87.688 3.365 87.436 3.242Q87.184 3.119 87.045 2.885Q86.906 2.650 86.906 2.326M91.516 3.287L89.660 3.287L89.660 2.990Q89.934 2.990 90.102 2.943Q90.270 2.896 90.270 2.728L90.270-1.432Q90.270-1.647 90.207-1.742Q90.145-1.838 90.025-1.859Q89.906-1.881 89.660-1.881L89.660-2.178L90.883-2.264L90.883 0.439Q91.008 0.228 91.195 0.078Q91.383-0.072 91.609-0.156Q91.836-0.240 92.082-0.240Q93.250-0.240 93.250 0.838L93.250 2.728Q93.250 2.896 93.420 2.943Q93.590 2.990 93.859 2.990L93.859 3.287L92.004 3.287L92.004 2.990Q92.277 2.990 92.445 2.943Q92.613 2.896 92.613 2.728L92.613 0.853Q92.613 0.471 92.492 0.242Q92.371 0.014 92.020 0.014Q91.707 0.014 91.453 0.176Q91.199 0.338 91.053 0.607Q90.906 0.877 90.906 1.174L90.906 2.728Q90.906 2.896 91.076 2.943Q91.246 2.990 91.516 2.990L91.516 3.287M94.305 1.533Q94.305 1.053 94.537 0.637Q94.770 0.221 95.180-0.029Q95.590-0.279 96.066-0.279Q96.797-0.279 97.195 0.162Q97.594 0.603 97.594 1.334Q97.594 1.439 97.500 1.463L95.051 1.463L95.051 1.533Q95.051 1.943 95.172 2.299Q95.293 2.654 95.564 2.871Q95.836 3.088 96.266 3.088Q96.629 3.088 96.926 2.859Q97.223 2.631 97.324 2.279Q97.332 2.232 97.418 2.217L97.500 2.217Q97.594 2.244 97.594 2.326Q97.594 2.334 97.586 2.365Q97.523 2.592 97.385 2.775Q97.246 2.959 97.055 3.092Q96.863 3.224 96.645 3.295Q96.426 3.365 96.188 3.365Q95.816 3.365 95.479 3.228Q95.141 3.092 94.873 2.840Q94.606 2.588 94.455 2.248Q94.305 1.908 94.305 1.533M95.059 1.224L97.020 1.224Q97.020 0.920 96.918 0.629Q96.816 0.338 96.600 0.156Q96.383-0.026 96.066-0.026Q95.766-0.026 95.535 0.162Q95.305 0.349 95.182 0.641Q95.059 0.932 95.059 1.224\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M102.506 3.256L101.436 0.400Q101.370 0.221 101.239 0.178Q101.108 0.135 100.850 0.135L100.850-0.162L102.530-0.162L102.530 0.135Q102.080 0.135 102.080 0.334Q102.084 0.349 102.086 0.367Q102.088 0.385 102.088 0.400L102.881 2.494L103.592 0.584Q103.557 0.490 103.557 0.445Q103.557 0.400 103.522 0.400Q103.455 0.221 103.325 0.178Q103.194 0.135 102.940 0.135L102.940-0.162L104.530-0.162L104.530 0.135Q104.080 0.135 104.080 0.334Q104.084 0.353 104.086 0.371Q104.088 0.389 104.088 0.400L104.920 2.615L105.674 0.615Q105.698 0.557 105.698 0.486Q105.698 0.326 105.561 0.230Q105.424 0.135 105.256 0.135L105.256-0.162L106.643-0.162L106.643 0.135Q106.409 0.135 106.231 0.262Q106.053 0.389 105.971 0.615L104.987 3.256Q104.932 3.365 104.819 3.365L104.760 3.365Q104.647 3.365 104.604 3.256L103.745 0.982L102.889 3.256Q102.850 3.365 102.729 3.365L102.674 3.365Q102.561 3.365 102.506 3.256\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M106.823 1.592Q106.823 1.088 107.079 0.656Q107.335 0.224 107.771-0.027Q108.206-0.279 108.706-0.279Q109.093-0.279 109.435-0.135Q109.776 0.010 110.038 0.271Q110.300 0.533 110.442 0.869Q110.585 1.205 110.585 1.592Q110.585 2.084 110.321 2.494Q110.058 2.904 109.628 3.135Q109.198 3.365 108.706 3.365Q108.214 3.365 107.780 3.133Q107.347 2.900 107.085 2.492Q106.823 2.084 106.823 1.592M108.706 3.088Q109.163 3.088 109.415 2.865Q109.667 2.642 109.755 2.291Q109.843 1.939 109.843 1.494Q109.843 1.064 109.749 0.726Q109.655 0.389 109.401 0.182Q109.147-0.026 108.706-0.026Q108.058-0.026 107.814 0.391Q107.569 0.807 107.569 1.494Q107.569 1.939 107.657 2.291Q107.745 2.642 107.997 2.865Q108.249 3.088 108.706 3.088M113.077 3.287L111.097 3.287L111.097 2.990Q111.366 2.990 111.534 2.945Q111.702 2.900 111.702 2.728L111.702 0.592Q111.702 0.377 111.640 0.281Q111.577 0.185 111.460 0.164Q111.343 0.142 111.097 0.142L111.097-0.154L112.265-0.240L112.265 0.545Q112.343 0.334 112.495 0.148Q112.647-0.037 112.847-0.139Q113.046-0.240 113.272-0.240Q113.519-0.240 113.710-0.096Q113.901 0.049 113.901 0.279Q113.901 0.435 113.796 0.545Q113.690 0.654 113.534 0.654Q113.378 0.654 113.269 0.545Q113.159 0.435 113.159 0.279Q113.159 0.119 113.265 0.014Q112.940 0.014 112.726 0.242Q112.511 0.471 112.415 0.810Q112.319 1.150 112.319 1.455L112.319 2.728Q112.319 2.896 112.546 2.943Q112.772 2.990 113.077 2.990L113.077 3.287M116.296 3.287L114.464 3.287L114.464 2.990Q114.737 2.990 114.905 2.943Q115.073 2.896 115.073 2.728L115.073-1.432Q115.073-1.647 115.011-1.742Q114.948-1.838 114.829-1.859Q114.710-1.881 114.464-1.881L114.464-2.178L115.687-2.264L115.687 2.728Q115.687 2.896 115.855 2.943Q116.022 2.990 116.296 2.990L116.296 3.287M118.558 3.365Q118.077 3.365 117.669 3.121Q117.261 2.877 117.022 2.463Q116.784 2.049 116.784 1.560Q116.784 1.068 117.042 0.652Q117.300 0.236 117.731-0.002Q118.163-0.240 118.655-0.240Q119.276-0.240 119.726 0.197L119.726-1.432Q119.726-1.647 119.663-1.742Q119.601-1.838 119.483-1.859Q119.366-1.881 119.120-1.881L119.120-2.178L120.343-2.264L120.343 2.545Q120.343 2.756 120.405 2.851Q120.468 2.947 120.585 2.969Q120.702 2.990 120.952 2.990L120.952 3.287L119.702 3.365L119.702 2.881Q119.237 3.365 118.558 3.365M118.624 3.111Q118.964 3.111 119.257 2.920Q119.550 2.728 119.702 2.432L119.702 0.599Q119.554 0.326 119.292 0.170Q119.030 0.014 118.718 0.014Q118.093 0.014 117.810 0.461Q117.526 0.908 117.526 1.568Q117.526 2.213 117.778 2.662Q118.030 3.111 118.624 3.111\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M75.606 12.787L73.828 12.787L73.828 12.490Q74.102 12.490 74.270 12.443Q74.438 12.396 74.438 12.228L74.438 10.092Q74.438 9.877 74.381 9.781Q74.324 9.685 74.211 9.664Q74.098 9.642 73.852 9.642L73.852 9.346L75.051 9.260L75.051 12.228Q75.051 12.396 75.197 12.443Q75.344 12.490 75.606 12.490L75.606 12.787M74.164 7.865Q74.164 7.674 74.299 7.543Q74.434 7.412 74.629 7.412Q74.750 7.412 74.854 7.475Q74.957 7.537 75.020 7.641Q75.082 7.744 75.082 7.865Q75.082 8.060 74.951 8.195Q74.820 8.330 74.629 8.330Q74.430 8.330 74.297 8.197Q74.164 8.064 74.164 7.865M76.149 12.779L76.149 11.557Q76.149 11.529 76.180 11.498Q76.211 11.467 76.235 11.467L76.340 11.467Q76.410 11.467 76.426 11.529Q76.488 11.850 76.627 12.090Q76.766 12.330 76.998 12.471Q77.231 12.611 77.539 12.611Q77.778 12.611 77.987 12.551Q78.195 12.490 78.332 12.342Q78.469 12.193 78.469 11.947Q78.469 11.693 78.258 11.527Q78.047 11.361 77.778 11.307L77.156 11.193Q76.750 11.115 76.449 10.859Q76.149 10.603 76.149 10.228Q76.149 9.861 76.350 9.639Q76.551 9.416 76.875 9.318Q77.199 9.221 77.539 9.221Q78.004 9.221 78.301 9.428L78.524 9.244Q78.547 9.221 78.578 9.221L78.629 9.221Q78.660 9.221 78.688 9.248Q78.715 9.275 78.715 9.307L78.715 10.291Q78.715 10.322 78.690 10.351Q78.664 10.381 78.629 10.381L78.524 10.381Q78.488 10.381 78.461 10.353Q78.434 10.326 78.434 10.291Q78.434 9.892 78.182 9.672Q77.930 9.451 77.531 9.451Q77.176 9.451 76.893 9.574Q76.610 9.697 76.610 10.002Q76.610 10.221 76.811 10.353Q77.012 10.486 77.258 10.529L77.883 10.642Q78.313 10.732 78.621 11.029Q78.930 11.326 78.930 11.740Q78.930 12.310 78.531 12.588Q78.133 12.865 77.539 12.865Q76.988 12.865 76.637 12.529L76.340 12.842Q76.317 12.865 76.281 12.865L76.235 12.865Q76.211 12.865 76.180 12.834Q76.149 12.803 76.149 12.779\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M84.208 12.787L82.376 12.787L82.376 12.490Q82.650 12.490 82.818 12.443Q82.986 12.396 82.986 12.228L82.986 8.068Q82.986 7.853 82.923 7.758Q82.861 7.662 82.742 7.641Q82.622 7.619 82.376 7.619L82.376 7.322L83.599 7.236L83.599 12.228Q83.599 12.396 83.767 12.443Q83.935 12.490 84.208 12.490L84.208 12.787M86.513 12.787L84.736 12.787L84.736 12.490Q85.009 12.490 85.177 12.443Q85.345 12.396 85.345 12.228L85.345 10.092Q85.345 9.877 85.288 9.781Q85.232 9.685 85.118 9.664Q85.005 9.642 84.759 9.642L84.759 9.346L85.958 9.260L85.958 12.228Q85.958 12.396 86.105 12.443Q86.251 12.490 86.513 12.490L86.513 12.787M85.072 7.865Q85.072 7.674 85.206 7.543Q85.341 7.412 85.536 7.412Q85.658 7.412 85.761 7.475Q85.865 7.537 85.927 7.641Q85.990 7.744 85.990 7.865Q85.990 8.060 85.859 8.195Q85.728 8.330 85.536 8.330Q85.337 8.330 85.204 8.197Q85.072 8.064 85.072 7.865M88.837 12.787L87.040 12.787L87.040 12.490Q87.310 12.490 87.478 12.445Q87.646 12.400 87.646 12.228L87.646 8.068Q87.646 7.853 87.583 7.758Q87.521 7.662 87.404 7.641Q87.286 7.619 87.040 7.619L87.040 7.322L88.263 7.236L88.263 11.002L89.361 10.115Q89.568 9.935 89.568 9.787Q89.568 9.721 89.515 9.678Q89.462 9.635 89.392 9.635L89.392 9.338L90.927 9.338L90.927 9.635Q90.396 9.635 89.798 10.115L89.189 10.611L90.263 12.010Q90.400 12.185 90.507 12.293Q90.615 12.400 90.749 12.445Q90.884 12.490 91.111 12.490L91.111 12.787L89.486 12.787L89.486 12.490Q89.728 12.490 89.728 12.338Q89.728 12.260 89.685 12.189Q89.642 12.119 89.560 12.010L88.759 10.963L88.232 11.389L88.232 12.228Q88.232 12.396 88.400 12.443Q88.568 12.490 88.837 12.490\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M91.266 11.033Q91.266 10.553 91.499 10.137Q91.731 9.721 92.141 9.471Q92.551 9.221 93.028 9.221Q93.758 9.221 94.157 9.662Q94.555 10.103 94.555 10.834Q94.555 10.939 94.462 10.963L92.012 10.963L92.012 11.033Q92.012 11.443 92.133 11.799Q92.255 12.154 92.526 12.371Q92.798 12.588 93.227 12.588Q93.591 12.588 93.887 12.359Q94.184 12.131 94.286 11.779Q94.294 11.732 94.380 11.717L94.462 11.717Q94.555 11.744 94.555 11.826Q94.555 11.834 94.548 11.865Q94.485 12.092 94.346 12.275Q94.208 12.459 94.016 12.592Q93.825 12.725 93.606 12.795Q93.387 12.865 93.149 12.865Q92.778 12.865 92.440 12.728Q92.102 12.592 91.835 12.340Q91.567 12.088 91.417 11.748Q91.266 11.408 91.266 11.033M92.020 10.725L93.981 10.725Q93.981 10.420 93.880 10.129Q93.778 9.838 93.561 9.656Q93.344 9.475 93.028 9.475Q92.727 9.475 92.497 9.662Q92.266 9.850 92.143 10.141Q92.020 10.432 92.020 10.725\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M99.807 12.787L97.951 12.787L97.951 12.490Q98.225 12.490 98.393 12.443Q98.561 12.396 98.561 12.228L98.561 10.092Q98.561 9.877 98.498 9.781Q98.436 9.685 98.317 9.664Q98.198 9.642 97.951 9.642L97.951 9.346L99.143 9.260L99.143 9.994Q99.256 9.779 99.450 9.611Q99.643 9.443 99.881 9.351Q100.119 9.260 100.373 9.260Q101.541 9.260 101.541 10.338L101.541 12.228Q101.541 12.396 101.711 12.443Q101.881 12.490 102.151 12.490L102.151 12.787L100.295 12.787L100.295 12.490Q100.569 12.490 100.737 12.443Q100.905 12.396 100.905 12.228L100.905 10.353Q100.905 9.971 100.784 9.742Q100.662 9.514 100.311 9.514Q99.998 9.514 99.744 9.676Q99.491 9.838 99.344 10.107Q99.198 10.377 99.198 10.674L99.198 12.228Q99.198 12.396 99.368 12.443Q99.537 12.490 99.807 12.490L99.807 12.787M102.596 11.092Q102.596 10.588 102.852 10.156Q103.108 9.725 103.543 9.473Q103.979 9.221 104.479 9.221Q104.866 9.221 105.207 9.365Q105.549 9.510 105.811 9.771Q106.073 10.033 106.215 10.369Q106.358 10.705 106.358 11.092Q106.358 11.584 106.094 11.994Q105.830 12.404 105.401 12.635Q104.971 12.865 104.479 12.865Q103.987 12.865 103.553 12.633Q103.119 12.400 102.858 11.992Q102.596 11.584 102.596 11.092M104.479 12.588Q104.936 12.588 105.188 12.365Q105.440 12.142 105.528 11.791Q105.616 11.439 105.616 10.994Q105.616 10.564 105.522 10.226Q105.428 9.889 105.174 9.682Q104.920 9.475 104.479 9.475Q103.830 9.475 103.586 9.891Q103.342 10.307 103.342 10.994Q103.342 11.439 103.430 11.791Q103.518 12.142 103.770 12.365Q104.022 12.588 104.479 12.588\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -37.997)\">\u003Cpath d=\"M108.200 12.756L107.130 9.900Q107.064 9.721 106.933 9.678Q106.802 9.635 106.544 9.635L106.544 9.338L108.224 9.338L108.224 9.635Q107.774 9.635 107.774 9.834Q107.778 9.850 107.780 9.867Q107.782 9.885 107.782 9.900L108.575 11.994L109.286 10.084Q109.251 9.990 109.251 9.945Q109.251 9.900 109.216 9.900Q109.149 9.721 109.019 9.678Q108.888 9.635 108.634 9.635L108.634 9.338L110.224 9.338L110.224 9.635Q109.774 9.635 109.774 9.834Q109.778 9.853 109.780 9.871Q109.782 9.889 109.782 9.900L110.614 12.115L111.368 10.115Q111.392 10.057 111.392 9.986Q111.392 9.826 111.255 9.730Q111.118 9.635 110.950 9.635L110.950 9.338L112.337 9.338L112.337 9.635Q112.103 9.635 111.925 9.762Q111.747 9.889 111.665 10.115L110.681 12.756Q110.626 12.865 110.513 12.865L110.454 12.865Q110.341 12.865 110.298 12.756L109.439 10.482L108.583 12.756Q108.544 12.865 108.423 12.865L108.368 12.865Q108.255 12.865 108.200 12.756\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M69.075 25.591h76.792V-2.862H69.075Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M66.616 3.256L65.546 0.400Q65.480 0.221 65.349 0.178Q65.218 0.135 64.960 0.135L64.960-0.162L66.640-0.162L66.640 0.135Q66.190 0.135 66.190 0.334Q66.194 0.349 66.196 0.367Q66.198 0.385 66.198 0.400L66.991 2.494L67.702 0.584Q67.667 0.490 67.667 0.445Q67.667 0.400 67.632 0.400Q67.565 0.221 67.435 0.178Q67.304 0.135 67.050 0.135L67.050-0.162L68.640-0.162L68.640 0.135Q68.190 0.135 68.190 0.334Q68.194 0.353 68.196 0.371Q68.198 0.389 68.198 0.400L69.030 2.615L69.784 0.615Q69.808 0.557 69.808 0.486Q69.808 0.326 69.671 0.230Q69.534 0.135 69.366 0.135L69.366-0.162L70.753-0.162L70.753 0.135Q70.519 0.135 70.341 0.262Q70.163 0.389 70.081 0.615L69.097 3.256Q69.042 3.365 68.929 3.365L68.870 3.365Q68.757 3.365 68.714 3.256L67.855 0.982L66.999 3.256Q66.960 3.365 66.839 3.365L66.784 3.365Q66.671 3.365 66.616 3.256M73.097 3.287L71.241 3.287L71.241 2.990Q71.515 2.990 71.683 2.943Q71.851 2.896 71.851 2.728L71.851-1.432Q71.851-1.647 71.788-1.742Q71.726-1.838 71.606-1.859Q71.487-1.881 71.241-1.881L71.241-2.178L72.464-2.264L72.464 0.439Q72.589 0.228 72.776 0.078Q72.964-0.072 73.190-0.156Q73.417-0.240 73.663-0.240Q74.831-0.240 74.831 0.838L74.831 2.728Q74.831 2.896 75.001 2.943Q75.171 2.990 75.440 2.990L75.440 3.287L73.585 3.287L73.585 2.990Q73.858 2.990 74.026 2.943Q74.194 2.896 74.194 2.728L74.194 0.853Q74.194 0.471 74.073 0.242Q73.952 0.014 73.601 0.014Q73.288 0.014 73.034 0.176Q72.780 0.338 72.634 0.607Q72.487 0.877 72.487 1.174L72.487 2.728Q72.487 2.896 72.657 2.943Q72.827 2.990 73.097 2.990L73.097 3.287M75.983 2.455Q75.983 1.971 76.386 1.676Q76.788 1.381 77.339 1.262Q77.890 1.142 78.382 1.142L78.382 0.853Q78.382 0.627 78.267 0.420Q78.151 0.213 77.954 0.094Q77.757-0.026 77.526-0.026Q77.101-0.026 76.815 0.080Q76.886 0.107 76.933 0.162Q76.980 0.217 77.005 0.287Q77.030 0.357 77.030 0.432Q77.030 0.537 76.980 0.629Q76.929 0.721 76.837 0.771Q76.745 0.822 76.640 0.822Q76.534 0.822 76.442 0.771Q76.351 0.721 76.300 0.629Q76.249 0.537 76.249 0.432Q76.249 0.014 76.638-0.133Q77.026-0.279 77.526-0.279Q77.858-0.279 78.212-0.149Q78.565-0.018 78.794 0.236Q79.022 0.490 79.022 0.838L79.022 2.639Q79.022 2.771 79.095 2.881Q79.167 2.990 79.296 2.990Q79.421 2.990 79.489 2.885Q79.558 2.779 79.558 2.639L79.558 2.127L79.839 2.127L79.839 2.639Q79.839 2.842 79.722 3Q79.605 3.158 79.423 3.242Q79.241 3.326 79.038 3.326Q78.808 3.326 78.655 3.154Q78.503 2.982 78.472 2.752Q78.312 3.033 78.003 3.199Q77.694 3.365 77.343 3.365Q76.831 3.365 76.407 3.142Q75.983 2.920 75.983 2.455M76.671 2.455Q76.671 2.740 76.897 2.926Q77.124 3.111 77.417 3.111Q77.663 3.111 77.888 2.994Q78.112 2.877 78.247 2.674Q78.382 2.471 78.382 2.217L78.382 1.385Q78.116 1.385 77.831 1.439Q77.546 1.494 77.274 1.623Q77.003 1.752 76.837 1.959Q76.671 2.166 76.671 2.455M80.757 2.326L80.757 0.135L80.054 0.135L80.054-0.119Q80.409-0.119 80.651-0.352Q80.894-0.584 81.005-0.932Q81.116-1.279 81.116-1.635L81.397-1.635L81.397-0.162L82.573-0.162L82.573 0.135L81.397 0.135L81.397 2.310Q81.397 2.631 81.517 2.859Q81.636 3.088 81.917 3.088Q82.097 3.088 82.214 2.965Q82.331 2.842 82.384 2.662Q82.437 2.482 82.437 2.310L82.437 1.838L82.718 1.838L82.718 2.326Q82.718 2.580 82.612 2.820Q82.507 3.060 82.310 3.213Q82.112 3.365 81.855 3.365Q81.538 3.365 81.286 3.242Q81.034 3.119 80.896 2.885Q80.757 2.650 80.757 2.326\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M88.141 3.287L86.363 3.287L86.363 2.990Q86.637 2.990 86.805 2.943Q86.973 2.896 86.973 2.728L86.973 0.592Q86.973 0.377 86.916 0.281Q86.859 0.185 86.746 0.164Q86.633 0.142 86.387 0.142L86.387-0.154L87.586-0.240L87.586 2.728Q87.586 2.896 87.732 2.943Q87.879 2.990 88.141 2.990L88.141 3.287M86.699-1.635Q86.699-1.826 86.834-1.957Q86.969-2.088 87.164-2.088Q87.285-2.088 87.389-2.026Q87.492-1.963 87.555-1.859Q87.617-1.756 87.617-1.635Q87.617-1.440 87.486-1.305Q87.356-1.170 87.164-1.170Q86.965-1.170 86.832-1.303Q86.699-1.436 86.699-1.635M89.266 2.326L89.266 0.135L88.563 0.135L88.563-0.119Q88.918-0.119 89.160-0.352Q89.402-0.584 89.514-0.932Q89.625-1.279 89.625-1.635L89.906-1.635L89.906-0.162L91.082-0.162L91.082 0.135L89.906 0.135L89.906 2.310Q89.906 2.631 90.025 2.859Q90.145 3.088 90.426 3.088Q90.606 3.088 90.723 2.965Q90.840 2.842 90.893 2.662Q90.945 2.482 90.945 2.310L90.945 1.838L91.227 1.838L91.227 2.326Q91.227 2.580 91.121 2.820Q91.016 3.060 90.818 3.213Q90.621 3.365 90.363 3.365Q90.047 3.365 89.795 3.242Q89.543 3.119 89.404 2.885Q89.266 2.650 89.266 2.326\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M96.367 3.256L95.297 0.400Q95.231 0.221 95.100 0.178Q94.969 0.135 94.711 0.135L94.711-0.162L96.391-0.162L96.391 0.135Q95.941 0.135 95.941 0.334Q95.945 0.349 95.947 0.367Q95.949 0.385 95.949 0.400L96.742 2.494L97.453 0.584Q97.418 0.490 97.418 0.445Q97.418 0.400 97.383 0.400Q97.316 0.221 97.186 0.178Q97.055 0.135 96.801 0.135L96.801-0.162L98.391-0.162L98.391 0.135Q97.941 0.135 97.941 0.334Q97.945 0.353 97.947 0.371Q97.949 0.389 97.949 0.400L98.781 2.615L99.535 0.615Q99.559 0.557 99.559 0.486Q99.559 0.326 99.422 0.230Q99.285 0.135 99.117 0.135L99.117-0.162L100.504-0.162L100.504 0.135Q100.270 0.135 100.092 0.262Q99.914 0.389 99.832 0.615L98.848 3.256Q98.793 3.365 98.680 3.365L98.621 3.365Q98.508 3.365 98.465 3.256L97.606 0.982L96.750 3.256Q96.711 3.365 96.590 3.365L96.535 3.365Q96.422 3.365 96.367 3.256M102.777 3.287L101 3.287L101 2.990Q101.273 2.990 101.441 2.943Q101.609 2.896 101.609 2.728L101.609 0.592Q101.609 0.377 101.553 0.281Q101.496 0.185 101.383 0.164Q101.270 0.142 101.023 0.142L101.023-0.154L102.223-0.240L102.223 2.728Q102.223 2.896 102.369 2.943Q102.516 2.990 102.777 2.990L102.777 3.287M101.336-1.635Q101.336-1.826 101.471-1.957Q101.606-2.088 101.801-2.088Q101.922-2.088 102.025-2.026Q102.129-1.963 102.191-1.859Q102.254-1.756 102.254-1.635Q102.254-1.440 102.123-1.305Q101.992-1.170 101.801-1.170Q101.602-1.170 101.469-1.303Q101.336-1.436 101.336-1.635M105.191 3.287L103.359 3.287L103.359 2.990Q103.633 2.990 103.801 2.943Q103.969 2.896 103.969 2.728L103.969-1.432Q103.969-1.647 103.906-1.742Q103.844-1.838 103.725-1.859Q103.606-1.881 103.359-1.881L103.359-2.178L104.582-2.264L104.582 2.728Q104.582 2.896 104.750 2.943Q104.918 2.990 105.191 2.990L105.191 3.287M107.551 3.287L105.719 3.287L105.719 2.990Q105.992 2.990 106.160 2.943Q106.328 2.896 106.328 2.728L106.328-1.432Q106.328-1.647 106.266-1.742Q106.203-1.838 106.084-1.859Q105.965-1.881 105.719-1.881L105.719-2.178L106.941-2.264L106.941 2.728Q106.941 2.896 107.109 2.943Q107.277 2.990 107.551 2.990\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M111.751 3.287L111.470 3.287L111.470-1.432Q111.470-1.647 111.408-1.742Q111.345-1.838 111.228-1.859Q111.111-1.881 110.865-1.881L110.865-2.178L112.087-2.264L112.087 0.224Q112.564-0.240 113.263-0.240Q113.744-0.240 114.152 0.004Q114.560 0.248 114.796 0.662Q115.033 1.076 115.033 1.560Q115.033 1.935 114.884 2.264Q114.736 2.592 114.466 2.844Q114.197 3.096 113.853 3.230Q113.509 3.365 113.150 3.365Q112.829 3.365 112.531 3.217Q112.232 3.068 112.025 2.807L111.751 3.287M112.111 0.615L112.111 2.455Q112.263 2.752 112.523 2.932Q112.783 3.111 113.095 3.111Q113.521 3.111 113.788 2.892Q114.056 2.674 114.171 2.328Q114.287 1.982 114.287 1.560Q114.287 0.912 114.038 0.463Q113.790 0.014 113.193 0.014Q112.857 0.014 112.568 0.172Q112.279 0.330 112.111 0.615\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M115.795 1.533Q115.795 1.053 116.028 0.637Q116.260 0.221 116.670-0.029Q117.080-0.279 117.557-0.279Q118.287-0.279 118.686 0.162Q119.084 0.603 119.084 1.334Q119.084 1.439 118.991 1.463L116.541 1.463L116.541 1.533Q116.541 1.943 116.662 2.299Q116.784 2.654 117.055 2.871Q117.327 3.088 117.756 3.088Q118.120 3.088 118.416 2.859Q118.713 2.631 118.815 2.279Q118.823 2.232 118.909 2.217L118.991 2.217Q119.084 2.244 119.084 2.326Q119.084 2.334 119.077 2.365Q119.014 2.592 118.875 2.775Q118.737 2.959 118.545 3.092Q118.354 3.224 118.135 3.295Q117.916 3.365 117.678 3.365Q117.307 3.365 116.969 3.228Q116.631 3.092 116.364 2.840Q116.096 2.588 115.946 2.248Q115.795 1.908 115.795 1.533M116.549 1.224L118.510 1.224Q118.510 0.920 118.409 0.629Q118.307 0.338 118.090 0.156Q117.873-0.026 117.557-0.026Q117.256-0.026 117.026 0.162Q116.795 0.349 116.672 0.641Q116.549 0.932 116.549 1.224\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M124.320 3.287L122.488 3.287L122.488 2.990Q122.762 2.990 122.930 2.943Q123.098 2.896 123.098 2.728L123.098-1.432Q123.098-1.647 123.035-1.742Q122.973-1.838 122.854-1.859Q122.734-1.881 122.488-1.881L122.488-2.178L123.711-2.264L123.711 2.728Q123.711 2.896 123.879 2.943Q124.047 2.990 124.320 2.990L124.320 3.287M126.625 3.287L124.848 3.287L124.848 2.990Q125.121 2.990 125.289 2.943Q125.457 2.896 125.457 2.728L125.457 0.592Q125.457 0.377 125.400 0.281Q125.344 0.185 125.231 0.164Q125.117 0.142 124.871 0.142L124.871-0.154L126.070-0.240L126.070 2.728Q126.070 2.896 126.217 2.943Q126.363 2.990 126.625 2.990L126.625 3.287M125.184-1.635Q125.184-1.826 125.318-1.957Q125.453-2.088 125.648-2.088Q125.770-2.088 125.873-2.026Q125.977-1.963 126.039-1.859Q126.102-1.756 126.102-1.635Q126.102-1.440 125.971-1.305Q125.840-1.170 125.648-1.170Q125.449-1.170 125.316-1.303Q125.184-1.436 125.184-1.635M128.949 3.287L127.152 3.287L127.152 2.990Q127.422 2.990 127.590 2.945Q127.758 2.900 127.758 2.728L127.758-1.432Q127.758-1.647 127.695-1.742Q127.633-1.838 127.516-1.859Q127.398-1.881 127.152-1.881L127.152-2.178L128.375-2.264L128.375 1.502L129.473 0.615Q129.680 0.435 129.680 0.287Q129.680 0.221 129.627 0.178Q129.574 0.135 129.504 0.135L129.504-0.162L131.039-0.162L131.039 0.135Q130.508 0.135 129.910 0.615L129.301 1.111L130.375 2.510Q130.512 2.685 130.619 2.793Q130.727 2.900 130.861 2.945Q130.996 2.990 131.223 2.990L131.223 3.287L129.598 3.287L129.598 2.990Q129.840 2.990 129.840 2.838Q129.840 2.760 129.797 2.689Q129.754 2.619 129.672 2.510L128.871 1.463L128.344 1.889L128.344 2.728Q128.344 2.896 128.512 2.943Q128.680 2.990 128.949 2.990\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M131.379 1.533Q131.379 1.053 131.612 0.637Q131.844 0.221 132.254-0.029Q132.664-0.279 133.141-0.279Q133.871-0.279 134.270 0.162Q134.668 0.603 134.668 1.334Q134.668 1.439 134.575 1.463L132.125 1.463L132.125 1.533Q132.125 1.943 132.246 2.299Q132.368 2.654 132.639 2.871Q132.911 3.088 133.340 3.088Q133.703 3.088 134 2.859Q134.297 2.631 134.399 2.279Q134.407 2.232 134.493 2.217L134.575 2.217Q134.668 2.244 134.668 2.326Q134.668 2.334 134.661 2.365Q134.598 2.592 134.459 2.775Q134.321 2.959 134.129 3.092Q133.938 3.224 133.719 3.295Q133.500 3.365 133.262 3.365Q132.891 3.365 132.553 3.228Q132.215 3.092 131.948 2.840Q131.680 2.588 131.530 2.248Q131.379 1.908 131.379 1.533M132.133 1.224L134.094 1.224Q134.094 0.920 133.993 0.629Q133.891 0.338 133.674 0.156Q133.457-0.026 133.141-0.026Q132.840-0.026 132.610 0.162Q132.379 0.349 132.256 0.641Q132.133 0.932 132.133 1.224\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M73.274 12.787L71.496 12.787L71.496 12.490Q71.770 12.490 71.938 12.443Q72.106 12.396 72.106 12.228L72.106 10.092Q72.106 9.877 72.049 9.781Q71.992 9.685 71.879 9.664Q71.766 9.642 71.520 9.642L71.520 9.346L72.719 9.260L72.719 12.228Q72.719 12.396 72.865 12.443Q73.012 12.490 73.274 12.490L73.274 12.787M71.832 7.865Q71.832 7.674 71.967 7.543Q72.102 7.412 72.297 7.412Q72.418 7.412 72.522 7.475Q72.625 7.537 72.688 7.641Q72.750 7.744 72.750 7.865Q72.750 8.060 72.619 8.195Q72.489 8.330 72.297 8.330Q72.098 8.330 71.965 8.197Q71.832 8.064 71.832 7.865M75.840 12.787L73.856 12.787L73.856 12.490Q74.129 12.490 74.297 12.443Q74.465 12.396 74.465 12.228L74.465 9.635L73.824 9.635L73.824 9.338L74.465 9.338L74.465 8.404Q74.465 8.139 74.582 7.902Q74.699 7.666 74.893 7.502Q75.086 7.338 75.334 7.246Q75.582 7.154 75.848 7.154Q76.133 7.154 76.358 7.312Q76.582 7.471 76.582 7.748Q76.582 7.904 76.477 8.014Q76.371 8.123 76.207 8.123Q76.051 8.123 75.942 8.014Q75.832 7.904 75.832 7.748Q75.832 7.541 75.992 7.435Q75.895 7.412 75.801 7.412Q75.571 7.412 75.399 7.568Q75.227 7.725 75.141 7.961Q75.055 8.197 75.055 8.420L75.055 9.338L76.024 9.338L76.024 9.635L75.078 9.635L75.078 12.228Q75.078 12.396 75.305 12.443Q75.531 12.490 75.840 12.490\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M81.730 12.787L79.265 12.787L79.265 12.490Q79.597 12.490 79.855 12.443Q80.113 12.396 80.113 12.228L80.113 7.885Q80.113 7.619 79.265 7.619L79.265 7.322L81.730 7.322L81.730 7.619Q80.878 7.619 80.878 7.885L80.878 12.228Q80.878 12.490 81.730 12.490\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M86.917 12.865Q86.436 12.865 86.028 12.621Q85.620 12.377 85.382 11.963Q85.143 11.549 85.143 11.060Q85.143 10.568 85.401 10.152Q85.659 9.736 86.091 9.498Q86.522 9.260 87.014 9.260Q87.635 9.260 88.085 9.697L88.085 8.068Q88.085 7.853 88.022 7.758Q87.960 7.662 87.842 7.641Q87.725 7.619 87.479 7.619L87.479 7.322L88.702 7.236L88.702 12.045Q88.702 12.256 88.764 12.351Q88.827 12.447 88.944 12.469Q89.061 12.490 89.311 12.490L89.311 12.787L88.061 12.865L88.061 12.381Q87.596 12.865 86.917 12.865M86.983 12.611Q87.323 12.611 87.616 12.420Q87.909 12.228 88.061 11.932L88.061 10.100Q87.913 9.826 87.651 9.670Q87.389 9.514 87.077 9.514Q86.452 9.514 86.169 9.961Q85.885 10.408 85.885 11.068Q85.885 11.713 86.137 12.162Q86.389 12.611 86.983 12.611M89.819 11.092Q89.819 10.588 90.075 10.156Q90.331 9.725 90.766 9.473Q91.202 9.221 91.702 9.221Q92.089 9.221 92.430 9.365Q92.772 9.510 93.034 9.771Q93.296 10.033 93.438 10.369Q93.581 10.705 93.581 11.092Q93.581 11.584 93.317 11.994Q93.053 12.404 92.624 12.635Q92.194 12.865 91.702 12.865Q91.210 12.865 90.776 12.633Q90.342 12.400 90.081 11.992Q89.819 11.584 89.819 11.092M91.702 12.588Q92.159 12.588 92.411 12.365Q92.663 12.142 92.751 11.791Q92.839 11.439 92.839 10.994Q92.839 10.564 92.745 10.226Q92.651 9.889 92.397 9.682Q92.143 9.475 91.702 9.475Q91.053 9.475 90.809 9.891Q90.565 10.307 90.565 10.994Q90.565 11.439 90.653 11.791Q90.741 12.142 90.993 12.365Q91.245 12.588 91.702 12.588\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M97.004 11.955Q97.004 11.471 97.406 11.176Q97.809 10.881 98.359 10.762Q98.910 10.642 99.402 10.642L99.402 10.353Q99.402 10.127 99.287 9.920Q99.172 9.713 98.975 9.594Q98.777 9.475 98.547 9.475Q98.121 9.475 97.836 9.580Q97.906 9.607 97.953 9.662Q98 9.717 98.025 9.787Q98.051 9.857 98.051 9.932Q98.051 10.037 98 10.129Q97.949 10.221 97.857 10.271Q97.766 10.322 97.660 10.322Q97.555 10.322 97.463 10.271Q97.371 10.221 97.320 10.129Q97.270 10.037 97.270 9.932Q97.270 9.514 97.658 9.367Q98.047 9.221 98.547 9.221Q98.879 9.221 99.232 9.351Q99.586 9.482 99.814 9.736Q100.043 9.990 100.043 10.338L100.043 12.139Q100.043 12.271 100.115 12.381Q100.188 12.490 100.316 12.490Q100.441 12.490 100.510 12.385Q100.578 12.279 100.578 12.139L100.578 11.627L100.859 11.627L100.859 12.139Q100.859 12.342 100.742 12.500Q100.625 12.658 100.443 12.742Q100.262 12.826 100.059 12.826Q99.828 12.826 99.676 12.654Q99.523 12.482 99.492 12.252Q99.332 12.533 99.023 12.699Q98.715 12.865 98.363 12.865Q97.852 12.865 97.428 12.642Q97.004 12.420 97.004 11.955M97.691 11.955Q97.691 12.240 97.918 12.426Q98.145 12.611 98.438 12.611Q98.684 12.611 98.908 12.494Q99.133 12.377 99.268 12.174Q99.402 11.971 99.402 11.717L99.402 10.885Q99.137 10.885 98.852 10.939Q98.566 10.994 98.295 11.123Q98.023 11.252 97.857 11.459Q97.691 11.666 97.691 11.955M101.195 11.060Q101.195 10.564 101.445 10.139Q101.695 9.713 102.115 9.467Q102.535 9.221 103.035 9.221Q103.574 9.221 103.965 9.346Q104.356 9.471 104.356 9.885Q104.356 9.990 104.305 10.082Q104.254 10.174 104.162 10.225Q104.070 10.275 103.961 10.275Q103.856 10.275 103.764 10.225Q103.672 10.174 103.621 10.082Q103.570 9.990 103.570 9.885Q103.570 9.662 103.738 9.557Q103.516 9.498 103.043 9.498Q102.746 9.498 102.531 9.637Q102.316 9.775 102.186 10.006Q102.055 10.236 101.996 10.506Q101.938 10.775 101.938 11.060Q101.938 11.455 102.070 11.805Q102.203 12.154 102.475 12.371Q102.746 12.588 103.145 12.588Q103.520 12.588 103.795 12.371Q104.070 12.154 104.172 11.795Q104.188 11.732 104.250 11.732L104.356 11.732Q104.391 11.732 104.416 11.760Q104.441 11.787 104.441 11.826L104.441 11.850Q104.309 12.330 103.924 12.598Q103.539 12.865 103.035 12.865Q102.672 12.865 102.338 12.728Q102.004 12.592 101.744 12.342Q101.484 12.092 101.340 11.756Q101.195 11.420 101.195 11.060M105.555 11.826L105.555 9.635L104.852 9.635L104.852 9.381Q105.207 9.381 105.449 9.148Q105.691 8.916 105.803 8.568Q105.914 8.221 105.914 7.865L106.195 7.865L106.195 9.338L107.371 9.338L107.371 9.635L106.195 9.635L106.195 11.810Q106.195 12.131 106.314 12.359Q106.434 12.588 106.715 12.588Q106.895 12.588 107.012 12.465Q107.129 12.342 107.182 12.162Q107.234 11.982 107.234 11.810L107.234 11.338L107.516 11.338L107.516 11.826Q107.516 12.080 107.410 12.320Q107.305 12.560 107.107 12.713Q106.910 12.865 106.652 12.865Q106.336 12.865 106.084 12.742Q105.832 12.619 105.693 12.385Q105.555 12.150 105.555 11.826M110.094 12.787L108.316 12.787L108.316 12.490Q108.590 12.490 108.758 12.443Q108.926 12.396 108.926 12.228L108.926 10.092Q108.926 9.877 108.869 9.781Q108.813 9.685 108.699 9.664Q108.586 9.642 108.340 9.642L108.340 9.346L109.539 9.260L109.539 12.228Q109.539 12.396 109.686 12.443Q109.832 12.490 110.094 12.490L110.094 12.787M108.652 7.865Q108.652 7.674 108.787 7.543Q108.922 7.412 109.117 7.412Q109.238 7.412 109.342 7.475Q109.445 7.537 109.508 7.641Q109.570 7.744 109.570 7.865Q109.570 8.060 109.439 8.195Q109.309 8.330 109.117 8.330Q108.918 8.330 108.785 8.197Q108.652 8.064 108.652 7.865M110.594 11.092Q110.594 10.588 110.850 10.156Q111.106 9.725 111.541 9.473Q111.977 9.221 112.477 9.221Q112.863 9.221 113.205 9.365Q113.547 9.510 113.809 9.771Q114.070 10.033 114.213 10.369Q114.356 10.705 114.356 11.092Q114.356 11.584 114.092 11.994Q113.828 12.404 113.398 12.635Q112.969 12.865 112.477 12.865Q111.984 12.865 111.551 12.633Q111.117 12.400 110.856 11.992Q110.594 11.584 110.594 11.092M112.477 12.588Q112.934 12.588 113.186 12.365Q113.438 12.142 113.525 11.791Q113.613 11.439 113.613 10.994Q113.613 10.564 113.520 10.226Q113.426 9.889 113.172 9.682Q112.918 9.475 112.477 9.475Q111.828 9.475 111.584 9.891Q111.340 10.307 111.340 10.994Q111.340 11.439 111.428 11.791Q111.516 12.142 111.768 12.365Q112.020 12.588 112.477 12.588M116.770 12.787L114.914 12.787L114.914 12.490Q115.188 12.490 115.356 12.443Q115.523 12.396 115.523 12.228L115.523 10.092Q115.523 9.877 115.461 9.781Q115.398 9.685 115.279 9.664Q115.160 9.642 114.914 9.642L114.914 9.346L116.106 9.260L116.106 9.994Q116.219 9.779 116.412 9.611Q116.606 9.443 116.844 9.351Q117.082 9.260 117.336 9.260Q118.504 9.260 118.504 10.338L118.504 12.228Q118.504 12.396 118.674 12.443Q118.844 12.490 119.113 12.490L119.113 12.787L117.258 12.787L117.258 12.490Q117.531 12.490 117.699 12.443Q117.867 12.396 117.867 12.228L117.867 10.353Q117.867 9.971 117.746 9.742Q117.625 9.514 117.273 9.514Q116.961 9.514 116.707 9.676Q116.453 9.838 116.307 10.107Q116.160 10.377 116.160 10.674L116.160 12.228Q116.160 12.396 116.330 12.443Q116.500 12.490 116.770 12.490\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 6.105)\">\u003Cpath d=\"M124.207 12.787L122.457 12.787L122.457 12.490Q123.156 12.490 123.344 12.010L125.145 7.185Q125.199 7.076 125.313 7.076L125.383 7.076Q125.496 7.076 125.551 7.185L127.441 12.228Q127.520 12.396 127.723 12.443Q127.926 12.490 128.238 12.490L128.238 12.787L126.016 12.787L126.016 12.490Q126.656 12.490 126.656 12.275Q126.656 12.256 126.654 12.246Q126.652 12.236 126.648 12.228L126.184 10.994L124.039 10.994L123.656 12.010Q123.652 12.025 123.647 12.055Q123.641 12.084 123.641 12.107Q123.641 12.248 123.731 12.332Q123.820 12.416 123.953 12.453Q124.086 12.490 124.207 12.490L124.207 12.787M125.113 8.131L124.145 10.697L126.070 10.697\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M52.724-25.624c0-6.286-26.443-11.381-59.064-11.381s-59.063 5.095-59.063 11.381S-38.96-14.243-6.34-14.243s59.064-5.095 59.064-11.381Zm-59.064 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M66.788 12.787L65.154 12.787L65.154 12.507Q65.383 12.507 65.532 12.473Q65.681 12.438 65.681 12.298L65.681 8.679Q65.681 8.409 65.573 8.347Q65.465 8.286 65.154 8.286L65.154 8.005L66.234 7.930L66.234 10.316Q66.340 10.131 66.518 9.989Q66.696 9.848 66.904 9.774Q67.113 9.701 67.338 9.701Q67.844 9.701 68.128 9.924Q68.412 10.148 68.412 10.644L68.412 12.298Q68.412 12.435 68.560 12.471Q68.709 12.507 68.935 12.507L68.935 12.787L67.304 12.787L67.304 12.507Q67.533 12.507 67.682 12.473Q67.831 12.438 67.831 12.298L67.831 10.658Q67.831 10.323 67.711 10.123Q67.591 9.923 67.277 9.923Q67.007 9.923 66.773 10.059Q66.539 10.196 66.400 10.430Q66.262 10.664 66.262 10.938L66.262 12.298Q66.262 12.435 66.412 12.471Q66.563 12.507 66.788 12.507L66.788 12.787M69.481 11.304Q69.481 10.962 69.616 10.663Q69.751 10.364 69.991 10.140Q70.230 9.916 70.548 9.791Q70.866 9.666 71.197 9.666Q71.642 9.666 72.042 9.882Q72.441 10.097 72.676 10.475Q72.910 10.852 72.910 11.304Q72.910 11.645 72.768 11.929Q72.626 12.213 72.382 12.420Q72.137 12.626 71.828 12.741Q71.519 12.855 71.197 12.855Q70.767 12.855 70.365 12.654Q69.963 12.452 69.722 12.100Q69.481 11.748 69.481 11.304M71.197 12.606Q71.799 12.606 72.023 12.228Q72.247 11.850 72.247 11.218Q72.247 10.606 72.012 10.247Q71.778 9.889 71.197 9.889Q70.145 9.889 70.145 11.218Q70.145 11.850 70.370 12.228Q70.596 12.606 71.197 12.606\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M74.682 12.760L73.701 10.261Q73.640 10.118 73.522 10.083Q73.404 10.049 73.188 10.049L73.188 9.769L74.668 9.769L74.668 10.049Q74.289 10.049 74.289 10.210Q74.289 10.220 74.303 10.261L75.017 12.093L75.690 10.388Q75.660 10.316 75.660 10.288Q75.660 10.261 75.632 10.261Q75.571 10.114 75.453 10.082Q75.335 10.049 75.123 10.049L75.123 9.769L76.521 9.769L76.521 10.049Q76.145 10.049 76.145 10.210Q76.145 10.241 76.152 10.261L76.907 12.199L77.594 10.449Q77.615 10.398 77.615 10.343Q77.615 10.203 77.502 10.126Q77.389 10.049 77.249 10.049L77.249 9.769L78.469 9.769L78.469 10.049Q78.264 10.049 78.109 10.155Q77.953 10.261 77.881 10.449L76.976 12.760Q76.941 12.855 76.829 12.855L76.760 12.855Q76.651 12.855 76.613 12.760L75.831 10.757L75.044 12.760Q75.010 12.855 74.897 12.855L74.829 12.855Q74.720 12.855 74.682 12.760\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M82.224 11.946L82.224 10.049L81.585 10.049L81.585 9.827Q81.903 9.827 82.120 9.617Q82.337 9.407 82.437 9.097Q82.538 8.788 82.538 8.480L82.805 8.480L82.805 9.769L83.882 9.769L83.882 10.049L82.805 10.049L82.805 11.933Q82.805 12.209 82.909 12.408Q83.013 12.606 83.273 12.606Q83.430 12.606 83.536 12.502Q83.642 12.397 83.692 12.244Q83.741 12.090 83.741 11.933L83.741 11.519L84.008 11.519L84.008 11.946Q84.008 12.172 83.909 12.382Q83.810 12.592 83.625 12.724Q83.441 12.855 83.212 12.855Q82.774 12.855 82.499 12.618Q82.224 12.380 82.224 11.946M86.500 12.787L84.866 12.787L84.866 12.507Q85.095 12.507 85.244 12.473Q85.392 12.438 85.392 12.298L85.392 8.679Q85.392 8.409 85.285 8.347Q85.177 8.286 84.866 8.286L84.866 8.005L85.946 7.930L85.946 10.316Q86.052 10.131 86.230 9.989Q86.407 9.848 86.616 9.774Q86.824 9.701 87.050 9.701Q87.556 9.701 87.840 9.924Q88.123 10.148 88.123 10.644L88.123 12.298Q88.123 12.435 88.272 12.471Q88.421 12.507 88.646 12.507L88.646 12.787L87.016 12.787L87.016 12.507Q87.245 12.507 87.393 12.473Q87.542 12.438 87.542 12.298L87.542 10.658Q87.542 10.323 87.423 10.123Q87.303 9.923 86.988 9.923Q86.718 9.923 86.484 10.059Q86.250 10.196 86.112 10.430Q85.973 10.664 85.973 10.938L85.973 12.298Q85.973 12.435 86.124 12.471Q86.274 12.507 86.500 12.507L86.500 12.787M89.193 11.252Q89.193 10.931 89.318 10.642Q89.443 10.353 89.668 10.130Q89.894 9.906 90.189 9.786Q90.485 9.666 90.803 9.666Q91.131 9.666 91.393 9.766Q91.654 9.865 91.830 10.047Q92.006 10.230 92.100 10.488Q92.194 10.746 92.194 11.078Q92.194 11.170 92.112 11.191L89.856 11.191L89.856 11.252Q89.856 11.840 90.140 12.223Q90.424 12.606 90.991 12.606Q91.312 12.606 91.581 12.413Q91.849 12.220 91.938 11.905Q91.945 11.864 92.020 11.850L92.112 11.850Q92.194 11.874 92.194 11.946Q92.194 11.953 92.187 11.980Q92.074 12.377 91.704 12.616Q91.333 12.855 90.909 12.855Q90.471 12.855 90.071 12.647Q89.672 12.438 89.432 12.071Q89.193 11.704 89.193 11.252M89.863 10.982L91.678 10.982Q91.678 10.705 91.581 10.453Q91.483 10.200 91.285 10.044Q91.087 9.889 90.803 9.889Q90.526 9.889 90.312 10.047Q90.099 10.206 89.981 10.461Q89.863 10.716 89.863 10.982\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M96.876 12.760L95.895 10.261Q95.834 10.118 95.716 10.083Q95.598 10.049 95.382 10.049L95.382 9.769L96.862 9.769L96.862 10.049Q96.483 10.049 96.483 10.210Q96.483 10.220 96.497 10.261L97.211 12.093L97.884 10.388Q97.854 10.316 97.854 10.288Q97.854 10.261 97.826 10.261Q97.765 10.114 97.647 10.082Q97.529 10.049 97.317 10.049L97.317 9.769L98.715 9.769L98.715 10.049Q98.339 10.049 98.339 10.210Q98.339 10.241 98.346 10.261L99.101 12.199L99.788 10.449Q99.809 10.398 99.809 10.343Q99.809 10.203 99.696 10.126Q99.583 10.049 99.443 10.049L99.443 9.769L100.663 9.769L100.663 10.049Q100.458 10.049 100.303 10.155Q100.147 10.261 100.075 10.449L99.170 12.760Q99.135 12.855 99.023 12.855L98.954 12.855Q98.845 12.855 98.807 12.760L98.025 10.757L97.238 12.760Q97.204 12.855 97.091 12.855L97.023 12.855Q96.914 12.855 96.876 12.760\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M100.941 11.304Q100.941 10.962 101.076 10.663Q101.211 10.364 101.451 10.140Q101.690 9.916 102.008 9.791Q102.326 9.666 102.657 9.666Q103.102 9.666 103.501 9.882Q103.901 10.097 104.136 10.475Q104.370 10.852 104.370 11.304Q104.370 11.645 104.228 11.929Q104.086 12.213 103.842 12.420Q103.597 12.626 103.288 12.741Q102.979 12.855 102.657 12.855Q102.227 12.855 101.825 12.654Q101.423 12.452 101.182 12.100Q100.941 11.748 100.941 11.304M102.657 12.606Q103.259 12.606 103.483 12.228Q103.707 11.850 103.707 11.218Q103.707 10.606 103.472 10.247Q103.238 9.889 102.657 9.889Q101.605 9.889 101.605 11.218Q101.605 11.850 101.830 12.228Q102.056 12.606 102.657 12.606M106.714 12.787L104.978 12.787L104.978 12.507Q105.207 12.507 105.356 12.473Q105.504 12.438 105.504 12.298L105.504 10.449Q105.504 10.179 105.397 10.118Q105.289 10.056 104.978 10.056L104.978 9.776L106.007 9.701L106.007 10.408Q106.137 10.100 106.379 9.901Q106.622 9.701 106.940 9.701Q107.159 9.701 107.330 9.825Q107.501 9.950 107.501 10.162Q107.501 10.299 107.401 10.398Q107.302 10.497 107.169 10.497Q107.032 10.497 106.933 10.398Q106.834 10.299 106.834 10.162Q106.834 10.022 106.933 9.923Q106.643 9.923 106.443 10.119Q106.243 10.316 106.150 10.610Q106.058 10.904 106.058 11.184L106.058 12.298Q106.058 12.507 106.714 12.507L106.714 12.787M109.753 12.787L108.150 12.787L108.150 12.507Q108.376 12.507 108.524 12.473Q108.673 12.438 108.673 12.298L108.673 8.679Q108.673 8.409 108.565 8.347Q108.458 8.286 108.150 8.286L108.150 8.005L109.227 7.930L109.227 12.298Q109.227 12.435 109.377 12.471Q109.527 12.507 109.753 12.507L109.753 12.787M110.348 11.276Q110.348 10.938 110.488 10.647Q110.628 10.357 110.872 10.143Q111.117 9.930 111.421 9.815Q111.725 9.701 112.050 9.701Q112.320 9.701 112.583 9.800Q112.846 9.899 113.038 10.077L113.038 8.679Q113.038 8.409 112.930 8.347Q112.822 8.286 112.511 8.286L112.511 8.005L113.588 7.930L113.588 12.114Q113.588 12.302 113.643 12.385Q113.697 12.469 113.798 12.488Q113.899 12.507 114.114 12.507L114.114 12.787L113.007 12.855L113.007 12.438Q112.590 12.855 111.964 12.855Q111.534 12.855 111.161 12.643Q110.789 12.432 110.568 12.071Q110.348 11.710 110.348 11.276M112.022 12.633Q112.231 12.633 112.417 12.561Q112.604 12.490 112.757 12.353Q112.911 12.216 113.007 12.038L113.007 10.429Q112.921 10.282 112.776 10.162Q112.631 10.042 112.462 9.983Q112.293 9.923 112.111 9.923Q111.551 9.923 111.283 10.312Q111.014 10.702 111.014 11.283Q111.014 11.854 111.248 12.244Q111.482 12.633 112.022 12.633\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M117.427 11.252Q117.427 10.931 117.552 10.642Q117.677 10.353 117.903 10.130Q118.128 9.906 118.424 9.786Q118.719 9.666 119.037 9.666Q119.365 9.666 119.627 9.766Q119.888 9.865 120.064 10.047Q120.240 10.230 120.334 10.488Q120.428 10.746 120.428 11.078Q120.428 11.170 120.346 11.191L118.091 11.191L118.091 11.252Q118.091 11.840 118.374 12.223Q118.658 12.606 119.225 12.606Q119.547 12.606 119.815 12.413Q120.083 12.220 120.172 11.905Q120.179 11.864 120.254 11.850L120.346 11.850Q120.428 11.874 120.428 11.946Q120.428 11.953 120.422 11.980Q120.309 12.377 119.938 12.616Q119.567 12.855 119.143 12.855Q118.706 12.855 118.306 12.647Q117.906 12.438 117.667 12.071Q117.427 11.704 117.427 11.252M118.097 10.982L119.912 10.982Q119.912 10.705 119.815 10.453Q119.717 10.200 119.519 10.044Q119.321 9.889 119.037 9.889Q118.760 9.889 118.547 10.047Q118.333 10.206 118.215 10.461Q118.097 10.716 118.097 10.982M122.606 12.760L121.478 10.261Q121.406 10.114 121.276 10.082Q121.146 10.049 120.917 10.049L120.917 9.769L122.431 9.769L122.431 10.049Q122.079 10.049 122.079 10.196Q122.079 10.241 122.090 10.261L122.954 12.179L123.734 10.449Q123.768 10.381 123.768 10.302Q123.768 10.189 123.684 10.119Q123.600 10.049 123.481 10.049L123.481 9.769L124.677 9.769L124.677 10.049Q124.458 10.049 124.287 10.152Q124.116 10.254 124.028 10.449L122.992 12.760Q122.944 12.855 122.838 12.855L122.759 12.855Q122.654 12.855 122.606 12.760\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M124.968 11.304Q124.968 10.962 125.103 10.663Q125.238 10.364 125.478 10.140Q125.717 9.916 126.035 9.791Q126.353 9.666 126.684 9.666Q127.129 9.666 127.528 9.882Q127.928 10.097 128.163 10.475Q128.397 10.852 128.397 11.304Q128.397 11.645 128.255 11.929Q128.113 12.213 127.869 12.420Q127.624 12.626 127.315 12.741Q127.006 12.855 126.684 12.855Q126.254 12.855 125.852 12.654Q125.450 12.452 125.209 12.100Q124.968 11.748 124.968 11.304M126.684 12.606Q127.286 12.606 127.510 12.228Q127.734 11.850 127.734 11.218Q127.734 10.606 127.499 10.247Q127.265 9.889 126.684 9.889Q125.632 9.889 125.632 11.218Q125.632 11.850 125.857 12.228Q126.083 12.606 126.684 12.606M130.659 12.787L129.056 12.787L129.056 12.507Q129.282 12.507 129.431 12.473Q129.579 12.438 129.579 12.298L129.579 8.679Q129.579 8.409 129.472 8.347Q129.364 8.286 129.056 8.286L129.056 8.005L130.133 7.930L130.133 12.298Q130.133 12.435 130.283 12.471Q130.434 12.507 130.659 12.507L130.659 12.787M132.843 12.760L131.716 10.261Q131.644 10.114 131.514 10.082Q131.384 10.049 131.155 10.049L131.155 9.769L132.669 9.769L132.669 10.049Q132.317 10.049 132.317 10.196Q132.317 10.241 132.327 10.261L133.192 12.179L133.971 10.449Q134.006 10.381 134.006 10.302Q134.006 10.189 133.922 10.119Q133.838 10.049 133.718 10.049L133.718 9.769L134.915 9.769L134.915 10.049Q134.696 10.049 134.525 10.152Q134.354 10.254 134.265 10.449L133.230 12.760Q133.182 12.855 133.076 12.855L132.997 12.855Q132.891 12.855 132.843 12.760\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -35.98)\">\u003Cpath d=\"M135.205 11.252Q135.205 10.931 135.330 10.642Q135.455 10.353 135.681 10.130Q135.906 9.906 136.202 9.786Q136.497 9.666 136.815 9.666Q137.143 9.666 137.405 9.766Q137.666 9.865 137.842 10.047Q138.018 10.230 138.112 10.488Q138.206 10.746 138.206 11.078Q138.206 11.170 138.124 11.191L135.869 11.191L135.869 11.252Q135.869 11.840 136.152 12.223Q136.436 12.606 137.003 12.606Q137.325 12.606 137.593 12.413Q137.861 12.220 137.950 11.905Q137.957 11.864 138.032 11.850L138.124 11.850Q138.206 11.874 138.206 11.946Q138.206 11.953 138.200 11.980Q138.087 12.377 137.716 12.616Q137.345 12.855 136.921 12.855Q136.484 12.855 136.084 12.647Q135.684 12.438 135.445 12.071Q135.205 11.704 135.205 11.252M135.875 10.982L137.690 10.982Q137.690 10.705 137.593 10.453Q137.495 10.200 137.297 10.044Q137.099 9.889 136.815 9.889Q136.538 9.889 136.325 10.047Q136.111 10.206 135.993 10.461Q135.875 10.716 135.875 10.982M138.794 12.780L138.794 11.717Q138.794 11.693 138.822 11.666Q138.849 11.639 138.873 11.639L138.982 11.639Q139.047 11.639 139.061 11.697Q139.157 12.131 139.403 12.382Q139.649 12.633 140.062 12.633Q140.404 12.633 140.657 12.500Q140.910 12.367 140.910 12.059Q140.910 11.902 140.816 11.787Q140.722 11.673 140.584 11.604Q140.445 11.536 140.278 11.498L139.697 11.399Q139.341 11.331 139.068 11.110Q138.794 10.890 138.794 10.548Q138.794 10.299 138.905 10.124Q139.016 9.950 139.203 9.851Q139.389 9.752 139.604 9.709Q139.820 9.666 140.062 9.666Q140.476 9.666 140.756 9.848L140.972 9.673Q140.982 9.670 140.989 9.668Q140.995 9.666 141.006 9.666L141.057 9.666Q141.084 9.666 141.108 9.690Q141.132 9.714 141.132 9.742L141.132 10.589Q141.132 10.610 141.108 10.637Q141.084 10.664 141.057 10.664L140.944 10.664Q140.917 10.664 140.891 10.639Q140.866 10.613 140.866 10.589Q140.866 10.353 140.760 10.189Q140.654 10.025 140.471 9.943Q140.288 9.861 140.056 9.861Q139.727 9.861 139.471 9.964Q139.215 10.066 139.215 10.343Q139.215 10.538 139.398 10.647Q139.580 10.757 139.809 10.798L140.384 10.904Q140.630 10.952 140.843 11.080Q141.057 11.208 141.194 11.411Q141.330 11.615 141.330 11.864Q141.330 12.377 140.965 12.616Q140.599 12.855 140.062 12.855Q139.567 12.855 139.235 12.561L138.969 12.835Q138.948 12.855 138.921 12.855L138.873 12.855Q138.849 12.855 138.822 12.828Q138.794 12.801 138.794 12.780\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M47.009 4.251c0-6.285-23.885-11.38-53.349-11.38S-59.688-2.035-59.688 4.25-35.803 15.633-6.34 15.633c29.464 0 53.349-5.096 53.349-11.382Zm-53.349 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-105.522 -6.786)\">\u003Cpath d=\"M66.494 12.760L65.513 10.261Q65.452 10.118 65.334 10.083Q65.216 10.049 65 10.049L65 9.769L66.480 9.769L66.480 10.049Q66.101 10.049 66.101 10.210Q66.101 10.220 66.115 10.261L66.829 12.093L67.502 10.388Q67.472 10.316 67.472 10.288Q67.472 10.261 67.444 10.261Q67.383 10.114 67.265 10.082Q67.147 10.049 66.935 10.049L66.935 9.769L68.333 9.769L68.333 10.049Q67.957 10.049 67.957 10.210Q67.957 10.241 67.964 10.261L68.719 12.199L69.406 10.449Q69.427 10.398 69.427 10.343Q69.427 10.203 69.314 10.126Q69.201 10.049 69.061 10.049L69.061 9.769L70.281 9.769L70.281 10.049Q70.076 10.049 69.921 10.155Q69.765 10.261 69.693 10.449L68.788 12.760Q68.753 12.855 68.641 12.855L68.572 12.855Q68.463 12.855 68.425 12.760L67.643 10.757L66.856 12.760Q66.822 12.855 66.709 12.855L66.641 12.855Q66.532 12.855 66.494 12.760M72.493 12.787L70.859 12.787L70.859 12.507Q71.088 12.507 71.237 12.473Q71.385 12.438 71.385 12.298L71.385 8.679Q71.385 8.409 71.278 8.347Q71.170 8.286 70.859 8.286L70.859 8.005L71.939 7.930L71.939 10.316Q72.045 10.131 72.223 9.989Q72.400 9.848 72.609 9.774Q72.817 9.701 73.043 9.701Q73.549 9.701 73.833 9.924Q74.116 10.148 74.116 10.644L74.116 12.298Q74.116 12.435 74.265 12.471Q74.414 12.507 74.639 12.507L74.639 12.787L73.009 12.787L73.009 12.507Q73.238 12.507 73.386 12.473Q73.535 12.438 73.535 12.298L73.535 10.658Q73.535 10.323 73.416 10.123Q73.296 9.923 72.981 9.923Q72.711 9.923 72.477 10.059Q72.243 10.196 72.105 10.430Q71.966 10.664 71.966 10.938L71.966 12.298Q71.966 12.435 72.117 12.471Q72.267 12.507 72.493 12.507L72.493 12.787M75.285 12.059Q75.285 11.727 75.509 11.500Q75.733 11.273 76.076 11.145Q76.420 11.016 76.792 10.964Q77.165 10.911 77.469 10.911L77.469 10.658Q77.469 10.453 77.362 10.273Q77.254 10.094 77.073 9.991Q76.892 9.889 76.683 9.889Q76.276 9.889 76.041 9.981Q76.129 10.018 76.176 10.102Q76.222 10.186 76.222 10.288Q76.222 10.384 76.176 10.463Q76.129 10.541 76.049 10.586Q75.969 10.630 75.880 10.630Q75.730 10.630 75.629 10.533Q75.528 10.435 75.528 10.288Q75.528 9.666 76.683 9.666Q76.895 9.666 77.145 9.730Q77.394 9.793 77.596 9.912Q77.797 10.032 77.924 10.217Q78.050 10.401 78.050 10.644L78.050 12.220Q78.050 12.336 78.112 12.432Q78.173 12.527 78.286 12.527Q78.396 12.527 78.460 12.433Q78.525 12.339 78.525 12.220L78.525 11.772L78.792 11.772L78.792 12.220Q78.792 12.490 78.565 12.655Q78.337 12.821 78.057 12.821Q77.849 12.821 77.712 12.667Q77.575 12.514 77.551 12.298Q77.404 12.565 77.122 12.710Q76.840 12.855 76.516 12.855Q76.239 12.855 75.955 12.780Q75.671 12.705 75.478 12.526Q75.285 12.346 75.285 12.059M75.900 12.059Q75.900 12.233 76.001 12.363Q76.102 12.493 76.258 12.563Q76.413 12.633 76.577 12.633Q76.796 12.633 77.004 12.536Q77.213 12.438 77.341 12.257Q77.469 12.076 77.469 11.850L77.469 11.122Q77.145 11.122 76.779 11.213Q76.413 11.304 76.157 11.516Q75.900 11.727 75.900 12.059M79.735 11.946L79.735 10.049L79.096 10.049L79.096 9.827Q79.414 9.827 79.631 9.617Q79.848 9.407 79.949 9.097Q80.050 8.788 80.050 8.480L80.316 8.480L80.316 9.769L81.393 9.769L81.393 10.049L80.316 10.049L80.316 11.933Q80.316 12.209 80.421 12.408Q80.525 12.606 80.785 12.606Q80.942 12.606 81.048 12.502Q81.154 12.397 81.203 12.244Q81.253 12.090 81.253 11.933L81.253 11.519L81.520 11.519L81.520 11.946Q81.520 12.172 81.420 12.382Q81.321 12.592 81.137 12.724Q80.952 12.855 80.723 12.855Q80.286 12.855 80.011 12.618Q79.735 12.380 79.735 11.946\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -6.786)\">\u003Cpath d=\"M86.719 12.787L85.085 12.787L85.085 12.507Q85.314 12.507 85.463 12.473Q85.612 12.438 85.612 12.298L85.612 10.449Q85.612 10.179 85.504 10.118Q85.396 10.056 85.085 10.056L85.085 9.776L86.145 9.701L86.145 10.350Q86.316 10.042 86.620 9.871Q86.924 9.701 87.269 9.701Q87.669 9.701 87.946 9.841Q88.223 9.981 88.308 10.329Q88.476 10.036 88.775 9.868Q89.074 9.701 89.419 9.701Q89.925 9.701 90.209 9.924Q90.493 10.148 90.493 10.644L90.493 12.298Q90.493 12.435 90.641 12.471Q90.790 12.507 91.015 12.507L91.015 12.787L89.385 12.787L89.385 12.507Q89.611 12.507 89.761 12.471Q89.911 12.435 89.911 12.298L89.911 10.658Q89.911 10.323 89.792 10.123Q89.672 9.923 89.358 9.923Q89.088 9.923 88.854 10.059Q88.619 10.196 88.481 10.430Q88.343 10.664 88.343 10.938L88.343 12.298Q88.343 12.435 88.491 12.471Q88.640 12.507 88.866 12.507L88.866 12.787L87.235 12.787L87.235 12.507Q87.464 12.507 87.613 12.473Q87.762 12.438 87.762 12.298L87.762 10.658Q87.762 10.323 87.642 10.123Q87.522 9.923 87.208 9.923Q86.938 9.923 86.704 10.059Q86.470 10.196 86.331 10.430Q86.193 10.664 86.193 10.938L86.193 12.298Q86.193 12.435 86.343 12.471Q86.494 12.507 86.719 12.507\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -6.786)\">\u003Cpath d=\"M91.726 13.922Q91.856 13.990 91.993 13.990Q92.164 13.990 92.314 13.901Q92.465 13.812 92.576 13.667Q92.687 13.522 92.765 13.354L93.029 12.787L91.860 10.261Q91.785 10.114 91.655 10.082Q91.525 10.049 91.292 10.049L91.292 9.769L92.813 9.769L92.813 10.049Q92.465 10.049 92.465 10.196Q92.468 10.217 92.470 10.234Q92.472 10.251 92.472 10.261L93.329 12.120L94.102 10.449Q94.136 10.381 94.136 10.302Q94.136 10.189 94.052 10.119Q93.969 10.049 93.856 10.049L93.856 9.769L95.052 9.769L95.052 10.049Q94.833 10.049 94.661 10.153Q94.488 10.258 94.396 10.449L93.059 13.354Q92.889 13.724 92.619 13.970Q92.348 14.216 91.993 14.216Q91.723 14.216 91.504 14.050Q91.285 13.884 91.285 13.621Q91.285 13.484 91.378 13.395Q91.470 13.307 91.610 13.307Q91.747 13.307 91.836 13.395Q91.925 13.484 91.925 13.621Q91.925 13.724 91.872 13.802Q91.819 13.881 91.726 13.922\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -6.786)\">\u003Cpath d=\"M98.346 12.059Q98.346 11.727 98.569 11.500Q98.793 11.273 99.137 11.145Q99.480 11.016 99.853 10.964Q100.225 10.911 100.530 10.911L100.530 10.658Q100.530 10.453 100.422 10.273Q100.314 10.094 100.133 9.991Q99.952 9.889 99.744 9.889Q99.337 9.889 99.101 9.981Q99.190 10.018 99.236 10.102Q99.282 10.186 99.282 10.288Q99.282 10.384 99.236 10.463Q99.190 10.541 99.109 10.586Q99.029 10.630 98.940 10.630Q98.790 10.630 98.689 10.533Q98.588 10.435 98.588 10.288Q98.588 9.666 99.744 9.666Q99.955 9.666 100.205 9.730Q100.454 9.793 100.656 9.912Q100.858 10.032 100.984 10.217Q101.111 10.401 101.111 10.644L101.111 12.220Q101.111 12.336 101.172 12.432Q101.234 12.527 101.347 12.527Q101.456 12.527 101.521 12.433Q101.586 12.339 101.586 12.220L101.586 11.772L101.852 11.772L101.852 12.220Q101.852 12.490 101.625 12.655Q101.398 12.821 101.118 12.821Q100.909 12.821 100.772 12.667Q100.636 12.514 100.612 12.298Q100.465 12.565 100.183 12.710Q99.901 12.855 99.576 12.855Q99.299 12.855 99.015 12.780Q98.732 12.705 98.539 12.526Q98.346 12.346 98.346 12.059M98.961 12.059Q98.961 12.233 99.062 12.363Q99.162 12.493 99.318 12.563Q99.473 12.633 99.638 12.633Q99.856 12.633 100.065 12.536Q100.273 12.438 100.401 12.257Q100.530 12.076 100.530 11.850L100.530 11.122Q100.205 11.122 99.839 11.213Q99.473 11.304 99.217 11.516Q98.961 11.727 98.961 12.059M102.269 11.276Q102.269 10.948 102.404 10.647Q102.539 10.347 102.775 10.126Q103.011 9.906 103.315 9.786Q103.619 9.666 103.944 9.666Q104.450 9.666 104.799 9.769Q105.147 9.871 105.147 10.247Q105.147 10.394 105.050 10.495Q104.952 10.596 104.806 10.596Q104.652 10.596 104.553 10.497Q104.453 10.398 104.453 10.247Q104.453 10.059 104.594 9.967Q104.392 9.916 103.951 9.916Q103.596 9.916 103.367 10.112Q103.138 10.309 103.037 10.618Q102.936 10.928 102.936 11.276Q102.936 11.625 103.062 11.931Q103.189 12.237 103.443 12.421Q103.698 12.606 104.054 12.606Q104.276 12.606 104.460 12.522Q104.645 12.438 104.780 12.283Q104.915 12.127 104.973 11.919Q104.987 11.864 105.041 11.864L105.154 11.864Q105.185 11.864 105.207 11.888Q105.229 11.912 105.229 11.946L105.229 11.967Q105.144 12.254 104.956 12.452Q104.768 12.650 104.503 12.753Q104.238 12.855 103.944 12.855Q103.514 12.855 103.126 12.649Q102.738 12.442 102.504 12.079Q102.269 11.717 102.269 11.276M106.344 11.946L106.344 10.049L105.704 10.049L105.704 9.827Q106.022 9.827 106.239 9.617Q106.456 9.407 106.557 9.097Q106.658 8.788 106.658 8.480L106.925 8.480L106.925 9.769L108.001 9.769L108.001 10.049L106.925 10.049L106.925 11.933Q106.925 12.209 107.029 12.408Q107.133 12.606 107.393 12.606Q107.550 12.606 107.656 12.502Q107.762 12.397 107.812 12.244Q107.861 12.090 107.861 11.933L107.861 11.519L108.128 11.519L108.128 11.946Q108.128 12.172 108.029 12.382Q107.930 12.592 107.745 12.724Q107.560 12.855 107.331 12.855Q106.894 12.855 106.619 12.618Q106.344 12.380 106.344 11.946M110.555 12.787L109.003 12.787L109.003 12.507Q109.228 12.507 109.377 12.473Q109.526 12.438 109.526 12.298L109.526 10.449Q109.526 10.261 109.478 10.177Q109.430 10.094 109.333 10.075Q109.235 10.056 109.023 10.056L109.023 9.776L110.079 9.701L110.079 12.298Q110.079 12.438 110.211 12.473Q110.343 12.507 110.555 12.507L110.555 12.787M109.283 8.480Q109.283 8.309 109.406 8.190Q109.529 8.070 109.700 8.070Q109.868 8.070 109.991 8.190Q110.114 8.309 110.114 8.480Q110.114 8.655 109.991 8.778Q109.868 8.901 109.700 8.901Q109.529 8.901 109.406 8.778Q109.283 8.655 109.283 8.480M111.160 11.304Q111.160 10.962 111.295 10.663Q111.430 10.364 111.669 10.140Q111.908 9.916 112.226 9.791Q112.544 9.666 112.875 9.666Q113.320 9.666 113.720 9.882Q114.119 10.097 114.354 10.475Q114.588 10.852 114.588 11.304Q114.588 11.645 114.446 11.929Q114.304 12.213 114.060 12.420Q113.815 12.626 113.506 12.741Q113.197 12.855 112.875 12.855Q112.445 12.855 112.043 12.654Q111.641 12.452 111.400 12.100Q111.160 11.748 111.160 11.304M112.875 12.606Q113.477 12.606 113.701 12.228Q113.925 11.850 113.925 11.218Q113.925 10.606 113.691 10.247Q113.456 9.889 112.875 9.889Q111.823 9.889 111.823 11.218Q111.823 11.850 112.048 12.228Q112.274 12.606 112.875 12.606M116.864 12.787L115.230 12.787L115.230 12.507Q115.459 12.507 115.608 12.473Q115.757 12.438 115.757 12.298L115.757 10.449Q115.757 10.179 115.649 10.118Q115.541 10.056 115.230 10.056L115.230 9.776L116.290 9.701L116.290 10.350Q116.461 10.042 116.765 9.871Q117.069 9.701 117.414 9.701Q117.920 9.701 118.204 9.924Q118.488 10.148 118.488 10.644L118.488 12.298Q118.488 12.435 118.636 12.471Q118.785 12.507 119.011 12.507L119.011 12.787L117.380 12.787L117.380 12.507Q117.609 12.507 117.758 12.473Q117.907 12.438 117.907 12.298L117.907 10.658Q117.907 10.323 117.787 10.123Q117.667 9.923 117.353 9.923Q117.083 9.923 116.849 10.059Q116.615 10.196 116.476 10.430Q116.338 10.664 116.338 10.938L116.338 12.298Q116.338 12.435 116.488 12.471Q116.639 12.507 116.864 12.507L116.864 12.787M119.598 12.780L119.598 11.717Q119.598 11.693 119.626 11.666Q119.653 11.639 119.677 11.639L119.786 11.639Q119.851 11.639 119.865 11.697Q119.961 12.131 120.207 12.382Q120.453 12.633 120.867 12.633Q121.208 12.633 121.461 12.500Q121.714 12.367 121.714 12.059Q121.714 11.902 121.620 11.787Q121.526 11.673 121.388 11.604Q121.249 11.536 121.082 11.498L120.501 11.399Q120.145 11.331 119.872 11.110Q119.598 10.890 119.598 10.548Q119.598 10.299 119.710 10.124Q119.821 9.950 120.007 9.851Q120.193 9.752 120.409 9.709Q120.624 9.666 120.867 9.666Q121.280 9.666 121.560 9.848L121.776 9.673Q121.786 9.670 121.793 9.668Q121.800 9.666 121.810 9.666L121.861 9.666Q121.889 9.666 121.912 9.690Q121.936 9.714 121.936 9.742L121.936 10.589Q121.936 10.610 121.912 10.637Q121.889 10.664 121.861 10.664L121.748 10.664Q121.721 10.664 121.695 10.639Q121.670 10.613 121.670 10.589Q121.670 10.353 121.564 10.189Q121.458 10.025 121.275 9.943Q121.092 9.861 120.860 9.861Q120.532 9.861 120.275 9.964Q120.019 10.066 120.019 10.343Q120.019 10.538 120.202 10.647Q120.385 10.757 120.614 10.798L121.188 10.904Q121.434 10.952 121.648 11.080Q121.861 11.208 121.998 11.411Q122.135 11.615 122.135 11.864Q122.135 12.377 121.769 12.616Q121.403 12.855 120.867 12.855Q120.371 12.855 120.039 12.561L119.773 12.835Q119.752 12.855 119.725 12.855L119.677 12.855Q119.653 12.855 119.626 12.828Q119.598 12.801 119.598 12.780\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -6.786)\">\u003Cpath d=\"M125.483 11.276Q125.483 10.938 125.624 10.647Q125.764 10.357 126.008 10.143Q126.252 9.930 126.557 9.815Q126.861 9.701 127.186 9.701Q127.456 9.701 127.719 9.800Q127.982 9.899 128.173 10.077L128.173 8.679Q128.173 8.409 128.066 8.347Q127.958 8.286 127.647 8.286L127.647 8.005L128.724 7.930L128.724 12.114Q128.724 12.302 128.778 12.385Q128.833 12.469 128.934 12.488Q129.035 12.507 129.250 12.507L129.250 12.787L128.143 12.855L128.143 12.438Q127.726 12.855 127.100 12.855Q126.669 12.855 126.297 12.643Q125.924 12.432 125.704 12.071Q125.483 11.710 125.483 11.276M127.158 12.633Q127.367 12.633 127.553 12.561Q127.739 12.490 127.893 12.353Q128.047 12.216 128.143 12.038L128.143 10.429Q128.057 10.282 127.912 10.162Q127.767 10.042 127.597 9.983Q127.428 9.923 127.247 9.923Q126.687 9.923 126.418 10.312Q126.150 10.702 126.150 11.283Q126.150 11.854 126.384 12.244Q126.618 12.633 127.158 12.633M129.858 11.304Q129.858 10.962 129.993 10.663Q130.128 10.364 130.368 10.140Q130.607 9.916 130.925 9.791Q131.243 9.666 131.574 9.666Q132.019 9.666 132.419 9.882Q132.818 10.097 133.053 10.475Q133.287 10.852 133.287 11.304Q133.287 11.645 133.145 11.929Q133.003 12.213 132.759 12.420Q132.514 12.626 132.205 12.741Q131.896 12.855 131.574 12.855Q131.144 12.855 130.742 12.654Q130.340 12.452 130.099 12.100Q129.858 11.748 129.858 11.304M131.574 12.606Q132.176 12.606 132.400 12.228Q132.624 11.850 132.624 11.218Q132.624 10.606 132.389 10.247Q132.155 9.889 131.574 9.889Q130.522 9.889 130.522 11.218Q130.522 11.850 130.747 12.228Q130.973 12.606 131.574 12.606\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M36.34 52.621c0-6.286-19.108-11.381-42.68-11.381-23.57 0-42.679 5.095-42.679 11.381s19.108 11.381 42.68 11.381c23.57 0 42.679-5.095 42.679-11.38Zm-42.68 0\"\u002F>\u003Cg transform=\"translate(-79.827 41.584)\">\u003Cpath d=\"M65.065 13.320Q65.065 13.074 65.262 12.890Q65.459 12.705 65.715 12.626Q65.578 12.514 65.506 12.353Q65.435 12.192 65.435 12.011Q65.435 11.690 65.646 11.444Q65.312 11.146 65.312 10.736Q65.312 10.275 65.701 9.988Q66.091 9.701 66.569 9.701Q67.041 9.701 67.376 9.947Q67.550 9.793 67.761 9.711Q67.971 9.629 68.200 9.629Q68.364 9.629 68.485 9.736Q68.606 9.844 68.606 10.008Q68.606 10.104 68.535 10.176Q68.463 10.247 68.371 10.247Q68.271 10.247 68.201 10.174Q68.131 10.100 68.131 10.001Q68.131 9.947 68.145 9.916L68.152 9.902Q68.159 9.882 68.167 9.871Q68.176 9.861 68.179 9.854Q67.824 9.854 67.537 10.077Q67.824 10.370 67.824 10.736Q67.824 11.051 67.639 11.283Q67.455 11.516 67.166 11.644Q66.877 11.772 66.569 11.772Q66.368 11.772 66.176 11.722Q65.985 11.673 65.807 11.563Q65.715 11.690 65.715 11.833Q65.715 12.015 65.843 12.150Q65.971 12.285 66.156 12.285L66.788 12.285Q67.236 12.285 67.605 12.356Q67.974 12.428 68.234 12.657Q68.494 12.886 68.494 13.320Q68.494 13.641 68.198 13.843Q67.902 14.045 67.499 14.134Q67.096 14.223 66.781 14.223Q66.463 14.223 66.060 14.134Q65.657 14.045 65.361 13.843Q65.065 13.641 65.065 13.320M65.520 13.320Q65.520 13.549 65.739 13.698Q65.958 13.847 66.250 13.915Q66.542 13.983 66.781 13.983Q66.945 13.983 67.154 13.947Q67.362 13.912 67.569 13.831Q67.776 13.751 67.907 13.623Q68.039 13.495 68.039 13.320Q68.039 12.968 67.658 12.874Q67.277 12.780 66.774 12.780L66.156 12.780Q65.917 12.780 65.718 12.931Q65.520 13.081 65.520 13.320M66.569 11.533Q67.236 11.533 67.236 10.736Q67.236 9.936 66.569 9.936Q65.899 9.936 65.899 10.736Q65.899 11.533 66.569 11.533M69.047 11.304Q69.047 10.962 69.182 10.663Q69.317 10.364 69.557 10.140Q69.796 9.916 70.114 9.791Q70.432 9.666 70.763 9.666Q71.208 9.666 71.607 9.882Q72.007 10.097 72.241 10.475Q72.476 10.852 72.476 11.304Q72.476 11.645 72.334 11.929Q72.192 12.213 71.948 12.420Q71.703 12.626 71.394 12.741Q71.084 12.855 70.763 12.855Q70.333 12.855 69.931 12.654Q69.529 12.452 69.288 12.100Q69.047 11.748 69.047 11.304M70.763 12.606Q71.365 12.606 71.589 12.228Q71.813 11.850 71.813 11.218Q71.813 10.606 71.578 10.247Q71.344 9.889 70.763 9.889Q69.710 9.889 69.710 11.218Q69.710 11.850 69.936 12.228Q70.162 12.606 70.763 12.606M73.128 12.059Q73.128 11.727 73.352 11.500Q73.576 11.273 73.920 11.145Q74.263 11.016 74.636 10.964Q75.008 10.911 75.313 10.911L75.313 10.658Q75.313 10.453 75.205 10.273Q75.097 10.094 74.916 9.991Q74.735 9.889 74.526 9.889Q74.120 9.889 73.884 9.981Q73.973 10.018 74.019 10.102Q74.065 10.186 74.065 10.288Q74.065 10.384 74.019 10.463Q73.973 10.541 73.892 10.586Q73.812 10.630 73.723 10.630Q73.573 10.630 73.472 10.533Q73.371 10.435 73.371 10.288Q73.371 9.666 74.526 9.666Q74.738 9.666 74.988 9.730Q75.237 9.793 75.439 9.912Q75.641 10.032 75.767 10.217Q75.894 10.401 75.894 10.644L75.894 12.220Q75.894 12.336 75.955 12.432Q76.017 12.527 76.129 12.527Q76.239 12.527 76.304 12.433Q76.369 12.339 76.369 12.220L76.369 11.772L76.635 11.772L76.635 12.220Q76.635 12.490 76.408 12.655Q76.181 12.821 75.900 12.821Q75.692 12.821 75.555 12.667Q75.418 12.514 75.395 12.298Q75.248 12.565 74.966 12.710Q74.684 12.855 74.359 12.855Q74.082 12.855 73.798 12.780Q73.515 12.705 73.322 12.526Q73.128 12.346 73.128 12.059M73.744 12.059Q73.744 12.233 73.844 12.363Q73.945 12.493 74.101 12.563Q74.256 12.633 74.420 12.633Q74.639 12.633 74.848 12.536Q75.056 12.438 75.184 12.257Q75.313 12.076 75.313 11.850L75.313 11.122Q74.988 11.122 74.622 11.213Q74.256 11.304 74 11.516Q73.744 11.727 73.744 12.059M78.720 12.787L77.117 12.787L77.117 12.507Q77.343 12.507 77.491 12.473Q77.640 12.438 77.640 12.298L77.640 8.679Q77.640 8.409 77.532 8.347Q77.425 8.286 77.117 8.286L77.117 8.005L78.194 7.930L78.194 12.298Q78.194 12.435 78.344 12.471Q78.495 12.507 78.720 12.507L78.720 12.787M79.315 12.780L79.315 11.717Q79.315 11.693 79.342 11.666Q79.370 11.639 79.394 11.639L79.503 11.639Q79.568 11.639 79.582 11.697Q79.677 12.131 79.923 12.382Q80.169 12.633 80.583 12.633Q80.925 12.633 81.178 12.500Q81.431 12.367 81.431 12.059Q81.431 11.902 81.337 11.787Q81.243 11.673 81.104 11.604Q80.966 11.536 80.798 11.498L80.217 11.399Q79.862 11.331 79.588 11.110Q79.315 10.890 79.315 10.548Q79.315 10.299 79.426 10.124Q79.537 9.950 79.723 9.851Q79.910 9.752 80.125 9.709Q80.340 9.666 80.583 9.666Q80.997 9.666 81.277 9.848L81.492 9.673Q81.502 9.670 81.509 9.668Q81.516 9.666 81.526 9.666L81.578 9.666Q81.605 9.666 81.629 9.690Q81.653 9.714 81.653 9.742L81.653 10.589Q81.653 10.610 81.629 10.637Q81.605 10.664 81.578 10.664L81.465 10.664Q81.438 10.664 81.412 10.639Q81.386 10.613 81.386 10.589Q81.386 10.353 81.280 10.189Q81.174 10.025 80.991 9.943Q80.809 9.861 80.576 9.861Q80.248 9.861 79.992 9.964Q79.735 10.066 79.735 10.343Q79.735 10.538 79.918 10.647Q80.101 10.757 80.330 10.798L80.904 10.904Q81.150 10.952 81.364 11.080Q81.578 11.208 81.714 11.411Q81.851 11.615 81.851 11.864Q81.851 12.377 81.485 12.616Q81.120 12.855 80.583 12.855Q80.087 12.855 79.756 12.561L79.489 12.835Q79.469 12.855 79.441 12.855L79.394 12.855Q79.370 12.855 79.342 12.828Q79.315 12.801 79.315 12.780\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M70.483 72.538h73.977V44.086H70.483Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M68.533 3.256L67.463 0.400Q67.397 0.221 67.266 0.178Q67.135 0.135 66.877 0.135L66.877-0.162L68.557-0.162L68.557 0.135Q68.107 0.135 68.107 0.334Q68.111 0.349 68.113 0.367Q68.115 0.385 68.115 0.400L68.908 2.494L69.619 0.584Q69.584 0.490 69.584 0.445Q69.584 0.400 69.549 0.400Q69.482 0.221 69.352 0.178Q69.221 0.135 68.967 0.135L68.967-0.162L70.557-0.162L70.557 0.135Q70.107 0.135 70.107 0.334Q70.111 0.353 70.113 0.371Q70.115 0.389 70.115 0.400L70.947 2.615L71.701 0.615Q71.725 0.557 71.725 0.486Q71.725 0.326 71.588 0.230Q71.451 0.135 71.283 0.135L71.283-0.162L72.670-0.162L72.670 0.135Q72.436 0.135 72.258 0.262Q72.080 0.389 71.998 0.615L71.014 3.256Q70.959 3.365 70.846 3.365L70.787 3.365Q70.674 3.365 70.631 3.256L69.772 0.982L68.916 3.256Q68.877 3.365 68.756 3.365L68.701 3.365Q68.588 3.365 68.533 3.256M75.014 3.287L73.158 3.287L73.158 2.990Q73.432 2.990 73.600 2.943Q73.768 2.896 73.768 2.728L73.768-1.432Q73.768-1.647 73.705-1.742Q73.643-1.838 73.523-1.859Q73.404-1.881 73.158-1.881L73.158-2.178L74.381-2.264L74.381 0.439Q74.506 0.228 74.693 0.078Q74.881-0.072 75.107-0.156Q75.334-0.240 75.580-0.240Q76.748-0.240 76.748 0.838L76.748 2.728Q76.748 2.896 76.918 2.943Q77.088 2.990 77.357 2.990L77.357 3.287L75.502 3.287L75.502 2.990Q75.775 2.990 75.943 2.943Q76.111 2.896 76.111 2.728L76.111 0.853Q76.111 0.471 75.990 0.242Q75.869 0.014 75.518 0.014Q75.205 0.014 74.951 0.176Q74.697 0.338 74.551 0.607Q74.404 0.877 74.404 1.174L74.404 2.728Q74.404 2.896 74.574 2.943Q74.744 2.990 75.014 2.990L75.014 3.287M77.900 2.455Q77.900 1.971 78.303 1.676Q78.705 1.381 79.256 1.262Q79.807 1.142 80.299 1.142L80.299 0.853Q80.299 0.627 80.184 0.420Q80.068 0.213 79.871 0.094Q79.674-0.026 79.443-0.026Q79.018-0.026 78.732 0.080Q78.803 0.107 78.850 0.162Q78.897 0.217 78.922 0.287Q78.947 0.357 78.947 0.432Q78.947 0.537 78.897 0.629Q78.846 0.721 78.754 0.771Q78.662 0.822 78.557 0.822Q78.451 0.822 78.359 0.771Q78.268 0.721 78.217 0.629Q78.166 0.537 78.166 0.432Q78.166 0.014 78.555-0.133Q78.943-0.279 79.443-0.279Q79.775-0.279 80.129-0.149Q80.482-0.018 80.711 0.236Q80.939 0.490 80.939 0.838L80.939 2.639Q80.939 2.771 81.012 2.881Q81.084 2.990 81.213 2.990Q81.338 2.990 81.406 2.885Q81.475 2.779 81.475 2.639L81.475 2.127L81.756 2.127L81.756 2.639Q81.756 2.842 81.639 3Q81.522 3.158 81.340 3.242Q81.158 3.326 80.955 3.326Q80.725 3.326 80.572 3.154Q80.420 2.982 80.389 2.752Q80.229 3.033 79.920 3.199Q79.611 3.365 79.260 3.365Q78.748 3.365 78.324 3.142Q77.900 2.920 77.900 2.455M78.588 2.455Q78.588 2.740 78.814 2.926Q79.041 3.111 79.334 3.111Q79.580 3.111 79.805 2.994Q80.029 2.877 80.164 2.674Q80.299 2.471 80.299 2.217L80.299 1.385Q80.033 1.385 79.748 1.439Q79.463 1.494 79.191 1.623Q78.920 1.752 78.754 1.959Q78.588 2.166 78.588 2.455M82.674 2.326L82.674 0.135L81.971 0.135L81.971-0.119Q82.326-0.119 82.568-0.352Q82.811-0.584 82.922-0.932Q83.033-1.279 83.033-1.635L83.314-1.635L83.314-0.162L84.490-0.162L84.490 0.135L83.314 0.135L83.314 2.310Q83.314 2.631 83.434 2.859Q83.553 3.088 83.834 3.088Q84.014 3.088 84.131 2.965Q84.248 2.842 84.301 2.662Q84.354 2.482 84.354 2.310L84.354 1.838L84.635 1.838L84.635 2.326Q84.635 2.580 84.529 2.820Q84.424 3.060 84.227 3.213Q84.029 3.365 83.772 3.365Q83.455 3.365 83.203 3.242Q82.951 3.119 82.813 2.885Q82.674 2.650 82.674 2.326\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M88.295 2.455Q88.295 1.971 88.697 1.676Q89.100 1.381 89.650 1.262Q90.201 1.142 90.693 1.142L90.693 0.853Q90.693 0.627 90.578 0.420Q90.463 0.213 90.266 0.094Q90.068-0.026 89.838-0.026Q89.412-0.026 89.127 0.080Q89.197 0.107 89.244 0.162Q89.291 0.217 89.316 0.287Q89.342 0.357 89.342 0.432Q89.342 0.537 89.291 0.629Q89.240 0.721 89.148 0.771Q89.057 0.822 88.951 0.822Q88.846 0.822 88.754 0.771Q88.662 0.721 88.611 0.629Q88.561 0.537 88.561 0.432Q88.561 0.014 88.949-0.133Q89.338-0.279 89.838-0.279Q90.170-0.279 90.523-0.149Q90.877-0.018 91.105 0.236Q91.334 0.490 91.334 0.838L91.334 2.639Q91.334 2.771 91.406 2.881Q91.479 2.990 91.607 2.990Q91.732 2.990 91.801 2.885Q91.869 2.779 91.869 2.639L91.869 2.127L92.150 2.127L92.150 2.639Q92.150 2.842 92.033 3Q91.916 3.158 91.734 3.242Q91.553 3.326 91.350 3.326Q91.119 3.326 90.967 3.154Q90.814 2.982 90.783 2.752Q90.623 3.033 90.314 3.199Q90.006 3.365 89.654 3.365Q89.143 3.365 88.719 3.142Q88.295 2.920 88.295 2.455M88.982 2.455Q88.982 2.740 89.209 2.926Q89.436 3.111 89.729 3.111Q89.975 3.111 90.199 2.994Q90.424 2.877 90.559 2.674Q90.693 2.471 90.693 2.217L90.693 1.385Q90.428 1.385 90.143 1.439Q89.857 1.494 89.586 1.623Q89.314 1.752 89.148 1.959Q88.982 2.166 88.982 2.455M92.486 1.560Q92.486 1.064 92.736 0.639Q92.986 0.213 93.406-0.033Q93.826-0.279 94.326-0.279Q94.865-0.279 95.256-0.154Q95.647-0.029 95.647 0.385Q95.647 0.490 95.596 0.582Q95.545 0.674 95.453 0.724Q95.361 0.775 95.252 0.775Q95.147 0.775 95.055 0.724Q94.963 0.674 94.912 0.582Q94.861 0.490 94.861 0.385Q94.861 0.162 95.029 0.057Q94.807-0.002 94.334-0.002Q94.037-0.002 93.822 0.137Q93.607 0.275 93.477 0.506Q93.346 0.736 93.287 1.006Q93.229 1.275 93.229 1.560Q93.229 1.955 93.361 2.305Q93.494 2.654 93.766 2.871Q94.037 3.088 94.436 3.088Q94.811 3.088 95.086 2.871Q95.361 2.654 95.463 2.295Q95.479 2.232 95.541 2.232L95.647 2.232Q95.682 2.232 95.707 2.260Q95.732 2.287 95.732 2.326L95.732 2.349Q95.600 2.830 95.215 3.098Q94.830 3.365 94.326 3.365Q93.963 3.365 93.629 3.228Q93.295 3.092 93.035 2.842Q92.775 2.592 92.631 2.256Q92.486 1.920 92.486 1.560M96.846 2.326L96.846 0.135L96.143 0.135L96.143-0.119Q96.498-0.119 96.740-0.352Q96.982-0.584 97.094-0.932Q97.205-1.279 97.205-1.635L97.486-1.635L97.486-0.162L98.662-0.162L98.662 0.135L97.486 0.135L97.486 2.310Q97.486 2.631 97.605 2.859Q97.725 3.088 98.006 3.088Q98.186 3.088 98.303 2.965Q98.420 2.842 98.473 2.662Q98.525 2.482 98.525 2.310L98.525 1.838L98.807 1.838L98.807 2.326Q98.807 2.580 98.701 2.820Q98.596 3.060 98.398 3.213Q98.201 3.365 97.943 3.365Q97.627 3.365 97.375 3.242Q97.123 3.119 96.984 2.885Q96.846 2.650 96.846 2.326M101.385 3.287L99.607 3.287L99.607 2.990Q99.881 2.990 100.049 2.943Q100.217 2.896 100.217 2.728L100.217 0.592Q100.217 0.377 100.160 0.281Q100.104 0.185 99.990 0.164Q99.877 0.142 99.631 0.142L99.631-0.154L100.830-0.240L100.830 2.728Q100.830 2.896 100.977 2.943Q101.123 2.990 101.385 2.990L101.385 3.287M99.943-1.635Q99.943-1.826 100.078-1.957Q100.213-2.088 100.408-2.088Q100.529-2.088 100.633-2.026Q100.736-1.963 100.799-1.859Q100.861-1.756 100.861-1.635Q100.861-1.440 100.730-1.305Q100.600-1.170 100.408-1.170Q100.209-1.170 100.076-1.303Q99.943-1.436 99.943-1.635M101.885 1.592Q101.885 1.088 102.141 0.656Q102.397 0.224 102.832-0.027Q103.268-0.279 103.768-0.279Q104.154-0.279 104.496-0.135Q104.838 0.010 105.100 0.271Q105.361 0.533 105.504 0.869Q105.647 1.205 105.647 1.592Q105.647 2.084 105.383 2.494Q105.119 2.904 104.689 3.135Q104.260 3.365 103.768 3.365Q103.275 3.365 102.842 3.133Q102.408 2.900 102.147 2.492Q101.885 2.084 101.885 1.592M103.768 3.088Q104.225 3.088 104.477 2.865Q104.729 2.642 104.816 2.291Q104.904 1.939 104.904 1.494Q104.904 1.064 104.811 0.726Q104.717 0.389 104.463 0.182Q104.209-0.026 103.768-0.026Q103.119-0.026 102.875 0.391Q102.631 0.807 102.631 1.494Q102.631 1.939 102.719 2.291Q102.807 2.642 103.059 2.865Q103.311 3.088 103.768 3.088M108.061 3.287L106.205 3.287L106.205 2.990Q106.479 2.990 106.647 2.943Q106.814 2.896 106.814 2.728L106.814 0.592Q106.814 0.377 106.752 0.281Q106.689 0.185 106.570 0.164Q106.451 0.142 106.205 0.142L106.205-0.154L107.397-0.240L107.397 0.494Q107.510 0.279 107.703 0.111Q107.897-0.057 108.135-0.149Q108.373-0.240 108.627-0.240Q109.795-0.240 109.795 0.838L109.795 2.728Q109.795 2.896 109.965 2.943Q110.135 2.990 110.404 2.990L110.404 3.287L108.549 3.287L108.549 2.990Q108.822 2.990 108.990 2.943Q109.158 2.896 109.158 2.728L109.158 0.853Q109.158 0.471 109.037 0.242Q108.916 0.014 108.564 0.014Q108.252 0.014 107.998 0.176Q107.744 0.338 107.598 0.607Q107.451 0.877 107.451 1.174L107.451 2.728Q107.451 2.896 107.621 2.943Q107.791 2.990 108.061 2.990\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M116.222 3.287L113.757 3.287L113.757 2.990Q114.089 2.990 114.347 2.943Q114.605 2.896 114.605 2.728L114.605-1.615Q114.605-1.881 113.757-1.881L113.757-2.178L116.222-2.178L116.222-1.881Q115.370-1.881 115.370-1.615L115.370 2.728Q115.370 2.990 116.222 2.990\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M65.073 12.779L65.073 11.557Q65.073 11.529 65.105 11.498Q65.136 11.467 65.159 11.467L65.265 11.467Q65.335 11.467 65.351 11.529Q65.413 11.850 65.552 12.090Q65.690 12.330 65.923 12.471Q66.155 12.611 66.464 12.611Q66.702 12.611 66.911 12.551Q67.120 12.490 67.257 12.342Q67.394 12.193 67.394 11.947Q67.394 11.693 67.183 11.527Q66.972 11.361 66.702 11.307L66.081 11.193Q65.675 11.115 65.374 10.859Q65.073 10.603 65.073 10.228Q65.073 9.861 65.274 9.639Q65.476 9.416 65.800 9.318Q66.124 9.221 66.464 9.221Q66.929 9.221 67.226 9.428L67.448 9.244Q67.472 9.221 67.503 9.221L67.554 9.221Q67.585 9.221 67.612 9.248Q67.640 9.275 67.640 9.307L67.640 10.291Q67.640 10.322 67.614 10.351Q67.589 10.381 67.554 10.381L67.448 10.381Q67.413 10.381 67.386 10.353Q67.358 10.326 67.358 10.291Q67.358 9.892 67.106 9.672Q66.855 9.451 66.456 9.451Q66.101 9.451 65.817 9.574Q65.534 9.697 65.534 10.002Q65.534 10.221 65.735 10.353Q65.937 10.486 66.183 10.529L66.808 10.642Q67.237 10.732 67.546 11.029Q67.855 11.326 67.855 11.740Q67.855 12.310 67.456 12.588Q67.058 12.865 66.464 12.865Q65.913 12.865 65.562 12.529L65.265 12.842Q65.241 12.865 65.206 12.865L65.159 12.865Q65.136 12.865 65.105 12.834Q65.073 12.803 65.073 12.779M70.312 12.787L68.456 12.787L68.456 12.490Q68.730 12.490 68.897 12.443Q69.065 12.396 69.065 12.228L69.065 8.068Q69.065 7.853 69.003 7.758Q68.940 7.662 68.821 7.641Q68.702 7.619 68.456 7.619L68.456 7.322L69.679 7.236L69.679 9.939Q69.804 9.728 69.991 9.578Q70.179 9.428 70.405 9.344Q70.632 9.260 70.878 9.260Q72.046 9.260 72.046 10.338L72.046 12.228Q72.046 12.396 72.216 12.443Q72.386 12.490 72.655 12.490L72.655 12.787L70.800 12.787L70.800 12.490Q71.073 12.490 71.241 12.443Q71.409 12.396 71.409 12.228L71.409 10.353Q71.409 9.971 71.288 9.742Q71.167 9.514 70.815 9.514Q70.503 9.514 70.249 9.676Q69.995 9.838 69.849 10.107Q69.702 10.377 69.702 10.674L69.702 12.228Q69.702 12.396 69.872 12.443Q70.042 12.490 70.312 12.490L70.312 12.787M73.101 11.092Q73.101 10.588 73.356 10.156Q73.612 9.725 74.048 9.473Q74.483 9.221 74.983 9.221Q75.370 9.221 75.712 9.365Q76.054 9.510 76.315 9.771Q76.577 10.033 76.720 10.369Q76.862 10.705 76.862 11.092Q76.862 11.584 76.599 11.994Q76.335 12.404 75.905 12.635Q75.476 12.865 74.983 12.865Q74.491 12.865 74.058 12.633Q73.624 12.400 73.362 11.992Q73.101 11.584 73.101 11.092M74.983 12.588Q75.440 12.588 75.692 12.365Q75.944 12.142 76.032 11.791Q76.120 11.439 76.120 10.994Q76.120 10.564 76.026 10.226Q75.933 9.889 75.679 9.682Q75.425 9.475 74.983 9.475Q74.335 9.475 74.091 9.891Q73.847 10.307 73.847 10.994Q73.847 11.439 73.935 11.791Q74.022 12.142 74.274 12.365Q74.526 12.588 74.983 12.588M78.030 11.834L78.030 10.092Q78.030 9.877 77.968 9.781Q77.905 9.685 77.786 9.664Q77.667 9.642 77.421 9.642L77.421 9.346L78.667 9.260L78.667 11.810L78.667 11.834Q78.667 12.146 78.722 12.308Q78.776 12.471 78.927 12.541Q79.077 12.611 79.397 12.611Q79.827 12.611 80.101 12.273Q80.374 11.935 80.374 11.490L80.374 10.092Q80.374 9.877 80.312 9.781Q80.249 9.685 80.130 9.664Q80.011 9.642 79.765 9.642L79.765 9.346L81.011 9.260L81.011 12.045Q81.011 12.256 81.073 12.351Q81.136 12.447 81.255 12.469Q81.374 12.490 81.620 12.490L81.620 12.787L80.397 12.865L80.397 12.244Q80.230 12.533 79.948 12.699Q79.667 12.865 79.347 12.865Q78.030 12.865 78.030 11.834M83.980 12.787L82.147 12.787L82.147 12.490Q82.421 12.490 82.589 12.443Q82.757 12.396 82.757 12.228L82.757 8.068Q82.757 7.853 82.694 7.758Q82.632 7.662 82.513 7.641Q82.394 7.619 82.147 7.619L82.147 7.322L83.370 7.236L83.370 12.228Q83.370 12.396 83.538 12.443Q83.706 12.490 83.980 12.490L83.980 12.787M86.241 12.865Q85.761 12.865 85.353 12.621Q84.944 12.377 84.706 11.963Q84.468 11.549 84.468 11.060Q84.468 10.568 84.726 10.152Q84.983 9.736 85.415 9.498Q85.847 9.260 86.339 9.260Q86.960 9.260 87.409 9.697L87.409 8.068Q87.409 7.853 87.347 7.758Q87.284 7.662 87.167 7.641Q87.050 7.619 86.804 7.619L86.804 7.322L88.026 7.236L88.026 12.045Q88.026 12.256 88.089 12.351Q88.151 12.447 88.269 12.469Q88.386 12.490 88.636 12.490L88.636 12.787L87.386 12.865L87.386 12.381Q86.921 12.865 86.241 12.865M86.308 12.611Q86.647 12.611 86.940 12.420Q87.233 12.228 87.386 11.932L87.386 10.100Q87.237 9.826 86.976 9.670Q86.714 9.514 86.401 9.514Q85.776 9.514 85.493 9.961Q85.210 10.408 85.210 11.068Q85.210 11.713 85.462 12.162Q85.714 12.611 86.308 12.611\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M93.812 12.865Q93.331 12.865 92.923 12.621Q92.515 12.377 92.277 11.963Q92.038 11.549 92.038 11.060Q92.038 10.568 92.296 10.152Q92.554 9.736 92.986 9.498Q93.417 9.260 93.909 9.260Q94.530 9.260 94.980 9.697L94.980 8.068Q94.980 7.853 94.917 7.758Q94.855 7.662 94.737 7.641Q94.620 7.619 94.374 7.619L94.374 7.322L95.597 7.236L95.597 12.045Q95.597 12.256 95.659 12.351Q95.722 12.447 95.839 12.469Q95.956 12.490 96.206 12.490L96.206 12.787L94.956 12.865L94.956 12.381Q94.491 12.865 93.812 12.865M93.878 12.611Q94.218 12.611 94.511 12.420Q94.804 12.228 94.956 11.932L94.956 10.100Q94.808 9.826 94.546 9.670Q94.284 9.514 93.972 9.514Q93.347 9.514 93.064 9.961Q92.780 10.408 92.780 11.068Q92.780 11.713 93.032 12.162Q93.284 12.611 93.878 12.611M96.714 11.092Q96.714 10.588 96.970 10.156Q97.226 9.725 97.661 9.473Q98.097 9.221 98.597 9.221Q98.984 9.221 99.325 9.365Q99.667 9.510 99.929 9.771Q100.191 10.033 100.333 10.369Q100.476 10.705 100.476 11.092Q100.476 11.584 100.212 11.994Q99.948 12.404 99.519 12.635Q99.089 12.865 98.597 12.865Q98.105 12.865 97.671 12.633Q97.237 12.400 96.976 11.992Q96.714 11.584 96.714 11.092M98.597 12.588Q99.054 12.588 99.306 12.365Q99.558 12.142 99.646 11.791Q99.734 11.439 99.734 10.994Q99.734 10.564 99.640 10.226Q99.546 9.889 99.292 9.682Q99.038 9.475 98.597 9.475Q97.948 9.475 97.704 9.891Q97.460 10.307 97.460 10.994Q97.460 11.439 97.548 11.791Q97.636 12.142 97.888 12.365Q98.140 12.588 98.597 12.588\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M105.730 12.787L103.874 12.787L103.874 12.490Q104.148 12.490 104.316 12.443Q104.484 12.396 104.484 12.228L104.484 10.092Q104.484 9.877 104.421 9.781Q104.359 9.685 104.240 9.664Q104.121 9.642 103.874 9.642L103.874 9.346L105.066 9.260L105.066 9.994Q105.179 9.779 105.373 9.611Q105.566 9.443 105.804 9.351Q106.042 9.260 106.296 9.260Q107.464 9.260 107.464 10.338L107.464 12.228Q107.464 12.396 107.634 12.443Q107.804 12.490 108.074 12.490L108.074 12.787L106.218 12.787L106.218 12.490Q106.492 12.490 106.660 12.443Q106.828 12.396 106.828 12.228L106.828 10.353Q106.828 9.971 106.707 9.742Q106.585 9.514 106.234 9.514Q105.921 9.514 105.667 9.676Q105.414 9.838 105.267 10.107Q105.121 10.377 105.121 10.674L105.121 12.228Q105.121 12.396 105.291 12.443Q105.460 12.490 105.730 12.490L105.730 12.787M108.519 11.092Q108.519 10.588 108.775 10.156Q109.031 9.725 109.466 9.473Q109.902 9.221 110.402 9.221Q110.789 9.221 111.130 9.365Q111.472 9.510 111.734 9.771Q111.996 10.033 112.138 10.369Q112.281 10.705 112.281 11.092Q112.281 11.584 112.017 11.994Q111.753 12.404 111.324 12.635Q110.894 12.865 110.402 12.865Q109.910 12.865 109.476 12.633Q109.042 12.400 108.781 11.992Q108.519 11.584 108.519 11.092M110.402 12.588Q110.859 12.588 111.111 12.365Q111.363 12.142 111.451 11.791Q111.539 11.439 111.539 10.994Q111.539 10.564 111.445 10.226Q111.351 9.889 111.097 9.682Q110.843 9.475 110.402 9.475Q109.753 9.475 109.509 9.891Q109.265 10.307 109.265 10.994Q109.265 11.439 109.353 11.791Q109.441 12.142 109.693 12.365Q109.945 12.588 110.402 12.588\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 53.052)\">\u003Cpath d=\"M114.123 12.756L113.053 9.900Q112.987 9.721 112.856 9.678Q112.725 9.635 112.467 9.635L112.467 9.338L114.147 9.338L114.147 9.635Q113.697 9.635 113.697 9.834Q113.701 9.850 113.703 9.867Q113.705 9.885 113.705 9.900L114.498 11.994L115.209 10.084Q115.174 9.990 115.174 9.945Q115.174 9.900 115.139 9.900Q115.072 9.721 114.942 9.678Q114.811 9.635 114.557 9.635L114.557 9.338L116.147 9.338L116.147 9.635Q115.697 9.635 115.697 9.834Q115.701 9.853 115.703 9.871Q115.705 9.889 115.705 9.900L116.537 12.115L117.291 10.115Q117.315 10.057 117.315 9.986Q117.315 9.826 117.178 9.730Q117.041 9.635 116.873 9.635L116.873 9.338L118.260 9.338L118.260 9.635Q118.026 9.635 117.848 9.762Q117.670 9.889 117.588 10.115L116.604 12.756Q116.549 12.865 116.436 12.865L116.377 12.865Q116.264 12.865 116.221 12.756L115.362 10.482L114.506 12.756Q114.467 12.865 114.346 12.865L114.291 12.865Q114.178 12.865 114.123 12.756\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M208.666-47.164H107.47v-2.6\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471-47.164 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m52.924-25.624 14.953-6.127\"\u002F>\u003Cpath stroke=\"none\" d=\"m70.283-32.737-4.638-.348 2.232 1.334-.655 2.516\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m47.209 4.251 19.196 6.303\"\u002F>\u003Cpath stroke=\"none\" d=\"M68.875 11.365 65.572 8.09l.833 2.463-2.13 1.49\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471-18.31v12.648\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471-3.062 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471 25.791v15.495\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471 43.886 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m36.54 52.621 31.18 5.259\"\u002F>\u003Cpath stroke=\"none\" d=\"m70.283 58.312-3.756-2.743 1.192 2.31-1.884 1.792\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471 72.738v14.227h101.195v-.246\"\u002F>\u003Cpath stroke=\"none\" d=\"m208.666 84.12-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">A goal-based agent. On top of the model it keeps a goal, and it predicts what the world will be like if it takes an action A, choosing the action that leads toward the goal. This requires reasoning about the future.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:461.751px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 346.313 188.397\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-51.864 100.991h233.313V-58.344H-51.864Z\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-113.523 74.98)\">\u003Cpath d=\"M66.831 21.323L65.081 21.323L65.081 21.026Q65.780 21.026 65.968 20.546L67.769 15.721Q67.823 15.612 67.937 15.612L68.007 15.612Q68.120 15.612 68.175 15.721L70.065 20.764Q70.144 20.932 70.347 20.979Q70.550 21.026 70.862 21.026L70.862 21.323L68.640 21.323L68.640 21.026Q69.280 21.026 69.280 20.811Q69.280 20.792 69.278 20.782Q69.276 20.772 69.272 20.764L68.808 19.530L66.663 19.530L66.280 20.546Q66.276 20.561 66.271 20.591Q66.265 20.620 66.265 20.643Q66.265 20.784 66.355 20.868Q66.444 20.952 66.577 20.989Q66.710 21.026 66.831 21.026L66.831 21.323M67.737 16.667L66.769 19.233L68.694 19.233L67.737 16.667M71.390 21.932Q71.390 21.651 71.601 21.440Q71.812 21.229 72.097 21.139Q71.940 21.014 71.862 20.825Q71.784 20.636 71.784 20.436Q71.784 20.081 72.015 19.788Q71.647 19.448 71.647 18.979Q71.647 18.628 71.851 18.358Q72.054 18.089 72.374 17.942Q72.694 17.796 73.038 17.796Q73.558 17.796 73.929 18.077Q74.292 17.706 74.839 17.706Q75.019 17.706 75.146 17.833Q75.272 17.960 75.272 18.139Q75.272 18.245 75.194 18.323Q75.116 18.401 75.007 18.401Q74.897 18.401 74.821 18.325Q74.745 18.249 74.745 18.139Q74.745 18.038 74.784 17.987Q74.792 17.979 74.796 17.973Q74.800 17.968 74.800 17.964Q74.425 17.964 74.105 18.218Q74.425 18.557 74.425 18.979Q74.425 19.249 74.308 19.466Q74.190 19.682 73.985 19.841Q73.780 19.999 73.538 20.081Q73.296 20.163 73.038 20.163Q72.819 20.163 72.606 20.104Q72.394 20.046 72.198 19.925Q72.105 20.065 72.105 20.245Q72.105 20.452 72.241 20.604Q72.378 20.757 72.585 20.757L73.280 20.757Q73.769 20.757 74.181 20.841Q74.593 20.925 74.872 21.182Q75.151 21.440 75.151 21.932Q75.151 22.296 74.831 22.528Q74.511 22.761 74.069 22.862Q73.628 22.964 73.272 22.964Q72.917 22.964 72.474 22.862Q72.030 22.761 71.710 22.528Q71.390 22.296 71.390 21.932M71.894 21.932Q71.894 22.128 72.038 22.276Q72.183 22.425 72.396 22.514Q72.608 22.604 72.849 22.651Q73.089 22.698 73.272 22.698Q73.515 22.698 73.845 22.620Q74.175 22.542 74.411 22.368Q74.647 22.194 74.647 21.932Q74.647 21.526 74.237 21.417Q73.827 21.307 73.265 21.307L72.585 21.307Q72.315 21.307 72.105 21.485Q71.894 21.663 71.894 21.932M73.038 19.897Q73.761 19.897 73.761 18.979Q73.761 18.057 73.038 18.057Q72.312 18.057 72.312 18.979Q72.312 19.897 73.038 19.897M75.636 19.569Q75.636 19.089 75.868 18.673Q76.101 18.257 76.511 18.007Q76.921 17.757 77.397 17.757Q78.128 17.757 78.526 18.198Q78.925 18.639 78.925 19.370Q78.925 19.475 78.831 19.499L76.382 19.499L76.382 19.569Q76.382 19.979 76.503 20.335Q76.624 20.690 76.896 20.907Q77.167 21.124 77.597 21.124Q77.960 21.124 78.257 20.895Q78.554 20.667 78.655 20.315Q78.663 20.268 78.749 20.253L78.831 20.253Q78.925 20.280 78.925 20.362Q78.925 20.370 78.917 20.401Q78.855 20.628 78.716 20.811Q78.577 20.995 78.386 21.128Q78.194 21.261 77.976 21.331Q77.757 21.401 77.519 21.401Q77.147 21.401 76.810 21.264Q76.472 21.128 76.204 20.876Q75.937 20.624 75.786 20.284Q75.636 19.944 75.636 19.569M76.390 19.261L78.351 19.261Q78.351 18.956 78.249 18.665Q78.147 18.374 77.931 18.192Q77.714 18.011 77.397 18.011Q77.097 18.011 76.866 18.198Q76.636 18.386 76.513 18.677Q76.390 18.968 76.390 19.261M81.343 21.323L79.487 21.323L79.487 21.026Q79.761 21.026 79.929 20.979Q80.097 20.932 80.097 20.764L80.097 18.628Q80.097 18.413 80.034 18.317Q79.972 18.221 79.853 18.200Q79.733 18.178 79.487 18.178L79.487 17.882L80.679 17.796L80.679 18.530Q80.792 18.315 80.985 18.147Q81.179 17.979 81.417 17.887Q81.655 17.796 81.909 17.796Q83.077 17.796 83.077 18.874L83.077 20.764Q83.077 20.932 83.247 20.979Q83.417 21.026 83.687 21.026L83.687 21.323L81.831 21.323L81.831 21.026Q82.105 21.026 82.272 20.979Q82.440 20.932 82.440 20.764L82.440 18.889Q82.440 18.507 82.319 18.278Q82.198 18.050 81.847 18.050Q81.534 18.050 81.280 18.212Q81.026 18.374 80.880 18.643Q80.733 18.913 80.733 19.210L80.733 20.764Q80.733 20.932 80.903 20.979Q81.073 21.026 81.343 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-113.523 74.98)\">\u003Cpath d=\"M84.536 20.362L84.536 18.171L83.833 18.171L83.833 17.917Q84.189 17.917 84.431 17.684Q84.673 17.452 84.784 17.104Q84.896 16.757 84.896 16.401L85.177 16.401L85.177 17.874L86.353 17.874L86.353 18.171L85.177 18.171L85.177 20.346Q85.177 20.667 85.296 20.895Q85.415 21.124 85.696 21.124Q85.876 21.124 85.993 21.001Q86.111 20.878 86.163 20.698Q86.216 20.518 86.216 20.346L86.216 19.874L86.497 19.874L86.497 20.362Q86.497 20.616 86.392 20.856Q86.286 21.096 86.089 21.249Q85.892 21.401 85.634 21.401Q85.318 21.401 85.066 21.278Q84.814 21.155 84.675 20.921Q84.536 20.686 84.536 20.362\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M208.866 100.991h58.977V-58.344h-58.977Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr9\" font-size=\"9\">\u003Cg transform=\"translate(147.406 3.075)\">\u003Cpath d=\"M70.426 21.323L65.117 21.323L65.117 21.007Q66.036 21.007 66.036 20.712L66.036 15.786Q66.036 15.491 65.117 15.491L65.117 15.175L70.307 15.175L70.562 17.236L70.272 17.236Q70.202 16.643 70.087 16.311Q69.973 15.979 69.764 15.803Q69.556 15.628 69.211 15.560Q68.866 15.491 68.255 15.491L67.341 15.491Q67.090 15.491 66.985 15.540Q66.879 15.588 66.879 15.786L66.879 17.974L67.565 17.974Q68.044 17.974 68.266 17.900Q68.488 17.825 68.580 17.610Q68.672 17.394 68.672 16.924L68.958 16.924L68.958 19.341L68.672 19.341Q68.672 18.871 68.580 18.656Q68.488 18.440 68.266 18.365Q68.044 18.291 67.565 18.291L66.879 18.291L66.879 20.712Q66.879 20.906 66.985 20.956Q67.090 21.007 67.341 21.007L68.321 21.007Q68.958 21.007 69.347 20.910Q69.736 20.813 69.956 20.591Q70.175 20.369 70.296 19.991Q70.417 19.614 70.527 18.963L70.813 18.963L70.426 21.323M73.471 21.323L71.384 21.323L71.384 21.007Q71.691 21.007 71.883 20.954Q72.074 20.901 72.074 20.712L72.074 18.264Q72.074 18.023 72.003 17.915Q71.933 17.807 71.799 17.783Q71.665 17.759 71.384 17.759L71.384 17.443L72.724 17.346L72.724 18.181Q72.922 17.799 73.276 17.572Q73.629 17.346 74.056 17.346Q75.334 17.346 75.334 18.559L75.334 20.712Q75.334 20.901 75.526 20.954Q75.717 21.007 76.024 21.007L76.024 21.323L73.937 21.323L73.937 21.007Q74.249 21.007 74.440 20.954Q74.631 20.901 74.631 20.712L74.631 18.594Q74.631 18.335 74.587 18.113Q74.543 17.891 74.398 17.748Q74.253 17.605 73.994 17.605Q73.651 17.605 73.370 17.794Q73.089 17.983 72.933 18.295Q72.777 18.607 72.777 18.954L72.777 20.712Q72.777 20.901 72.970 20.954Q73.164 21.007 73.471 21.007\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(147.406 3.075)\">\u003Cpath d=\"M78.201 21.305L76.870 18.058Q76.782 17.860 76.617 17.810Q76.452 17.759 76.149 17.759L76.149 17.443L78.074 17.443L78.074 17.759Q77.582 17.759 77.582 17.974Q77.582 17.996 77.599 18.058L78.615 20.532L79.524 18.308Q79.559 18.225 79.559 18.128Q79.559 17.957 79.436 17.858Q79.313 17.759 79.146 17.759L79.146 17.443L80.658 17.443L80.658 17.759Q80.372 17.759 80.159 17.902Q79.946 18.045 79.841 18.308L78.606 21.305Q78.562 21.424 78.434 21.424L78.373 21.424Q78.245 21.424 78.201 21.305M83.141 21.323L81.155 21.323L81.155 21.007Q81.462 21.007 81.653 20.954Q81.844 20.901 81.844 20.712L81.844 18.264Q81.844 18.018 81.779 17.913Q81.713 17.807 81.587 17.783Q81.462 17.759 81.190 17.759L81.190 17.443L82.521 17.346L82.521 20.712Q82.521 20.906 82.686 20.956Q82.851 21.007 83.141 21.007L83.141 21.323M81.541 15.799Q81.541 15.593 81.691 15.443Q81.840 15.294 82.042 15.294Q82.174 15.294 82.291 15.364Q82.407 15.434 82.477 15.551Q82.548 15.667 82.548 15.799Q82.548 16.001 82.398 16.151Q82.249 16.300 82.042 16.300Q81.840 16.300 81.691 16.151Q81.541 16.001 81.541 15.799M85.896 21.323L83.664 21.323L83.664 21.007Q83.976 21.007 84.167 20.954Q84.358 20.901 84.358 20.712L84.358 18.264Q84.358 18.023 84.288 17.915Q84.218 17.807 84.084 17.783Q83.949 17.759 83.664 17.759L83.664 17.443L84.978 17.346L84.978 18.207Q85.140 17.816 85.408 17.581Q85.677 17.346 86.068 17.346Q86.340 17.346 86.555 17.509Q86.771 17.671 86.771 17.930Q86.771 18.106 86.652 18.225Q86.533 18.344 86.358 18.344Q86.177 18.344 86.059 18.225Q85.940 18.106 85.940 17.930Q85.940 17.715 86.094 17.605L86.076 17.605Q85.698 17.605 85.466 17.867Q85.233 18.128 85.134 18.515Q85.035 18.902 85.035 19.262L85.035 20.712Q85.035 20.901 85.292 20.954Q85.549 21.007 85.896 21.007L85.896 21.323M87.289 19.416Q87.289 18.849 87.562 18.361Q87.834 17.873 88.304 17.581Q88.775 17.289 89.342 17.289Q89.763 17.289 90.139 17.458Q90.515 17.627 90.792 17.919Q91.069 18.212 91.227 18.607Q91.385 19.003 91.385 19.416Q91.385 19.965 91.106 20.427Q90.827 20.888 90.359 21.156Q89.891 21.424 89.342 21.424Q88.788 21.424 88.318 21.156Q87.847 20.888 87.568 20.427Q87.289 19.965 87.289 19.416M89.342 21.134Q89.838 21.134 90.115 20.873Q90.392 20.611 90.484 20.207Q90.576 19.802 90.576 19.306Q90.576 18.831 90.478 18.442Q90.379 18.053 90.106 17.803Q89.834 17.552 89.342 17.552Q88.630 17.552 88.366 18.047Q88.102 18.541 88.102 19.306Q88.102 20.106 88.357 20.620Q88.612 21.134 89.342 21.134M94.035 21.323L91.948 21.323L91.948 21.007Q92.255 21.007 92.446 20.954Q92.637 20.901 92.637 20.712L92.637 18.264Q92.637 18.023 92.567 17.915Q92.497 17.807 92.363 17.783Q92.229 17.759 91.948 17.759L91.948 17.443L93.288 17.346L93.288 18.181Q93.486 17.799 93.839 17.572Q94.193 17.346 94.619 17.346Q95.898 17.346 95.898 18.559L95.898 20.712Q95.898 20.901 96.089 20.954Q96.281 21.007 96.588 21.007L96.588 21.323L94.501 21.323L94.501 21.007Q94.813 21.007 95.004 20.954Q95.195 20.901 95.195 20.712L95.195 18.594Q95.195 18.335 95.151 18.113Q95.107 17.891 94.962 17.748Q94.817 17.605 94.558 17.605Q94.215 17.605 93.934 17.794Q93.653 17.983 93.497 18.295Q93.341 18.607 93.341 18.954L93.341 20.712Q93.341 20.901 93.534 20.954Q93.727 21.007 94.035 21.007L94.035 21.323M99.172 21.323L97.085 21.323L97.085 21.007Q97.392 21.007 97.584 20.954Q97.775 20.901 97.775 20.712L97.775 18.264Q97.775 18.023 97.704 17.915Q97.634 17.807 97.500 17.783Q97.366 17.759 97.085 17.759L97.085 17.443L98.425 17.346L98.425 18.181Q98.623 17.803 98.983 17.574Q99.344 17.346 99.765 17.346Q100.811 17.346 100.996 18.155Q101.198 17.785 101.556 17.566Q101.914 17.346 102.332 17.346Q102.956 17.346 103.281 17.640Q103.606 17.935 103.606 18.559L103.606 20.712Q103.606 20.901 103.800 20.954Q103.993 21.007 104.301 21.007L104.301 21.323L102.213 21.323L102.213 21.007Q102.521 21.007 102.714 20.954Q102.907 20.901 102.907 20.712L102.907 18.594Q102.907 18.163 102.780 17.884Q102.653 17.605 102.266 17.605Q101.923 17.605 101.640 17.794Q101.356 17.983 101.200 18.295Q101.044 18.607 101.044 18.954L101.044 20.712Q101.044 20.901 101.235 20.954Q101.427 21.007 101.734 21.007L101.734 21.323L99.647 21.323L99.647 21.007Q99.959 21.007 100.150 20.954Q100.341 20.901 100.341 20.712L100.341 18.594Q100.341 18.335 100.297 18.113Q100.253 17.891 100.108 17.748Q99.963 17.605 99.704 17.605Q99.168 17.605 98.823 18.012Q98.478 18.418 98.478 18.954L98.478 20.712Q98.478 20.901 98.671 20.954Q98.865 21.007 99.172 21.007L99.172 21.323M106.801 21.424Q106.243 21.424 105.771 21.141Q105.298 20.857 105.023 20.380Q104.749 19.904 104.749 19.350Q104.749 18.954 104.892 18.579Q105.034 18.203 105.292 17.915Q105.549 17.627 105.907 17.458Q106.265 17.289 106.669 17.289Q107.214 17.289 107.585 17.526Q107.957 17.763 108.144 18.181Q108.330 18.598 108.330 19.135Q108.330 19.187 108.306 19.225Q108.282 19.262 108.234 19.262L105.562 19.262L105.562 19.341Q105.562 20.088 105.874 20.611Q106.186 21.134 106.885 21.134Q107.289 21.134 107.610 20.877Q107.930 20.620 108.053 20.216Q108.071 20.136 108.155 20.136L108.234 20.136Q108.273 20.136 108.302 20.167Q108.330 20.198 108.330 20.242L108.330 20.277Q108.225 20.620 108.003 20.879Q107.781 21.138 107.467 21.281Q107.153 21.424 106.801 21.424M105.571 19.011L107.684 19.011Q107.684 18.743 107.632 18.497Q107.579 18.251 107.458 18.029Q107.337 17.807 107.139 17.680Q106.942 17.552 106.669 17.552Q106.326 17.552 106.074 17.777Q105.821 18.001 105.696 18.339Q105.571 18.677 105.571 19.011M110.989 21.323L108.902 21.323L108.902 21.007Q109.209 21.007 109.400 20.954Q109.592 20.901 109.592 20.712L109.592 18.264Q109.592 18.023 109.521 17.915Q109.451 17.807 109.317 17.783Q109.183 17.759 108.902 17.759L108.902 17.443L110.242 17.346L110.242 18.181Q110.440 17.799 110.793 17.572Q111.147 17.346 111.573 17.346Q112.852 17.346 112.852 18.559L112.852 20.712Q112.852 20.901 113.043 20.954Q113.235 21.007 113.542 21.007L113.542 21.323L111.455 21.323L111.455 21.007Q111.767 21.007 111.958 20.954Q112.149 20.901 112.149 20.712L112.149 18.594Q112.149 18.335 112.105 18.113Q112.061 17.891 111.916 17.748Q111.771 17.605 111.512 17.605Q111.169 17.605 110.888 17.794Q110.607 17.983 110.451 18.295Q110.295 18.607 110.295 18.954L110.295 20.712Q110.295 20.901 110.488 20.954Q110.681 21.007 110.989 21.007\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(147.406 3.075)\">\u003Cpath d=\"M114.443 20.251L114.443 17.759L113.678 17.759L113.678 17.500Q114.083 17.500 114.349 17.234Q114.614 16.968 114.735 16.568Q114.856 16.168 114.856 15.786L115.146 15.786L115.146 17.443L116.434 17.443L116.434 17.759L115.146 17.759L115.146 20.216Q115.146 20.585 115.271 20.859Q115.397 21.134 115.722 21.134Q116.021 21.134 116.159 20.840Q116.298 20.545 116.298 20.216L116.298 19.693L116.583 19.693L116.583 20.251Q116.583 20.528 116.473 20.800Q116.363 21.073 116.150 21.248Q115.937 21.424 115.656 21.424Q115.296 21.424 115.023 21.286Q114.751 21.147 114.597 20.884Q114.443 20.620 114.443 20.251\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(57.412 -85.477)\">\u003Cpath d=\"M65.281 21.385L65.281 19.812Q65.281 19.785 65.306 19.759Q65.332 19.734 65.359 19.734L65.472 19.734Q65.500 19.734 65.523 19.761Q65.547 19.788 65.547 19.812Q65.547 20.157 65.679 20.421Q65.811 20.684 66.040 20.853Q66.269 21.022 66.571 21.103Q66.874 21.183 67.215 21.183Q67.482 21.183 67.718 21.055Q67.954 20.927 68.099 20.704Q68.244 20.482 68.244 20.216Q68.244 19.993 68.138 19.797Q68.032 19.600 67.851 19.465Q67.670 19.330 67.444 19.279L66.416 19.047Q66.105 18.975 65.845 18.789Q65.585 18.602 65.433 18.331Q65.281 18.059 65.281 17.744Q65.281 17.358 65.494 17.051Q65.708 16.743 66.055 16.572Q66.402 16.401 66.781 16.401Q67.010 16.401 67.239 16.454Q67.468 16.507 67.667 16.615Q67.865 16.722 68.019 16.886L68.313 16.446Q68.336 16.401 68.377 16.401L68.425 16.401Q68.456 16.401 68.478 16.427Q68.500 16.452 68.500 16.480L68.500 18.055Q68.500 18.076 68.477 18.103Q68.453 18.131 68.425 18.131L68.313 18.131Q68.251 18.131 68.237 18.055Q68.196 17.642 68.015 17.322Q67.834 17.003 67.523 16.828Q67.212 16.654 66.781 16.654Q66.532 16.654 66.292 16.765Q66.053 16.876 65.903 17.074Q65.752 17.273 65.752 17.536Q65.752 17.748 65.860 17.929Q65.968 18.110 66.144 18.230Q66.320 18.349 66.528 18.390L67.557 18.619Q67.875 18.691 68.142 18.896Q68.408 19.101 68.560 19.395Q68.712 19.689 68.712 20.021Q68.712 20.414 68.507 20.749Q68.302 21.084 67.957 21.273Q67.612 21.463 67.215 21.463Q66.795 21.463 66.416 21.350Q66.036 21.238 65.766 20.988L65.472 21.422Q65.445 21.463 65.407 21.463L65.359 21.463Q65.332 21.463 65.306 21.438Q65.281 21.412 65.281 21.385M69.481 19.788Q69.481 19.467 69.606 19.178Q69.731 18.889 69.957 18.666Q70.182 18.442 70.478 18.322Q70.773 18.202 71.091 18.202Q71.419 18.202 71.681 18.302Q71.942 18.401 72.118 18.583Q72.294 18.766 72.388 19.024Q72.482 19.282 72.482 19.614Q72.482 19.706 72.400 19.727L70.145 19.727L70.145 19.788Q70.145 20.376 70.428 20.759Q70.712 21.142 71.279 21.142Q71.601 21.142 71.869 20.949Q72.137 20.756 72.226 20.441Q72.233 20.400 72.308 20.386L72.400 20.386Q72.482 20.410 72.482 20.482Q72.482 20.489 72.476 20.516Q72.363 20.913 71.992 21.152Q71.621 21.391 71.197 21.391Q70.760 21.391 70.360 21.183Q69.960 20.974 69.721 20.607Q69.481 20.240 69.481 19.788M70.151 19.518L71.966 19.518Q71.966 19.241 71.869 18.989Q71.771 18.736 71.573 18.580Q71.375 18.425 71.091 18.425Q70.814 18.425 70.601 18.583Q70.387 18.742 70.269 18.997Q70.151 19.252 70.151 19.518M74.752 21.323L73.118 21.323L73.118 21.043Q73.347 21.043 73.496 21.009Q73.645 20.974 73.645 20.834L73.645 18.985Q73.645 18.715 73.537 18.654Q73.429 18.592 73.118 18.592L73.118 18.312L74.178 18.237L74.178 18.886Q74.349 18.578 74.653 18.407Q74.957 18.237 75.302 18.237Q75.808 18.237 76.092 18.460Q76.375 18.684 76.375 19.180L76.375 20.834Q76.375 20.971 76.524 21.007Q76.673 21.043 76.898 21.043L76.898 21.323L75.268 21.323L75.268 21.043Q75.497 21.043 75.646 21.009Q75.794 20.974 75.794 20.834L75.794 19.194Q75.794 18.859 75.675 18.659Q75.555 18.459 75.241 18.459Q74.971 18.459 74.737 18.595Q74.502 18.732 74.364 18.966Q74.226 19.200 74.226 19.474L74.226 20.834Q74.226 20.971 74.376 21.007Q74.526 21.043 74.752 21.043L74.752 21.323M77.486 21.316L77.486 20.253Q77.486 20.229 77.514 20.202Q77.541 20.175 77.565 20.175L77.674 20.175Q77.739 20.175 77.753 20.233Q77.849 20.667 78.095 20.918Q78.341 21.169 78.754 21.169Q79.096 21.169 79.349 21.036Q79.602 20.903 79.602 20.595Q79.602 20.438 79.508 20.323Q79.414 20.209 79.276 20.140Q79.137 20.072 78.970 20.034L78.389 19.935Q78.033 19.867 77.760 19.646Q77.486 19.426 77.486 19.084Q77.486 18.835 77.597 18.660Q77.709 18.486 77.895 18.387Q78.081 18.288 78.296 18.245Q78.512 18.202 78.754 18.202Q79.168 18.202 79.448 18.384L79.664 18.209Q79.674 18.206 79.681 18.204Q79.688 18.202 79.698 18.202L79.749 18.202Q79.776 18.202 79.800 18.226Q79.824 18.250 79.824 18.278L79.824 19.125Q79.824 19.146 79.800 19.173Q79.776 19.200 79.749 19.200L79.636 19.200Q79.609 19.200 79.583 19.175Q79.558 19.149 79.558 19.125Q79.558 18.889 79.452 18.725Q79.346 18.561 79.163 18.479Q78.980 18.397 78.748 18.397Q78.419 18.397 78.163 18.500Q77.907 18.602 77.907 18.879Q77.907 19.074 78.090 19.183Q78.272 19.293 78.501 19.334L79.076 19.440Q79.322 19.488 79.535 19.616Q79.749 19.744 79.886 19.947Q80.022 20.151 80.022 20.400Q80.022 20.913 79.657 21.152Q79.291 21.391 78.754 21.391Q78.259 21.391 77.927 21.097L77.661 21.371Q77.640 21.391 77.613 21.391L77.565 21.391Q77.541 21.391 77.514 21.364Q77.486 21.337 77.486 21.316M80.610 19.840Q80.610 19.498 80.745 19.199Q80.880 18.900 81.120 18.676Q81.359 18.452 81.677 18.327Q81.995 18.202 82.326 18.202Q82.771 18.202 83.170 18.418Q83.570 18.633 83.804 19.011Q84.039 19.388 84.039 19.840Q84.039 20.181 83.897 20.465Q83.755 20.749 83.511 20.956Q83.266 21.162 82.957 21.277Q82.647 21.391 82.326 21.391Q81.896 21.391 81.494 21.190Q81.092 20.988 80.851 20.636Q80.610 20.284 80.610 19.840M82.326 21.142Q82.928 21.142 83.152 20.764Q83.375 20.386 83.375 19.754Q83.375 19.142 83.141 18.783Q82.907 18.425 82.326 18.425Q81.273 18.425 81.273 19.754Q81.273 20.386 81.499 20.764Q81.725 21.142 82.326 21.142M86.383 21.323L84.647 21.323L84.647 21.043Q84.876 21.043 85.025 21.009Q85.173 20.974 85.173 20.834L85.173 18.985Q85.173 18.715 85.066 18.654Q84.958 18.592 84.647 18.592L84.647 18.312L85.676 18.237L85.676 18.944Q85.806 18.636 86.048 18.437Q86.291 18.237 86.609 18.237Q86.828 18.237 86.999 18.361Q87.169 18.486 87.169 18.698Q87.169 18.835 87.070 18.934Q86.971 19.033 86.838 19.033Q86.701 19.033 86.602 18.934Q86.503 18.835 86.503 18.698Q86.503 18.558 86.602 18.459Q86.312 18.459 86.112 18.655Q85.912 18.852 85.819 19.146Q85.727 19.440 85.727 19.720L85.727 20.834Q85.727 21.043 86.383 21.043L86.383 21.323M87.754 21.316L87.754 20.253Q87.754 20.229 87.781 20.202Q87.809 20.175 87.833 20.175L87.942 20.175Q88.007 20.175 88.021 20.233Q88.116 20.667 88.362 20.918Q88.608 21.169 89.022 21.169Q89.364 21.169 89.617 21.036Q89.870 20.903 89.870 20.595Q89.870 20.438 89.776 20.323Q89.682 20.209 89.543 20.140Q89.405 20.072 89.237 20.034L88.656 19.935Q88.301 19.867 88.027 19.646Q87.754 19.426 87.754 19.084Q87.754 18.835 87.865 18.660Q87.976 18.486 88.162 18.387Q88.349 18.288 88.564 18.245Q88.779 18.202 89.022 18.202Q89.436 18.202 89.716 18.384L89.931 18.209Q89.941 18.206 89.948 18.204Q89.955 18.202 89.965 18.202L90.017 18.202Q90.044 18.202 90.068 18.226Q90.092 18.250 90.092 18.278L90.092 19.125Q90.092 19.146 90.068 19.173Q90.044 19.200 90.017 19.200L89.904 19.200Q89.876 19.200 89.851 19.175Q89.825 19.149 89.825 19.125Q89.825 18.889 89.719 18.725Q89.613 18.561 89.430 18.479Q89.248 18.397 89.015 18.397Q88.687 18.397 88.431 18.500Q88.174 18.602 88.174 18.879Q88.174 19.074 88.357 19.183Q88.540 19.293 88.769 19.334L89.343 19.440Q89.589 19.488 89.803 19.616Q90.017 19.744 90.153 19.947Q90.290 20.151 90.290 20.400Q90.290 20.913 89.924 21.152Q89.559 21.391 89.022 21.391Q88.526 21.391 88.195 21.097L87.928 21.371Q87.908 21.391 87.880 21.391L87.833 21.391Q87.809 21.391 87.781 21.364Q87.754 21.337 87.754 21.316\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(74.465 73.524)\">\u003Cpath d=\"M66.696 21.323L65.106 21.323L65.106 21.043Q65.749 21.043 65.906 20.643L67.550 16.428Q67.584 16.333 67.697 16.333L67.779 16.333Q67.889 16.333 67.930 16.428L69.649 20.834Q69.717 20.974 69.907 21.009Q70.097 21.043 70.370 21.043L70.370 21.323L68.371 21.323L68.371 21.043Q68.935 21.043 68.935 20.868Q68.935 20.851 68.933 20.844Q68.931 20.838 68.928 20.834L68.507 19.768L66.549 19.768L66.207 20.643Q66.193 20.643 66.193 20.721Q66.193 20.882 66.356 20.962Q66.518 21.043 66.696 21.043L66.696 21.323M67.530 17.249L66.662 19.488L68.405 19.488L67.530 17.249M71.006 19.812Q71.006 19.484 71.141 19.183Q71.276 18.883 71.512 18.662Q71.748 18.442 72.052 18.322Q72.356 18.202 72.681 18.202Q73.187 18.202 73.535 18.305Q73.884 18.407 73.884 18.783Q73.884 18.930 73.786 19.031Q73.689 19.132 73.542 19.132Q73.388 19.132 73.289 19.033Q73.190 18.934 73.190 18.783Q73.190 18.595 73.330 18.503Q73.128 18.452 72.688 18.452Q72.332 18.452 72.103 18.648Q71.874 18.845 71.773 19.154Q71.672 19.464 71.672 19.812Q71.672 20.161 71.799 20.467Q71.925 20.773 72.180 20.957Q72.435 21.142 72.790 21.142Q73.012 21.142 73.197 21.058Q73.381 20.974 73.516 20.819Q73.651 20.663 73.709 20.455Q73.723 20.400 73.778 20.400L73.891 20.400Q73.921 20.400 73.944 20.424Q73.966 20.448 73.966 20.482L73.966 20.503Q73.880 20.790 73.692 20.988Q73.504 21.186 73.240 21.289Q72.975 21.391 72.681 21.391Q72.250 21.391 71.862 21.185Q71.474 20.978 71.240 20.615Q71.006 20.253 71.006 19.812M75.080 20.482L75.080 18.585L74.441 18.585L74.441 18.363Q74.759 18.363 74.976 18.153Q75.193 17.943 75.294 17.633Q75.395 17.324 75.395 17.016L75.661 17.016L75.661 18.305L76.738 18.305L76.738 18.585L75.661 18.585L75.661 20.469Q75.661 20.745 75.765 20.944Q75.870 21.142 76.129 21.142Q76.287 21.142 76.393 21.038Q76.499 20.933 76.548 20.780Q76.598 20.626 76.598 20.469L76.598 20.055L76.864 20.055L76.864 20.482Q76.864 20.708 76.765 20.918Q76.666 21.128 76.481 21.260Q76.297 21.391 76.068 21.391Q75.630 21.391 75.355 21.154Q75.080 20.916 75.080 20.482M78.249 20.489L78.249 18.985Q78.249 18.715 78.141 18.654Q78.033 18.592 77.722 18.592L77.722 18.312L78.830 18.237L78.830 20.469L78.830 20.489Q78.830 20.769 78.881 20.913Q78.932 21.056 79.074 21.113Q79.216 21.169 79.503 21.169Q79.756 21.169 79.961 21.029Q80.166 20.889 80.282 20.663Q80.398 20.438 80.398 20.188L80.398 18.985Q80.398 18.715 80.291 18.654Q80.183 18.592 79.872 18.592L79.872 18.312L80.980 18.237L80.980 20.650Q80.980 20.841 81.032 20.923Q81.085 21.005 81.186 21.024Q81.287 21.043 81.502 21.043L81.502 21.323L80.426 21.391L80.426 20.827Q80.316 21.009 80.171 21.132Q80.026 21.255 79.840 21.323Q79.653 21.391 79.452 21.391Q78.249 21.391 78.249 20.489M82.148 20.595Q82.148 20.263 82.372 20.036Q82.596 19.809 82.940 19.681Q83.283 19.552 83.656 19.500Q84.028 19.447 84.333 19.447L84.333 19.194Q84.333 18.989 84.225 18.809Q84.117 18.630 83.936 18.527Q83.755 18.425 83.546 18.425Q83.140 18.425 82.904 18.517Q82.993 18.554 83.039 18.638Q83.085 18.722 83.085 18.824Q83.085 18.920 83.039 18.999Q82.993 19.077 82.912 19.122Q82.832 19.166 82.743 19.166Q82.593 19.166 82.492 19.069Q82.391 18.971 82.391 18.824Q82.391 18.202 83.546 18.202Q83.758 18.202 84.008 18.266Q84.257 18.329 84.459 18.448Q84.661 18.568 84.787 18.753Q84.914 18.937 84.914 19.180L84.914 20.756Q84.914 20.872 84.975 20.968Q85.037 21.063 85.149 21.063Q85.259 21.063 85.324 20.969Q85.389 20.875 85.389 20.756L85.389 20.308L85.655 20.308L85.655 20.756Q85.655 21.026 85.428 21.191Q85.201 21.357 84.920 21.357Q84.712 21.357 84.575 21.203Q84.438 21.050 84.415 20.834Q84.268 21.101 83.986 21.246Q83.704 21.391 83.379 21.391Q83.102 21.391 82.818 21.316Q82.535 21.241 82.342 21.062Q82.148 20.882 82.148 20.595M82.764 20.595Q82.764 20.769 82.865 20.899Q82.965 21.029 83.121 21.099Q83.276 21.169 83.440 21.169Q83.659 21.169 83.868 21.072Q84.076 20.974 84.204 20.793Q84.333 20.612 84.333 20.386L84.333 19.658Q84.008 19.658 83.642 19.749Q83.276 19.840 83.020 20.052Q82.764 20.263 82.764 20.595M86.599 20.482L86.599 18.585L85.959 18.585L85.959 18.363Q86.277 18.363 86.494 18.153Q86.711 17.943 86.812 17.633Q86.913 17.324 86.913 17.016L87.180 17.016L87.180 18.305L88.256 18.305L88.256 18.585L87.180 18.585L87.180 20.469Q87.180 20.745 87.284 20.944Q87.388 21.142 87.648 21.142Q87.805 21.142 87.911 21.038Q88.017 20.933 88.067 20.780Q88.116 20.626 88.116 20.469L88.116 20.055L88.383 20.055L88.383 20.482Q88.383 20.708 88.284 20.918Q88.185 21.128 88 21.260Q87.815 21.391 87.586 21.391Q87.149 21.391 86.874 21.154Q86.599 20.916 86.599 20.482M89.152 19.840Q89.152 19.498 89.287 19.199Q89.422 18.900 89.661 18.676Q89.900 18.452 90.218 18.327Q90.536 18.202 90.868 18.202Q91.312 18.202 91.712 18.418Q92.112 18.633 92.346 19.011Q92.580 19.388 92.580 19.840Q92.580 20.181 92.438 20.465Q92.296 20.749 92.052 20.956Q91.808 21.162 91.498 21.277Q91.189 21.391 90.868 21.391Q90.437 21.391 90.035 21.190Q89.634 20.988 89.393 20.636Q89.152 20.284 89.152 19.840M90.868 21.142Q91.469 21.142 91.693 20.764Q91.917 20.386 91.917 19.754Q91.917 19.142 91.683 18.783Q91.449 18.425 90.868 18.425Q89.815 18.425 89.815 19.754Q89.815 20.386 90.041 20.764Q90.266 21.142 90.868 21.142M94.925 21.323L93.188 21.323L93.188 21.043Q93.417 21.043 93.566 21.009Q93.715 20.974 93.715 20.834L93.715 18.985Q93.715 18.715 93.607 18.654Q93.500 18.592 93.188 18.592L93.188 18.312L94.217 18.237L94.217 18.944Q94.347 18.636 94.590 18.437Q94.833 18.237 95.150 18.237Q95.369 18.237 95.540 18.361Q95.711 18.486 95.711 18.698Q95.711 18.835 95.612 18.934Q95.513 19.033 95.379 19.033Q95.243 19.033 95.144 18.934Q95.044 18.835 95.044 18.698Q95.044 18.558 95.144 18.459Q94.853 18.459 94.653 18.655Q94.453 18.852 94.361 19.146Q94.269 19.440 94.269 19.720L94.269 20.834Q94.269 21.043 94.925 21.043L94.925 21.323M96.295 21.316L96.295 20.253Q96.295 20.229 96.323 20.202Q96.350 20.175 96.374 20.175L96.483 20.175Q96.548 20.175 96.562 20.233Q96.658 20.667 96.904 20.918Q97.150 21.169 97.563 21.169Q97.905 21.169 98.158 21.036Q98.411 20.903 98.411 20.595Q98.411 20.438 98.317 20.323Q98.223 20.209 98.085 20.140Q97.946 20.072 97.779 20.034L97.198 19.935Q96.842 19.867 96.569 19.646Q96.295 19.426 96.295 19.084Q96.295 18.835 96.407 18.660Q96.518 18.486 96.704 18.387Q96.890 18.288 97.105 18.245Q97.321 18.202 97.563 18.202Q97.977 18.202 98.257 18.384L98.473 18.209Q98.483 18.206 98.490 18.204Q98.497 18.202 98.507 18.202L98.558 18.202Q98.585 18.202 98.609 18.226Q98.633 18.250 98.633 18.278L98.633 19.125Q98.633 19.146 98.609 19.173Q98.585 19.200 98.558 19.200L98.445 19.200Q98.418 19.200 98.392 19.175Q98.367 19.149 98.367 19.125Q98.367 18.889 98.261 18.725Q98.155 18.561 97.972 18.479Q97.789 18.397 97.557 18.397Q97.229 18.397 96.972 18.500Q96.716 18.602 96.716 18.879Q96.716 19.074 96.899 19.183Q97.082 19.293 97.311 19.334L97.885 19.440Q98.131 19.488 98.344 19.616Q98.558 19.744 98.695 19.947Q98.832 20.151 98.832 20.400Q98.832 20.913 98.466 21.152Q98.100 21.391 97.563 21.391Q97.068 21.391 96.736 21.097L96.470 21.371Q96.449 21.391 96.422 21.391L96.374 21.391Q96.350 21.391 96.323 21.364Q96.295 21.337 96.295 21.316\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M70.483-19.933h73.977v-28.453H70.483Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M66.616 11.792L65.546 8.936Q65.480 8.757 65.349 8.714Q65.218 8.671 64.960 8.671L64.960 8.374L66.640 8.374L66.640 8.671Q66.190 8.671 66.190 8.870Q66.194 8.886 66.196 8.903Q66.198 8.921 66.198 8.936L66.991 11.030L67.702 9.120Q67.667 9.026 67.667 8.981Q67.667 8.936 67.632 8.936Q67.565 8.757 67.435 8.714Q67.304 8.671 67.050 8.671L67.050 8.374L68.640 8.374L68.640 8.671Q68.190 8.671 68.190 8.870Q68.194 8.889 68.196 8.907Q68.198 8.925 68.198 8.936L69.030 11.151L69.784 9.151Q69.808 9.093 69.808 9.022Q69.808 8.862 69.671 8.766Q69.534 8.671 69.366 8.671L69.366 8.374L70.753 8.374L70.753 8.671Q70.519 8.671 70.341 8.798Q70.163 8.925 70.081 9.151L69.097 11.792Q69.042 11.901 68.929 11.901L68.870 11.901Q68.757 11.901 68.714 11.792L67.855 9.518L66.999 11.792Q66.960 11.901 66.839 11.901L66.784 11.901Q66.671 11.901 66.616 11.792M73.097 11.823L71.241 11.823L71.241 11.526Q71.515 11.526 71.683 11.479Q71.851 11.432 71.851 11.264L71.851 7.104Q71.851 6.889 71.788 6.794Q71.726 6.698 71.606 6.677Q71.487 6.655 71.241 6.655L71.241 6.358L72.464 6.272L72.464 8.975Q72.589 8.764 72.776 8.614Q72.964 8.464 73.190 8.380Q73.417 8.296 73.663 8.296Q74.831 8.296 74.831 9.374L74.831 11.264Q74.831 11.432 75.001 11.479Q75.171 11.526 75.440 11.526L75.440 11.823L73.585 11.823L73.585 11.526Q73.858 11.526 74.026 11.479Q74.194 11.432 74.194 11.264L74.194 9.389Q74.194 9.007 74.073 8.778Q73.952 8.550 73.601 8.550Q73.288 8.550 73.034 8.712Q72.780 8.874 72.634 9.143Q72.487 9.413 72.487 9.710L72.487 11.264Q72.487 11.432 72.657 11.479Q72.827 11.526 73.097 11.526L73.097 11.823M75.983 10.991Q75.983 10.507 76.386 10.212Q76.788 9.917 77.339 9.798Q77.890 9.678 78.382 9.678L78.382 9.389Q78.382 9.163 78.267 8.956Q78.151 8.749 77.954 8.630Q77.757 8.511 77.526 8.511Q77.101 8.511 76.815 8.616Q76.886 8.643 76.933 8.698Q76.980 8.753 77.005 8.823Q77.030 8.893 77.030 8.968Q77.030 9.073 76.980 9.165Q76.929 9.257 76.837 9.307Q76.745 9.358 76.640 9.358Q76.534 9.358 76.442 9.307Q76.351 9.257 76.300 9.165Q76.249 9.073 76.249 8.968Q76.249 8.550 76.638 8.403Q77.026 8.257 77.526 8.257Q77.858 8.257 78.212 8.387Q78.565 8.518 78.794 8.772Q79.022 9.026 79.022 9.374L79.022 11.175Q79.022 11.307 79.095 11.417Q79.167 11.526 79.296 11.526Q79.421 11.526 79.489 11.421Q79.558 11.315 79.558 11.175L79.558 10.663L79.839 10.663L79.839 11.175Q79.839 11.378 79.722 11.536Q79.605 11.694 79.423 11.778Q79.241 11.862 79.038 11.862Q78.808 11.862 78.655 11.690Q78.503 11.518 78.472 11.288Q78.312 11.569 78.003 11.735Q77.694 11.901 77.343 11.901Q76.831 11.901 76.407 11.678Q75.983 11.456 75.983 10.991M76.671 10.991Q76.671 11.276 76.897 11.462Q77.124 11.647 77.417 11.647Q77.663 11.647 77.888 11.530Q78.112 11.413 78.247 11.210Q78.382 11.007 78.382 10.753L78.382 9.921Q78.116 9.921 77.831 9.975Q77.546 10.030 77.274 10.159Q77.003 10.288 76.837 10.495Q76.671 10.702 76.671 10.991M80.757 10.862L80.757 8.671L80.054 8.671L80.054 8.417Q80.409 8.417 80.651 8.184Q80.894 7.952 81.005 7.604Q81.116 7.257 81.116 6.901L81.397 6.901L81.397 8.374L82.573 8.374L82.573 8.671L81.397 8.671L81.397 10.846Q81.397 11.167 81.517 11.395Q81.636 11.624 81.917 11.624Q82.097 11.624 82.214 11.501Q82.331 11.378 82.384 11.198Q82.437 11.018 82.437 10.846L82.437 10.374L82.718 10.374L82.718 10.862Q82.718 11.116 82.612 11.356Q82.507 11.596 82.310 11.749Q82.112 11.901 81.855 11.901Q81.538 11.901 81.286 11.778Q81.034 11.655 80.896 11.421Q80.757 11.186 80.757 10.862\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M86.906 10.862L86.906 8.671L86.203 8.671L86.203 8.417Q86.559 8.417 86.801 8.184Q87.043 7.952 87.154 7.604Q87.266 7.257 87.266 6.901L87.547 6.901L87.547 8.374L88.723 8.374L88.723 8.671L87.547 8.671L87.547 10.846Q87.547 11.167 87.666 11.395Q87.785 11.624 88.066 11.624Q88.246 11.624 88.363 11.501Q88.481 11.378 88.533 11.198Q88.586 11.018 88.586 10.846L88.586 10.374L88.867 10.374L88.867 10.862Q88.867 11.116 88.762 11.356Q88.656 11.596 88.459 11.749Q88.262 11.901 88.004 11.901Q87.688 11.901 87.436 11.778Q87.184 11.655 87.045 11.421Q86.906 11.186 86.906 10.862M91.516 11.823L89.660 11.823L89.660 11.526Q89.934 11.526 90.102 11.479Q90.270 11.432 90.270 11.264L90.270 7.104Q90.270 6.889 90.207 6.794Q90.145 6.698 90.025 6.677Q89.906 6.655 89.660 6.655L89.660 6.358L90.883 6.272L90.883 8.975Q91.008 8.764 91.195 8.614Q91.383 8.464 91.609 8.380Q91.836 8.296 92.082 8.296Q93.250 8.296 93.250 9.374L93.250 11.264Q93.250 11.432 93.420 11.479Q93.590 11.526 93.859 11.526L93.859 11.823L92.004 11.823L92.004 11.526Q92.277 11.526 92.445 11.479Q92.613 11.432 92.613 11.264L92.613 9.389Q92.613 9.007 92.492 8.778Q92.371 8.550 92.020 8.550Q91.707 8.550 91.453 8.712Q91.199 8.874 91.053 9.143Q90.906 9.413 90.906 9.710L90.906 11.264Q90.906 11.432 91.076 11.479Q91.246 11.526 91.516 11.526L91.516 11.823M94.305 10.069Q94.305 9.589 94.537 9.173Q94.770 8.757 95.180 8.507Q95.590 8.257 96.066 8.257Q96.797 8.257 97.195 8.698Q97.594 9.139 97.594 9.870Q97.594 9.975 97.500 9.999L95.051 9.999L95.051 10.069Q95.051 10.479 95.172 10.835Q95.293 11.190 95.564 11.407Q95.836 11.624 96.266 11.624Q96.629 11.624 96.926 11.395Q97.223 11.167 97.324 10.815Q97.332 10.768 97.418 10.753L97.500 10.753Q97.594 10.780 97.594 10.862Q97.594 10.870 97.586 10.901Q97.523 11.128 97.385 11.311Q97.246 11.495 97.055 11.628Q96.863 11.761 96.645 11.831Q96.426 11.901 96.188 11.901Q95.816 11.901 95.479 11.764Q95.141 11.628 94.873 11.376Q94.606 11.124 94.455 10.784Q94.305 10.444 94.305 10.069M95.059 9.761L97.020 9.761Q97.020 9.456 96.918 9.165Q96.816 8.874 96.600 8.692Q96.383 8.511 96.066 8.511Q95.766 8.511 95.535 8.698Q95.305 8.886 95.182 9.177Q95.059 9.468 95.059 9.761\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M102.506 11.792L101.436 8.936Q101.370 8.757 101.239 8.714Q101.108 8.671 100.850 8.671L100.850 8.374L102.530 8.374L102.530 8.671Q102.080 8.671 102.080 8.870Q102.084 8.886 102.086 8.903Q102.088 8.921 102.088 8.936L102.881 11.030L103.592 9.120Q103.557 9.026 103.557 8.981Q103.557 8.936 103.522 8.936Q103.455 8.757 103.325 8.714Q103.194 8.671 102.940 8.671L102.940 8.374L104.530 8.374L104.530 8.671Q104.080 8.671 104.080 8.870Q104.084 8.889 104.086 8.907Q104.088 8.925 104.088 8.936L104.920 11.151L105.674 9.151Q105.698 9.093 105.698 9.022Q105.698 8.862 105.561 8.766Q105.424 8.671 105.256 8.671L105.256 8.374L106.643 8.374L106.643 8.671Q106.409 8.671 106.231 8.798Q106.053 8.925 105.971 9.151L104.987 11.792Q104.932 11.901 104.819 11.901L104.760 11.901Q104.647 11.901 104.604 11.792L103.745 9.518L102.889 11.792Q102.850 11.901 102.729 11.901L102.674 11.901Q102.561 11.901 102.506 11.792\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M106.823 10.128Q106.823 9.624 107.079 9.192Q107.335 8.761 107.771 8.509Q108.206 8.257 108.706 8.257Q109.093 8.257 109.435 8.401Q109.776 8.546 110.038 8.807Q110.300 9.069 110.442 9.405Q110.585 9.741 110.585 10.128Q110.585 10.620 110.321 11.030Q110.058 11.440 109.628 11.671Q109.198 11.901 108.706 11.901Q108.214 11.901 107.780 11.669Q107.347 11.436 107.085 11.028Q106.823 10.620 106.823 10.128M108.706 11.624Q109.163 11.624 109.415 11.401Q109.667 11.178 109.755 10.827Q109.843 10.475 109.843 10.030Q109.843 9.600 109.749 9.262Q109.655 8.925 109.401 8.718Q109.147 8.511 108.706 8.511Q108.058 8.511 107.814 8.927Q107.569 9.343 107.569 10.030Q107.569 10.475 107.657 10.827Q107.745 11.178 107.997 11.401Q108.249 11.624 108.706 11.624M113.077 11.823L111.097 11.823L111.097 11.526Q111.366 11.526 111.534 11.481Q111.702 11.436 111.702 11.264L111.702 9.128Q111.702 8.913 111.640 8.817Q111.577 8.721 111.460 8.700Q111.343 8.678 111.097 8.678L111.097 8.382L112.265 8.296L112.265 9.081Q112.343 8.870 112.495 8.684Q112.647 8.499 112.847 8.397Q113.046 8.296 113.272 8.296Q113.519 8.296 113.710 8.440Q113.901 8.585 113.901 8.815Q113.901 8.971 113.796 9.081Q113.690 9.190 113.534 9.190Q113.378 9.190 113.269 9.081Q113.159 8.971 113.159 8.815Q113.159 8.655 113.265 8.550Q112.940 8.550 112.726 8.778Q112.511 9.007 112.415 9.346Q112.319 9.686 112.319 9.991L112.319 11.264Q112.319 11.432 112.546 11.479Q112.772 11.526 113.077 11.526L113.077 11.823M116.296 11.823L114.464 11.823L114.464 11.526Q114.737 11.526 114.905 11.479Q115.073 11.432 115.073 11.264L115.073 7.104Q115.073 6.889 115.011 6.794Q114.948 6.698 114.829 6.677Q114.710 6.655 114.464 6.655L114.464 6.358L115.687 6.272L115.687 11.264Q115.687 11.432 115.855 11.479Q116.022 11.526 116.296 11.526L116.296 11.823M118.558 11.901Q118.077 11.901 117.669 11.657Q117.261 11.413 117.022 10.999Q116.784 10.585 116.784 10.096Q116.784 9.604 117.042 9.188Q117.300 8.772 117.731 8.534Q118.163 8.296 118.655 8.296Q119.276 8.296 119.726 8.733L119.726 7.104Q119.726 6.889 119.663 6.794Q119.601 6.698 119.483 6.677Q119.366 6.655 119.120 6.655L119.120 6.358L120.343 6.272L120.343 11.081Q120.343 11.292 120.405 11.387Q120.468 11.483 120.585 11.505Q120.702 11.526 120.952 11.526L120.952 11.823L119.702 11.901L119.702 11.417Q119.237 11.901 118.558 11.901M118.624 11.647Q118.964 11.647 119.257 11.456Q119.550 11.264 119.702 10.968L119.702 9.136Q119.554 8.862 119.292 8.706Q119.030 8.550 118.718 8.550Q118.093 8.550 117.810 8.997Q117.526 9.444 117.526 10.104Q117.526 10.749 117.778 11.198Q118.030 11.647 118.624 11.647\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M75.606 21.323L73.828 21.323L73.828 21.026Q74.102 21.026 74.270 20.979Q74.438 20.932 74.438 20.764L74.438 18.628Q74.438 18.413 74.381 18.317Q74.324 18.221 74.211 18.200Q74.098 18.178 73.852 18.178L73.852 17.882L75.051 17.796L75.051 20.764Q75.051 20.932 75.197 20.979Q75.344 21.026 75.606 21.026L75.606 21.323M74.164 16.401Q74.164 16.210 74.299 16.079Q74.434 15.948 74.629 15.948Q74.750 15.948 74.854 16.011Q74.957 16.073 75.020 16.177Q75.082 16.280 75.082 16.401Q75.082 16.596 74.951 16.731Q74.820 16.866 74.629 16.866Q74.430 16.866 74.297 16.733Q74.164 16.600 74.164 16.401M76.149 21.315L76.149 20.093Q76.149 20.065 76.180 20.034Q76.211 20.003 76.235 20.003L76.340 20.003Q76.410 20.003 76.426 20.065Q76.488 20.386 76.627 20.626Q76.766 20.866 76.998 21.007Q77.231 21.147 77.539 21.147Q77.778 21.147 77.987 21.087Q78.195 21.026 78.332 20.878Q78.469 20.729 78.469 20.483Q78.469 20.229 78.258 20.063Q78.047 19.897 77.778 19.843L77.156 19.729Q76.750 19.651 76.449 19.395Q76.149 19.139 76.149 18.764Q76.149 18.397 76.350 18.175Q76.551 17.952 76.875 17.854Q77.199 17.757 77.539 17.757Q78.004 17.757 78.301 17.964L78.524 17.780Q78.547 17.757 78.578 17.757L78.629 17.757Q78.660 17.757 78.688 17.784Q78.715 17.811 78.715 17.843L78.715 18.827Q78.715 18.858 78.690 18.887Q78.664 18.917 78.629 18.917L78.524 18.917Q78.488 18.917 78.461 18.889Q78.434 18.862 78.434 18.827Q78.434 18.428 78.182 18.208Q77.930 17.987 77.531 17.987Q77.176 17.987 76.893 18.110Q76.610 18.233 76.610 18.538Q76.610 18.757 76.811 18.889Q77.012 19.022 77.258 19.065L77.883 19.178Q78.313 19.268 78.621 19.565Q78.930 19.862 78.930 20.276Q78.930 20.846 78.531 21.124Q78.133 21.401 77.539 21.401Q76.988 21.401 76.637 21.065L76.340 21.378Q76.317 21.401 76.281 21.401L76.235 21.401Q76.211 21.401 76.180 21.370Q76.149 21.339 76.149 21.315\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M84.208 21.323L82.376 21.323L82.376 21.026Q82.650 21.026 82.818 20.979Q82.986 20.932 82.986 20.764L82.986 16.604Q82.986 16.389 82.923 16.294Q82.861 16.198 82.742 16.177Q82.622 16.155 82.376 16.155L82.376 15.858L83.599 15.772L83.599 20.764Q83.599 20.932 83.767 20.979Q83.935 21.026 84.208 21.026L84.208 21.323M86.513 21.323L84.736 21.323L84.736 21.026Q85.009 21.026 85.177 20.979Q85.345 20.932 85.345 20.764L85.345 18.628Q85.345 18.413 85.288 18.317Q85.232 18.221 85.118 18.200Q85.005 18.178 84.759 18.178L84.759 17.882L85.958 17.796L85.958 20.764Q85.958 20.932 86.105 20.979Q86.251 21.026 86.513 21.026L86.513 21.323M85.072 16.401Q85.072 16.210 85.206 16.079Q85.341 15.948 85.536 15.948Q85.658 15.948 85.761 16.011Q85.865 16.073 85.927 16.177Q85.990 16.280 85.990 16.401Q85.990 16.596 85.859 16.731Q85.728 16.866 85.536 16.866Q85.337 16.866 85.204 16.733Q85.072 16.600 85.072 16.401M88.837 21.323L87.040 21.323L87.040 21.026Q87.310 21.026 87.478 20.981Q87.646 20.936 87.646 20.764L87.646 16.604Q87.646 16.389 87.583 16.294Q87.521 16.198 87.404 16.177Q87.286 16.155 87.040 16.155L87.040 15.858L88.263 15.772L88.263 19.538L89.361 18.651Q89.568 18.471 89.568 18.323Q89.568 18.257 89.515 18.214Q89.462 18.171 89.392 18.171L89.392 17.874L90.927 17.874L90.927 18.171Q90.396 18.171 89.798 18.651L89.189 19.147L90.263 20.546Q90.400 20.721 90.507 20.829Q90.615 20.936 90.749 20.981Q90.884 21.026 91.111 21.026L91.111 21.323L89.486 21.323L89.486 21.026Q89.728 21.026 89.728 20.874Q89.728 20.796 89.685 20.725Q89.642 20.655 89.560 20.546L88.759 19.499L88.232 19.925L88.232 20.764Q88.232 20.932 88.400 20.979Q88.568 21.026 88.837 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M91.266 19.569Q91.266 19.089 91.499 18.673Q91.731 18.257 92.141 18.007Q92.551 17.757 93.028 17.757Q93.758 17.757 94.157 18.198Q94.555 18.639 94.555 19.370Q94.555 19.475 94.462 19.499L92.012 19.499L92.012 19.569Q92.012 19.979 92.133 20.335Q92.255 20.690 92.526 20.907Q92.798 21.124 93.227 21.124Q93.591 21.124 93.887 20.895Q94.184 20.667 94.286 20.315Q94.294 20.268 94.380 20.253L94.462 20.253Q94.555 20.280 94.555 20.362Q94.555 20.370 94.548 20.401Q94.485 20.628 94.346 20.811Q94.208 20.995 94.016 21.128Q93.825 21.261 93.606 21.331Q93.387 21.401 93.149 21.401Q92.778 21.401 92.440 21.264Q92.102 21.128 91.835 20.876Q91.567 20.624 91.417 20.284Q91.266 19.944 91.266 19.569M92.020 19.261L93.981 19.261Q93.981 18.956 93.880 18.665Q93.778 18.374 93.561 18.192Q93.344 18.011 93.028 18.011Q92.727 18.011 92.497 18.198Q92.266 18.386 92.143 18.677Q92.020 18.968 92.020 19.261\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M99.807 21.323L97.951 21.323L97.951 21.026Q98.225 21.026 98.393 20.979Q98.561 20.932 98.561 20.764L98.561 18.628Q98.561 18.413 98.498 18.317Q98.436 18.221 98.317 18.200Q98.198 18.178 97.951 18.178L97.951 17.882L99.143 17.796L99.143 18.530Q99.256 18.315 99.450 18.147Q99.643 17.979 99.881 17.887Q100.119 17.796 100.373 17.796Q101.541 17.796 101.541 18.874L101.541 20.764Q101.541 20.932 101.711 20.979Q101.881 21.026 102.151 21.026L102.151 21.323L100.295 21.323L100.295 21.026Q100.569 21.026 100.737 20.979Q100.905 20.932 100.905 20.764L100.905 18.889Q100.905 18.507 100.784 18.278Q100.662 18.050 100.311 18.050Q99.998 18.050 99.744 18.212Q99.491 18.374 99.344 18.643Q99.198 18.913 99.198 19.210L99.198 20.764Q99.198 20.932 99.368 20.979Q99.537 21.026 99.807 21.026L99.807 21.323M102.596 19.628Q102.596 19.124 102.852 18.692Q103.108 18.261 103.543 18.009Q103.979 17.757 104.479 17.757Q104.866 17.757 105.207 17.901Q105.549 18.046 105.811 18.307Q106.073 18.569 106.215 18.905Q106.358 19.241 106.358 19.628Q106.358 20.120 106.094 20.530Q105.830 20.940 105.401 21.171Q104.971 21.401 104.479 21.401Q103.987 21.401 103.553 21.169Q103.119 20.936 102.858 20.528Q102.596 20.120 102.596 19.628M104.479 21.124Q104.936 21.124 105.188 20.901Q105.440 20.678 105.528 20.327Q105.616 19.975 105.616 19.530Q105.616 19.100 105.522 18.762Q105.428 18.425 105.174 18.218Q104.920 18.011 104.479 18.011Q103.830 18.011 103.586 18.427Q103.342 18.843 103.342 19.530Q103.342 19.975 103.430 20.327Q103.518 20.678 103.770 20.901Q104.022 21.124 104.479 21.124\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(14.46 -47.955)\">\u003Cpath d=\"M108.200 21.292L107.130 18.436Q107.064 18.257 106.933 18.214Q106.802 18.171 106.544 18.171L106.544 17.874L108.224 17.874L108.224 18.171Q107.774 18.171 107.774 18.370Q107.778 18.386 107.780 18.403Q107.782 18.421 107.782 18.436L108.575 20.530L109.286 18.620Q109.251 18.526 109.251 18.481Q109.251 18.436 109.216 18.436Q109.149 18.257 109.019 18.214Q108.888 18.171 108.634 18.171L108.634 17.874L110.224 17.874L110.224 18.171Q109.774 18.171 109.774 18.370Q109.778 18.389 109.780 18.407Q109.782 18.425 109.782 18.436L110.614 20.651L111.368 18.651Q111.392 18.593 111.392 18.522Q111.392 18.362 111.255 18.266Q111.118 18.171 110.950 18.171L110.950 17.874L112.337 17.874L112.337 18.171Q112.103 18.171 111.925 18.298Q111.747 18.425 111.665 18.651L110.681 21.292Q110.626 21.401 110.513 21.401L110.454 21.401Q110.341 21.401 110.298 21.292L109.439 19.018L108.583 21.292Q108.544 21.401 108.423 21.401L108.368 21.401Q108.255 21.401 108.200 21.292\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M69.075 19.9h76.792V-8.551H69.075Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M66.616 11.792L65.546 8.936Q65.480 8.757 65.349 8.714Q65.218 8.671 64.960 8.671L64.960 8.374L66.640 8.374L66.640 8.671Q66.190 8.671 66.190 8.870Q66.194 8.886 66.196 8.903Q66.198 8.921 66.198 8.936L66.991 11.030L67.702 9.120Q67.667 9.026 67.667 8.981Q67.667 8.936 67.632 8.936Q67.565 8.757 67.435 8.714Q67.304 8.671 67.050 8.671L67.050 8.374L68.640 8.374L68.640 8.671Q68.190 8.671 68.190 8.870Q68.194 8.889 68.196 8.907Q68.198 8.925 68.198 8.936L69.030 11.151L69.784 9.151Q69.808 9.093 69.808 9.022Q69.808 8.862 69.671 8.766Q69.534 8.671 69.366 8.671L69.366 8.374L70.753 8.374L70.753 8.671Q70.519 8.671 70.341 8.798Q70.163 8.925 70.081 9.151L69.097 11.792Q69.042 11.901 68.929 11.901L68.870 11.901Q68.757 11.901 68.714 11.792L67.855 9.518L66.999 11.792Q66.960 11.901 66.839 11.901L66.784 11.901Q66.671 11.901 66.616 11.792M73.097 11.823L71.241 11.823L71.241 11.526Q71.515 11.526 71.683 11.479Q71.851 11.432 71.851 11.264L71.851 7.104Q71.851 6.889 71.788 6.794Q71.726 6.698 71.606 6.677Q71.487 6.655 71.241 6.655L71.241 6.358L72.464 6.272L72.464 8.975Q72.589 8.764 72.776 8.614Q72.964 8.464 73.190 8.380Q73.417 8.296 73.663 8.296Q74.831 8.296 74.831 9.374L74.831 11.264Q74.831 11.432 75.001 11.479Q75.171 11.526 75.440 11.526L75.440 11.823L73.585 11.823L73.585 11.526Q73.858 11.526 74.026 11.479Q74.194 11.432 74.194 11.264L74.194 9.389Q74.194 9.007 74.073 8.778Q73.952 8.550 73.601 8.550Q73.288 8.550 73.034 8.712Q72.780 8.874 72.634 9.143Q72.487 9.413 72.487 9.710L72.487 11.264Q72.487 11.432 72.657 11.479Q72.827 11.526 73.097 11.526L73.097 11.823M75.983 10.991Q75.983 10.507 76.386 10.212Q76.788 9.917 77.339 9.798Q77.890 9.678 78.382 9.678L78.382 9.389Q78.382 9.163 78.267 8.956Q78.151 8.749 77.954 8.630Q77.757 8.511 77.526 8.511Q77.101 8.511 76.815 8.616Q76.886 8.643 76.933 8.698Q76.980 8.753 77.005 8.823Q77.030 8.893 77.030 8.968Q77.030 9.073 76.980 9.165Q76.929 9.257 76.837 9.307Q76.745 9.358 76.640 9.358Q76.534 9.358 76.442 9.307Q76.351 9.257 76.300 9.165Q76.249 9.073 76.249 8.968Q76.249 8.550 76.638 8.403Q77.026 8.257 77.526 8.257Q77.858 8.257 78.212 8.387Q78.565 8.518 78.794 8.772Q79.022 9.026 79.022 9.374L79.022 11.175Q79.022 11.307 79.095 11.417Q79.167 11.526 79.296 11.526Q79.421 11.526 79.489 11.421Q79.558 11.315 79.558 11.175L79.558 10.663L79.839 10.663L79.839 11.175Q79.839 11.378 79.722 11.536Q79.605 11.694 79.423 11.778Q79.241 11.862 79.038 11.862Q78.808 11.862 78.655 11.690Q78.503 11.518 78.472 11.288Q78.312 11.569 78.003 11.735Q77.694 11.901 77.343 11.901Q76.831 11.901 76.407 11.678Q75.983 11.456 75.983 10.991M76.671 10.991Q76.671 11.276 76.897 11.462Q77.124 11.647 77.417 11.647Q77.663 11.647 77.888 11.530Q78.112 11.413 78.247 11.210Q78.382 11.007 78.382 10.753L78.382 9.921Q78.116 9.921 77.831 9.975Q77.546 10.030 77.274 10.159Q77.003 10.288 76.837 10.495Q76.671 10.702 76.671 10.991M80.757 10.862L80.757 8.671L80.054 8.671L80.054 8.417Q80.409 8.417 80.651 8.184Q80.894 7.952 81.005 7.604Q81.116 7.257 81.116 6.901L81.397 6.901L81.397 8.374L82.573 8.374L82.573 8.671L81.397 8.671L81.397 10.846Q81.397 11.167 81.517 11.395Q81.636 11.624 81.917 11.624Q82.097 11.624 82.214 11.501Q82.331 11.378 82.384 11.198Q82.437 11.018 82.437 10.846L82.437 10.374L82.718 10.374L82.718 10.862Q82.718 11.116 82.612 11.356Q82.507 11.596 82.310 11.749Q82.112 11.901 81.855 11.901Q81.538 11.901 81.286 11.778Q81.034 11.655 80.896 11.421Q80.757 11.186 80.757 10.862\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M88.141 11.823L86.363 11.823L86.363 11.526Q86.637 11.526 86.805 11.479Q86.973 11.432 86.973 11.264L86.973 9.128Q86.973 8.913 86.916 8.817Q86.859 8.721 86.746 8.700Q86.633 8.678 86.387 8.678L86.387 8.382L87.586 8.296L87.586 11.264Q87.586 11.432 87.732 11.479Q87.879 11.526 88.141 11.526L88.141 11.823M86.699 6.901Q86.699 6.710 86.834 6.579Q86.969 6.448 87.164 6.448Q87.285 6.448 87.389 6.511Q87.492 6.573 87.555 6.677Q87.617 6.780 87.617 6.901Q87.617 7.096 87.486 7.231Q87.356 7.366 87.164 7.366Q86.965 7.366 86.832 7.233Q86.699 7.100 86.699 6.901M89.266 10.862L89.266 8.671L88.563 8.671L88.563 8.417Q88.918 8.417 89.160 8.184Q89.402 7.952 89.514 7.604Q89.625 7.257 89.625 6.901L89.906 6.901L89.906 8.374L91.082 8.374L91.082 8.671L89.906 8.671L89.906 10.846Q89.906 11.167 90.025 11.395Q90.145 11.624 90.426 11.624Q90.606 11.624 90.723 11.501Q90.840 11.378 90.893 11.198Q90.945 11.018 90.945 10.846L90.945 10.374L91.227 10.374L91.227 10.862Q91.227 11.116 91.121 11.356Q91.016 11.596 90.818 11.749Q90.621 11.901 90.363 11.901Q90.047 11.901 89.795 11.778Q89.543 11.655 89.404 11.421Q89.266 11.186 89.266 10.862\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M96.367 11.792L95.297 8.936Q95.231 8.757 95.100 8.714Q94.969 8.671 94.711 8.671L94.711 8.374L96.391 8.374L96.391 8.671Q95.941 8.671 95.941 8.870Q95.945 8.886 95.947 8.903Q95.949 8.921 95.949 8.936L96.742 11.030L97.453 9.120Q97.418 9.026 97.418 8.981Q97.418 8.936 97.383 8.936Q97.316 8.757 97.186 8.714Q97.055 8.671 96.801 8.671L96.801 8.374L98.391 8.374L98.391 8.671Q97.941 8.671 97.941 8.870Q97.945 8.889 97.947 8.907Q97.949 8.925 97.949 8.936L98.781 11.151L99.535 9.151Q99.559 9.093 99.559 9.022Q99.559 8.862 99.422 8.766Q99.285 8.671 99.117 8.671L99.117 8.374L100.504 8.374L100.504 8.671Q100.270 8.671 100.092 8.798Q99.914 8.925 99.832 9.151L98.848 11.792Q98.793 11.901 98.680 11.901L98.621 11.901Q98.508 11.901 98.465 11.792L97.606 9.518L96.750 11.792Q96.711 11.901 96.590 11.901L96.535 11.901Q96.422 11.901 96.367 11.792M102.777 11.823L101 11.823L101 11.526Q101.273 11.526 101.441 11.479Q101.609 11.432 101.609 11.264L101.609 9.128Q101.609 8.913 101.553 8.817Q101.496 8.721 101.383 8.700Q101.270 8.678 101.023 8.678L101.023 8.382L102.223 8.296L102.223 11.264Q102.223 11.432 102.369 11.479Q102.516 11.526 102.777 11.526L102.777 11.823M101.336 6.901Q101.336 6.710 101.471 6.579Q101.606 6.448 101.801 6.448Q101.922 6.448 102.025 6.511Q102.129 6.573 102.191 6.677Q102.254 6.780 102.254 6.901Q102.254 7.096 102.123 7.231Q101.992 7.366 101.801 7.366Q101.602 7.366 101.469 7.233Q101.336 7.100 101.336 6.901M105.191 11.823L103.359 11.823L103.359 11.526Q103.633 11.526 103.801 11.479Q103.969 11.432 103.969 11.264L103.969 7.104Q103.969 6.889 103.906 6.794Q103.844 6.698 103.725 6.677Q103.606 6.655 103.359 6.655L103.359 6.358L104.582 6.272L104.582 11.264Q104.582 11.432 104.750 11.479Q104.918 11.526 105.191 11.526L105.191 11.823M107.551 11.823L105.719 11.823L105.719 11.526Q105.992 11.526 106.160 11.479Q106.328 11.432 106.328 11.264L106.328 7.104Q106.328 6.889 106.266 6.794Q106.203 6.698 106.084 6.677Q105.965 6.655 105.719 6.655L105.719 6.358L106.941 6.272L106.941 11.264Q106.941 11.432 107.109 11.479Q107.277 11.526 107.551 11.526\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M111.751 11.823L111.470 11.823L111.470 7.104Q111.470 6.889 111.408 6.794Q111.345 6.698 111.228 6.677Q111.111 6.655 110.865 6.655L110.865 6.358L112.087 6.272L112.087 8.761Q112.564 8.296 113.263 8.296Q113.744 8.296 114.152 8.540Q114.560 8.784 114.796 9.198Q115.033 9.612 115.033 10.096Q115.033 10.471 114.884 10.800Q114.736 11.128 114.466 11.380Q114.197 11.632 113.853 11.766Q113.509 11.901 113.150 11.901Q112.829 11.901 112.531 11.753Q112.232 11.604 112.025 11.343L111.751 11.823M112.111 9.151L112.111 10.991Q112.263 11.288 112.523 11.468Q112.783 11.647 113.095 11.647Q113.521 11.647 113.788 11.428Q114.056 11.210 114.171 10.864Q114.287 10.518 114.287 10.096Q114.287 9.448 114.038 8.999Q113.790 8.550 113.193 8.550Q112.857 8.550 112.568 8.708Q112.279 8.866 112.111 9.151\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M115.795 10.069Q115.795 9.589 116.028 9.173Q116.260 8.757 116.670 8.507Q117.080 8.257 117.557 8.257Q118.287 8.257 118.686 8.698Q119.084 9.139 119.084 9.870Q119.084 9.975 118.991 9.999L116.541 9.999L116.541 10.069Q116.541 10.479 116.662 10.835Q116.784 11.190 117.055 11.407Q117.327 11.624 117.756 11.624Q118.120 11.624 118.416 11.395Q118.713 11.167 118.815 10.815Q118.823 10.768 118.909 10.753L118.991 10.753Q119.084 10.780 119.084 10.862Q119.084 10.870 119.077 10.901Q119.014 11.128 118.875 11.311Q118.737 11.495 118.545 11.628Q118.354 11.761 118.135 11.831Q117.916 11.901 117.678 11.901Q117.307 11.901 116.969 11.764Q116.631 11.628 116.364 11.376Q116.096 11.124 115.946 10.784Q115.795 10.444 115.795 10.069M116.549 9.761L118.510 9.761Q118.510 9.456 118.409 9.165Q118.307 8.874 118.090 8.692Q117.873 8.511 117.557 8.511Q117.256 8.511 117.026 8.698Q116.795 8.886 116.672 9.177Q116.549 9.468 116.549 9.761\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M124.320 11.823L122.488 11.823L122.488 11.526Q122.762 11.526 122.930 11.479Q123.098 11.432 123.098 11.264L123.098 7.104Q123.098 6.889 123.035 6.794Q122.973 6.698 122.854 6.677Q122.734 6.655 122.488 6.655L122.488 6.358L123.711 6.272L123.711 11.264Q123.711 11.432 123.879 11.479Q124.047 11.526 124.320 11.526L124.320 11.823M126.625 11.823L124.848 11.823L124.848 11.526Q125.121 11.526 125.289 11.479Q125.457 11.432 125.457 11.264L125.457 9.128Q125.457 8.913 125.400 8.817Q125.344 8.721 125.231 8.700Q125.117 8.678 124.871 8.678L124.871 8.382L126.070 8.296L126.070 11.264Q126.070 11.432 126.217 11.479Q126.363 11.526 126.625 11.526L126.625 11.823M125.184 6.901Q125.184 6.710 125.318 6.579Q125.453 6.448 125.648 6.448Q125.770 6.448 125.873 6.511Q125.977 6.573 126.039 6.677Q126.102 6.780 126.102 6.901Q126.102 7.096 125.971 7.231Q125.840 7.366 125.648 7.366Q125.449 7.366 125.316 7.233Q125.184 7.100 125.184 6.901M128.949 11.823L127.152 11.823L127.152 11.526Q127.422 11.526 127.590 11.481Q127.758 11.436 127.758 11.264L127.758 7.104Q127.758 6.889 127.695 6.794Q127.633 6.698 127.516 6.677Q127.398 6.655 127.152 6.655L127.152 6.358L128.375 6.272L128.375 10.038L129.473 9.151Q129.680 8.971 129.680 8.823Q129.680 8.757 129.627 8.714Q129.574 8.671 129.504 8.671L129.504 8.374L131.039 8.374L131.039 8.671Q130.508 8.671 129.910 9.151L129.301 9.647L130.375 11.046Q130.512 11.221 130.619 11.329Q130.727 11.436 130.861 11.481Q130.996 11.526 131.223 11.526L131.223 11.823L129.598 11.823L129.598 11.526Q129.840 11.526 129.840 11.374Q129.840 11.296 129.797 11.225Q129.754 11.155 129.672 11.046L128.871 9.999L128.344 10.425L128.344 11.264Q128.344 11.432 128.512 11.479Q128.680 11.526 128.949 11.526\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M131.379 10.069Q131.379 9.589 131.612 9.173Q131.844 8.757 132.254 8.507Q132.664 8.257 133.141 8.257Q133.871 8.257 134.270 8.698Q134.668 9.139 134.668 9.870Q134.668 9.975 134.575 9.999L132.125 9.999L132.125 10.069Q132.125 10.479 132.246 10.835Q132.368 11.190 132.639 11.407Q132.911 11.624 133.340 11.624Q133.703 11.624 134 11.395Q134.297 11.167 134.399 10.815Q134.407 10.768 134.493 10.753L134.575 10.753Q134.668 10.780 134.668 10.862Q134.668 10.870 134.661 10.901Q134.598 11.128 134.459 11.311Q134.321 11.495 134.129 11.628Q133.938 11.761 133.719 11.831Q133.500 11.901 133.262 11.901Q132.891 11.901 132.553 11.764Q132.215 11.628 131.948 11.376Q131.680 11.124 131.530 10.784Q131.379 10.444 131.379 10.069M132.133 9.761L134.094 9.761Q134.094 9.456 133.993 9.165Q133.891 8.874 133.674 8.692Q133.457 8.511 133.141 8.511Q132.840 8.511 132.610 8.698Q132.379 8.886 132.256 9.177Q132.133 9.468 132.133 9.761\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M73.274 21.323L71.496 21.323L71.496 21.026Q71.770 21.026 71.938 20.979Q72.106 20.932 72.106 20.764L72.106 18.628Q72.106 18.413 72.049 18.317Q71.992 18.221 71.879 18.200Q71.766 18.178 71.520 18.178L71.520 17.882L72.719 17.796L72.719 20.764Q72.719 20.932 72.865 20.979Q73.012 21.026 73.274 21.026L73.274 21.323M71.832 16.401Q71.832 16.210 71.967 16.079Q72.102 15.948 72.297 15.948Q72.418 15.948 72.522 16.011Q72.625 16.073 72.688 16.177Q72.750 16.280 72.750 16.401Q72.750 16.596 72.619 16.731Q72.489 16.866 72.297 16.866Q72.098 16.866 71.965 16.733Q71.832 16.600 71.832 16.401M75.840 21.323L73.856 21.323L73.856 21.026Q74.129 21.026 74.297 20.979Q74.465 20.932 74.465 20.764L74.465 18.171L73.824 18.171L73.824 17.874L74.465 17.874L74.465 16.940Q74.465 16.675 74.582 16.438Q74.699 16.202 74.893 16.038Q75.086 15.874 75.334 15.782Q75.582 15.690 75.848 15.690Q76.133 15.690 76.358 15.848Q76.582 16.007 76.582 16.284Q76.582 16.440 76.477 16.550Q76.371 16.659 76.207 16.659Q76.051 16.659 75.942 16.550Q75.832 16.440 75.832 16.284Q75.832 16.077 75.992 15.971Q75.895 15.948 75.801 15.948Q75.571 15.948 75.399 16.104Q75.227 16.261 75.141 16.497Q75.055 16.733 75.055 16.956L75.055 17.874L76.024 17.874L76.024 18.171L75.078 18.171L75.078 20.764Q75.078 20.932 75.305 20.979Q75.531 21.026 75.840 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M81.730 21.323L79.265 21.323L79.265 21.026Q79.597 21.026 79.855 20.979Q80.113 20.932 80.113 20.764L80.113 16.421Q80.113 16.155 79.265 16.155L79.265 15.858L81.730 15.858L81.730 16.155Q80.878 16.155 80.878 16.421L80.878 20.764Q80.878 21.026 81.730 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M86.917 21.401Q86.436 21.401 86.028 21.157Q85.620 20.913 85.382 20.499Q85.143 20.085 85.143 19.596Q85.143 19.104 85.401 18.688Q85.659 18.272 86.091 18.034Q86.522 17.796 87.014 17.796Q87.635 17.796 88.085 18.233L88.085 16.604Q88.085 16.389 88.022 16.294Q87.960 16.198 87.842 16.177Q87.725 16.155 87.479 16.155L87.479 15.858L88.702 15.772L88.702 20.581Q88.702 20.792 88.764 20.887Q88.827 20.983 88.944 21.005Q89.061 21.026 89.311 21.026L89.311 21.323L88.061 21.401L88.061 20.917Q87.596 21.401 86.917 21.401M86.983 21.147Q87.323 21.147 87.616 20.956Q87.909 20.764 88.061 20.468L88.061 18.636Q87.913 18.362 87.651 18.206Q87.389 18.050 87.077 18.050Q86.452 18.050 86.169 18.497Q85.885 18.944 85.885 19.604Q85.885 20.249 86.137 20.698Q86.389 21.147 86.983 21.147M89.819 19.628Q89.819 19.124 90.075 18.692Q90.331 18.261 90.766 18.009Q91.202 17.757 91.702 17.757Q92.089 17.757 92.430 17.901Q92.772 18.046 93.034 18.307Q93.296 18.569 93.438 18.905Q93.581 19.241 93.581 19.628Q93.581 20.120 93.317 20.530Q93.053 20.940 92.624 21.171Q92.194 21.401 91.702 21.401Q91.210 21.401 90.776 21.169Q90.342 20.936 90.081 20.528Q89.819 20.120 89.819 19.628M91.702 21.124Q92.159 21.124 92.411 20.901Q92.663 20.678 92.751 20.327Q92.839 19.975 92.839 19.530Q92.839 19.100 92.745 18.762Q92.651 18.425 92.397 18.218Q92.143 18.011 91.702 18.011Q91.053 18.011 90.809 18.427Q90.565 18.843 90.565 19.530Q90.565 19.975 90.653 20.327Q90.741 20.678 90.993 20.901Q91.245 21.124 91.702 21.124\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M97.004 20.491Q97.004 20.007 97.406 19.712Q97.809 19.417 98.359 19.298Q98.910 19.178 99.402 19.178L99.402 18.889Q99.402 18.663 99.287 18.456Q99.172 18.249 98.975 18.130Q98.777 18.011 98.547 18.011Q98.121 18.011 97.836 18.116Q97.906 18.143 97.953 18.198Q98 18.253 98.025 18.323Q98.051 18.393 98.051 18.468Q98.051 18.573 98 18.665Q97.949 18.757 97.857 18.807Q97.766 18.858 97.660 18.858Q97.555 18.858 97.463 18.807Q97.371 18.757 97.320 18.665Q97.270 18.573 97.270 18.468Q97.270 18.050 97.658 17.903Q98.047 17.757 98.547 17.757Q98.879 17.757 99.232 17.887Q99.586 18.018 99.814 18.272Q100.043 18.526 100.043 18.874L100.043 20.675Q100.043 20.807 100.115 20.917Q100.188 21.026 100.316 21.026Q100.441 21.026 100.510 20.921Q100.578 20.815 100.578 20.675L100.578 20.163L100.859 20.163L100.859 20.675Q100.859 20.878 100.742 21.036Q100.625 21.194 100.443 21.278Q100.262 21.362 100.059 21.362Q99.828 21.362 99.676 21.190Q99.523 21.018 99.492 20.788Q99.332 21.069 99.023 21.235Q98.715 21.401 98.363 21.401Q97.852 21.401 97.428 21.178Q97.004 20.956 97.004 20.491M97.691 20.491Q97.691 20.776 97.918 20.962Q98.145 21.147 98.438 21.147Q98.684 21.147 98.908 21.030Q99.133 20.913 99.268 20.710Q99.402 20.507 99.402 20.253L99.402 19.421Q99.137 19.421 98.852 19.475Q98.566 19.530 98.295 19.659Q98.023 19.788 97.857 19.995Q97.691 20.202 97.691 20.491M101.195 19.596Q101.195 19.100 101.445 18.675Q101.695 18.249 102.115 18.003Q102.535 17.757 103.035 17.757Q103.574 17.757 103.965 17.882Q104.356 18.007 104.356 18.421Q104.356 18.526 104.305 18.618Q104.254 18.710 104.162 18.761Q104.070 18.811 103.961 18.811Q103.856 18.811 103.764 18.761Q103.672 18.710 103.621 18.618Q103.570 18.526 103.570 18.421Q103.570 18.198 103.738 18.093Q103.516 18.034 103.043 18.034Q102.746 18.034 102.531 18.173Q102.316 18.311 102.186 18.542Q102.055 18.772 101.996 19.042Q101.938 19.311 101.938 19.596Q101.938 19.991 102.070 20.341Q102.203 20.690 102.475 20.907Q102.746 21.124 103.145 21.124Q103.520 21.124 103.795 20.907Q104.070 20.690 104.172 20.331Q104.188 20.268 104.250 20.268L104.356 20.268Q104.391 20.268 104.416 20.296Q104.441 20.323 104.441 20.362L104.441 20.386Q104.309 20.866 103.924 21.134Q103.539 21.401 103.035 21.401Q102.672 21.401 102.338 21.264Q102.004 21.128 101.744 20.878Q101.484 20.628 101.340 20.292Q101.195 19.956 101.195 19.596M105.555 20.362L105.555 18.171L104.852 18.171L104.852 17.917Q105.207 17.917 105.449 17.684Q105.691 17.452 105.803 17.104Q105.914 16.757 105.914 16.401L106.195 16.401L106.195 17.874L107.371 17.874L107.371 18.171L106.195 18.171L106.195 20.346Q106.195 20.667 106.314 20.895Q106.434 21.124 106.715 21.124Q106.895 21.124 107.012 21.001Q107.129 20.878 107.182 20.698Q107.234 20.518 107.234 20.346L107.234 19.874L107.516 19.874L107.516 20.362Q107.516 20.616 107.410 20.856Q107.305 21.096 107.107 21.249Q106.910 21.401 106.652 21.401Q106.336 21.401 106.084 21.278Q105.832 21.155 105.693 20.921Q105.555 20.686 105.555 20.362M110.094 21.323L108.316 21.323L108.316 21.026Q108.590 21.026 108.758 20.979Q108.926 20.932 108.926 20.764L108.926 18.628Q108.926 18.413 108.869 18.317Q108.813 18.221 108.699 18.200Q108.586 18.178 108.340 18.178L108.340 17.882L109.539 17.796L109.539 20.764Q109.539 20.932 109.686 20.979Q109.832 21.026 110.094 21.026L110.094 21.323M108.652 16.401Q108.652 16.210 108.787 16.079Q108.922 15.948 109.117 15.948Q109.238 15.948 109.342 16.011Q109.445 16.073 109.508 16.177Q109.570 16.280 109.570 16.401Q109.570 16.596 109.439 16.731Q109.309 16.866 109.117 16.866Q108.918 16.866 108.785 16.733Q108.652 16.600 108.652 16.401M110.594 19.628Q110.594 19.124 110.850 18.692Q111.106 18.261 111.541 18.009Q111.977 17.757 112.477 17.757Q112.863 17.757 113.205 17.901Q113.547 18.046 113.809 18.307Q114.070 18.569 114.213 18.905Q114.356 19.241 114.356 19.628Q114.356 20.120 114.092 20.530Q113.828 20.940 113.398 21.171Q112.969 21.401 112.477 21.401Q111.984 21.401 111.551 21.169Q111.117 20.936 110.856 20.528Q110.594 20.120 110.594 19.628M112.477 21.124Q112.934 21.124 113.186 20.901Q113.438 20.678 113.525 20.327Q113.613 19.975 113.613 19.530Q113.613 19.100 113.520 18.762Q113.426 18.425 113.172 18.218Q112.918 18.011 112.477 18.011Q111.828 18.011 111.584 18.427Q111.340 18.843 111.340 19.530Q111.340 19.975 111.428 20.327Q111.516 20.678 111.768 20.901Q112.020 21.124 112.477 21.124M116.770 21.323L114.914 21.323L114.914 21.026Q115.188 21.026 115.356 20.979Q115.523 20.932 115.523 20.764L115.523 18.628Q115.523 18.413 115.461 18.317Q115.398 18.221 115.279 18.200Q115.160 18.178 114.914 18.178L114.914 17.882L116.106 17.796L116.106 18.530Q116.219 18.315 116.412 18.147Q116.606 17.979 116.844 17.887Q117.082 17.796 117.336 17.796Q118.504 17.796 118.504 18.874L118.504 20.764Q118.504 20.932 118.674 20.979Q118.844 21.026 119.113 21.026L119.113 21.323L117.258 21.323L117.258 21.026Q117.531 21.026 117.699 20.979Q117.867 20.932 117.867 20.764L117.867 18.889Q117.867 18.507 117.746 18.278Q117.625 18.050 117.273 18.050Q116.961 18.050 116.707 18.212Q116.453 18.374 116.307 18.643Q116.160 18.913 116.160 19.210L116.160 20.764Q116.160 20.932 116.330 20.979Q116.500 21.026 116.770 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(7.616 -8.121)\">\u003Cpath d=\"M124.207 21.323L122.457 21.323L122.457 21.026Q123.156 21.026 123.344 20.546L125.145 15.721Q125.199 15.612 125.313 15.612L125.383 15.612Q125.496 15.612 125.551 15.721L127.441 20.764Q127.520 20.932 127.723 20.979Q127.926 21.026 128.238 21.026L128.238 21.323L126.016 21.323L126.016 21.026Q126.656 21.026 126.656 20.811Q126.656 20.792 126.654 20.782Q126.652 20.772 126.648 20.764L126.184 19.530L124.039 19.530L123.656 20.546Q123.652 20.561 123.647 20.591Q123.641 20.620 123.641 20.643Q123.641 20.784 123.731 20.868Q123.820 20.952 123.953 20.989Q124.086 21.026 124.207 21.026L124.207 21.323M125.113 16.667L124.145 19.233L126.070 19.233\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M67.19 59.735h80.562V31.282H67.191Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M66.960 11.823L65.105 11.823L65.105 11.526Q65.378 11.526 65.546 11.479Q65.714 11.432 65.714 11.264L65.714 7.104Q65.714 6.889 65.651 6.794Q65.589 6.698 65.470 6.677Q65.351 6.655 65.105 6.655L65.105 6.358L66.327 6.272L66.327 8.975Q66.452 8.764 66.640 8.614Q66.827 8.464 67.054 8.380Q67.280 8.296 67.526 8.296Q68.694 8.296 68.694 9.374L68.694 11.264Q68.694 11.432 68.864 11.479Q69.034 11.526 69.304 11.526L69.304 11.823L67.448 11.823L67.448 11.526Q67.722 11.526 67.890 11.479Q68.058 11.432 68.058 11.264L68.058 9.389Q68.058 9.007 67.937 8.778Q67.815 8.550 67.464 8.550Q67.151 8.550 66.897 8.712Q66.644 8.874 66.497 9.143Q66.351 9.413 66.351 9.710L66.351 11.264Q66.351 11.432 66.521 11.479Q66.690 11.526 66.960 11.526L66.960 11.823M69.749 10.128Q69.749 9.624 70.005 9.192Q70.261 8.761 70.696 8.509Q71.132 8.257 71.632 8.257Q72.019 8.257 72.360 8.401Q72.702 8.546 72.964 8.807Q73.226 9.069 73.368 9.405Q73.511 9.741 73.511 10.128Q73.511 10.620 73.247 11.030Q72.983 11.440 72.554 11.671Q72.124 11.901 71.632 11.901Q71.140 11.901 70.706 11.669Q70.272 11.436 70.011 11.028Q69.749 10.620 69.749 10.128M71.632 11.624Q72.089 11.624 72.341 11.401Q72.593 11.178 72.681 10.827Q72.769 10.475 72.769 10.030Q72.769 9.600 72.675 9.262Q72.581 8.925 72.327 8.718Q72.073 8.511 71.632 8.511Q70.983 8.511 70.739 8.927Q70.495 9.343 70.495 10.030Q70.495 10.475 70.583 10.827Q70.671 11.178 70.923 11.401Q71.175 11.624 71.632 11.624\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M75.353 11.792L74.283 8.936Q74.216 8.757 74.086 8.714Q73.955 8.671 73.697 8.671L73.697 8.374L75.377 8.374L75.377 8.671Q74.927 8.671 74.927 8.870Q74.931 8.886 74.933 8.903Q74.935 8.921 74.935 8.936L75.728 11.030L76.439 9.120Q76.404 9.026 76.404 8.981Q76.404 8.936 76.369 8.936Q76.302 8.757 76.172 8.714Q76.041 8.671 75.787 8.671L75.787 8.374L77.377 8.374L77.377 8.671Q76.927 8.671 76.927 8.870Q76.931 8.889 76.933 8.907Q76.935 8.925 76.935 8.936L77.767 11.151L78.521 9.151Q78.545 9.093 78.545 9.022Q78.545 8.862 78.408 8.766Q78.271 8.671 78.103 8.671L78.103 8.374L79.490 8.374L79.490 8.671Q79.256 8.671 79.078 8.798Q78.900 8.925 78.818 9.151L77.834 11.792Q77.779 11.901 77.666 11.901L77.607 11.901Q77.494 11.901 77.451 11.792L76.591 9.518L75.736 11.792Q75.697 11.901 75.576 11.901L75.521 11.901Q75.408 11.901 75.353 11.792\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M84.669 11.823L82.814 11.823L82.814 11.526Q83.087 11.526 83.255 11.479Q83.423 11.432 83.423 11.264L83.423 7.104Q83.423 6.889 83.360 6.794Q83.298 6.698 83.179 6.677Q83.060 6.655 82.814 6.655L82.814 6.358L84.036 6.272L84.036 8.975Q84.161 8.764 84.349 8.614Q84.536 8.464 84.763 8.380Q84.989 8.296 85.235 8.296Q86.403 8.296 86.403 9.374L86.403 11.264Q86.403 11.432 86.573 11.479Q86.743 11.526 87.013 11.526L87.013 11.823L85.157 11.823L85.157 11.526Q85.431 11.526 85.599 11.479Q85.767 11.432 85.767 11.264L85.767 9.389Q85.767 9.007 85.646 8.778Q85.524 8.550 85.173 8.550Q84.860 8.550 84.606 8.712Q84.353 8.874 84.206 9.143Q84.060 9.413 84.060 9.710L84.060 11.264Q84.060 11.432 84.230 11.479Q84.399 11.526 84.669 11.526L84.669 11.823M87.556 10.991Q87.556 10.507 87.958 10.212Q88.360 9.917 88.911 9.798Q89.462 9.678 89.954 9.678L89.954 9.389Q89.954 9.163 89.839 8.956Q89.724 8.749 89.526 8.630Q89.329 8.511 89.099 8.511Q88.673 8.511 88.388 8.616Q88.458 8.643 88.505 8.698Q88.552 8.753 88.577 8.823Q88.603 8.893 88.603 8.968Q88.603 9.073 88.552 9.165Q88.501 9.257 88.409 9.307Q88.317 9.358 88.212 9.358Q88.106 9.358 88.015 9.307Q87.923 9.257 87.872 9.165Q87.821 9.073 87.821 8.968Q87.821 8.550 88.210 8.403Q88.599 8.257 89.099 8.257Q89.431 8.257 89.784 8.387Q90.138 8.518 90.366 8.772Q90.595 9.026 90.595 9.374L90.595 11.175Q90.595 11.307 90.667 11.417Q90.739 11.526 90.868 11.526Q90.993 11.526 91.062 11.421Q91.130 11.315 91.130 11.175L91.130 10.663L91.411 10.663L91.411 11.175Q91.411 11.378 91.294 11.536Q91.177 11.694 90.995 11.778Q90.814 11.862 90.610 11.862Q90.380 11.862 90.228 11.690Q90.075 11.518 90.044 11.288Q89.884 11.569 89.575 11.735Q89.267 11.901 88.915 11.901Q88.403 11.901 87.980 11.678Q87.556 11.456 87.556 10.991M88.243 10.991Q88.243 11.276 88.470 11.462Q88.696 11.647 88.989 11.647Q89.235 11.647 89.460 11.530Q89.685 11.413 89.819 11.210Q89.954 11.007 89.954 10.753L89.954 9.921Q89.689 9.921 89.403 9.975Q89.118 10.030 88.847 10.159Q88.575 10.288 88.409 10.495Q88.243 10.702 88.243 10.991M93.587 13.374L91.731 13.374L91.731 13.081Q92.001 13.081 92.169 13.036Q92.337 12.991 92.337 12.815L92.337 8.991Q92.337 8.784 92.181 8.731Q92.024 8.678 91.731 8.678L91.731 8.382L92.954 8.296L92.954 8.761Q93.185 8.538 93.499 8.417Q93.814 8.296 94.153 8.296Q94.626 8.296 95.030 8.542Q95.435 8.788 95.667 9.204Q95.899 9.620 95.899 10.096Q95.899 10.471 95.751 10.800Q95.603 11.128 95.333 11.380Q95.064 11.632 94.720 11.766Q94.376 11.901 94.017 11.901Q93.728 11.901 93.456 11.780Q93.185 11.659 92.978 11.448L92.978 12.815Q92.978 12.991 93.146 13.036Q93.314 13.081 93.587 13.081L93.587 13.374M92.978 9.159L92.978 10.999Q93.130 11.288 93.392 11.468Q93.653 11.647 93.962 11.647Q94.247 11.647 94.470 11.509Q94.692 11.370 94.845 11.139Q94.997 10.909 95.075 10.637Q95.153 10.366 95.153 10.096Q95.153 9.764 95.028 9.407Q94.903 9.050 94.655 8.813Q94.407 8.577 94.060 8.577Q93.735 8.577 93.440 8.733Q93.146 8.889 92.978 9.159M98.306 13.374L96.450 13.374L96.450 13.081Q96.720 13.081 96.888 13.036Q97.056 12.991 97.056 12.815L97.056 8.991Q97.056 8.784 96.899 8.731Q96.743 8.678 96.450 8.678L96.450 8.382L97.673 8.296L97.673 8.761Q97.903 8.538 98.218 8.417Q98.532 8.296 98.872 8.296Q99.345 8.296 99.749 8.542Q100.153 8.788 100.386 9.204Q100.618 9.620 100.618 10.096Q100.618 10.471 100.470 10.800Q100.321 11.128 100.052 11.380Q99.782 11.632 99.439 11.766Q99.095 11.901 98.735 11.901Q98.446 11.901 98.175 11.780Q97.903 11.659 97.696 11.448L97.696 12.815Q97.696 12.991 97.864 13.036Q98.032 13.081 98.306 13.081L98.306 13.374M97.696 9.159L97.696 10.999Q97.849 11.288 98.110 11.468Q98.372 11.647 98.681 11.647Q98.966 11.647 99.189 11.509Q99.411 11.370 99.564 11.139Q99.716 10.909 99.794 10.637Q99.872 10.366 99.872 10.096Q99.872 9.764 99.747 9.407Q99.622 9.050 99.374 8.813Q99.126 8.577 98.778 8.577Q98.454 8.577 98.159 8.733Q97.864 8.889 97.696 9.159\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M101.338 13.120Q101.452 13.198 101.627 13.198Q101.916 13.198 102.137 12.985Q102.358 12.772 102.483 12.471L102.772 11.823L101.498 8.936Q101.416 8.761 101.272 8.716Q101.127 8.671 100.858 8.671L100.858 8.374L102.577 8.374L102.577 8.671Q102.155 8.671 102.155 8.854Q102.155 8.866 102.170 8.936L103.108 11.061L103.940 9.151Q103.979 9.061 103.979 8.983Q103.979 8.843 103.877 8.757Q103.776 8.671 103.635 8.671L103.635 8.374L104.987 8.374L104.987 8.671Q104.733 8.671 104.539 8.796Q104.346 8.921 104.241 9.151L102.795 12.471Q102.682 12.725 102.516 12.948Q102.350 13.171 102.121 13.313Q101.893 13.456 101.627 13.456Q101.330 13.456 101.090 13.264Q100.850 13.073 100.850 12.784Q100.850 12.628 100.955 12.526Q101.061 12.425 101.209 12.425Q101.315 12.425 101.395 12.471Q101.475 12.518 101.522 12.596Q101.569 12.675 101.569 12.784Q101.569 12.905 101.508 12.993Q101.448 13.081 101.338 13.120\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M110.763 11.823L108.298 11.823L108.298 11.526Q108.630 11.526 108.888 11.479Q109.146 11.432 109.146 11.264L109.146 6.921Q109.146 6.655 108.298 6.655L108.298 6.358L110.763 6.358L110.763 6.655Q109.911 6.655 109.911 6.921L109.911 11.264Q109.911 11.526 110.763 11.526\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M115.720 11.792L114.650 8.936Q114.584 8.757 114.453 8.714Q114.322 8.671 114.064 8.671L114.064 8.374L115.744 8.374L115.744 8.671Q115.294 8.671 115.294 8.870Q115.298 8.886 115.300 8.903Q115.302 8.921 115.302 8.936L116.095 11.030L116.806 9.120Q116.771 9.026 116.771 8.981Q116.771 8.936 116.736 8.936Q116.669 8.757 116.539 8.714Q116.408 8.671 116.154 8.671L116.154 8.374L117.744 8.374L117.744 8.671Q117.294 8.671 117.294 8.870Q117.298 8.889 117.300 8.907Q117.302 8.925 117.302 8.936L118.134 11.151L118.888 9.151Q118.912 9.093 118.912 9.022Q118.912 8.862 118.775 8.766Q118.638 8.671 118.470 8.671L118.470 8.374L119.857 8.374L119.857 8.671Q119.623 8.671 119.445 8.798Q119.267 8.925 119.185 9.151L118.201 11.792Q118.146 11.901 118.033 11.901L117.974 11.901Q117.861 11.901 117.818 11.792L116.959 9.518L116.103 11.792Q116.064 11.901 115.943 11.901L115.888 11.901Q115.775 11.901 115.720 11.792M122.130 11.823L120.353 11.823L120.353 11.526Q120.626 11.526 120.794 11.479Q120.962 11.432 120.962 11.264L120.962 9.128Q120.962 8.913 120.906 8.817Q120.849 8.721 120.736 8.700Q120.623 8.678 120.376 8.678L120.376 8.382L121.576 8.296L121.576 11.264Q121.576 11.432 121.722 11.479Q121.869 11.526 122.130 11.526L122.130 11.823M120.689 6.901Q120.689 6.710 120.824 6.579Q120.959 6.448 121.154 6.448Q121.275 6.448 121.378 6.511Q121.482 6.573 121.544 6.677Q121.607 6.780 121.607 6.901Q121.607 7.096 121.476 7.231Q121.345 7.366 121.154 7.366Q120.955 7.366 120.822 7.233Q120.689 7.100 120.689 6.901M124.544 11.823L122.712 11.823L122.712 11.526Q122.986 11.526 123.154 11.479Q123.322 11.432 123.322 11.264L123.322 7.104Q123.322 6.889 123.259 6.794Q123.197 6.698 123.078 6.677Q122.959 6.655 122.712 6.655L122.712 6.358L123.935 6.272L123.935 11.264Q123.935 11.432 124.103 11.479Q124.271 11.526 124.544 11.526L124.544 11.823M126.904 11.823L125.072 11.823L125.072 11.526Q125.345 11.526 125.513 11.479Q125.681 11.432 125.681 11.264L125.681 7.104Q125.681 6.889 125.619 6.794Q125.556 6.698 125.437 6.677Q125.318 6.655 125.072 6.655L125.072 6.358L126.294 6.272L126.294 11.264Q126.294 11.432 126.462 11.479Q126.630 11.526 126.904 11.526\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M131.104 11.823L130.823 11.823L130.823 7.104Q130.823 6.889 130.761 6.794Q130.698 6.698 130.581 6.677Q130.464 6.655 130.218 6.655L130.218 6.358L131.440 6.272L131.440 8.761Q131.917 8.296 132.616 8.296Q133.097 8.296 133.505 8.540Q133.913 8.784 134.149 9.198Q134.386 9.612 134.386 10.096Q134.386 10.471 134.237 10.800Q134.089 11.128 133.819 11.380Q133.550 11.632 133.206 11.766Q132.862 11.901 132.503 11.901Q132.182 11.901 131.884 11.753Q131.585 11.604 131.378 11.343L131.104 11.823M131.464 9.151L131.464 10.991Q131.616 11.288 131.876 11.468Q132.136 11.647 132.448 11.647Q132.874 11.647 133.141 11.428Q133.409 11.210 133.524 10.864Q133.639 10.518 133.639 10.096Q133.639 9.448 133.391 8.999Q133.143 8.550 132.546 8.550Q132.210 8.550 131.921 8.708Q131.632 8.866 131.464 9.151\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M135.148 10.069Q135.148 9.589 135.381 9.173Q135.613 8.757 136.023 8.507Q136.433 8.257 136.910 8.257Q137.640 8.257 138.039 8.698Q138.437 9.139 138.437 9.870Q138.437 9.975 138.344 9.999L135.894 9.999L135.894 10.069Q135.894 10.479 136.015 10.835Q136.137 11.190 136.408 11.407Q136.680 11.624 137.109 11.624Q137.472 11.624 137.769 11.395Q138.066 11.167 138.168 10.815Q138.176 10.768 138.262 10.753L138.344 10.753Q138.437 10.780 138.437 10.862Q138.437 10.870 138.430 10.901Q138.367 11.128 138.228 11.311Q138.090 11.495 137.898 11.628Q137.707 11.761 137.488 11.831Q137.269 11.901 137.031 11.901Q136.660 11.901 136.322 11.764Q135.984 11.628 135.717 11.376Q135.449 11.124 135.299 10.784Q135.148 10.444 135.148 10.069M135.902 9.761L137.863 9.761Q137.863 9.456 137.762 9.165Q137.660 8.874 137.443 8.692Q137.226 8.511 136.910 8.511Q136.609 8.511 136.379 8.698Q136.148 8.886 136.025 9.177Q135.902 9.468 135.902 9.761\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M76.756 21.323L74.978 21.323L74.978 21.026Q75.252 21.026 75.420 20.979Q75.588 20.932 75.588 20.764L75.588 18.628Q75.588 18.413 75.531 18.317Q75.474 18.221 75.361 18.200Q75.248 18.178 75.002 18.178L75.002 17.882L76.201 17.796L76.201 20.764Q76.201 20.932 76.347 20.979Q76.494 21.026 76.756 21.026L76.756 21.323M75.314 16.401Q75.314 16.210 75.449 16.079Q75.584 15.948 75.779 15.948Q75.900 15.948 76.004 16.011Q76.107 16.073 76.170 16.177Q76.232 16.280 76.232 16.401Q76.232 16.596 76.101 16.731Q75.971 16.866 75.779 16.866Q75.580 16.866 75.447 16.733Q75.314 16.600 75.314 16.401M79.185 21.323L77.330 21.323L77.330 21.026Q77.603 21.026 77.771 20.979Q77.939 20.932 77.939 20.764L77.939 18.628Q77.939 18.413 77.877 18.317Q77.814 18.221 77.695 18.200Q77.576 18.178 77.330 18.178L77.330 17.882L78.521 17.796L78.521 18.530Q78.635 18.315 78.828 18.147Q79.021 17.979 79.260 17.887Q79.498 17.796 79.752 17.796Q80.920 17.796 80.920 18.874L80.920 20.764Q80.920 20.932 81.090 20.979Q81.260 21.026 81.529 21.026L81.529 21.323L79.674 21.323L79.674 21.026Q79.947 21.026 80.115 20.979Q80.283 20.932 80.283 20.764L80.283 18.889Q80.283 18.507 80.162 18.278Q80.041 18.050 79.689 18.050Q79.377 18.050 79.123 18.212Q78.869 18.374 78.722 18.643Q78.576 18.913 78.576 19.210L78.576 20.764Q78.576 20.932 78.746 20.979Q78.916 21.026 79.185 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M84.856 21.315L84.856 20.093Q84.856 20.065 84.888 20.034Q84.919 20.003 84.942 20.003L85.048 20.003Q85.118 20.003 85.134 20.065Q85.196 20.386 85.335 20.626Q85.473 20.866 85.706 21.007Q85.938 21.147 86.247 21.147Q86.485 21.147 86.694 21.087Q86.903 21.026 87.040 20.878Q87.177 20.729 87.177 20.483Q87.177 20.229 86.966 20.063Q86.755 19.897 86.485 19.843L85.864 19.729Q85.458 19.651 85.157 19.395Q84.856 19.139 84.856 18.764Q84.856 18.397 85.057 18.175Q85.259 17.952 85.583 17.854Q85.907 17.757 86.247 17.757Q86.712 17.757 87.009 17.964L87.231 17.780Q87.255 17.757 87.286 17.757L87.337 17.757Q87.368 17.757 87.395 17.784Q87.423 17.811 87.423 17.843L87.423 18.827Q87.423 18.858 87.397 18.887Q87.372 18.917 87.337 18.917L87.231 18.917Q87.196 18.917 87.169 18.889Q87.141 18.862 87.141 18.827Q87.141 18.428 86.889 18.208Q86.638 17.987 86.239 17.987Q85.884 17.987 85.600 18.110Q85.317 18.233 85.317 18.538Q85.317 18.757 85.518 18.889Q85.720 19.022 85.966 19.065L86.591 19.178Q87.020 19.268 87.329 19.565Q87.638 19.862 87.638 20.276Q87.638 20.846 87.239 21.124Q86.841 21.401 86.247 21.401Q85.696 21.401 85.345 21.065L85.048 21.378Q85.024 21.401 84.989 21.401L84.942 21.401Q84.919 21.401 84.888 21.370Q84.856 21.339 84.856 21.315M88.848 20.370L88.848 18.628Q88.848 18.413 88.786 18.317Q88.723 18.221 88.604 18.200Q88.485 18.178 88.239 18.178L88.239 17.882L89.485 17.796L89.485 20.346L89.485 20.370Q89.485 20.682 89.540 20.844Q89.595 21.007 89.745 21.077Q89.895 21.147 90.216 21.147Q90.645 21.147 90.919 20.809Q91.192 20.471 91.192 20.026L91.192 18.628Q91.192 18.413 91.130 18.317Q91.067 18.221 90.948 18.200Q90.829 18.178 90.583 18.178L90.583 17.882L91.829 17.796L91.829 20.581Q91.829 20.792 91.891 20.887Q91.954 20.983 92.073 21.005Q92.192 21.026 92.438 21.026L92.438 21.323L91.216 21.401L91.216 20.780Q91.048 21.069 90.766 21.235Q90.485 21.401 90.165 21.401Q88.848 21.401 88.848 20.370M92.927 19.596Q92.927 19.100 93.177 18.675Q93.427 18.249 93.846 18.003Q94.266 17.757 94.766 17.757Q95.305 17.757 95.696 17.882Q96.087 18.007 96.087 18.421Q96.087 18.526 96.036 18.618Q95.985 18.710 95.893 18.761Q95.802 18.811 95.692 18.811Q95.587 18.811 95.495 18.761Q95.403 18.710 95.352 18.618Q95.302 18.526 95.302 18.421Q95.302 18.198 95.470 18.093Q95.247 18.034 94.774 18.034Q94.477 18.034 94.263 18.173Q94.048 18.311 93.917 18.542Q93.786 18.772 93.727 19.042Q93.669 19.311 93.669 19.596Q93.669 19.991 93.802 20.341Q93.934 20.690 94.206 20.907Q94.477 21.124 94.876 21.124Q95.251 21.124 95.526 20.907Q95.802 20.690 95.903 20.331Q95.919 20.268 95.981 20.268L96.087 20.268Q96.122 20.268 96.147 20.296Q96.173 20.323 96.173 20.362L96.173 20.386Q96.040 20.866 95.655 21.134Q95.270 21.401 94.766 21.401Q94.403 21.401 94.069 21.264Q93.735 21.128 93.475 20.878Q93.216 20.628 93.071 20.292Q92.927 19.956 92.927 19.596\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M98.359 21.323L96.504 21.323L96.504 21.026Q96.777 21.026 96.945 20.979Q97.113 20.932 97.113 20.764L97.113 16.604Q97.113 16.389 97.050 16.294Q96.988 16.198 96.869 16.177Q96.750 16.155 96.504 16.155L96.504 15.858L97.726 15.772L97.726 18.475Q97.851 18.264 98.039 18.114Q98.226 17.964 98.453 17.880Q98.679 17.796 98.925 17.796Q100.093 17.796 100.093 18.874L100.093 20.764Q100.093 20.932 100.263 20.979Q100.433 21.026 100.703 21.026L100.703 21.323L98.847 21.323L98.847 21.026Q99.121 21.026 99.289 20.979Q99.457 20.932 99.457 20.764L99.457 18.889Q99.457 18.507 99.336 18.278Q99.214 18.050 98.863 18.050Q98.550 18.050 98.296 18.212Q98.043 18.374 97.896 18.643Q97.750 18.913 97.750 19.210L97.750 20.764Q97.750 20.932 97.920 20.979Q98.089 21.026 98.359 21.026\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M104.083 20.491Q104.083 20.007 104.485 19.712Q104.888 19.417 105.438 19.298Q105.989 19.178 106.481 19.178L106.481 18.889Q106.481 18.663 106.366 18.456Q106.251 18.249 106.054 18.130Q105.856 18.011 105.626 18.011Q105.200 18.011 104.915 18.116Q104.985 18.143 105.032 18.198Q105.079 18.253 105.104 18.323Q105.130 18.393 105.130 18.468Q105.130 18.573 105.079 18.665Q105.028 18.757 104.936 18.807Q104.845 18.858 104.739 18.858Q104.634 18.858 104.542 18.807Q104.450 18.757 104.399 18.665Q104.349 18.573 104.349 18.468Q104.349 18.050 104.737 17.903Q105.126 17.757 105.626 17.757Q105.958 17.757 106.311 17.887Q106.665 18.018 106.893 18.272Q107.122 18.526 107.122 18.874L107.122 20.675Q107.122 20.807 107.194 20.917Q107.267 21.026 107.395 21.026Q107.520 21.026 107.589 20.921Q107.657 20.815 107.657 20.675L107.657 20.163L107.938 20.163L107.938 20.675Q107.938 20.878 107.821 21.036Q107.704 21.194 107.522 21.278Q107.341 21.362 107.138 21.362Q106.907 21.362 106.755 21.190Q106.602 21.018 106.571 20.788Q106.411 21.069 106.102 21.235Q105.794 21.401 105.442 21.401Q104.931 21.401 104.507 21.178Q104.083 20.956 104.083 20.491M104.770 20.491Q104.770 20.776 104.997 20.962Q105.224 21.147 105.517 21.147Q105.763 21.147 105.987 21.030Q106.212 20.913 106.347 20.710Q106.481 20.507 106.481 20.253L106.481 19.421Q106.216 19.421 105.931 19.475Q105.645 19.530 105.374 19.659Q105.102 19.788 104.936 19.995Q104.770 20.202 104.770 20.491\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(5.731 31.713)\">\u003Cpath d=\"M111.112 21.315L111.112 20.093Q111.112 20.065 111.144 20.034Q111.175 20.003 111.198 20.003L111.304 20.003Q111.374 20.003 111.390 20.065Q111.452 20.386 111.591 20.626Q111.729 20.866 111.962 21.007Q112.194 21.147 112.503 21.147Q112.741 21.147 112.950 21.087Q113.159 21.026 113.296 20.878Q113.433 20.729 113.433 20.483Q113.433 20.229 113.222 20.063Q113.011 19.897 112.741 19.843L112.120 19.729Q111.714 19.651 111.413 19.395Q111.112 19.139 111.112 18.764Q111.112 18.397 111.313 18.175Q111.515 17.952 111.839 17.854Q112.163 17.757 112.503 17.757Q112.968 17.757 113.265 17.964L113.487 17.780Q113.511 17.757 113.542 17.757L113.593 17.757Q113.624 17.757 113.651 17.784Q113.679 17.811 113.679 17.843L113.679 18.827Q113.679 18.858 113.653 18.887Q113.628 18.917 113.593 18.917L113.487 18.917Q113.452 18.917 113.425 18.889Q113.397 18.862 113.397 18.827Q113.397 18.428 113.145 18.208Q112.894 17.987 112.495 17.987Q112.140 17.987 111.856 18.110Q111.573 18.233 111.573 18.538Q111.573 18.757 111.774 18.889Q111.976 19.022 112.222 19.065L112.847 19.178Q113.276 19.268 113.585 19.565Q113.894 19.862 113.894 20.276Q113.894 20.846 113.495 21.124Q113.097 21.401 112.503 21.401Q111.952 21.401 111.601 21.065L111.304 21.378Q111.280 21.401 111.245 21.401L111.198 21.401Q111.175 21.401 111.144 21.370Q111.112 21.339 111.112 21.315M115.046 20.362L115.046 18.171L114.343 18.171L114.343 17.917Q114.698 17.917 114.940 17.684Q115.183 17.452 115.294 17.104Q115.405 16.757 115.405 16.401L115.686 16.401L115.686 17.874L116.862 17.874L116.862 18.171L115.686 18.171L115.686 20.346Q115.686 20.667 115.806 20.895Q115.925 21.124 116.206 21.124Q116.386 21.124 116.503 21.001Q116.620 20.878 116.673 20.698Q116.726 20.518 116.726 20.346L116.726 19.874L117.007 19.874L117.007 20.362Q117.007 20.616 116.901 20.856Q116.796 21.096 116.599 21.249Q116.401 21.401 116.144 21.401Q115.827 21.401 115.575 21.278Q115.323 21.155 115.185 20.921Q115.046 20.686 115.046 20.362M117.823 20.491Q117.823 20.007 118.226 19.712Q118.628 19.417 119.179 19.298Q119.729 19.178 120.222 19.178L120.222 18.889Q120.222 18.663 120.106 18.456Q119.991 18.249 119.794 18.130Q119.597 18.011 119.366 18.011Q118.940 18.011 118.655 18.116Q118.726 18.143 118.772 18.198Q118.819 18.253 118.845 18.323Q118.870 18.393 118.870 18.468Q118.870 18.573 118.819 18.665Q118.769 18.757 118.677 18.807Q118.585 18.858 118.479 18.858Q118.374 18.858 118.282 18.807Q118.190 18.757 118.140 18.665Q118.089 18.573 118.089 18.468Q118.089 18.050 118.477 17.903Q118.866 17.757 119.366 17.757Q119.698 17.757 120.052 17.887Q120.405 18.018 120.634 18.272Q120.862 18.526 120.862 18.874L120.862 20.675Q120.862 20.807 120.935 20.917Q121.007 21.026 121.136 21.026Q121.261 21.026 121.329 20.921Q121.397 20.815 121.397 20.675L121.397 20.163L121.679 20.163L121.679 20.675Q121.679 20.878 121.561 21.036Q121.444 21.194 121.263 21.278Q121.081 21.362 120.878 21.362Q120.647 21.362 120.495 21.190Q120.343 21.018 120.311 20.788Q120.151 21.069 119.843 21.235Q119.534 21.401 119.183 21.401Q118.671 21.401 118.247 21.178Q117.823 20.956 117.823 20.491M118.511 20.491Q118.511 20.776 118.737 20.962Q118.964 21.147 119.257 21.147Q119.503 21.147 119.727 21.030Q119.952 20.913 120.087 20.710Q120.222 20.507 120.222 20.253L120.222 19.421Q119.956 19.421 119.671 19.475Q119.386 19.530 119.114 19.659Q118.843 19.788 118.677 19.995Q118.511 20.202 118.511 20.491M122.597 20.362L122.597 18.171L121.894 18.171L121.894 17.917Q122.249 17.917 122.491 17.684Q122.733 17.452 122.845 17.104Q122.956 16.757 122.956 16.401L123.237 16.401L123.237 17.874L124.413 17.874L124.413 18.171L123.237 18.171L123.237 20.346Q123.237 20.667 123.356 20.895Q123.476 21.124 123.757 21.124Q123.936 21.124 124.054 21.001Q124.171 20.878 124.224 20.698Q124.276 20.518 124.276 20.346L124.276 19.874L124.558 19.874L124.558 20.362Q124.558 20.616 124.452 20.856Q124.347 21.096 124.149 21.249Q123.952 21.401 123.694 21.401Q123.378 21.401 123.126 21.278Q122.874 21.155 122.735 20.921Q122.597 20.686 122.597 20.362M125.276 19.569Q125.276 19.089 125.509 18.673Q125.741 18.257 126.151 18.007Q126.561 17.757 127.038 17.757Q127.769 17.757 128.167 18.198Q128.565 18.639 128.565 19.370Q128.565 19.475 128.472 19.499L126.022 19.499L126.022 19.569Q126.022 19.979 126.144 20.335Q126.265 20.690 126.536 20.907Q126.808 21.124 127.237 21.124Q127.601 21.124 127.897 20.895Q128.194 20.667 128.296 20.315Q128.304 20.268 128.390 20.253L128.472 20.253Q128.565 20.280 128.565 20.362Q128.565 20.370 128.558 20.401Q128.495 20.628 128.356 20.811Q128.218 20.995 128.026 21.128Q127.835 21.261 127.616 21.331Q127.397 21.401 127.159 21.401Q126.788 21.401 126.450 21.264Q126.112 21.128 125.845 20.876Q125.577 20.624 125.427 20.284Q125.276 19.944 125.276 19.569M126.030 19.261L127.991 19.261Q127.991 18.956 127.890 18.665Q127.788 18.374 127.571 18.192Q127.354 18.011 127.038 18.011Q126.737 18.011 126.507 18.198Q126.276 18.386 126.153 18.677Q126.030 18.968 126.030 19.261\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M52.724-27.046c0-6.286-26.443-11.381-59.064-11.381s-59.063 5.095-59.063 11.38S-38.96-15.664-6.34-15.664s59.064-5.096 59.064-11.381Zm-59.064 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M66.788 21.323L65.154 21.323L65.154 21.043Q65.383 21.043 65.532 21.009Q65.681 20.974 65.681 20.834L65.681 17.215Q65.681 16.945 65.573 16.883Q65.465 16.822 65.154 16.822L65.154 16.541L66.234 16.466L66.234 18.852Q66.340 18.667 66.518 18.525Q66.696 18.384 66.904 18.310Q67.113 18.237 67.338 18.237Q67.844 18.237 68.128 18.460Q68.412 18.684 68.412 19.180L68.412 20.834Q68.412 20.971 68.560 21.007Q68.709 21.043 68.935 21.043L68.935 21.323L67.304 21.323L67.304 21.043Q67.533 21.043 67.682 21.009Q67.831 20.974 67.831 20.834L67.831 19.194Q67.831 18.859 67.711 18.659Q67.591 18.459 67.277 18.459Q67.007 18.459 66.773 18.595Q66.539 18.732 66.400 18.966Q66.262 19.200 66.262 19.474L66.262 20.834Q66.262 20.971 66.412 21.007Q66.563 21.043 66.788 21.043L66.788 21.323M69.481 19.840Q69.481 19.498 69.616 19.199Q69.751 18.900 69.991 18.676Q70.230 18.452 70.548 18.327Q70.866 18.202 71.197 18.202Q71.642 18.202 72.042 18.418Q72.441 18.633 72.676 19.011Q72.910 19.388 72.910 19.840Q72.910 20.181 72.768 20.465Q72.626 20.749 72.382 20.956Q72.137 21.162 71.828 21.277Q71.519 21.391 71.197 21.391Q70.767 21.391 70.365 21.190Q69.963 20.988 69.722 20.636Q69.481 20.284 69.481 19.840M71.197 21.142Q71.799 21.142 72.023 20.764Q72.247 20.386 72.247 19.754Q72.247 19.142 72.012 18.783Q71.778 18.425 71.197 18.425Q70.145 18.425 70.145 19.754Q70.145 20.386 70.370 20.764Q70.596 21.142 71.197 21.142\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M74.682 21.296L73.701 18.797Q73.640 18.654 73.522 18.619Q73.404 18.585 73.188 18.585L73.188 18.305L74.668 18.305L74.668 18.585Q74.289 18.585 74.289 18.746Q74.289 18.756 74.303 18.797L75.017 20.629L75.690 18.924Q75.660 18.852 75.660 18.824Q75.660 18.797 75.632 18.797Q75.571 18.650 75.453 18.618Q75.335 18.585 75.123 18.585L75.123 18.305L76.521 18.305L76.521 18.585Q76.145 18.585 76.145 18.746Q76.145 18.777 76.152 18.797L76.907 20.735L77.594 18.985Q77.615 18.934 77.615 18.879Q77.615 18.739 77.502 18.662Q77.389 18.585 77.249 18.585L77.249 18.305L78.469 18.305L78.469 18.585Q78.264 18.585 78.109 18.691Q77.953 18.797 77.881 18.985L76.976 21.296Q76.941 21.391 76.829 21.391L76.760 21.391Q76.651 21.391 76.613 21.296L75.831 19.293L75.044 21.296Q75.010 21.391 74.897 21.391L74.829 21.391Q74.720 21.391 74.682 21.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M82.224 20.482L82.224 18.585L81.585 18.585L81.585 18.363Q81.903 18.363 82.120 18.153Q82.337 17.943 82.437 17.633Q82.538 17.324 82.538 17.016L82.805 17.016L82.805 18.305L83.882 18.305L83.882 18.585L82.805 18.585L82.805 20.469Q82.805 20.745 82.909 20.944Q83.013 21.142 83.273 21.142Q83.430 21.142 83.536 21.038Q83.642 20.933 83.692 20.780Q83.741 20.626 83.741 20.469L83.741 20.055L84.008 20.055L84.008 20.482Q84.008 20.708 83.909 20.918Q83.810 21.128 83.625 21.260Q83.441 21.391 83.212 21.391Q82.774 21.391 82.499 21.154Q82.224 20.916 82.224 20.482M86.500 21.323L84.866 21.323L84.866 21.043Q85.095 21.043 85.244 21.009Q85.392 20.974 85.392 20.834L85.392 17.215Q85.392 16.945 85.285 16.883Q85.177 16.822 84.866 16.822L84.866 16.541L85.946 16.466L85.946 18.852Q86.052 18.667 86.230 18.525Q86.407 18.384 86.616 18.310Q86.824 18.237 87.050 18.237Q87.556 18.237 87.840 18.460Q88.123 18.684 88.123 19.180L88.123 20.834Q88.123 20.971 88.272 21.007Q88.421 21.043 88.646 21.043L88.646 21.323L87.016 21.323L87.016 21.043Q87.245 21.043 87.393 21.009Q87.542 20.974 87.542 20.834L87.542 19.194Q87.542 18.859 87.423 18.659Q87.303 18.459 86.988 18.459Q86.718 18.459 86.484 18.595Q86.250 18.732 86.112 18.966Q85.973 19.200 85.973 19.474L85.973 20.834Q85.973 20.971 86.124 21.007Q86.274 21.043 86.500 21.043L86.500 21.323M89.193 19.788Q89.193 19.467 89.318 19.178Q89.443 18.889 89.668 18.666Q89.894 18.442 90.189 18.322Q90.485 18.202 90.803 18.202Q91.131 18.202 91.393 18.302Q91.654 18.401 91.830 18.583Q92.006 18.766 92.100 19.024Q92.194 19.282 92.194 19.614Q92.194 19.706 92.112 19.727L89.856 19.727L89.856 19.788Q89.856 20.376 90.140 20.759Q90.424 21.142 90.991 21.142Q91.312 21.142 91.581 20.949Q91.849 20.756 91.938 20.441Q91.945 20.400 92.020 20.386L92.112 20.386Q92.194 20.410 92.194 20.482Q92.194 20.489 92.187 20.516Q92.074 20.913 91.704 21.152Q91.333 21.391 90.909 21.391Q90.471 21.391 90.071 21.183Q89.672 20.974 89.432 20.607Q89.193 20.240 89.193 19.788M89.863 19.518L91.678 19.518Q91.678 19.241 91.581 18.989Q91.483 18.736 91.285 18.580Q91.087 18.425 90.803 18.425Q90.526 18.425 90.312 18.583Q90.099 18.742 89.981 18.997Q89.863 19.252 89.863 19.518\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M96.876 21.296L95.895 18.797Q95.834 18.654 95.716 18.619Q95.598 18.585 95.382 18.585L95.382 18.305L96.862 18.305L96.862 18.585Q96.483 18.585 96.483 18.746Q96.483 18.756 96.497 18.797L97.211 20.629L97.884 18.924Q97.854 18.852 97.854 18.824Q97.854 18.797 97.826 18.797Q97.765 18.650 97.647 18.618Q97.529 18.585 97.317 18.585L97.317 18.305L98.715 18.305L98.715 18.585Q98.339 18.585 98.339 18.746Q98.339 18.777 98.346 18.797L99.101 20.735L99.788 18.985Q99.809 18.934 99.809 18.879Q99.809 18.739 99.696 18.662Q99.583 18.585 99.443 18.585L99.443 18.305L100.663 18.305L100.663 18.585Q100.458 18.585 100.303 18.691Q100.147 18.797 100.075 18.985L99.170 21.296Q99.135 21.391 99.023 21.391L98.954 21.391Q98.845 21.391 98.807 21.296L98.025 19.293L97.238 21.296Q97.204 21.391 97.091 21.391L97.023 21.391Q96.914 21.391 96.876 21.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M100.941 19.840Q100.941 19.498 101.076 19.199Q101.211 18.900 101.451 18.676Q101.690 18.452 102.008 18.327Q102.326 18.202 102.657 18.202Q103.102 18.202 103.501 18.418Q103.901 18.633 104.136 19.011Q104.370 19.388 104.370 19.840Q104.370 20.181 104.228 20.465Q104.086 20.749 103.842 20.956Q103.597 21.162 103.288 21.277Q102.979 21.391 102.657 21.391Q102.227 21.391 101.825 21.190Q101.423 20.988 101.182 20.636Q100.941 20.284 100.941 19.840M102.657 21.142Q103.259 21.142 103.483 20.764Q103.707 20.386 103.707 19.754Q103.707 19.142 103.472 18.783Q103.238 18.425 102.657 18.425Q101.605 18.425 101.605 19.754Q101.605 20.386 101.830 20.764Q102.056 21.142 102.657 21.142M106.714 21.323L104.978 21.323L104.978 21.043Q105.207 21.043 105.356 21.009Q105.504 20.974 105.504 20.834L105.504 18.985Q105.504 18.715 105.397 18.654Q105.289 18.592 104.978 18.592L104.978 18.312L106.007 18.237L106.007 18.944Q106.137 18.636 106.379 18.437Q106.622 18.237 106.940 18.237Q107.159 18.237 107.330 18.361Q107.501 18.486 107.501 18.698Q107.501 18.835 107.401 18.934Q107.302 19.033 107.169 19.033Q107.032 19.033 106.933 18.934Q106.834 18.835 106.834 18.698Q106.834 18.558 106.933 18.459Q106.643 18.459 106.443 18.655Q106.243 18.852 106.150 19.146Q106.058 19.440 106.058 19.720L106.058 20.834Q106.058 21.043 106.714 21.043L106.714 21.323M109.753 21.323L108.150 21.323L108.150 21.043Q108.376 21.043 108.524 21.009Q108.673 20.974 108.673 20.834L108.673 17.215Q108.673 16.945 108.565 16.883Q108.458 16.822 108.150 16.822L108.150 16.541L109.227 16.466L109.227 20.834Q109.227 20.971 109.377 21.007Q109.527 21.043 109.753 21.043L109.753 21.323M110.348 19.812Q110.348 19.474 110.488 19.183Q110.628 18.893 110.872 18.679Q111.117 18.466 111.421 18.351Q111.725 18.237 112.050 18.237Q112.320 18.237 112.583 18.336Q112.846 18.435 113.038 18.613L113.038 17.215Q113.038 16.945 112.930 16.883Q112.822 16.822 112.511 16.822L112.511 16.541L113.588 16.466L113.588 20.650Q113.588 20.838 113.643 20.921Q113.697 21.005 113.798 21.024Q113.899 21.043 114.114 21.043L114.114 21.323L113.007 21.391L113.007 20.974Q112.590 21.391 111.964 21.391Q111.534 21.391 111.161 21.179Q110.789 20.968 110.568 20.607Q110.348 20.246 110.348 19.812M112.022 21.169Q112.231 21.169 112.417 21.097Q112.604 21.026 112.757 20.889Q112.911 20.752 113.007 20.574L113.007 18.965Q112.921 18.818 112.776 18.698Q112.631 18.578 112.462 18.519Q112.293 18.459 112.111 18.459Q111.551 18.459 111.283 18.848Q111.014 19.238 111.014 19.819Q111.014 20.390 111.248 20.780Q111.482 21.169 112.022 21.169\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M117.427 19.788Q117.427 19.467 117.552 19.178Q117.677 18.889 117.903 18.666Q118.128 18.442 118.424 18.322Q118.719 18.202 119.037 18.202Q119.365 18.202 119.627 18.302Q119.888 18.401 120.064 18.583Q120.240 18.766 120.334 19.024Q120.428 19.282 120.428 19.614Q120.428 19.706 120.346 19.727L118.091 19.727L118.091 19.788Q118.091 20.376 118.374 20.759Q118.658 21.142 119.225 21.142Q119.547 21.142 119.815 20.949Q120.083 20.756 120.172 20.441Q120.179 20.400 120.254 20.386L120.346 20.386Q120.428 20.410 120.428 20.482Q120.428 20.489 120.422 20.516Q120.309 20.913 119.938 21.152Q119.567 21.391 119.143 21.391Q118.706 21.391 118.306 21.183Q117.906 20.974 117.667 20.607Q117.427 20.240 117.427 19.788M118.097 19.518L119.912 19.518Q119.912 19.241 119.815 18.989Q119.717 18.736 119.519 18.580Q119.321 18.425 119.037 18.425Q118.760 18.425 118.547 18.583Q118.333 18.742 118.215 18.997Q118.097 19.252 118.097 19.518M122.606 21.296L121.478 18.797Q121.406 18.650 121.276 18.618Q121.146 18.585 120.917 18.585L120.917 18.305L122.431 18.305L122.431 18.585Q122.079 18.585 122.079 18.732Q122.079 18.777 122.090 18.797L122.954 20.715L123.734 18.985Q123.768 18.917 123.768 18.838Q123.768 18.725 123.684 18.655Q123.600 18.585 123.481 18.585L123.481 18.305L124.677 18.305L124.677 18.585Q124.458 18.585 124.287 18.688Q124.116 18.790 124.028 18.985L122.992 21.296Q122.944 21.391 122.838 21.391L122.759 21.391Q122.654 21.391 122.606 21.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M124.968 19.840Q124.968 19.498 125.103 19.199Q125.238 18.900 125.478 18.676Q125.717 18.452 126.035 18.327Q126.353 18.202 126.684 18.202Q127.129 18.202 127.528 18.418Q127.928 18.633 128.163 19.011Q128.397 19.388 128.397 19.840Q128.397 20.181 128.255 20.465Q128.113 20.749 127.869 20.956Q127.624 21.162 127.315 21.277Q127.006 21.391 126.684 21.391Q126.254 21.391 125.852 21.190Q125.450 20.988 125.209 20.636Q124.968 20.284 124.968 19.840M126.684 21.142Q127.286 21.142 127.510 20.764Q127.734 20.386 127.734 19.754Q127.734 19.142 127.499 18.783Q127.265 18.425 126.684 18.425Q125.632 18.425 125.632 19.754Q125.632 20.386 125.857 20.764Q126.083 21.142 126.684 21.142M130.659 21.323L129.056 21.323L129.056 21.043Q129.282 21.043 129.431 21.009Q129.579 20.974 129.579 20.834L129.579 17.215Q129.579 16.945 129.472 16.883Q129.364 16.822 129.056 16.822L129.056 16.541L130.133 16.466L130.133 20.834Q130.133 20.971 130.283 21.007Q130.434 21.043 130.659 21.043L130.659 21.323M132.843 21.296L131.716 18.797Q131.644 18.650 131.514 18.618Q131.384 18.585 131.155 18.585L131.155 18.305L132.669 18.305L132.669 18.585Q132.317 18.585 132.317 18.732Q132.317 18.777 132.327 18.797L133.192 20.715L133.971 18.985Q134.006 18.917 134.006 18.838Q134.006 18.725 133.922 18.655Q133.838 18.585 133.718 18.585L133.718 18.305L134.915 18.305L134.915 18.585Q134.696 18.585 134.525 18.688Q134.354 18.790 134.265 18.985L133.230 21.296Q133.182 21.391 133.076 21.391L132.997 21.391Q132.891 21.391 132.843 21.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-109.563 -45.939)\">\u003Cpath d=\"M135.205 19.788Q135.205 19.467 135.330 19.178Q135.455 18.889 135.681 18.666Q135.906 18.442 136.202 18.322Q136.497 18.202 136.815 18.202Q137.143 18.202 137.405 18.302Q137.666 18.401 137.842 18.583Q138.018 18.766 138.112 19.024Q138.206 19.282 138.206 19.614Q138.206 19.706 138.124 19.727L135.869 19.727L135.869 19.788Q135.869 20.376 136.152 20.759Q136.436 21.142 137.003 21.142Q137.325 21.142 137.593 20.949Q137.861 20.756 137.950 20.441Q137.957 20.400 138.032 20.386L138.124 20.386Q138.206 20.410 138.206 20.482Q138.206 20.489 138.200 20.516Q138.087 20.913 137.716 21.152Q137.345 21.391 136.921 21.391Q136.484 21.391 136.084 21.183Q135.684 20.974 135.445 20.607Q135.205 20.240 135.205 19.788M135.875 19.518L137.690 19.518Q137.690 19.241 137.593 18.989Q137.495 18.736 137.297 18.580Q137.099 18.425 136.815 18.425Q136.538 18.425 136.325 18.583Q136.111 18.742 135.993 18.997Q135.875 19.252 135.875 19.518M138.794 21.316L138.794 20.253Q138.794 20.229 138.822 20.202Q138.849 20.175 138.873 20.175L138.982 20.175Q139.047 20.175 139.061 20.233Q139.157 20.667 139.403 20.918Q139.649 21.169 140.062 21.169Q140.404 21.169 140.657 21.036Q140.910 20.903 140.910 20.595Q140.910 20.438 140.816 20.323Q140.722 20.209 140.584 20.140Q140.445 20.072 140.278 20.034L139.697 19.935Q139.341 19.867 139.068 19.646Q138.794 19.426 138.794 19.084Q138.794 18.835 138.905 18.660Q139.016 18.486 139.203 18.387Q139.389 18.288 139.604 18.245Q139.820 18.202 140.062 18.202Q140.476 18.202 140.756 18.384L140.972 18.209Q140.982 18.206 140.989 18.204Q140.995 18.202 141.006 18.202L141.057 18.202Q141.084 18.202 141.108 18.226Q141.132 18.250 141.132 18.278L141.132 19.125Q141.132 19.146 141.108 19.173Q141.084 19.200 141.057 19.200L140.944 19.200Q140.917 19.200 140.891 19.175Q140.866 19.149 140.866 19.125Q140.866 18.889 140.760 18.725Q140.654 18.561 140.471 18.479Q140.288 18.397 140.056 18.397Q139.727 18.397 139.471 18.500Q139.215 18.602 139.215 18.879Q139.215 19.074 139.398 19.183Q139.580 19.293 139.809 19.334L140.384 19.440Q140.630 19.488 140.843 19.616Q141.057 19.744 141.194 19.947Q141.330 20.151 141.330 20.400Q141.330 20.913 140.965 21.152Q140.599 21.391 140.062 21.391Q139.567 21.391 139.235 21.097L138.969 21.371Q138.948 21.391 138.921 21.391L138.873 21.391Q138.849 21.391 138.822 21.364Q138.794 21.337 138.794 21.316\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M47.009 2.83c0-6.286-23.885-11.382-53.349-11.382S-59.688-3.456-59.688 2.83-35.803 14.21-6.34 14.21c29.464 0 53.349-5.095 53.349-11.38Zm-53.349 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-105.522 -16.744)\">\u003Cpath d=\"M66.494 21.296L65.513 18.797Q65.452 18.654 65.334 18.619Q65.216 18.585 65 18.585L65 18.305L66.480 18.305L66.480 18.585Q66.101 18.585 66.101 18.746Q66.101 18.756 66.115 18.797L66.829 20.629L67.502 18.924Q67.472 18.852 67.472 18.824Q67.472 18.797 67.444 18.797Q67.383 18.650 67.265 18.618Q67.147 18.585 66.935 18.585L66.935 18.305L68.333 18.305L68.333 18.585Q67.957 18.585 67.957 18.746Q67.957 18.777 67.964 18.797L68.719 20.735L69.406 18.985Q69.427 18.934 69.427 18.879Q69.427 18.739 69.314 18.662Q69.201 18.585 69.061 18.585L69.061 18.305L70.281 18.305L70.281 18.585Q70.076 18.585 69.921 18.691Q69.765 18.797 69.693 18.985L68.788 21.296Q68.753 21.391 68.641 21.391L68.572 21.391Q68.463 21.391 68.425 21.296L67.643 19.293L66.856 21.296Q66.822 21.391 66.709 21.391L66.641 21.391Q66.532 21.391 66.494 21.296M72.493 21.323L70.859 21.323L70.859 21.043Q71.088 21.043 71.237 21.009Q71.385 20.974 71.385 20.834L71.385 17.215Q71.385 16.945 71.278 16.883Q71.170 16.822 70.859 16.822L70.859 16.541L71.939 16.466L71.939 18.852Q72.045 18.667 72.223 18.525Q72.400 18.384 72.609 18.310Q72.817 18.237 73.043 18.237Q73.549 18.237 73.833 18.460Q74.116 18.684 74.116 19.180L74.116 20.834Q74.116 20.971 74.265 21.007Q74.414 21.043 74.639 21.043L74.639 21.323L73.009 21.323L73.009 21.043Q73.238 21.043 73.386 21.009Q73.535 20.974 73.535 20.834L73.535 19.194Q73.535 18.859 73.416 18.659Q73.296 18.459 72.981 18.459Q72.711 18.459 72.477 18.595Q72.243 18.732 72.105 18.966Q71.966 19.200 71.966 19.474L71.966 20.834Q71.966 20.971 72.117 21.007Q72.267 21.043 72.493 21.043L72.493 21.323M75.285 20.595Q75.285 20.263 75.509 20.036Q75.733 19.809 76.076 19.681Q76.420 19.552 76.792 19.500Q77.165 19.447 77.469 19.447L77.469 19.194Q77.469 18.989 77.362 18.809Q77.254 18.630 77.073 18.527Q76.892 18.425 76.683 18.425Q76.276 18.425 76.041 18.517Q76.129 18.554 76.176 18.638Q76.222 18.722 76.222 18.824Q76.222 18.920 76.176 18.999Q76.129 19.077 76.049 19.122Q75.969 19.166 75.880 19.166Q75.730 19.166 75.629 19.069Q75.528 18.971 75.528 18.824Q75.528 18.202 76.683 18.202Q76.895 18.202 77.145 18.266Q77.394 18.329 77.596 18.448Q77.797 18.568 77.924 18.753Q78.050 18.937 78.050 19.180L78.050 20.756Q78.050 20.872 78.112 20.968Q78.173 21.063 78.286 21.063Q78.396 21.063 78.460 20.969Q78.525 20.875 78.525 20.756L78.525 20.308L78.792 20.308L78.792 20.756Q78.792 21.026 78.565 21.191Q78.337 21.357 78.057 21.357Q77.849 21.357 77.712 21.203Q77.575 21.050 77.551 20.834Q77.404 21.101 77.122 21.246Q76.840 21.391 76.516 21.391Q76.239 21.391 75.955 21.316Q75.671 21.241 75.478 21.062Q75.285 20.882 75.285 20.595M75.900 20.595Q75.900 20.769 76.001 20.899Q76.102 21.029 76.258 21.099Q76.413 21.169 76.577 21.169Q76.796 21.169 77.004 21.072Q77.213 20.974 77.341 20.793Q77.469 20.612 77.469 20.386L77.469 19.658Q77.145 19.658 76.779 19.749Q76.413 19.840 76.157 20.052Q75.900 20.263 75.900 20.595M79.735 20.482L79.735 18.585L79.096 18.585L79.096 18.363Q79.414 18.363 79.631 18.153Q79.848 17.943 79.949 17.633Q80.050 17.324 80.050 17.016L80.316 17.016L80.316 18.305L81.393 18.305L81.393 18.585L80.316 18.585L80.316 20.469Q80.316 20.745 80.421 20.944Q80.525 21.142 80.785 21.142Q80.942 21.142 81.048 21.038Q81.154 20.933 81.203 20.780Q81.253 20.626 81.253 20.469L81.253 20.055L81.520 20.055L81.520 20.482Q81.520 20.708 81.420 20.918Q81.321 21.128 81.137 21.260Q80.952 21.391 80.723 21.391Q80.286 21.391 80.011 21.154Q79.735 20.916 79.735 20.482\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -16.744)\">\u003Cpath d=\"M86.719 21.323L85.085 21.323L85.085 21.043Q85.314 21.043 85.463 21.009Q85.612 20.974 85.612 20.834L85.612 18.985Q85.612 18.715 85.504 18.654Q85.396 18.592 85.085 18.592L85.085 18.312L86.145 18.237L86.145 18.886Q86.316 18.578 86.620 18.407Q86.924 18.237 87.269 18.237Q87.669 18.237 87.946 18.377Q88.223 18.517 88.308 18.865Q88.476 18.572 88.775 18.404Q89.074 18.237 89.419 18.237Q89.925 18.237 90.209 18.460Q90.493 18.684 90.493 19.180L90.493 20.834Q90.493 20.971 90.641 21.007Q90.790 21.043 91.015 21.043L91.015 21.323L89.385 21.323L89.385 21.043Q89.611 21.043 89.761 21.007Q89.911 20.971 89.911 20.834L89.911 19.194Q89.911 18.859 89.792 18.659Q89.672 18.459 89.358 18.459Q89.088 18.459 88.854 18.595Q88.619 18.732 88.481 18.966Q88.343 19.200 88.343 19.474L88.343 20.834Q88.343 20.971 88.491 21.007Q88.640 21.043 88.866 21.043L88.866 21.323L87.235 21.323L87.235 21.043Q87.464 21.043 87.613 21.009Q87.762 20.974 87.762 20.834L87.762 19.194Q87.762 18.859 87.642 18.659Q87.522 18.459 87.208 18.459Q86.938 18.459 86.704 18.595Q86.470 18.732 86.331 18.966Q86.193 19.200 86.193 19.474L86.193 20.834Q86.193 20.971 86.343 21.007Q86.494 21.043 86.719 21.043\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -16.744)\">\u003Cpath d=\"M91.726 22.458Q91.856 22.526 91.993 22.526Q92.164 22.526 92.314 22.437Q92.465 22.348 92.576 22.203Q92.687 22.058 92.765 21.890L93.029 21.323L91.860 18.797Q91.785 18.650 91.655 18.618Q91.525 18.585 91.292 18.585L91.292 18.305L92.813 18.305L92.813 18.585Q92.465 18.585 92.465 18.732Q92.468 18.753 92.470 18.770Q92.472 18.787 92.472 18.797L93.329 20.656L94.102 18.985Q94.136 18.917 94.136 18.838Q94.136 18.725 94.052 18.655Q93.969 18.585 93.856 18.585L93.856 18.305L95.052 18.305L95.052 18.585Q94.833 18.585 94.661 18.689Q94.488 18.794 94.396 18.985L93.059 21.890Q92.889 22.260 92.619 22.506Q92.348 22.752 91.993 22.752Q91.723 22.752 91.504 22.586Q91.285 22.420 91.285 22.157Q91.285 22.020 91.378 21.931Q91.470 21.843 91.610 21.843Q91.747 21.843 91.836 21.931Q91.925 22.020 91.925 22.157Q91.925 22.260 91.872 22.338Q91.819 22.417 91.726 22.458\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -16.744)\">\u003Cpath d=\"M98.346 20.595Q98.346 20.263 98.569 20.036Q98.793 19.809 99.137 19.681Q99.480 19.552 99.853 19.500Q100.225 19.447 100.530 19.447L100.530 19.194Q100.530 18.989 100.422 18.809Q100.314 18.630 100.133 18.527Q99.952 18.425 99.744 18.425Q99.337 18.425 99.101 18.517Q99.190 18.554 99.236 18.638Q99.282 18.722 99.282 18.824Q99.282 18.920 99.236 18.999Q99.190 19.077 99.109 19.122Q99.029 19.166 98.940 19.166Q98.790 19.166 98.689 19.069Q98.588 18.971 98.588 18.824Q98.588 18.202 99.744 18.202Q99.955 18.202 100.205 18.266Q100.454 18.329 100.656 18.448Q100.858 18.568 100.984 18.753Q101.111 18.937 101.111 19.180L101.111 20.756Q101.111 20.872 101.172 20.968Q101.234 21.063 101.347 21.063Q101.456 21.063 101.521 20.969Q101.586 20.875 101.586 20.756L101.586 20.308L101.852 20.308L101.852 20.756Q101.852 21.026 101.625 21.191Q101.398 21.357 101.118 21.357Q100.909 21.357 100.772 21.203Q100.636 21.050 100.612 20.834Q100.465 21.101 100.183 21.246Q99.901 21.391 99.576 21.391Q99.299 21.391 99.015 21.316Q98.732 21.241 98.539 21.062Q98.346 20.882 98.346 20.595M98.961 20.595Q98.961 20.769 99.062 20.899Q99.162 21.029 99.318 21.099Q99.473 21.169 99.638 21.169Q99.856 21.169 100.065 21.072Q100.273 20.974 100.401 20.793Q100.530 20.612 100.530 20.386L100.530 19.658Q100.205 19.658 99.839 19.749Q99.473 19.840 99.217 20.052Q98.961 20.263 98.961 20.595M102.269 19.812Q102.269 19.484 102.404 19.183Q102.539 18.883 102.775 18.662Q103.011 18.442 103.315 18.322Q103.619 18.202 103.944 18.202Q104.450 18.202 104.799 18.305Q105.147 18.407 105.147 18.783Q105.147 18.930 105.050 19.031Q104.952 19.132 104.806 19.132Q104.652 19.132 104.553 19.033Q104.453 18.934 104.453 18.783Q104.453 18.595 104.594 18.503Q104.392 18.452 103.951 18.452Q103.596 18.452 103.367 18.648Q103.138 18.845 103.037 19.154Q102.936 19.464 102.936 19.812Q102.936 20.161 103.062 20.467Q103.189 20.773 103.443 20.957Q103.698 21.142 104.054 21.142Q104.276 21.142 104.460 21.058Q104.645 20.974 104.780 20.819Q104.915 20.663 104.973 20.455Q104.987 20.400 105.041 20.400L105.154 20.400Q105.185 20.400 105.207 20.424Q105.229 20.448 105.229 20.482L105.229 20.503Q105.144 20.790 104.956 20.988Q104.768 21.186 104.503 21.289Q104.238 21.391 103.944 21.391Q103.514 21.391 103.126 21.185Q102.738 20.978 102.504 20.615Q102.269 20.253 102.269 19.812M106.344 20.482L106.344 18.585L105.704 18.585L105.704 18.363Q106.022 18.363 106.239 18.153Q106.456 17.943 106.557 17.633Q106.658 17.324 106.658 17.016L106.925 17.016L106.925 18.305L108.001 18.305L108.001 18.585L106.925 18.585L106.925 20.469Q106.925 20.745 107.029 20.944Q107.133 21.142 107.393 21.142Q107.550 21.142 107.656 21.038Q107.762 20.933 107.812 20.780Q107.861 20.626 107.861 20.469L107.861 20.055L108.128 20.055L108.128 20.482Q108.128 20.708 108.029 20.918Q107.930 21.128 107.745 21.260Q107.560 21.391 107.331 21.391Q106.894 21.391 106.619 21.154Q106.344 20.916 106.344 20.482M110.555 21.323L109.003 21.323L109.003 21.043Q109.228 21.043 109.377 21.009Q109.526 20.974 109.526 20.834L109.526 18.985Q109.526 18.797 109.478 18.713Q109.430 18.630 109.333 18.611Q109.235 18.592 109.023 18.592L109.023 18.312L110.079 18.237L110.079 20.834Q110.079 20.974 110.211 21.009Q110.343 21.043 110.555 21.043L110.555 21.323M109.283 17.016Q109.283 16.845 109.406 16.726Q109.529 16.606 109.700 16.606Q109.868 16.606 109.991 16.726Q110.114 16.845 110.114 17.016Q110.114 17.191 109.991 17.314Q109.868 17.437 109.700 17.437Q109.529 17.437 109.406 17.314Q109.283 17.191 109.283 17.016M111.160 19.840Q111.160 19.498 111.295 19.199Q111.430 18.900 111.669 18.676Q111.908 18.452 112.226 18.327Q112.544 18.202 112.875 18.202Q113.320 18.202 113.720 18.418Q114.119 18.633 114.354 19.011Q114.588 19.388 114.588 19.840Q114.588 20.181 114.446 20.465Q114.304 20.749 114.060 20.956Q113.815 21.162 113.506 21.277Q113.197 21.391 112.875 21.391Q112.445 21.391 112.043 21.190Q111.641 20.988 111.400 20.636Q111.160 20.284 111.160 19.840M112.875 21.142Q113.477 21.142 113.701 20.764Q113.925 20.386 113.925 19.754Q113.925 19.142 113.691 18.783Q113.456 18.425 112.875 18.425Q111.823 18.425 111.823 19.754Q111.823 20.386 112.048 20.764Q112.274 21.142 112.875 21.142M116.864 21.323L115.230 21.323L115.230 21.043Q115.459 21.043 115.608 21.009Q115.757 20.974 115.757 20.834L115.757 18.985Q115.757 18.715 115.649 18.654Q115.541 18.592 115.230 18.592L115.230 18.312L116.290 18.237L116.290 18.886Q116.461 18.578 116.765 18.407Q117.069 18.237 117.414 18.237Q117.920 18.237 118.204 18.460Q118.488 18.684 118.488 19.180L118.488 20.834Q118.488 20.971 118.636 21.007Q118.785 21.043 119.011 21.043L119.011 21.323L117.380 21.323L117.380 21.043Q117.609 21.043 117.758 21.009Q117.907 20.974 117.907 20.834L117.907 19.194Q117.907 18.859 117.787 18.659Q117.667 18.459 117.353 18.459Q117.083 18.459 116.849 18.595Q116.615 18.732 116.476 18.966Q116.338 19.200 116.338 19.474L116.338 20.834Q116.338 20.971 116.488 21.007Q116.639 21.043 116.864 21.043L116.864 21.323M119.598 21.316L119.598 20.253Q119.598 20.229 119.626 20.202Q119.653 20.175 119.677 20.175L119.786 20.175Q119.851 20.175 119.865 20.233Q119.961 20.667 120.207 20.918Q120.453 21.169 120.867 21.169Q121.208 21.169 121.461 21.036Q121.714 20.903 121.714 20.595Q121.714 20.438 121.620 20.323Q121.526 20.209 121.388 20.140Q121.249 20.072 121.082 20.034L120.501 19.935Q120.145 19.867 119.872 19.646Q119.598 19.426 119.598 19.084Q119.598 18.835 119.710 18.660Q119.821 18.486 120.007 18.387Q120.193 18.288 120.409 18.245Q120.624 18.202 120.867 18.202Q121.280 18.202 121.560 18.384L121.776 18.209Q121.786 18.206 121.793 18.204Q121.800 18.202 121.810 18.202L121.861 18.202Q121.889 18.202 121.912 18.226Q121.936 18.250 121.936 18.278L121.936 19.125Q121.936 19.146 121.912 19.173Q121.889 19.200 121.861 19.200L121.748 19.200Q121.721 19.200 121.695 19.175Q121.670 19.149 121.670 19.125Q121.670 18.889 121.564 18.725Q121.458 18.561 121.275 18.479Q121.092 18.397 120.860 18.397Q120.532 18.397 120.275 18.500Q120.019 18.602 120.019 18.879Q120.019 19.074 120.202 19.183Q120.385 19.293 120.614 19.334L121.188 19.440Q121.434 19.488 121.648 19.616Q121.861 19.744 121.998 19.947Q122.135 20.151 122.135 20.400Q122.135 20.913 121.769 21.152Q121.403 21.391 120.867 21.391Q120.371 21.391 120.039 21.097L119.773 21.371Q119.752 21.391 119.725 21.391L119.677 21.391Q119.653 21.391 119.626 21.364Q119.598 21.337 119.598 21.316\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-105.522 -16.744)\">\u003Cpath d=\"M125.483 19.812Q125.483 19.474 125.624 19.183Q125.764 18.893 126.008 18.679Q126.252 18.466 126.557 18.351Q126.861 18.237 127.186 18.237Q127.456 18.237 127.719 18.336Q127.982 18.435 128.173 18.613L128.173 17.215Q128.173 16.945 128.066 16.883Q127.958 16.822 127.647 16.822L127.647 16.541L128.724 16.466L128.724 20.650Q128.724 20.838 128.778 20.921Q128.833 21.005 128.934 21.024Q129.035 21.043 129.250 21.043L129.250 21.323L128.143 21.391L128.143 20.974Q127.726 21.391 127.100 21.391Q126.669 21.391 126.297 21.179Q125.924 20.968 125.704 20.607Q125.483 20.246 125.483 19.812M127.158 21.169Q127.367 21.169 127.553 21.097Q127.739 21.026 127.893 20.889Q128.047 20.752 128.143 20.574L128.143 18.965Q128.057 18.818 127.912 18.698Q127.767 18.578 127.597 18.519Q127.428 18.459 127.247 18.459Q126.687 18.459 126.418 18.848Q126.150 19.238 126.150 19.819Q126.150 20.390 126.384 20.780Q126.618 21.169 127.158 21.169M129.858 19.840Q129.858 19.498 129.993 19.199Q130.128 18.900 130.368 18.676Q130.607 18.452 130.925 18.327Q131.243 18.202 131.574 18.202Q132.019 18.202 132.419 18.418Q132.818 18.633 133.053 19.011Q133.287 19.388 133.287 19.840Q133.287 20.181 133.145 20.465Q133.003 20.749 132.759 20.956Q132.514 21.162 132.205 21.277Q131.896 21.391 131.574 21.391Q131.144 21.391 130.742 21.190Q130.340 20.988 130.099 20.636Q129.858 20.284 129.858 19.840M131.574 21.142Q132.176 21.142 132.400 20.764Q132.624 20.386 132.624 19.754Q132.624 19.142 132.389 18.783Q132.155 18.425 131.574 18.425Q130.522 18.425 130.522 19.754Q130.522 20.386 130.747 20.764Q130.973 21.142 131.574 21.142\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M36.34 46.93c0-6.285-19.108-11.38-42.68-11.38-23.57 0-42.679 5.095-42.679 11.38s19.108 11.382 42.68 11.382c23.57 0 42.679-5.096 42.679-11.381Zm-42.68 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-81.854 27.357)\">\u003Cpath d=\"M65.681 20.489L65.681 18.985Q65.681 18.715 65.573 18.654Q65.465 18.592 65.154 18.592L65.154 18.312L66.262 18.237L66.262 20.469L66.262 20.489Q66.262 20.769 66.313 20.913Q66.364 21.056 66.506 21.113Q66.648 21.169 66.935 21.169Q67.188 21.169 67.393 21.029Q67.598 20.889 67.714 20.663Q67.831 20.438 67.831 20.188L67.831 18.985Q67.831 18.715 67.723 18.654Q67.615 18.592 67.304 18.592L67.304 18.312L68.412 18.237L68.412 20.650Q68.412 20.841 68.465 20.923Q68.518 21.005 68.618 21.024Q68.719 21.043 68.935 21.043L68.935 21.323L67.858 21.391L67.858 20.827Q67.749 21.009 67.603 21.132Q67.458 21.255 67.272 21.323Q67.085 21.391 66.884 21.391Q65.681 21.391 65.681 20.489M70.049 20.482L70.049 18.585L69.410 18.585L69.410 18.363Q69.728 18.363 69.945 18.153Q70.162 17.943 70.262 17.633Q70.363 17.324 70.363 17.016L70.630 17.016L70.630 18.305L71.707 18.305L71.707 18.585L70.630 18.585L70.630 20.469Q70.630 20.745 70.734 20.944Q70.838 21.142 71.098 21.142Q71.255 21.142 71.361 21.038Q71.467 20.933 71.517 20.780Q71.566 20.626 71.566 20.469L71.566 20.055L71.833 20.055L71.833 20.482Q71.833 20.708 71.734 20.918Q71.635 21.128 71.450 21.260Q71.266 21.391 71.037 21.391Q70.599 21.391 70.324 21.154Q70.049 20.916 70.049 20.482M74.260 21.323L72.708 21.323L72.708 21.043Q72.934 21.043 73.082 21.009Q73.231 20.974 73.231 20.834L73.231 18.985Q73.231 18.797 73.183 18.713Q73.135 18.630 73.038 18.611Q72.940 18.592 72.729 18.592L72.729 18.312L73.785 18.237L73.785 20.834Q73.785 20.974 73.916 21.009Q74.048 21.043 74.260 21.043L74.260 21.323M72.988 17.016Q72.988 16.845 73.111 16.726Q73.234 16.606 73.405 16.606Q73.573 16.606 73.696 16.726Q73.819 16.845 73.819 17.016Q73.819 17.191 73.696 17.314Q73.573 17.437 73.405 17.437Q73.234 17.437 73.111 17.314Q72.988 17.191 72.988 17.016M76.574 21.323L74.971 21.323L74.971 21.043Q75.196 21.043 75.345 21.009Q75.494 20.974 75.494 20.834L75.494 17.215Q75.494 16.945 75.386 16.883Q75.278 16.822 74.971 16.822L74.971 16.541L76.047 16.466L76.047 20.834Q76.047 20.971 76.198 21.007Q76.348 21.043 76.574 21.043L76.574 21.323M78.785 21.323L77.233 21.323L77.233 21.043Q77.459 21.043 77.608 21.009Q77.756 20.974 77.756 20.834L77.756 18.985Q77.756 18.797 77.709 18.713Q77.661 18.630 77.563 18.611Q77.466 18.592 77.254 18.592L77.254 18.312L78.310 18.237L78.310 20.834Q78.310 20.974 78.442 21.009Q78.573 21.043 78.785 21.043L78.785 21.323M77.514 17.016Q77.514 16.845 77.637 16.726Q77.760 16.606 77.931 16.606Q78.098 16.606 78.221 16.726Q78.344 16.845 78.344 17.016Q78.344 17.191 78.221 17.314Q78.098 17.437 77.931 17.437Q77.760 17.437 77.637 17.314Q77.514 17.191 77.514 17.016M79.958 20.482L79.958 18.585L79.318 18.585L79.318 18.363Q79.636 18.363 79.853 18.153Q80.070 17.943 80.171 17.633Q80.272 17.324 80.272 17.016L80.539 17.016L80.539 18.305L81.615 18.305L81.615 18.585L80.539 18.585L80.539 20.469Q80.539 20.745 80.643 20.944Q80.747 21.142 81.007 21.142Q81.164 21.142 81.270 21.038Q81.376 20.933 81.426 20.780Q81.475 20.626 81.475 20.469L81.475 20.055L81.742 20.055L81.742 20.482Q81.742 20.708 81.643 20.918Q81.543 21.128 81.359 21.260Q81.174 21.391 80.945 21.391Q80.508 21.391 80.233 21.154Q79.958 20.916 79.958 20.482\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-81.854 27.357)\">\u003Cpath d=\"M82.684 22.458Q82.814 22.526 82.951 22.526Q83.122 22.526 83.272 22.437Q83.423 22.348 83.534 22.203Q83.645 22.058 83.723 21.890L83.987 21.323L82.818 18.797Q82.743 18.650 82.613 18.618Q82.483 18.585 82.250 18.585L82.250 18.305L83.771 18.305L83.771 18.585Q83.423 18.585 83.423 18.732Q83.426 18.753 83.428 18.770Q83.430 18.787 83.430 18.797L84.287 20.656L85.060 18.985Q85.094 18.917 85.094 18.838Q85.094 18.725 85.010 18.655Q84.927 18.585 84.814 18.585L84.814 18.305L86.010 18.305L86.010 18.585Q85.791 18.585 85.619 18.689Q85.446 18.794 85.354 18.985L84.017 21.890Q83.847 22.260 83.577 22.506Q83.306 22.752 82.951 22.752Q82.681 22.752 82.462 22.586Q82.243 22.420 82.243 22.157Q82.243 22.020 82.336 21.931Q82.428 21.843 82.568 21.843Q82.705 21.843 82.794 21.931Q82.883 22.020 82.883 22.157Q82.883 22.260 82.830 22.338Q82.777 22.417 82.684 22.458\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M70.483 95.3h73.977V66.849H70.483Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M68.533 11.792L67.463 8.936Q67.397 8.757 67.266 8.714Q67.135 8.671 66.877 8.671L66.877 8.374L68.557 8.374L68.557 8.671Q68.107 8.671 68.107 8.870Q68.111 8.886 68.113 8.903Q68.115 8.921 68.115 8.936L68.908 11.030L69.619 9.120Q69.584 9.026 69.584 8.981Q69.584 8.936 69.549 8.936Q69.482 8.757 69.352 8.714Q69.221 8.671 68.967 8.671L68.967 8.374L70.557 8.374L70.557 8.671Q70.107 8.671 70.107 8.870Q70.111 8.889 70.113 8.907Q70.115 8.925 70.115 8.936L70.947 11.151L71.701 9.151Q71.725 9.093 71.725 9.022Q71.725 8.862 71.588 8.766Q71.451 8.671 71.283 8.671L71.283 8.374L72.670 8.374L72.670 8.671Q72.436 8.671 72.258 8.798Q72.080 8.925 71.998 9.151L71.014 11.792Q70.959 11.901 70.846 11.901L70.787 11.901Q70.674 11.901 70.631 11.792L69.772 9.518L68.916 11.792Q68.877 11.901 68.756 11.901L68.701 11.901Q68.588 11.901 68.533 11.792M75.014 11.823L73.158 11.823L73.158 11.526Q73.432 11.526 73.600 11.479Q73.768 11.432 73.768 11.264L73.768 7.104Q73.768 6.889 73.705 6.794Q73.643 6.698 73.523 6.677Q73.404 6.655 73.158 6.655L73.158 6.358L74.381 6.272L74.381 8.975Q74.506 8.764 74.693 8.614Q74.881 8.464 75.107 8.380Q75.334 8.296 75.580 8.296Q76.748 8.296 76.748 9.374L76.748 11.264Q76.748 11.432 76.918 11.479Q77.088 11.526 77.357 11.526L77.357 11.823L75.502 11.823L75.502 11.526Q75.775 11.526 75.943 11.479Q76.111 11.432 76.111 11.264L76.111 9.389Q76.111 9.007 75.990 8.778Q75.869 8.550 75.518 8.550Q75.205 8.550 74.951 8.712Q74.697 8.874 74.551 9.143Q74.404 9.413 74.404 9.710L74.404 11.264Q74.404 11.432 74.574 11.479Q74.744 11.526 75.014 11.526L75.014 11.823M77.900 10.991Q77.900 10.507 78.303 10.212Q78.705 9.917 79.256 9.798Q79.807 9.678 80.299 9.678L80.299 9.389Q80.299 9.163 80.184 8.956Q80.068 8.749 79.871 8.630Q79.674 8.511 79.443 8.511Q79.018 8.511 78.732 8.616Q78.803 8.643 78.850 8.698Q78.897 8.753 78.922 8.823Q78.947 8.893 78.947 8.968Q78.947 9.073 78.897 9.165Q78.846 9.257 78.754 9.307Q78.662 9.358 78.557 9.358Q78.451 9.358 78.359 9.307Q78.268 9.257 78.217 9.165Q78.166 9.073 78.166 8.968Q78.166 8.550 78.555 8.403Q78.943 8.257 79.443 8.257Q79.775 8.257 80.129 8.387Q80.482 8.518 80.711 8.772Q80.939 9.026 80.939 9.374L80.939 11.175Q80.939 11.307 81.012 11.417Q81.084 11.526 81.213 11.526Q81.338 11.526 81.406 11.421Q81.475 11.315 81.475 11.175L81.475 10.663L81.756 10.663L81.756 11.175Q81.756 11.378 81.639 11.536Q81.522 11.694 81.340 11.778Q81.158 11.862 80.955 11.862Q80.725 11.862 80.572 11.690Q80.420 11.518 80.389 11.288Q80.229 11.569 79.920 11.735Q79.611 11.901 79.260 11.901Q78.748 11.901 78.324 11.678Q77.900 11.456 77.900 10.991M78.588 10.991Q78.588 11.276 78.814 11.462Q79.041 11.647 79.334 11.647Q79.580 11.647 79.805 11.530Q80.029 11.413 80.164 11.210Q80.299 11.007 80.299 10.753L80.299 9.921Q80.033 9.921 79.748 9.975Q79.463 10.030 79.191 10.159Q78.920 10.288 78.754 10.495Q78.588 10.702 78.588 10.991M82.674 10.862L82.674 8.671L81.971 8.671L81.971 8.417Q82.326 8.417 82.568 8.184Q82.811 7.952 82.922 7.604Q83.033 7.257 83.033 6.901L83.314 6.901L83.314 8.374L84.490 8.374L84.490 8.671L83.314 8.671L83.314 10.846Q83.314 11.167 83.434 11.395Q83.553 11.624 83.834 11.624Q84.014 11.624 84.131 11.501Q84.248 11.378 84.301 11.198Q84.354 11.018 84.354 10.846L84.354 10.374L84.635 10.374L84.635 10.862Q84.635 11.116 84.529 11.356Q84.424 11.596 84.227 11.749Q84.029 11.901 83.772 11.901Q83.455 11.901 83.203 11.778Q82.951 11.655 82.813 11.421Q82.674 11.186 82.674 10.862\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M88.295 10.991Q88.295 10.507 88.697 10.212Q89.100 9.917 89.650 9.798Q90.201 9.678 90.693 9.678L90.693 9.389Q90.693 9.163 90.578 8.956Q90.463 8.749 90.266 8.630Q90.068 8.511 89.838 8.511Q89.412 8.511 89.127 8.616Q89.197 8.643 89.244 8.698Q89.291 8.753 89.316 8.823Q89.342 8.893 89.342 8.968Q89.342 9.073 89.291 9.165Q89.240 9.257 89.148 9.307Q89.057 9.358 88.951 9.358Q88.846 9.358 88.754 9.307Q88.662 9.257 88.611 9.165Q88.561 9.073 88.561 8.968Q88.561 8.550 88.949 8.403Q89.338 8.257 89.838 8.257Q90.170 8.257 90.523 8.387Q90.877 8.518 91.105 8.772Q91.334 9.026 91.334 9.374L91.334 11.175Q91.334 11.307 91.406 11.417Q91.479 11.526 91.607 11.526Q91.732 11.526 91.801 11.421Q91.869 11.315 91.869 11.175L91.869 10.663L92.150 10.663L92.150 11.175Q92.150 11.378 92.033 11.536Q91.916 11.694 91.734 11.778Q91.553 11.862 91.350 11.862Q91.119 11.862 90.967 11.690Q90.814 11.518 90.783 11.288Q90.623 11.569 90.314 11.735Q90.006 11.901 89.654 11.901Q89.143 11.901 88.719 11.678Q88.295 11.456 88.295 10.991M88.982 10.991Q88.982 11.276 89.209 11.462Q89.436 11.647 89.729 11.647Q89.975 11.647 90.199 11.530Q90.424 11.413 90.559 11.210Q90.693 11.007 90.693 10.753L90.693 9.921Q90.428 9.921 90.143 9.975Q89.857 10.030 89.586 10.159Q89.314 10.288 89.148 10.495Q88.982 10.702 88.982 10.991M92.486 10.096Q92.486 9.600 92.736 9.175Q92.986 8.749 93.406 8.503Q93.826 8.257 94.326 8.257Q94.865 8.257 95.256 8.382Q95.647 8.507 95.647 8.921Q95.647 9.026 95.596 9.118Q95.545 9.210 95.453 9.261Q95.361 9.311 95.252 9.311Q95.147 9.311 95.055 9.261Q94.963 9.210 94.912 9.118Q94.861 9.026 94.861 8.921Q94.861 8.698 95.029 8.593Q94.807 8.534 94.334 8.534Q94.037 8.534 93.822 8.673Q93.607 8.811 93.477 9.042Q93.346 9.272 93.287 9.542Q93.229 9.811 93.229 10.096Q93.229 10.491 93.361 10.841Q93.494 11.190 93.766 11.407Q94.037 11.624 94.436 11.624Q94.811 11.624 95.086 11.407Q95.361 11.190 95.463 10.831Q95.479 10.768 95.541 10.768L95.647 10.768Q95.682 10.768 95.707 10.796Q95.732 10.823 95.732 10.862L95.732 10.886Q95.600 11.366 95.215 11.634Q94.830 11.901 94.326 11.901Q93.963 11.901 93.629 11.764Q93.295 11.628 93.035 11.378Q92.775 11.128 92.631 10.792Q92.486 10.456 92.486 10.096M96.846 10.862L96.846 8.671L96.143 8.671L96.143 8.417Q96.498 8.417 96.740 8.184Q96.982 7.952 97.094 7.604Q97.205 7.257 97.205 6.901L97.486 6.901L97.486 8.374L98.662 8.374L98.662 8.671L97.486 8.671L97.486 10.846Q97.486 11.167 97.605 11.395Q97.725 11.624 98.006 11.624Q98.186 11.624 98.303 11.501Q98.420 11.378 98.473 11.198Q98.525 11.018 98.525 10.846L98.525 10.374L98.807 10.374L98.807 10.862Q98.807 11.116 98.701 11.356Q98.596 11.596 98.398 11.749Q98.201 11.901 97.943 11.901Q97.627 11.901 97.375 11.778Q97.123 11.655 96.984 11.421Q96.846 11.186 96.846 10.862M101.385 11.823L99.607 11.823L99.607 11.526Q99.881 11.526 100.049 11.479Q100.217 11.432 100.217 11.264L100.217 9.128Q100.217 8.913 100.160 8.817Q100.104 8.721 99.990 8.700Q99.877 8.678 99.631 8.678L99.631 8.382L100.830 8.296L100.830 11.264Q100.830 11.432 100.977 11.479Q101.123 11.526 101.385 11.526L101.385 11.823M99.943 6.901Q99.943 6.710 100.078 6.579Q100.213 6.448 100.408 6.448Q100.529 6.448 100.633 6.511Q100.736 6.573 100.799 6.677Q100.861 6.780 100.861 6.901Q100.861 7.096 100.730 7.231Q100.600 7.366 100.408 7.366Q100.209 7.366 100.076 7.233Q99.943 7.100 99.943 6.901M101.885 10.128Q101.885 9.624 102.141 9.192Q102.397 8.761 102.832 8.509Q103.268 8.257 103.768 8.257Q104.154 8.257 104.496 8.401Q104.838 8.546 105.100 8.807Q105.361 9.069 105.504 9.405Q105.647 9.741 105.647 10.128Q105.647 10.620 105.383 11.030Q105.119 11.440 104.689 11.671Q104.260 11.901 103.768 11.901Q103.275 11.901 102.842 11.669Q102.408 11.436 102.147 11.028Q101.885 10.620 101.885 10.128M103.768 11.624Q104.225 11.624 104.477 11.401Q104.729 11.178 104.816 10.827Q104.904 10.475 104.904 10.030Q104.904 9.600 104.811 9.262Q104.717 8.925 104.463 8.718Q104.209 8.511 103.768 8.511Q103.119 8.511 102.875 8.927Q102.631 9.343 102.631 10.030Q102.631 10.475 102.719 10.827Q102.807 11.178 103.059 11.401Q103.311 11.624 103.768 11.624M108.061 11.823L106.205 11.823L106.205 11.526Q106.479 11.526 106.647 11.479Q106.814 11.432 106.814 11.264L106.814 9.128Q106.814 8.913 106.752 8.817Q106.689 8.721 106.570 8.700Q106.451 8.678 106.205 8.678L106.205 8.382L107.397 8.296L107.397 9.030Q107.510 8.815 107.703 8.647Q107.897 8.479 108.135 8.387Q108.373 8.296 108.627 8.296Q109.795 8.296 109.795 9.374L109.795 11.264Q109.795 11.432 109.965 11.479Q110.135 11.526 110.404 11.526L110.404 11.823L108.549 11.823L108.549 11.526Q108.822 11.526 108.990 11.479Q109.158 11.432 109.158 11.264L109.158 9.389Q109.158 9.007 109.037 8.778Q108.916 8.550 108.564 8.550Q108.252 8.550 107.998 8.712Q107.744 8.874 107.598 9.143Q107.451 9.413 107.451 9.710L107.451 11.264Q107.451 11.432 107.621 11.479Q107.791 11.526 108.061 11.526\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M116.222 11.823L113.757 11.823L113.757 11.526Q114.089 11.526 114.347 11.479Q114.605 11.432 114.605 11.264L114.605 6.921Q114.605 6.655 113.757 6.655L113.757 6.358L116.222 6.358L116.222 6.655Q115.370 6.655 115.370 6.921L115.370 11.264Q115.370 11.526 116.222 11.526\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M65.073 21.315L65.073 20.093Q65.073 20.065 65.105 20.034Q65.136 20.003 65.159 20.003L65.265 20.003Q65.335 20.003 65.351 20.065Q65.413 20.386 65.552 20.626Q65.690 20.866 65.923 21.007Q66.155 21.147 66.464 21.147Q66.702 21.147 66.911 21.087Q67.120 21.026 67.257 20.878Q67.394 20.729 67.394 20.483Q67.394 20.229 67.183 20.063Q66.972 19.897 66.702 19.843L66.081 19.729Q65.675 19.651 65.374 19.395Q65.073 19.139 65.073 18.764Q65.073 18.397 65.274 18.175Q65.476 17.952 65.800 17.854Q66.124 17.757 66.464 17.757Q66.929 17.757 67.226 17.964L67.448 17.780Q67.472 17.757 67.503 17.757L67.554 17.757Q67.585 17.757 67.612 17.784Q67.640 17.811 67.640 17.843L67.640 18.827Q67.640 18.858 67.614 18.887Q67.589 18.917 67.554 18.917L67.448 18.917Q67.413 18.917 67.386 18.889Q67.358 18.862 67.358 18.827Q67.358 18.428 67.106 18.208Q66.855 17.987 66.456 17.987Q66.101 17.987 65.817 18.110Q65.534 18.233 65.534 18.538Q65.534 18.757 65.735 18.889Q65.937 19.022 66.183 19.065L66.808 19.178Q67.237 19.268 67.546 19.565Q67.855 19.862 67.855 20.276Q67.855 20.846 67.456 21.124Q67.058 21.401 66.464 21.401Q65.913 21.401 65.562 21.065L65.265 21.378Q65.241 21.401 65.206 21.401L65.159 21.401Q65.136 21.401 65.105 21.370Q65.073 21.339 65.073 21.315M70.312 21.323L68.456 21.323L68.456 21.026Q68.730 21.026 68.897 20.979Q69.065 20.932 69.065 20.764L69.065 16.604Q69.065 16.389 69.003 16.294Q68.940 16.198 68.821 16.177Q68.702 16.155 68.456 16.155L68.456 15.858L69.679 15.772L69.679 18.475Q69.804 18.264 69.991 18.114Q70.179 17.964 70.405 17.880Q70.632 17.796 70.878 17.796Q72.046 17.796 72.046 18.874L72.046 20.764Q72.046 20.932 72.216 20.979Q72.386 21.026 72.655 21.026L72.655 21.323L70.800 21.323L70.800 21.026Q71.073 21.026 71.241 20.979Q71.409 20.932 71.409 20.764L71.409 18.889Q71.409 18.507 71.288 18.278Q71.167 18.050 70.815 18.050Q70.503 18.050 70.249 18.212Q69.995 18.374 69.849 18.643Q69.702 18.913 69.702 19.210L69.702 20.764Q69.702 20.932 69.872 20.979Q70.042 21.026 70.312 21.026L70.312 21.323M73.101 19.628Q73.101 19.124 73.356 18.692Q73.612 18.261 74.048 18.009Q74.483 17.757 74.983 17.757Q75.370 17.757 75.712 17.901Q76.054 18.046 76.315 18.307Q76.577 18.569 76.720 18.905Q76.862 19.241 76.862 19.628Q76.862 20.120 76.599 20.530Q76.335 20.940 75.905 21.171Q75.476 21.401 74.983 21.401Q74.491 21.401 74.058 21.169Q73.624 20.936 73.362 20.528Q73.101 20.120 73.101 19.628M74.983 21.124Q75.440 21.124 75.692 20.901Q75.944 20.678 76.032 20.327Q76.120 19.975 76.120 19.530Q76.120 19.100 76.026 18.762Q75.933 18.425 75.679 18.218Q75.425 18.011 74.983 18.011Q74.335 18.011 74.091 18.427Q73.847 18.843 73.847 19.530Q73.847 19.975 73.935 20.327Q74.022 20.678 74.274 20.901Q74.526 21.124 74.983 21.124M78.030 20.370L78.030 18.628Q78.030 18.413 77.968 18.317Q77.905 18.221 77.786 18.200Q77.667 18.178 77.421 18.178L77.421 17.882L78.667 17.796L78.667 20.346L78.667 20.370Q78.667 20.682 78.722 20.844Q78.776 21.007 78.927 21.077Q79.077 21.147 79.397 21.147Q79.827 21.147 80.101 20.809Q80.374 20.471 80.374 20.026L80.374 18.628Q80.374 18.413 80.312 18.317Q80.249 18.221 80.130 18.200Q80.011 18.178 79.765 18.178L79.765 17.882L81.011 17.796L81.011 20.581Q81.011 20.792 81.073 20.887Q81.136 20.983 81.255 21.005Q81.374 21.026 81.620 21.026L81.620 21.323L80.397 21.401L80.397 20.780Q80.230 21.069 79.948 21.235Q79.667 21.401 79.347 21.401Q78.030 21.401 78.030 20.370M83.980 21.323L82.147 21.323L82.147 21.026Q82.421 21.026 82.589 20.979Q82.757 20.932 82.757 20.764L82.757 16.604Q82.757 16.389 82.694 16.294Q82.632 16.198 82.513 16.177Q82.394 16.155 82.147 16.155L82.147 15.858L83.370 15.772L83.370 20.764Q83.370 20.932 83.538 20.979Q83.706 21.026 83.980 21.026L83.980 21.323M86.241 21.401Q85.761 21.401 85.353 21.157Q84.944 20.913 84.706 20.499Q84.468 20.085 84.468 19.596Q84.468 19.104 84.726 18.688Q84.983 18.272 85.415 18.034Q85.847 17.796 86.339 17.796Q86.960 17.796 87.409 18.233L87.409 16.604Q87.409 16.389 87.347 16.294Q87.284 16.198 87.167 16.177Q87.050 16.155 86.804 16.155L86.804 15.858L88.026 15.772L88.026 20.581Q88.026 20.792 88.089 20.887Q88.151 20.983 88.269 21.005Q88.386 21.026 88.636 21.026L88.636 21.323L87.386 21.401L87.386 20.917Q86.921 21.401 86.241 21.401M86.308 21.147Q86.647 21.147 86.940 20.956Q87.233 20.764 87.386 20.468L87.386 18.636Q87.237 18.362 86.976 18.206Q86.714 18.050 86.401 18.050Q85.776 18.050 85.493 18.497Q85.210 18.944 85.210 19.604Q85.210 20.249 85.462 20.698Q85.714 21.147 86.308 21.147\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M93.812 21.401Q93.331 21.401 92.923 21.157Q92.515 20.913 92.277 20.499Q92.038 20.085 92.038 19.596Q92.038 19.104 92.296 18.688Q92.554 18.272 92.986 18.034Q93.417 17.796 93.909 17.796Q94.530 17.796 94.980 18.233L94.980 16.604Q94.980 16.389 94.917 16.294Q94.855 16.198 94.737 16.177Q94.620 16.155 94.374 16.155L94.374 15.858L95.597 15.772L95.597 20.581Q95.597 20.792 95.659 20.887Q95.722 20.983 95.839 21.005Q95.956 21.026 96.206 21.026L96.206 21.323L94.956 21.401L94.956 20.917Q94.491 21.401 93.812 21.401M93.878 21.147Q94.218 21.147 94.511 20.956Q94.804 20.764 94.956 20.468L94.956 18.636Q94.808 18.362 94.546 18.206Q94.284 18.050 93.972 18.050Q93.347 18.050 93.064 18.497Q92.780 18.944 92.780 19.604Q92.780 20.249 93.032 20.698Q93.284 21.147 93.878 21.147M96.714 19.628Q96.714 19.124 96.970 18.692Q97.226 18.261 97.661 18.009Q98.097 17.757 98.597 17.757Q98.984 17.757 99.325 17.901Q99.667 18.046 99.929 18.307Q100.191 18.569 100.333 18.905Q100.476 19.241 100.476 19.628Q100.476 20.120 100.212 20.530Q99.948 20.940 99.519 21.171Q99.089 21.401 98.597 21.401Q98.105 21.401 97.671 21.169Q97.237 20.936 96.976 20.528Q96.714 20.120 96.714 19.628M98.597 21.124Q99.054 21.124 99.306 20.901Q99.558 20.678 99.646 20.327Q99.734 19.975 99.734 19.530Q99.734 19.100 99.640 18.762Q99.546 18.425 99.292 18.218Q99.038 18.011 98.597 18.011Q97.948 18.011 97.704 18.427Q97.460 18.843 97.460 19.530Q97.460 19.975 97.548 20.327Q97.636 20.678 97.888 20.901Q98.140 21.124 98.597 21.124\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M105.730 21.323L103.874 21.323L103.874 21.026Q104.148 21.026 104.316 20.979Q104.484 20.932 104.484 20.764L104.484 18.628Q104.484 18.413 104.421 18.317Q104.359 18.221 104.240 18.200Q104.121 18.178 103.874 18.178L103.874 17.882L105.066 17.796L105.066 18.530Q105.179 18.315 105.373 18.147Q105.566 17.979 105.804 17.887Q106.042 17.796 106.296 17.796Q107.464 17.796 107.464 18.874L107.464 20.764Q107.464 20.932 107.634 20.979Q107.804 21.026 108.074 21.026L108.074 21.323L106.218 21.323L106.218 21.026Q106.492 21.026 106.660 20.979Q106.828 20.932 106.828 20.764L106.828 18.889Q106.828 18.507 106.707 18.278Q106.585 18.050 106.234 18.050Q105.921 18.050 105.667 18.212Q105.414 18.374 105.267 18.643Q105.121 18.913 105.121 19.210L105.121 20.764Q105.121 20.932 105.291 20.979Q105.460 21.026 105.730 21.026L105.730 21.323M108.519 19.628Q108.519 19.124 108.775 18.692Q109.031 18.261 109.466 18.009Q109.902 17.757 110.402 17.757Q110.789 17.757 111.130 17.901Q111.472 18.046 111.734 18.307Q111.996 18.569 112.138 18.905Q112.281 19.241 112.281 19.628Q112.281 20.120 112.017 20.530Q111.753 20.940 111.324 21.171Q110.894 21.401 110.402 21.401Q109.910 21.401 109.476 21.169Q109.042 20.936 108.781 20.528Q108.519 20.120 108.519 19.628M110.402 21.124Q110.859 21.124 111.111 20.901Q111.363 20.678 111.451 20.327Q111.539 19.975 111.539 19.530Q111.539 19.100 111.445 18.762Q111.351 18.425 111.097 18.218Q110.843 18.011 110.402 18.011Q109.753 18.011 109.509 18.427Q109.265 18.843 109.265 19.530Q109.265 19.975 109.353 20.327Q109.441 20.678 109.693 20.901Q109.945 21.124 110.402 21.124\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(15.856 67.279)\">\u003Cpath d=\"M114.123 21.292L113.053 18.436Q112.987 18.257 112.856 18.214Q112.725 18.171 112.467 18.171L112.467 17.874L114.147 17.874L114.147 18.171Q113.697 18.171 113.697 18.370Q113.701 18.386 113.703 18.403Q113.705 18.421 113.705 18.436L114.498 20.530L115.209 18.620Q115.174 18.526 115.174 18.481Q115.174 18.436 115.139 18.436Q115.072 18.257 114.942 18.214Q114.811 18.171 114.557 18.171L114.557 17.874L116.147 17.874L116.147 18.171Q115.697 18.171 115.697 18.370Q115.701 18.389 115.703 18.407Q115.705 18.425 115.705 18.436L116.537 20.651L117.291 18.651Q117.315 18.593 117.315 18.522Q117.315 18.362 117.178 18.266Q117.041 18.171 116.873 18.171L116.873 17.874L118.260 17.874L118.260 18.171Q118.026 18.171 117.848 18.298Q117.670 18.425 117.588 18.651L116.604 21.292Q116.549 21.401 116.436 21.401L116.377 21.401Q116.264 21.401 116.221 21.292L115.362 19.018L114.506 21.292Q114.467 21.401 114.346 21.401L114.291 21.401Q114.178 21.401 114.123 21.292\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M208.666-47.164H107.47v1.178\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471-48.586-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m52.924-27.046 14.953-6.128\"\u002F>\u003Cpath stroke=\"none\" d=\"m70.283-34.16-4.638-.347 2.232 1.333-.655 2.516\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m47.209 2.83 19.089 2.506\"\u002F>\u003Cpath stroke=\"none\" d=\"m68.875 5.674-3.853-2.603 1.276 2.265-1.818 1.859\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471-19.733v8.38\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471-8.752 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471 20.1v8.382\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471 31.082 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m36.54 46.93 27.854-1.3\"\u002F>\u003Cpath stroke=\"none\" d=\"m66.99 45.508-4.251-1.883 1.655 2.005-1.461 2.15\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471 59.935v4.113\"\u002F>\u003Cpath stroke=\"none\" d=\"m107.471 66.648 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M107.471 95.5v14.227h101.195v-5.936\"\u002F>\u003Cpath stroke=\"none\" d=\"m208.666 101.191-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">A utility-based agent. It predicts the outcome of each action and scores how desirable the resulting state is by a utility function, choosing the action of highest expected utility — the average utility over possible outcomes, weighted by their probability.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:451.552px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 338.664 175.967\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-65.203 97.097H173.8V-62.24H-65.203Z\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-116.369 74.98)\">\u003Cpath d=\"M56.337 17.429L54.587 17.429L54.587 17.132Q55.286 17.132 55.474 16.652L57.275 11.827Q57.329 11.718 57.443 11.718L57.513 11.718Q57.626 11.718 57.681 11.827L59.571 16.870Q59.650 17.038 59.853 17.085Q60.056 17.132 60.368 17.132L60.368 17.429L58.146 17.429L58.146 17.132Q58.786 17.132 58.786 16.917Q58.786 16.898 58.784 16.888Q58.782 16.878 58.778 16.870L58.314 15.636L56.169 15.636L55.786 16.652Q55.782 16.667 55.777 16.697Q55.771 16.726 55.771 16.749Q55.771 16.890 55.861 16.974Q55.950 17.058 56.083 17.095Q56.216 17.132 56.337 17.132L56.337 17.429M57.243 12.773L56.275 15.339L58.200 15.339L57.243 12.773M60.896 18.038Q60.896 17.757 61.107 17.546Q61.318 17.335 61.603 17.245Q61.446 17.120 61.368 16.931Q61.290 16.741 61.290 16.542Q61.290 16.187 61.521 15.894Q61.153 15.554 61.153 15.085Q61.153 14.734 61.357 14.464Q61.560 14.195 61.880 14.048Q62.200 13.902 62.544 13.902Q63.064 13.902 63.435 14.183Q63.798 13.812 64.345 13.812Q64.525 13.812 64.652 13.939Q64.778 14.066 64.778 14.245Q64.778 14.351 64.700 14.429Q64.622 14.507 64.513 14.507Q64.403 14.507 64.327 14.431Q64.251 14.355 64.251 14.245Q64.251 14.144 64.290 14.093Q64.298 14.085 64.302 14.079Q64.306 14.074 64.306 14.070Q63.931 14.070 63.611 14.324Q63.931 14.663 63.931 15.085Q63.931 15.355 63.814 15.572Q63.696 15.788 63.491 15.947Q63.286 16.105 63.044 16.187Q62.802 16.269 62.544 16.269Q62.325 16.269 62.112 16.210Q61.900 16.152 61.704 16.031Q61.611 16.171 61.611 16.351Q61.611 16.558 61.747 16.710Q61.884 16.863 62.091 16.863L62.786 16.863Q63.275 16.863 63.687 16.947Q64.099 17.031 64.378 17.288Q64.657 17.546 64.657 18.038Q64.657 18.402 64.337 18.634Q64.017 18.866 63.575 18.968Q63.134 19.070 62.778 19.070Q62.423 19.070 61.980 18.968Q61.536 18.866 61.216 18.634Q60.896 18.402 60.896 18.038M61.400 18.038Q61.400 18.234 61.544 18.382Q61.689 18.531 61.902 18.620Q62.114 18.710 62.355 18.757Q62.595 18.804 62.778 18.804Q63.021 18.804 63.351 18.726Q63.681 18.648 63.917 18.474Q64.153 18.300 64.153 18.038Q64.153 17.632 63.743 17.523Q63.333 17.413 62.771 17.413L62.091 17.413Q61.821 17.413 61.611 17.591Q61.400 17.769 61.400 18.038M62.544 16.003Q63.267 16.003 63.267 15.085Q63.267 14.163 62.544 14.163Q61.818 14.163 61.818 15.085Q61.818 16.003 62.544 16.003M65.142 15.675Q65.142 15.195 65.374 14.779Q65.607 14.363 66.017 14.113Q66.427 13.863 66.903 13.863Q67.634 13.863 68.032 14.304Q68.431 14.745 68.431 15.476Q68.431 15.581 68.337 15.605L65.888 15.605L65.888 15.675Q65.888 16.085 66.009 16.441Q66.130 16.796 66.402 17.013Q66.673 17.230 67.103 17.230Q67.466 17.230 67.763 17.001Q68.060 16.773 68.161 16.421Q68.169 16.374 68.255 16.359L68.337 16.359Q68.431 16.386 68.431 16.468Q68.431 16.476 68.423 16.507Q68.361 16.734 68.222 16.917Q68.083 17.101 67.892 17.234Q67.700 17.366 67.482 17.437Q67.263 17.507 67.025 17.507Q66.653 17.507 66.316 17.370Q65.978 17.234 65.710 16.982Q65.443 16.730 65.292 16.390Q65.142 16.050 65.142 15.675M65.896 15.366L67.857 15.366Q67.857 15.062 67.755 14.771Q67.653 14.480 67.437 14.298Q67.220 14.116 66.903 14.116Q66.603 14.116 66.372 14.304Q66.142 14.491 66.019 14.783Q65.896 15.074 65.896 15.366M70.849 17.429L68.993 17.429L68.993 17.132Q69.267 17.132 69.435 17.085Q69.603 17.038 69.603 16.870L69.603 14.734Q69.603 14.519 69.540 14.423Q69.478 14.327 69.359 14.306Q69.239 14.284 68.993 14.284L68.993 13.988L70.185 13.902L70.185 14.636Q70.298 14.421 70.491 14.253Q70.685 14.085 70.923 13.993Q71.161 13.902 71.415 13.902Q72.583 13.902 72.583 14.980L72.583 16.870Q72.583 17.038 72.753 17.085Q72.923 17.132 73.193 17.132L73.193 17.429L71.337 17.429L71.337 17.132Q71.611 17.132 71.778 17.085Q71.946 17.038 71.946 16.870L71.946 14.995Q71.946 14.613 71.825 14.384Q71.704 14.156 71.353 14.156Q71.040 14.156 70.786 14.318Q70.532 14.480 70.386 14.749Q70.239 15.019 70.239 15.316L70.239 16.870Q70.239 17.038 70.409 17.085Q70.579 17.132 70.849 17.132\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-116.369 74.98)\">\u003Cpath d=\"M74.042 16.468L74.042 14.277L73.339 14.277L73.339 14.023Q73.695 14.023 73.937 13.790Q74.179 13.558 74.290 13.210Q74.402 12.863 74.402 12.507L74.683 12.507L74.683 13.980L75.859 13.980L75.859 14.277L74.683 14.277L74.683 16.452Q74.683 16.773 74.802 17.001Q74.921 17.230 75.202 17.230Q75.382 17.230 75.499 17.107Q75.617 16.984 75.669 16.804Q75.722 16.624 75.722 16.452L75.722 15.980L76.003 15.980L76.003 16.468Q76.003 16.722 75.898 16.962Q75.792 17.202 75.595 17.355Q75.398 17.507 75.140 17.507Q74.824 17.507 74.572 17.384Q74.320 17.261 74.181 17.027Q74.042 16.792 74.042 16.468\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M201.216 97.097h58.978V-62.24h-58.978Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr9\" font-size=\"9\">\u003Cg transform=\"translate(150.251 3.075)\">\u003Cpath d=\"M59.932 17.429L54.623 17.429L54.623 17.113Q55.542 17.113 55.542 16.818L55.542 11.892Q55.542 11.597 54.623 11.597L54.623 11.281L59.813 11.281L60.068 13.342L59.778 13.342Q59.708 12.749 59.593 12.417Q59.479 12.085 59.270 11.909Q59.062 11.734 58.717 11.666Q58.372 11.597 57.761 11.597L56.847 11.597Q56.596 11.597 56.491 11.646Q56.385 11.694 56.385 11.892L56.385 14.080L57.071 14.080Q57.550 14.080 57.772 14.006Q57.994 13.931 58.086 13.716Q58.178 13.500 58.178 13.030L58.464 13.030L58.464 15.447L58.178 15.447Q58.178 14.977 58.086 14.762Q57.994 14.546 57.772 14.471Q57.550 14.397 57.071 14.397L56.385 14.397L56.385 16.818Q56.385 17.012 56.491 17.062Q56.596 17.113 56.847 17.113L57.827 17.113Q58.464 17.113 58.853 17.016Q59.242 16.919 59.462 16.697Q59.681 16.475 59.802 16.097Q59.923 15.720 60.033 15.069L60.319 15.069L59.932 17.429M62.977 17.429L60.890 17.429L60.890 17.113Q61.197 17.113 61.389 17.060Q61.580 17.007 61.580 16.818L61.580 14.370Q61.580 14.129 61.509 14.021Q61.439 13.913 61.305 13.889Q61.171 13.865 60.890 13.865L60.890 13.549L62.230 13.452L62.230 14.287Q62.428 13.905 62.782 13.678Q63.135 13.452 63.562 13.452Q64.840 13.452 64.840 14.665L64.840 16.818Q64.840 17.007 65.032 17.060Q65.223 17.113 65.530 17.113L65.530 17.429L63.443 17.429L63.443 17.113Q63.755 17.113 63.946 17.060Q64.137 17.007 64.137 16.818L64.137 14.700Q64.137 14.441 64.093 14.219Q64.049 13.997 63.904 13.854Q63.759 13.711 63.500 13.711Q63.157 13.711 62.876 13.900Q62.595 14.089 62.439 14.401Q62.283 14.713 62.283 15.060L62.283 16.818Q62.283 17.007 62.476 17.060Q62.670 17.113 62.977 17.113\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(150.251 3.075)\">\u003Cpath d=\"M67.707 17.411L66.376 14.164Q66.288 13.966 66.123 13.916Q65.958 13.865 65.655 13.865L65.655 13.549L67.580 13.549L67.580 13.865Q67.088 13.865 67.088 14.080Q67.088 14.102 67.105 14.164L68.121 16.638L69.030 14.414Q69.065 14.331 69.065 14.234Q69.065 14.063 68.942 13.964Q68.819 13.865 68.652 13.865L68.652 13.549L70.164 13.549L70.164 13.865Q69.878 13.865 69.665 14.008Q69.452 14.151 69.347 14.414L68.112 17.411Q68.068 17.530 67.940 17.530L67.879 17.530Q67.751 17.530 67.707 17.411M72.647 17.429L70.661 17.429L70.661 17.113Q70.968 17.113 71.159 17.060Q71.350 17.007 71.350 16.818L71.350 14.370Q71.350 14.124 71.285 14.019Q71.219 13.913 71.093 13.889Q70.968 13.865 70.696 13.865L70.696 13.549L72.027 13.452L72.027 16.818Q72.027 17.012 72.192 17.062Q72.357 17.113 72.647 17.113L72.647 17.429M71.047 11.905Q71.047 11.699 71.197 11.549Q71.346 11.400 71.548 11.400Q71.680 11.400 71.797 11.470Q71.913 11.540 71.983 11.657Q72.054 11.773 72.054 11.905Q72.054 12.107 71.904 12.257Q71.755 12.406 71.548 12.406Q71.346 12.406 71.197 12.257Q71.047 12.107 71.047 11.905M75.402 17.429L73.170 17.429L73.170 17.113Q73.482 17.113 73.673 17.060Q73.864 17.007 73.864 16.818L73.864 14.370Q73.864 14.129 73.794 14.021Q73.724 13.913 73.590 13.889Q73.455 13.865 73.170 13.865L73.170 13.549L74.484 13.452L74.484 14.313Q74.646 13.922 74.914 13.687Q75.183 13.452 75.574 13.452Q75.846 13.452 76.061 13.615Q76.277 13.777 76.277 14.036Q76.277 14.212 76.158 14.331Q76.039 14.450 75.864 14.450Q75.683 14.450 75.565 14.331Q75.446 14.212 75.446 14.036Q75.446 13.821 75.600 13.711L75.582 13.711Q75.204 13.711 74.972 13.973Q74.739 14.234 74.640 14.621Q74.541 15.008 74.541 15.368L74.541 16.818Q74.541 17.007 74.798 17.060Q75.055 17.113 75.402 17.113L75.402 17.429M76.795 15.522Q76.795 14.955 77.068 14.467Q77.340 13.979 77.810 13.687Q78.281 13.395 78.848 13.395Q79.269 13.395 79.645 13.564Q80.021 13.733 80.298 14.025Q80.575 14.318 80.733 14.713Q80.891 15.109 80.891 15.522Q80.891 16.071 80.612 16.533Q80.333 16.994 79.865 17.262Q79.397 17.530 78.848 17.530Q78.294 17.530 77.824 17.262Q77.353 16.994 77.074 16.533Q76.795 16.071 76.795 15.522M78.848 17.240Q79.344 17.240 79.621 16.979Q79.898 16.717 79.990 16.313Q80.082 15.908 80.082 15.412Q80.082 14.937 79.984 14.548Q79.885 14.159 79.612 13.909Q79.340 13.658 78.848 13.658Q78.136 13.658 77.872 14.153Q77.608 14.647 77.608 15.412Q77.608 16.212 77.863 16.726Q78.118 17.240 78.848 17.240M83.541 17.429L81.454 17.429L81.454 17.113Q81.761 17.113 81.952 17.060Q82.143 17.007 82.143 16.818L82.143 14.370Q82.143 14.129 82.073 14.021Q82.003 13.913 81.869 13.889Q81.735 13.865 81.454 13.865L81.454 13.549L82.794 13.452L82.794 14.287Q82.992 13.905 83.345 13.678Q83.699 13.452 84.125 13.452Q85.404 13.452 85.404 14.665L85.404 16.818Q85.404 17.007 85.595 17.060Q85.787 17.113 86.094 17.113L86.094 17.429L84.007 17.429L84.007 17.113Q84.319 17.113 84.510 17.060Q84.701 17.007 84.701 16.818L84.701 14.700Q84.701 14.441 84.657 14.219Q84.613 13.997 84.468 13.854Q84.323 13.711 84.064 13.711Q83.721 13.711 83.440 13.900Q83.159 14.089 83.003 14.401Q82.847 14.713 82.847 15.060L82.847 16.818Q82.847 17.007 83.040 17.060Q83.233 17.113 83.541 17.113L83.541 17.429M88.678 17.429L86.591 17.429L86.591 17.113Q86.898 17.113 87.090 17.060Q87.281 17.007 87.281 16.818L87.281 14.370Q87.281 14.129 87.210 14.021Q87.140 13.913 87.006 13.889Q86.872 13.865 86.591 13.865L86.591 13.549L87.931 13.452L87.931 14.287Q88.129 13.909 88.489 13.680Q88.850 13.452 89.271 13.452Q90.317 13.452 90.502 14.261Q90.704 13.891 91.062 13.672Q91.420 13.452 91.838 13.452Q92.462 13.452 92.787 13.746Q93.112 14.041 93.112 14.665L93.112 16.818Q93.112 17.007 93.306 17.060Q93.499 17.113 93.807 17.113L93.807 17.429L91.719 17.429L91.719 17.113Q92.027 17.113 92.220 17.060Q92.413 17.007 92.413 16.818L92.413 14.700Q92.413 14.269 92.286 13.990Q92.159 13.711 91.772 13.711Q91.429 13.711 91.146 13.900Q90.862 14.089 90.706 14.401Q90.550 14.713 90.550 15.060L90.550 16.818Q90.550 17.007 90.741 17.060Q90.933 17.113 91.240 17.113L91.240 17.429L89.153 17.429L89.153 17.113Q89.465 17.113 89.656 17.060Q89.847 17.007 89.847 16.818L89.847 14.700Q89.847 14.441 89.803 14.219Q89.759 13.997 89.614 13.854Q89.469 13.711 89.210 13.711Q88.674 13.711 88.329 14.118Q87.984 14.524 87.984 15.060L87.984 16.818Q87.984 17.007 88.177 17.060Q88.371 17.113 88.678 17.113L88.678 17.429M96.307 17.530Q95.749 17.530 95.277 17.247Q94.804 16.963 94.529 16.486Q94.255 16.010 94.255 15.456Q94.255 15.060 94.398 14.685Q94.540 14.309 94.798 14.021Q95.055 13.733 95.413 13.564Q95.771 13.395 96.175 13.395Q96.720 13.395 97.091 13.632Q97.463 13.869 97.650 14.287Q97.836 14.704 97.836 15.241Q97.836 15.293 97.812 15.331Q97.788 15.368 97.740 15.368L95.068 15.368L95.068 15.447Q95.068 16.194 95.380 16.717Q95.692 17.240 96.391 17.240Q96.795 17.240 97.116 16.983Q97.436 16.726 97.559 16.322Q97.577 16.242 97.661 16.242L97.740 16.242Q97.779 16.242 97.808 16.273Q97.836 16.304 97.836 16.348L97.836 16.383Q97.731 16.726 97.509 16.985Q97.287 17.244 96.973 17.387Q96.659 17.530 96.307 17.530M95.077 15.117L97.190 15.117Q97.190 14.849 97.138 14.603Q97.085 14.357 96.964 14.135Q96.843 13.913 96.645 13.786Q96.448 13.658 96.175 13.658Q95.832 13.658 95.580 13.883Q95.327 14.107 95.202 14.445Q95.077 14.783 95.077 15.117M100.495 17.429L98.408 17.429L98.408 17.113Q98.715 17.113 98.906 17.060Q99.098 17.007 99.098 16.818L99.098 14.370Q99.098 14.129 99.027 14.021Q98.957 13.913 98.823 13.889Q98.689 13.865 98.408 13.865L98.408 13.549L99.748 13.452L99.748 14.287Q99.946 13.905 100.299 13.678Q100.653 13.452 101.079 13.452Q102.358 13.452 102.358 14.665L102.358 16.818Q102.358 17.007 102.549 17.060Q102.741 17.113 103.048 17.113L103.048 17.429L100.961 17.429L100.961 17.113Q101.273 17.113 101.464 17.060Q101.655 17.007 101.655 16.818L101.655 14.700Q101.655 14.441 101.611 14.219Q101.567 13.997 101.422 13.854Q101.277 13.711 101.018 13.711Q100.675 13.711 100.394 13.900Q100.113 14.089 99.957 14.401Q99.801 14.713 99.801 15.060L99.801 16.818Q99.801 17.007 99.994 17.060Q100.187 17.113 100.495 17.113\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(150.251 3.075)\">\u003Cpath d=\"M103.948 16.357L103.948 13.865L103.183 13.865L103.183 13.606Q103.588 13.606 103.854 13.340Q104.119 13.074 104.240 12.674Q104.361 12.274 104.361 11.892L104.651 11.892L104.651 13.549L105.939 13.549L105.939 13.865L104.651 13.865L104.651 16.322Q104.651 16.691 104.776 16.965Q104.902 17.240 105.227 17.240Q105.526 17.240 105.664 16.946Q105.803 16.651 105.803 16.322L105.803 15.799L106.088 15.799L106.088 16.357Q106.088 16.634 105.978 16.906Q105.868 17.179 105.655 17.354Q105.442 17.530 105.161 17.530Q104.801 17.530 104.528 17.392Q104.256 17.253 104.102 16.990Q103.948 16.726 103.948 16.357\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.270\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-52.65 -81.505)\">\u003Cpath d=\"M56.824 17.429L54.691 17.429L54.691 17.149Q55.412 17.149 55.412 16.940L55.412 13.139Q55.412 12.928 54.691 12.928L54.691 12.647L57.357 12.647Q57.767 12.647 58.188 12.801Q58.608 12.955 58.892 13.259Q59.175 13.563 59.175 13.977Q59.175 14.295 59.008 14.541Q58.840 14.787 58.564 14.953Q58.287 15.118 57.965 15.202Q57.644 15.286 57.357 15.286L56.103 15.286L56.103 16.940Q56.103 17.149 56.824 17.149L56.824 17.429M56.075 13.139L56.075 15.036L57.162 15.036Q57.771 15.036 58.085 14.799Q58.400 14.561 58.400 13.977Q58.400 13.584 58.254 13.350Q58.109 13.116 57.837 13.022Q57.566 12.928 57.162 12.928L56.441 12.928Q56.253 12.928 56.164 12.962Q56.075 12.996 56.075 13.139\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-52.65 -81.505)\">\u003Cpath d=\"M59.731 15.894Q59.731 15.573 59.856 15.284Q59.981 14.995 60.207 14.772Q60.432 14.548 60.728 14.428Q61.023 14.308 61.341 14.308Q61.669 14.308 61.931 14.408Q62.192 14.507 62.368 14.689Q62.544 14.872 62.638 15.130Q62.732 15.388 62.732 15.720Q62.732 15.812 62.650 15.833L60.395 15.833L60.395 15.894Q60.395 16.482 60.678 16.865Q60.962 17.248 61.529 17.248Q61.851 17.248 62.119 17.055Q62.387 16.862 62.476 16.547Q62.483 16.506 62.558 16.492L62.650 16.492Q62.732 16.516 62.732 16.588Q62.732 16.595 62.726 16.622Q62.613 17.019 62.242 17.258Q61.871 17.497 61.447 17.497Q61.010 17.497 60.610 17.289Q60.210 17.080 59.971 16.713Q59.731 16.346 59.731 15.894M60.401 15.624L62.216 15.624Q62.216 15.347 62.119 15.095Q62.021 14.842 61.823 14.686Q61.625 14.531 61.341 14.531Q61.064 14.531 60.851 14.689Q60.637 14.848 60.519 15.103Q60.401 15.358 60.401 15.624M65.070 17.429L63.334 17.429L63.334 17.149Q63.563 17.149 63.712 17.115Q63.860 17.080 63.860 16.940L63.860 15.091Q63.860 14.821 63.753 14.760Q63.645 14.698 63.334 14.698L63.334 14.418L64.363 14.343L64.363 15.050Q64.493 14.742 64.735 14.543Q64.978 14.343 65.296 14.343Q65.515 14.343 65.686 14.467Q65.856 14.592 65.856 14.804Q65.856 14.941 65.757 15.040Q65.658 15.139 65.525 15.139Q65.388 15.139 65.289 15.040Q65.190 14.941 65.190 14.804Q65.190 14.664 65.289 14.565Q64.999 14.565 64.799 14.761Q64.599 14.958 64.506 15.252Q64.414 15.546 64.414 15.826L64.414 16.940Q64.414 17.149 65.070 17.149L65.070 17.429M68.239 17.429L66.506 17.429L66.506 17.149Q66.731 17.149 66.880 17.115Q67.029 17.080 67.029 16.940L67.029 14.691L66.441 14.691L66.441 14.411L67.029 14.411L67.029 13.594Q67.029 13.276 67.207 13.028Q67.384 12.781 67.675 12.640Q67.965 12.500 68.276 12.500Q68.533 12.500 68.736 12.642Q68.939 12.784 68.939 13.027Q68.939 13.163 68.840 13.262Q68.741 13.362 68.604 13.362Q68.468 13.362 68.369 13.262Q68.270 13.163 68.270 13.027Q68.270 12.846 68.410 12.753Q68.331 12.726 68.232 12.726Q68.023 12.726 67.870 12.859Q67.716 12.992 67.635 13.196Q67.555 13.399 67.555 13.608L67.555 14.411L68.444 14.411L68.444 14.691L67.583 14.691L67.583 16.940Q67.583 17.149 68.239 17.149L68.239 17.429M68.878 15.946Q68.878 15.604 69.013 15.305Q69.148 15.006 69.387 14.782Q69.626 14.558 69.944 14.433Q70.262 14.308 70.594 14.308Q71.038 14.308 71.438 14.524Q71.838 14.739 72.072 15.117Q72.306 15.494 72.306 15.946Q72.306 16.287 72.164 16.571Q72.022 16.855 71.778 17.062Q71.534 17.268 71.224 17.383Q70.915 17.497 70.594 17.497Q70.163 17.497 69.761 17.296Q69.360 17.094 69.119 16.742Q68.878 16.390 68.878 15.946M70.594 17.248Q71.195 17.248 71.419 16.870Q71.643 16.492 71.643 15.860Q71.643 15.248 71.409 14.889Q71.175 14.531 70.594 14.531Q69.541 14.531 69.541 15.860Q69.541 16.492 69.767 16.870Q69.992 17.248 70.594 17.248M74.651 17.429L72.915 17.429L72.915 17.149Q73.144 17.149 73.292 17.115Q73.441 17.080 73.441 16.940L73.441 15.091Q73.441 14.821 73.333 14.760Q73.226 14.698 72.915 14.698L72.915 14.418L73.943 14.343L73.943 15.050Q74.073 14.742 74.316 14.543Q74.559 14.343 74.876 14.343Q75.095 14.343 75.266 14.467Q75.437 14.592 75.437 14.804Q75.437 14.941 75.338 15.040Q75.239 15.139 75.105 15.139Q74.969 15.139 74.870 15.040Q74.770 14.941 74.770 14.804Q74.770 14.664 74.870 14.565Q74.579 14.565 74.379 14.761Q74.179 14.958 74.087 15.252Q73.995 15.546 73.995 15.826L73.995 16.940Q73.995 17.149 74.651 17.149L74.651 17.429M77.703 17.429L76.069 17.429L76.069 17.149Q76.298 17.149 76.447 17.115Q76.596 17.080 76.596 16.940L76.596 15.091Q76.596 14.821 76.488 14.760Q76.380 14.698 76.069 14.698L76.069 14.418L77.129 14.343L77.129 14.992Q77.300 14.684 77.604 14.513Q77.908 14.343 78.253 14.343Q78.653 14.343 78.930 14.483Q79.207 14.623 79.292 14.971Q79.460 14.678 79.759 14.510Q80.058 14.343 80.403 14.343Q80.909 14.343 81.193 14.566Q81.477 14.790 81.477 15.286L81.477 16.940Q81.477 17.077 81.625 17.113Q81.774 17.149 82 17.149L82 17.429L80.369 17.429L80.369 17.149Q80.595 17.149 80.745 17.113Q80.895 17.077 80.895 16.940L80.895 15.300Q80.895 14.965 80.776 14.765Q80.656 14.565 80.342 14.565Q80.072 14.565 79.838 14.701Q79.604 14.838 79.465 15.072Q79.327 15.306 79.327 15.580L79.327 16.940Q79.327 17.077 79.475 17.113Q79.624 17.149 79.850 17.149L79.850 17.429L78.219 17.429L78.219 17.149Q78.448 17.149 78.597 17.115Q78.746 17.080 78.746 16.940L78.746 15.300Q78.746 14.965 78.626 14.765Q78.506 14.565 78.192 14.565Q77.922 14.565 77.688 14.701Q77.454 14.838 77.315 15.072Q77.177 15.306 77.177 15.580L77.177 16.940Q77.177 17.077 77.327 17.113Q77.478 17.149 77.703 17.149L77.703 17.429M82.645 16.701Q82.645 16.369 82.869 16.142Q83.093 15.915 83.437 15.787Q83.780 15.658 84.153 15.606Q84.525 15.553 84.830 15.553L84.830 15.300Q84.830 15.095 84.722 14.915Q84.614 14.736 84.433 14.633Q84.252 14.531 84.043 14.531Q83.637 14.531 83.401 14.623Q83.490 14.660 83.536 14.744Q83.582 14.828 83.582 14.930Q83.582 15.026 83.536 15.105Q83.490 15.183 83.409 15.228Q83.329 15.272 83.240 15.272Q83.090 15.272 82.989 15.175Q82.888 15.077 82.888 14.930Q82.888 14.308 84.043 14.308Q84.255 14.308 84.505 14.372Q84.754 14.435 84.956 14.554Q85.158 14.674 85.284 14.859Q85.411 15.043 85.411 15.286L85.411 16.862Q85.411 16.978 85.472 17.074Q85.534 17.169 85.646 17.169Q85.756 17.169 85.821 17.075Q85.886 16.981 85.886 16.862L85.886 16.414L86.152 16.414L86.152 16.862Q86.152 17.132 85.925 17.297Q85.698 17.463 85.417 17.463Q85.209 17.463 85.072 17.309Q84.936 17.156 84.912 16.940Q84.765 17.207 84.483 17.352Q84.201 17.497 83.876 17.497Q83.599 17.497 83.315 17.422Q83.032 17.347 82.839 17.168Q82.645 16.988 82.645 16.701M83.261 16.701Q83.261 16.875 83.362 17.005Q83.462 17.135 83.618 17.205Q83.773 17.275 83.937 17.275Q84.156 17.275 84.365 17.178Q84.573 17.080 84.701 16.899Q84.830 16.718 84.830 16.492L84.830 15.764Q84.505 15.764 84.139 15.855Q83.773 15.946 83.517 16.158Q83.261 16.369 83.261 16.701M88.251 17.429L86.617 17.429L86.617 17.149Q86.846 17.149 86.995 17.115Q87.144 17.080 87.144 16.940L87.144 15.091Q87.144 14.821 87.036 14.760Q86.928 14.698 86.617 14.698L86.617 14.418L87.677 14.343L87.677 14.992Q87.848 14.684 88.152 14.513Q88.456 14.343 88.801 14.343Q89.307 14.343 89.591 14.566Q89.875 14.790 89.875 15.286L89.875 16.940Q89.875 17.077 90.023 17.113Q90.172 17.149 90.397 17.149L90.397 17.429L88.767 17.429L88.767 17.149Q88.996 17.149 89.145 17.115Q89.293 17.080 89.293 16.940L89.293 15.300Q89.293 14.965 89.174 14.765Q89.054 14.565 88.740 14.565Q88.470 14.565 88.236 14.701Q88.001 14.838 87.863 15.072Q87.725 15.306 87.725 15.580L87.725 16.940Q87.725 17.077 87.875 17.113Q88.025 17.149 88.251 17.149L88.251 17.429M90.985 15.918Q90.985 15.590 91.120 15.289Q91.255 14.989 91.491 14.768Q91.727 14.548 92.031 14.428Q92.335 14.308 92.660 14.308Q93.166 14.308 93.515 14.411Q93.863 14.513 93.863 14.889Q93.863 15.036 93.766 15.137Q93.668 15.238 93.521 15.238Q93.368 15.238 93.269 15.139Q93.169 15.040 93.169 14.889Q93.169 14.701 93.310 14.609Q93.108 14.558 92.667 14.558Q92.312 14.558 92.083 14.754Q91.854 14.951 91.753 15.260Q91.652 15.570 91.652 15.918Q91.652 16.267 91.778 16.573Q91.905 16.879 92.159 17.063Q92.414 17.248 92.770 17.248Q92.992 17.248 93.176 17.164Q93.361 17.080 93.496 16.925Q93.631 16.769 93.689 16.561Q93.703 16.506 93.757 16.506L93.870 16.506Q93.901 16.506 93.923 16.530Q93.945 16.554 93.945 16.588L93.945 16.609Q93.860 16.896 93.672 17.094Q93.484 17.292 93.219 17.395Q92.954 17.497 92.660 17.497Q92.229 17.497 91.842 17.291Q91.454 17.084 91.219 16.721Q90.985 16.359 90.985 15.918M94.492 15.894Q94.492 15.573 94.617 15.284Q94.742 14.995 94.967 14.772Q95.193 14.548 95.489 14.428Q95.784 14.308 96.102 14.308Q96.430 14.308 96.692 14.408Q96.953 14.507 97.129 14.689Q97.305 14.872 97.399 15.130Q97.493 15.388 97.493 15.720Q97.493 15.812 97.411 15.833L95.155 15.833L95.155 15.894Q95.155 16.482 95.439 16.865Q95.723 17.248 96.290 17.248Q96.611 17.248 96.880 17.055Q97.148 16.862 97.237 16.547Q97.244 16.506 97.319 16.492L97.411 16.492Q97.493 16.516 97.493 16.588Q97.493 16.595 97.486 16.622Q97.374 17.019 97.003 17.258Q96.632 17.497 96.208 17.497Q95.770 17.497 95.371 17.289Q94.971 17.080 94.731 16.713Q94.492 16.346 94.492 15.894M95.162 15.624L96.977 15.624Q96.977 15.347 96.880 15.095Q96.782 14.842 96.584 14.686Q96.386 14.531 96.102 14.531Q95.825 14.531 95.612 14.689Q95.398 14.848 95.280 15.103Q95.162 15.358 95.162 15.624\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-52.65 -81.505)\">\u003Cpath d=\"M100.821 17.422L100.821 16.359Q100.821 16.335 100.849 16.308Q100.876 16.281 100.900 16.281L101.009 16.281Q101.074 16.281 101.088 16.339Q101.184 16.773 101.430 17.024Q101.676 17.275 102.090 17.275Q102.431 17.275 102.684 17.142Q102.937 17.009 102.937 16.701Q102.937 16.544 102.843 16.429Q102.749 16.315 102.611 16.246Q102.472 16.178 102.305 16.140L101.724 16.041Q101.368 15.973 101.095 15.752Q100.821 15.532 100.821 15.190Q100.821 14.941 100.933 14.766Q101.044 14.592 101.230 14.493Q101.416 14.394 101.632 14.351Q101.847 14.308 102.090 14.308Q102.503 14.308 102.783 14.490L102.999 14.315Q103.009 14.312 103.016 14.310Q103.023 14.308 103.033 14.308L103.084 14.308Q103.111 14.308 103.135 14.332Q103.159 14.356 103.159 14.384L103.159 15.231Q103.159 15.252 103.135 15.279Q103.111 15.306 103.084 15.306L102.971 15.306Q102.944 15.306 102.918 15.281Q102.893 15.255 102.893 15.231Q102.893 14.995 102.787 14.831Q102.681 14.667 102.498 14.585Q102.315 14.503 102.083 14.503Q101.755 14.503 101.498 14.606Q101.242 14.708 101.242 14.985Q101.242 15.180 101.425 15.289Q101.608 15.399 101.837 15.440L102.411 15.546Q102.657 15.594 102.871 15.722Q103.084 15.850 103.221 16.053Q103.358 16.257 103.358 16.506Q103.358 17.019 102.992 17.258Q102.626 17.497 102.090 17.497Q101.594 17.497 101.262 17.203L100.996 17.477Q100.975 17.497 100.948 17.497L100.900 17.497Q100.876 17.497 100.849 17.470Q100.821 17.443 100.821 17.422M104.513 16.588L104.513 14.691L103.874 14.691L103.874 14.469Q104.192 14.469 104.409 14.259Q104.626 14.049 104.726 13.739Q104.827 13.430 104.827 13.122L105.094 13.122L105.094 14.411L106.171 14.411L106.171 14.691L105.094 14.691L105.094 16.575Q105.094 16.851 105.198 17.050Q105.302 17.248 105.562 17.248Q105.719 17.248 105.825 17.144Q105.931 17.039 105.981 16.886Q106.030 16.732 106.030 16.575L106.030 16.161L106.297 16.161L106.297 16.588Q106.297 16.814 106.198 17.024Q106.099 17.234 105.914 17.366Q105.730 17.497 105.501 17.497Q105.063 17.497 104.788 17.260Q104.513 17.022 104.513 16.588M107.165 16.701Q107.165 16.369 107.389 16.142Q107.613 15.915 107.956 15.787Q108.300 15.658 108.673 15.606Q109.045 15.553 109.349 15.553L109.349 15.300Q109.349 15.095 109.242 14.915Q109.134 14.736 108.953 14.633Q108.772 14.531 108.563 14.531Q108.156 14.531 107.921 14.623Q108.009 14.660 108.056 14.744Q108.102 14.828 108.102 14.930Q108.102 15.026 108.056 15.105Q108.009 15.183 107.929 15.228Q107.849 15.272 107.760 15.272Q107.610 15.272 107.509 15.175Q107.408 15.077 107.408 14.930Q107.408 14.308 108.563 14.308Q108.775 14.308 109.025 14.372Q109.274 14.435 109.476 14.554Q109.677 14.674 109.804 14.859Q109.930 15.043 109.930 15.286L109.930 16.862Q109.930 16.978 109.992 17.074Q110.053 17.169 110.166 17.169Q110.276 17.169 110.340 17.075Q110.405 16.981 110.405 16.862L110.405 16.414L110.672 16.414L110.672 16.862Q110.672 17.132 110.445 17.297Q110.217 17.463 109.937 17.463Q109.729 17.463 109.592 17.309Q109.455 17.156 109.431 16.940Q109.284 17.207 109.002 17.352Q108.720 17.497 108.396 17.497Q108.119 17.497 107.835 17.422Q107.551 17.347 107.358 17.168Q107.165 16.988 107.165 16.701M107.780 16.701Q107.780 16.875 107.881 17.005Q107.982 17.135 108.138 17.205Q108.293 17.275 108.457 17.275Q108.676 17.275 108.884 17.178Q109.093 17.080 109.221 16.899Q109.349 16.718 109.349 16.492L109.349 15.764Q109.025 15.764 108.659 15.855Q108.293 15.946 108.037 16.158Q107.780 16.369 107.780 16.701M112.771 17.429L111.137 17.429L111.137 17.149Q111.366 17.149 111.515 17.115Q111.663 17.080 111.663 16.940L111.663 15.091Q111.663 14.821 111.556 14.760Q111.448 14.698 111.137 14.698L111.137 14.418L112.196 14.343L112.196 14.992Q112.367 14.684 112.672 14.513Q112.976 14.343 113.321 14.343Q113.827 14.343 114.111 14.566Q114.394 14.790 114.394 15.286L114.394 16.940Q114.394 17.077 114.543 17.113Q114.692 17.149 114.917 17.149L114.917 17.429L113.287 17.429L113.287 17.149Q113.516 17.149 113.664 17.115Q113.813 17.080 113.813 16.940L113.813 15.300Q113.813 14.965 113.694 14.765Q113.574 14.565 113.259 14.565Q112.989 14.565 112.755 14.701Q112.521 14.838 112.383 15.072Q112.244 15.306 112.244 15.580L112.244 16.940Q112.244 17.077 112.395 17.113Q112.545 17.149 112.771 17.149L112.771 17.429M115.505 15.918Q115.505 15.580 115.645 15.289Q115.785 14.999 116.030 14.785Q116.274 14.572 116.578 14.457Q116.882 14.343 117.207 14.343Q117.477 14.343 117.740 14.442Q118.004 14.541 118.195 14.719L118.195 13.321Q118.195 13.051 118.087 12.989Q117.980 12.928 117.669 12.928L117.669 12.647L118.745 12.572L118.745 16.756Q118.745 16.944 118.800 17.027Q118.855 17.111 118.955 17.130Q119.056 17.149 119.272 17.149L119.272 17.429L118.164 17.497L118.164 17.080Q117.747 17.497 117.122 17.497Q116.691 17.497 116.319 17.285Q115.946 17.074 115.726 16.713Q115.505 16.352 115.505 15.918M117.180 17.275Q117.388 17.275 117.575 17.203Q117.761 17.132 117.915 16.995Q118.069 16.858 118.164 16.680L118.164 15.071Q118.079 14.924 117.934 14.804Q117.788 14.684 117.619 14.625Q117.450 14.565 117.269 14.565Q116.708 14.565 116.440 14.954Q116.172 15.344 116.172 15.925Q116.172 16.496 116.406 16.886Q116.640 17.275 117.180 17.275M119.979 16.701Q119.979 16.369 120.203 16.142Q120.427 15.915 120.770 15.787Q121.114 15.658 121.486 15.606Q121.859 15.553 122.163 15.553L122.163 15.300Q122.163 15.095 122.056 14.915Q121.948 14.736 121.767 14.633Q121.586 14.531 121.377 14.531Q120.970 14.531 120.735 14.623Q120.823 14.660 120.870 14.744Q120.916 14.828 120.916 14.930Q120.916 15.026 120.870 15.105Q120.823 15.183 120.743 15.228Q120.663 15.272 120.574 15.272Q120.424 15.272 120.323 15.175Q120.222 15.077 120.222 14.930Q120.222 14.308 121.377 14.308Q121.589 14.308 121.839 14.372Q122.088 14.435 122.290 14.554Q122.491 14.674 122.618 14.859Q122.744 15.043 122.744 15.286L122.744 16.862Q122.744 16.978 122.806 17.074Q122.867 17.169 122.980 17.169Q123.090 17.169 123.154 17.075Q123.219 16.981 123.219 16.862L123.219 16.414L123.486 16.414L123.486 16.862Q123.486 17.132 123.259 17.297Q123.031 17.463 122.751 17.463Q122.543 17.463 122.406 17.309Q122.269 17.156 122.245 16.940Q122.098 17.207 121.816 17.352Q121.534 17.497 121.210 17.497Q120.933 17.497 120.649 17.422Q120.365 17.347 120.172 17.168Q119.979 16.988 119.979 16.701M120.594 16.701Q120.594 16.875 120.695 17.005Q120.796 17.135 120.952 17.205Q121.107 17.275 121.271 17.275Q121.490 17.275 121.698 17.178Q121.907 17.080 122.035 16.899Q122.163 16.718 122.163 16.492L122.163 15.764Q121.839 15.764 121.473 15.855Q121.107 15.946 120.851 16.158Q120.594 16.369 120.594 16.701M125.653 17.429L123.917 17.429L123.917 17.149Q124.146 17.149 124.294 17.115Q124.443 17.080 124.443 16.940L124.443 15.091Q124.443 14.821 124.335 14.760Q124.228 14.698 123.917 14.698L123.917 14.418L124.945 14.343L124.945 15.050Q125.075 14.742 125.318 14.543Q125.561 14.343 125.879 14.343Q126.097 14.343 126.268 14.467Q126.439 14.592 126.439 14.804Q126.439 14.941 126.340 15.040Q126.241 15.139 126.108 15.139Q125.971 15.139 125.872 15.040Q125.773 14.941 125.773 14.804Q125.773 14.664 125.872 14.565Q125.581 14.565 125.381 14.761Q125.181 14.958 125.089 15.252Q124.997 15.546 124.997 15.826L124.997 16.940Q124.997 17.149 125.653 17.149L125.653 17.429M127.024 15.918Q127.024 15.580 127.164 15.289Q127.304 14.999 127.548 14.785Q127.793 14.572 128.097 14.457Q128.401 14.343 128.726 14.343Q128.996 14.343 129.259 14.442Q129.522 14.541 129.714 14.719L129.714 13.321Q129.714 13.051 129.606 12.989Q129.498 12.928 129.187 12.928L129.187 12.647L130.264 12.572L130.264 16.756Q130.264 16.944 130.319 17.027Q130.373 17.111 130.474 17.130Q130.575 17.149 130.790 17.149L130.790 17.429L129.683 17.497L129.683 17.080Q129.266 17.497 128.640 17.497Q128.210 17.497 127.837 17.285Q127.465 17.074 127.244 16.713Q127.024 16.352 127.024 15.918M128.698 17.275Q128.907 17.275 129.093 17.203Q129.279 17.132 129.433 16.995Q129.587 16.858 129.683 16.680L129.683 15.071Q129.597 14.924 129.452 14.804Q129.307 14.684 129.138 14.625Q128.968 14.565 128.787 14.565Q128.227 14.565 127.958 14.954Q127.690 15.344 127.690 15.925Q127.690 16.496 127.924 16.886Q128.158 17.275 128.698 17.275\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(57.412 -43.133)\">\u003Cpath d=\"M54.787 17.491L54.787 15.918Q54.787 15.891 54.812 15.865Q54.838 15.840 54.865 15.840L54.978 15.840Q55.006 15.840 55.029 15.867Q55.053 15.894 55.053 15.918Q55.053 16.263 55.185 16.527Q55.317 16.790 55.546 16.959Q55.775 17.128 56.077 17.209Q56.380 17.289 56.721 17.289Q56.988 17.289 57.224 17.161Q57.460 17.033 57.605 16.810Q57.750 16.588 57.750 16.322Q57.750 16.099 57.644 15.903Q57.538 15.706 57.357 15.571Q57.176 15.436 56.950 15.385L55.922 15.153Q55.611 15.081 55.351 14.895Q55.091 14.708 54.939 14.437Q54.787 14.165 54.787 13.850Q54.787 13.464 55 13.157Q55.214 12.849 55.561 12.678Q55.908 12.507 56.287 12.507Q56.516 12.507 56.745 12.560Q56.974 12.613 57.173 12.721Q57.371 12.828 57.525 12.992L57.819 12.552Q57.842 12.507 57.883 12.507L57.931 12.507Q57.962 12.507 57.984 12.533Q58.006 12.558 58.006 12.586L58.006 14.161Q58.006 14.182 57.983 14.209Q57.959 14.237 57.931 14.237L57.819 14.237Q57.757 14.237 57.743 14.161Q57.702 13.748 57.521 13.428Q57.340 13.109 57.029 12.934Q56.718 12.760 56.287 12.760Q56.038 12.760 55.798 12.871Q55.559 12.982 55.409 13.180Q55.258 13.379 55.258 13.642Q55.258 13.854 55.366 14.035Q55.474 14.216 55.650 14.336Q55.826 14.455 56.034 14.496L57.063 14.725Q57.381 14.797 57.648 15.002Q57.914 15.207 58.066 15.501Q58.218 15.795 58.218 16.127Q58.218 16.520 58.013 16.855Q57.808 17.190 57.463 17.379Q57.118 17.569 56.721 17.569Q56.301 17.569 55.922 17.456Q55.542 17.344 55.272 17.094L54.978 17.528Q54.951 17.569 54.913 17.569L54.865 17.569Q54.838 17.569 54.812 17.544Q54.787 17.518 54.787 17.491M58.987 15.894Q58.987 15.573 59.112 15.284Q59.237 14.995 59.463 14.772Q59.688 14.548 59.984 14.428Q60.279 14.308 60.597 14.308Q60.925 14.308 61.187 14.408Q61.448 14.507 61.624 14.689Q61.800 14.872 61.894 15.130Q61.988 15.388 61.988 15.720Q61.988 15.812 61.906 15.833L59.651 15.833L59.651 15.894Q59.651 16.482 59.934 16.865Q60.218 17.248 60.785 17.248Q61.107 17.248 61.375 17.055Q61.643 16.862 61.732 16.547Q61.739 16.506 61.814 16.492L61.906 16.492Q61.988 16.516 61.988 16.588Q61.988 16.595 61.982 16.622Q61.869 17.019 61.498 17.258Q61.127 17.497 60.703 17.497Q60.266 17.497 59.866 17.289Q59.466 17.080 59.227 16.713Q58.987 16.346 58.987 15.894M59.657 15.624L61.472 15.624Q61.472 15.347 61.375 15.095Q61.277 14.842 61.079 14.686Q60.881 14.531 60.597 14.531Q60.320 14.531 60.107 14.689Q59.893 14.848 59.775 15.103Q59.657 15.358 59.657 15.624M64.258 17.429L62.624 17.429L62.624 17.149Q62.853 17.149 63.002 17.115Q63.151 17.080 63.151 16.940L63.151 15.091Q63.151 14.821 63.043 14.760Q62.935 14.698 62.624 14.698L62.624 14.418L63.684 14.343L63.684 14.992Q63.855 14.684 64.159 14.513Q64.463 14.343 64.808 14.343Q65.314 14.343 65.598 14.566Q65.881 14.790 65.881 15.286L65.881 16.940Q65.881 17.077 66.030 17.113Q66.179 17.149 66.404 17.149L66.404 17.429L64.774 17.429L64.774 17.149Q65.003 17.149 65.152 17.115Q65.300 17.080 65.300 16.940L65.300 15.300Q65.300 14.965 65.181 14.765Q65.061 14.565 64.747 14.565Q64.477 14.565 64.243 14.701Q64.008 14.838 63.870 15.072Q63.732 15.306 63.732 15.580L63.732 16.940Q63.732 17.077 63.882 17.113Q64.032 17.149 64.258 17.149L64.258 17.429M66.992 17.422L66.992 16.359Q66.992 16.335 67.020 16.308Q67.047 16.281 67.071 16.281L67.180 16.281Q67.245 16.281 67.259 16.339Q67.355 16.773 67.601 17.024Q67.847 17.275 68.260 17.275Q68.602 17.275 68.855 17.142Q69.108 17.009 69.108 16.701Q69.108 16.544 69.014 16.429Q68.920 16.315 68.782 16.246Q68.643 16.178 68.476 16.140L67.895 16.041Q67.539 15.973 67.266 15.752Q66.992 15.532 66.992 15.190Q66.992 14.941 67.103 14.766Q67.215 14.592 67.401 14.493Q67.587 14.394 67.802 14.351Q68.018 14.308 68.260 14.308Q68.674 14.308 68.954 14.490L69.170 14.315Q69.180 14.312 69.187 14.310Q69.194 14.308 69.204 14.308L69.255 14.308Q69.282 14.308 69.306 14.332Q69.330 14.356 69.330 14.384L69.330 15.231Q69.330 15.252 69.306 15.279Q69.282 15.306 69.255 15.306L69.142 15.306Q69.115 15.306 69.089 15.281Q69.064 15.255 69.064 15.231Q69.064 14.995 68.958 14.831Q68.852 14.667 68.669 14.585Q68.486 14.503 68.254 14.503Q67.925 14.503 67.669 14.606Q67.413 14.708 67.413 14.985Q67.413 15.180 67.596 15.289Q67.778 15.399 68.007 15.440L68.582 15.546Q68.828 15.594 69.041 15.722Q69.255 15.850 69.392 16.053Q69.528 16.257 69.528 16.506Q69.528 17.019 69.163 17.258Q68.797 17.497 68.260 17.497Q67.765 17.497 67.433 17.203L67.167 17.477Q67.146 17.497 67.119 17.497L67.071 17.497Q67.047 17.497 67.020 17.470Q66.992 17.443 66.992 17.422M70.116 15.946Q70.116 15.604 70.251 15.305Q70.386 15.006 70.626 14.782Q70.865 14.558 71.183 14.433Q71.501 14.308 71.832 14.308Q72.277 14.308 72.676 14.524Q73.076 14.739 73.310 15.117Q73.545 15.494 73.545 15.946Q73.545 16.287 73.403 16.571Q73.261 16.855 73.017 17.062Q72.772 17.268 72.463 17.383Q72.153 17.497 71.832 17.497Q71.402 17.497 71 17.296Q70.598 17.094 70.357 16.742Q70.116 16.390 70.116 15.946M71.832 17.248Q72.434 17.248 72.658 16.870Q72.881 16.492 72.881 15.860Q72.881 15.248 72.647 14.889Q72.413 14.531 71.832 14.531Q70.779 14.531 70.779 15.860Q70.779 16.492 71.005 16.870Q71.231 17.248 71.832 17.248M75.889 17.429L74.153 17.429L74.153 17.149Q74.382 17.149 74.531 17.115Q74.679 17.080 74.679 16.940L74.679 15.091Q74.679 14.821 74.572 14.760Q74.464 14.698 74.153 14.698L74.153 14.418L75.182 14.343L75.182 15.050Q75.312 14.742 75.554 14.543Q75.797 14.343 76.115 14.343Q76.334 14.343 76.505 14.467Q76.675 14.592 76.675 14.804Q76.675 14.941 76.576 15.040Q76.477 15.139 76.344 15.139Q76.207 15.139 76.108 15.040Q76.009 14.941 76.009 14.804Q76.009 14.664 76.108 14.565Q75.818 14.565 75.618 14.761Q75.418 14.958 75.325 15.252Q75.233 15.546 75.233 15.826L75.233 16.940Q75.233 17.149 75.889 17.149L75.889 17.429M77.260 17.422L77.260 16.359Q77.260 16.335 77.287 16.308Q77.315 16.281 77.339 16.281L77.448 16.281Q77.513 16.281 77.527 16.339Q77.622 16.773 77.868 17.024Q78.114 17.275 78.528 17.275Q78.870 17.275 79.123 17.142Q79.376 17.009 79.376 16.701Q79.376 16.544 79.282 16.429Q79.188 16.315 79.049 16.246Q78.911 16.178 78.743 16.140L78.162 16.041Q77.807 15.973 77.533 15.752Q77.260 15.532 77.260 15.190Q77.260 14.941 77.371 14.766Q77.482 14.592 77.668 14.493Q77.855 14.394 78.070 14.351Q78.285 14.308 78.528 14.308Q78.942 14.308 79.222 14.490L79.437 14.315Q79.447 14.312 79.454 14.310Q79.461 14.308 79.471 14.308L79.523 14.308Q79.550 14.308 79.574 14.332Q79.598 14.356 79.598 14.384L79.598 15.231Q79.598 15.252 79.574 15.279Q79.550 15.306 79.523 15.306L79.410 15.306Q79.382 15.306 79.357 15.281Q79.331 15.255 79.331 15.231Q79.331 14.995 79.225 14.831Q79.119 14.667 78.936 14.585Q78.754 14.503 78.521 14.503Q78.193 14.503 77.937 14.606Q77.680 14.708 77.680 14.985Q77.680 15.180 77.863 15.289Q78.046 15.399 78.275 15.440L78.849 15.546Q79.095 15.594 79.309 15.722Q79.523 15.850 79.659 16.053Q79.796 16.257 79.796 16.506Q79.796 17.019 79.430 17.258Q79.065 17.497 78.528 17.497Q78.032 17.497 77.701 17.203L77.434 17.477Q77.414 17.497 77.386 17.497L77.339 17.497Q77.315 17.497 77.287 17.470Q77.260 17.443 77.260 17.422\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(48.858 72.1)\">\u003Cpath d=\"M56.202 17.429L54.612 17.429L54.612 17.149Q55.255 17.149 55.412 16.749L57.056 12.534Q57.090 12.439 57.203 12.439L57.285 12.439Q57.395 12.439 57.436 12.534L59.155 16.940Q59.223 17.080 59.413 17.115Q59.603 17.149 59.876 17.149L59.876 17.429L57.877 17.429L57.877 17.149Q58.441 17.149 58.441 16.974Q58.441 16.957 58.439 16.950Q58.437 16.944 58.434 16.940L58.013 15.874L56.055 15.874L55.713 16.749Q55.699 16.749 55.699 16.827Q55.699 16.988 55.862 17.068Q56.024 17.149 56.202 17.149L56.202 17.429M57.036 13.355L56.168 15.594L57.911 15.594L57.036 13.355M60.512 15.918Q60.512 15.590 60.647 15.289Q60.782 14.989 61.018 14.768Q61.254 14.548 61.558 14.428Q61.862 14.308 62.187 14.308Q62.693 14.308 63.041 14.411Q63.390 14.513 63.390 14.889Q63.390 15.036 63.292 15.137Q63.195 15.238 63.048 15.238Q62.894 15.238 62.795 15.139Q62.696 15.040 62.696 14.889Q62.696 14.701 62.836 14.609Q62.634 14.558 62.194 14.558Q61.838 14.558 61.609 14.754Q61.380 14.951 61.279 15.260Q61.178 15.570 61.178 15.918Q61.178 16.267 61.305 16.573Q61.431 16.879 61.686 17.063Q61.941 17.248 62.296 17.248Q62.518 17.248 62.703 17.164Q62.887 17.080 63.022 16.925Q63.157 16.769 63.215 16.561Q63.229 16.506 63.284 16.506L63.397 16.506Q63.427 16.506 63.450 16.530Q63.472 16.554 63.472 16.588L63.472 16.609Q63.386 16.896 63.198 17.094Q63.010 17.292 62.746 17.395Q62.481 17.497 62.187 17.497Q61.756 17.497 61.368 17.291Q60.980 17.084 60.746 16.721Q60.512 16.359 60.512 15.918M64.586 16.588L64.586 14.691L63.947 14.691L63.947 14.469Q64.265 14.469 64.482 14.259Q64.699 14.049 64.800 13.739Q64.901 13.430 64.901 13.122L65.167 13.122L65.167 14.411L66.244 14.411L66.244 14.691L65.167 14.691L65.167 16.575Q65.167 16.851 65.271 17.050Q65.376 17.248 65.635 17.248Q65.793 17.248 65.899 17.144Q66.005 17.039 66.054 16.886Q66.104 16.732 66.104 16.575L66.104 16.161L66.370 16.161L66.370 16.588Q66.370 16.814 66.271 17.024Q66.172 17.234 65.987 17.366Q65.803 17.497 65.574 17.497Q65.136 17.497 64.861 17.260Q64.586 17.022 64.586 16.588M67.755 16.595L67.755 15.091Q67.755 14.821 67.647 14.760Q67.539 14.698 67.228 14.698L67.228 14.418L68.336 14.343L68.336 16.575L68.336 16.595Q68.336 16.875 68.387 17.019Q68.438 17.162 68.580 17.219Q68.722 17.275 69.009 17.275Q69.262 17.275 69.467 17.135Q69.672 16.995 69.788 16.769Q69.904 16.544 69.904 16.294L69.904 15.091Q69.904 14.821 69.797 14.760Q69.689 14.698 69.378 14.698L69.378 14.418L70.486 14.343L70.486 16.756Q70.486 16.947 70.538 17.029Q70.591 17.111 70.692 17.130Q70.793 17.149 71.008 17.149L71.008 17.429L69.932 17.497L69.932 16.933Q69.822 17.115 69.677 17.238Q69.532 17.361 69.346 17.429Q69.159 17.497 68.958 17.497Q67.755 17.497 67.755 16.595M71.654 16.701Q71.654 16.369 71.878 16.142Q72.102 15.915 72.446 15.787Q72.789 15.658 73.162 15.606Q73.534 15.553 73.839 15.553L73.839 15.300Q73.839 15.095 73.731 14.915Q73.623 14.736 73.442 14.633Q73.261 14.531 73.052 14.531Q72.646 14.531 72.410 14.623Q72.499 14.660 72.545 14.744Q72.591 14.828 72.591 14.930Q72.591 15.026 72.545 15.105Q72.499 15.183 72.418 15.228Q72.338 15.272 72.249 15.272Q72.099 15.272 71.998 15.175Q71.897 15.077 71.897 14.930Q71.897 14.308 73.052 14.308Q73.264 14.308 73.514 14.372Q73.763 14.435 73.965 14.554Q74.167 14.674 74.293 14.859Q74.420 15.043 74.420 15.286L74.420 16.862Q74.420 16.978 74.481 17.074Q74.543 17.169 74.655 17.169Q74.765 17.169 74.830 17.075Q74.895 16.981 74.895 16.862L74.895 16.414L75.161 16.414L75.161 16.862Q75.161 17.132 74.934 17.297Q74.707 17.463 74.426 17.463Q74.218 17.463 74.081 17.309Q73.944 17.156 73.921 16.940Q73.774 17.207 73.492 17.352Q73.210 17.497 72.885 17.497Q72.608 17.497 72.324 17.422Q72.041 17.347 71.848 17.168Q71.654 16.988 71.654 16.701M72.270 16.701Q72.270 16.875 72.371 17.005Q72.471 17.135 72.627 17.205Q72.782 17.275 72.946 17.275Q73.165 17.275 73.374 17.178Q73.582 17.080 73.710 16.899Q73.839 16.718 73.839 16.492L73.839 15.764Q73.514 15.764 73.148 15.855Q72.782 15.946 72.526 16.158Q72.270 16.369 72.270 16.701M76.105 16.588L76.105 14.691L75.465 14.691L75.465 14.469Q75.783 14.469 76 14.259Q76.217 14.049 76.318 13.739Q76.419 13.430 76.419 13.122L76.686 13.122L76.686 14.411L77.762 14.411L77.762 14.691L76.686 14.691L76.686 16.575Q76.686 16.851 76.790 17.050Q76.894 17.248 77.154 17.248Q77.311 17.248 77.417 17.144Q77.523 17.039 77.573 16.886Q77.622 16.732 77.622 16.575L77.622 16.161L77.889 16.161L77.889 16.588Q77.889 16.814 77.790 17.024Q77.691 17.234 77.506 17.366Q77.321 17.497 77.092 17.497Q76.655 17.497 76.380 17.260Q76.105 17.022 76.105 16.588M78.658 15.946Q78.658 15.604 78.793 15.305Q78.928 15.006 79.167 14.782Q79.406 14.558 79.724 14.433Q80.042 14.308 80.374 14.308Q80.818 14.308 81.218 14.524Q81.618 14.739 81.852 15.117Q82.086 15.494 82.086 15.946Q82.086 16.287 81.944 16.571Q81.802 16.855 81.558 17.062Q81.314 17.268 81.004 17.383Q80.695 17.497 80.374 17.497Q79.943 17.497 79.541 17.296Q79.140 17.094 78.899 16.742Q78.658 16.390 78.658 15.946M80.374 17.248Q80.975 17.248 81.199 16.870Q81.423 16.492 81.423 15.860Q81.423 15.248 81.189 14.889Q80.955 14.531 80.374 14.531Q79.321 14.531 79.321 15.860Q79.321 16.492 79.547 16.870Q79.772 17.248 80.374 17.248M84.431 17.429L82.694 17.429L82.694 17.149Q82.923 17.149 83.072 17.115Q83.221 17.080 83.221 16.940L83.221 15.091Q83.221 14.821 83.113 14.760Q83.006 14.698 82.694 14.698L82.694 14.418L83.723 14.343L83.723 15.050Q83.853 14.742 84.096 14.543Q84.339 14.343 84.656 14.343Q84.875 14.343 85.046 14.467Q85.217 14.592 85.217 14.804Q85.217 14.941 85.118 15.040Q85.019 15.139 84.885 15.139Q84.749 15.139 84.650 15.040Q84.550 14.941 84.550 14.804Q84.550 14.664 84.650 14.565Q84.359 14.565 84.159 14.761Q83.959 14.958 83.867 15.252Q83.775 15.546 83.775 15.826L83.775 16.940Q83.775 17.149 84.431 17.149L84.431 17.429M85.801 17.422L85.801 16.359Q85.801 16.335 85.829 16.308Q85.856 16.281 85.880 16.281L85.989 16.281Q86.054 16.281 86.068 16.339Q86.164 16.773 86.410 17.024Q86.656 17.275 87.069 17.275Q87.411 17.275 87.664 17.142Q87.917 17.009 87.917 16.701Q87.917 16.544 87.823 16.429Q87.729 16.315 87.591 16.246Q87.452 16.178 87.285 16.140L86.704 16.041Q86.348 15.973 86.075 15.752Q85.801 15.532 85.801 15.190Q85.801 14.941 85.913 14.766Q86.024 14.592 86.210 14.493Q86.396 14.394 86.611 14.351Q86.827 14.308 87.069 14.308Q87.483 14.308 87.763 14.490L87.979 14.315Q87.989 14.312 87.996 14.310Q88.003 14.308 88.013 14.308L88.064 14.308Q88.091 14.308 88.115 14.332Q88.139 14.356 88.139 14.384L88.139 15.231Q88.139 15.252 88.115 15.279Q88.091 15.306 88.064 15.306L87.951 15.306Q87.924 15.306 87.898 15.281Q87.873 15.255 87.873 15.231Q87.873 14.995 87.767 14.831Q87.661 14.667 87.478 14.585Q87.295 14.503 87.063 14.503Q86.735 14.503 86.478 14.606Q86.222 14.708 86.222 14.985Q86.222 15.180 86.405 15.289Q86.588 15.399 86.817 15.440L87.391 15.546Q87.637 15.594 87.850 15.722Q88.064 15.850 88.201 16.053Q88.338 16.257 88.338 16.506Q88.338 17.019 87.972 17.258Q87.606 17.497 87.069 17.497Q86.574 17.497 86.242 17.203L85.976 17.477Q85.955 17.497 85.928 17.497L85.880 17.497Q85.856 17.497 85.829 17.470Q85.801 17.443 85.801 17.422\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M5.929-9.601h68.286V-40.9H5.93Z\"\u002F>\u003Cg transform=\"translate(-24.855 -39.946)\">\u003Cpath d=\"M54.771 14.695Q54.771 14.101 55.003 13.570Q55.236 13.038 55.652 12.638Q56.068 12.238 56.601 12.017Q57.134 11.796 57.739 11.796Q58.177 11.796 58.575 11.978Q58.974 12.159 59.282 12.491L59.755 11.827Q59.786 11.796 59.818 11.796L59.864 11.796Q59.892 11.796 59.923 11.827Q59.954 11.859 59.954 11.886L59.954 14.023Q59.954 14.046 59.923 14.077Q59.892 14.109 59.864 14.109L59.747 14.109Q59.720 14.109 59.689 14.077Q59.657 14.046 59.657 14.023Q59.657 13.757 59.515 13.404Q59.372 13.050 59.193 12.812Q58.939 12.480 58.589 12.286Q58.239 12.093 57.833 12.093Q57.329 12.093 56.876 12.312Q56.423 12.531 56.130 12.925Q55.634 13.593 55.634 14.695Q55.634 15.226 55.771 15.693Q55.907 16.159 56.183 16.525Q56.458 16.890 56.878 17.095Q57.298 17.300 57.841 17.300Q58.329 17.300 58.753 17.056Q59.177 16.812 59.425 16.392Q59.673 15.972 59.673 15.476Q59.673 15.441 59.702 15.415Q59.732 15.390 59.763 15.390L59.864 15.390Q59.907 15.390 59.931 15.419Q59.954 15.449 59.954 15.491Q59.954 15.929 59.778 16.318Q59.603 16.706 59.292 16.990Q58.982 17.273 58.571 17.435Q58.161 17.597 57.739 17.597Q57.150 17.597 56.609 17.376Q56.068 17.156 55.652 16.751Q55.236 16.347 55.003 15.818Q54.771 15.288 54.771 14.695M62.681 17.429L60.700 17.429L60.700 17.132Q60.970 17.132 61.138 17.087Q61.306 17.042 61.306 16.870L61.306 14.734Q61.306 14.519 61.243 14.423Q61.181 14.327 61.064 14.306Q60.946 14.284 60.700 14.284L60.700 13.988L61.868 13.902L61.868 14.687Q61.946 14.476 62.099 14.290Q62.251 14.105 62.450 14.003Q62.650 13.902 62.876 13.902Q63.122 13.902 63.314 14.046Q63.505 14.191 63.505 14.421Q63.505 14.577 63.400 14.687Q63.294 14.796 63.138 14.796Q62.982 14.796 62.872 14.687Q62.763 14.577 62.763 14.421Q62.763 14.261 62.868 14.156Q62.544 14.156 62.329 14.384Q62.114 14.613 62.019 14.952Q61.923 15.292 61.923 15.597L61.923 16.870Q61.923 17.038 62.150 17.085Q62.376 17.132 62.681 17.132L62.681 17.429M65.845 17.429L64.068 17.429L64.068 17.132Q64.341 17.132 64.509 17.085Q64.677 17.038 64.677 16.870L64.677 14.734Q64.677 14.519 64.620 14.423Q64.564 14.327 64.450 14.306Q64.337 14.284 64.091 14.284L64.091 13.988L65.290 13.902L65.290 16.870Q65.290 17.038 65.437 17.085Q65.583 17.132 65.845 17.132L65.845 17.429M64.403 12.507Q64.403 12.316 64.538 12.185Q64.673 12.054 64.868 12.054Q64.989 12.054 65.093 12.116Q65.196 12.179 65.259 12.283Q65.321 12.386 65.321 12.507Q65.321 12.702 65.191 12.837Q65.060 12.972 64.868 12.972Q64.669 12.972 64.536 12.839Q64.403 12.706 64.403 12.507M66.970 16.468L66.970 14.277L66.267 14.277L66.267 14.023Q66.622 14.023 66.864 13.790Q67.107 13.558 67.218 13.210Q67.329 12.863 67.329 12.507L67.611 12.507L67.611 13.980L68.786 13.980L68.786 14.277L67.611 14.277L67.611 16.452Q67.611 16.773 67.730 17.001Q67.849 17.230 68.130 17.230Q68.310 17.230 68.427 17.107Q68.544 16.984 68.597 16.804Q68.650 16.624 68.650 16.452L68.650 15.980L68.931 15.980L68.931 16.468Q68.931 16.722 68.825 16.962Q68.720 17.202 68.523 17.355Q68.325 17.507 68.068 17.507Q67.751 17.507 67.499 17.384Q67.247 17.261 67.109 17.027Q66.970 16.792 66.970 16.468M71.509 17.429L69.732 17.429L69.732 17.132Q70.005 17.132 70.173 17.085Q70.341 17.038 70.341 16.870L70.341 14.734Q70.341 14.519 70.284 14.423Q70.228 14.327 70.114 14.306Q70.001 14.284 69.755 14.284L69.755 13.988L70.954 13.902L70.954 16.870Q70.954 17.038 71.101 17.085Q71.247 17.132 71.509 17.132L71.509 17.429M70.068 12.507Q70.068 12.316 70.202 12.185Q70.337 12.054 70.532 12.054Q70.653 12.054 70.757 12.116Q70.861 12.179 70.923 12.283Q70.986 12.386 70.986 12.507Q70.986 12.702 70.855 12.837Q70.724 12.972 70.532 12.972Q70.333 12.972 70.200 12.839Q70.068 12.706 70.068 12.507M72.052 15.702Q72.052 15.206 72.302 14.781Q72.552 14.355 72.972 14.109Q73.392 13.863 73.892 13.863Q74.431 13.863 74.821 13.988Q75.212 14.113 75.212 14.527Q75.212 14.632 75.161 14.724Q75.111 14.816 75.019 14.866Q74.927 14.917 74.818 14.917Q74.712 14.917 74.620 14.866Q74.528 14.816 74.478 14.724Q74.427 14.632 74.427 14.527Q74.427 14.304 74.595 14.199Q74.372 14.140 73.900 14.140Q73.603 14.140 73.388 14.279Q73.173 14.417 73.042 14.648Q72.911 14.878 72.853 15.148Q72.794 15.417 72.794 15.702Q72.794 16.097 72.927 16.447Q73.060 16.796 73.331 17.013Q73.603 17.230 74.001 17.230Q74.376 17.230 74.652 17.013Q74.927 16.796 75.028 16.437Q75.044 16.374 75.107 16.374L75.212 16.374Q75.247 16.374 75.273 16.402Q75.298 16.429 75.298 16.468L75.298 16.491Q75.165 16.972 74.780 17.240Q74.396 17.507 73.892 17.507Q73.528 17.507 73.194 17.370Q72.861 17.234 72.601 16.984Q72.341 16.734 72.196 16.398Q72.052 16.062 72.052 15.702\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-36.75 45.882h68.286V14.584h-68.287Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-73.258 20.287)\">\u003Cpath d=\"M59.017 7.929L54.634 7.929L54.634 7.632Q54.954 7.632 55.198 7.585Q55.443 7.538 55.443 7.370L55.443 3.027Q55.443 2.855 55.198 2.808Q54.954 2.761 54.634 2.761L54.634 2.464L57.220 2.464L57.220 2.761Q56.208 2.761 56.208 3.027L56.208 7.370Q56.208 7.542 56.300 7.587Q56.392 7.632 56.611 7.632L57.298 7.632Q57.771 7.632 58.079 7.507Q58.388 7.382 58.566 7.152Q58.743 6.921 58.835 6.595Q58.927 6.269 58.970 5.816L59.251 5.816L59.017 7.929M59.841 6.175Q59.841 5.695 60.073 5.279Q60.306 4.863 60.716 4.613Q61.126 4.363 61.603 4.363Q62.333 4.363 62.732 4.804Q63.130 5.245 63.130 5.976Q63.130 6.081 63.036 6.105L60.587 6.105L60.587 6.175Q60.587 6.585 60.708 6.941Q60.829 7.296 61.101 7.513Q61.372 7.730 61.802 7.730Q62.165 7.730 62.462 7.501Q62.759 7.273 62.861 6.921Q62.868 6.874 62.954 6.859L63.036 6.859Q63.130 6.886 63.130 6.968Q63.130 6.976 63.122 7.007Q63.060 7.234 62.921 7.417Q62.782 7.601 62.591 7.734Q62.400 7.867 62.181 7.937Q61.962 8.007 61.724 8.007Q61.353 8.007 61.015 7.870Q60.677 7.734 60.409 7.482Q60.142 7.230 59.991 6.890Q59.841 6.550 59.841 6.175M60.595 5.867L62.556 5.867Q62.556 5.562 62.454 5.271Q62.353 4.980 62.136 4.798Q61.919 4.617 61.603 4.617Q61.302 4.617 61.071 4.804Q60.841 4.992 60.718 5.283Q60.595 5.574 60.595 5.867M63.716 7.097Q63.716 6.613 64.118 6.318Q64.521 6.023 65.071 5.904Q65.622 5.784 66.114 5.784L66.114 5.495Q66.114 5.269 65.999 5.062Q65.884 4.855 65.687 4.736Q65.489 4.617 65.259 4.617Q64.833 4.617 64.548 4.722Q64.618 4.749 64.665 4.804Q64.712 4.859 64.737 4.929Q64.763 4.999 64.763 5.074Q64.763 5.179 64.712 5.271Q64.661 5.363 64.569 5.413Q64.478 5.464 64.372 5.464Q64.267 5.464 64.175 5.413Q64.083 5.363 64.032 5.271Q63.982 5.179 63.982 5.074Q63.982 4.656 64.370 4.509Q64.759 4.363 65.259 4.363Q65.591 4.363 65.944 4.493Q66.298 4.624 66.527 4.878Q66.755 5.132 66.755 5.480L66.755 7.281Q66.755 7.413 66.827 7.523Q66.900 7.632 67.028 7.632Q67.153 7.632 67.222 7.527Q67.290 7.421 67.290 7.281L67.290 6.769L67.571 6.769L67.571 7.281Q67.571 7.484 67.454 7.642Q67.337 7.800 67.155 7.884Q66.974 7.968 66.771 7.968Q66.540 7.968 66.388 7.796Q66.236 7.624 66.204 7.394Q66.044 7.675 65.736 7.841Q65.427 8.007 65.075 8.007Q64.564 8.007 64.140 7.784Q63.716 7.562 63.716 7.097M64.403 7.097Q64.403 7.382 64.630 7.568Q64.857 7.753 65.150 7.753Q65.396 7.753 65.620 7.636Q65.845 7.519 65.980 7.316Q66.114 7.113 66.114 6.859L66.114 6.027Q65.849 6.027 65.564 6.081Q65.278 6.136 65.007 6.265Q64.736 6.394 64.569 6.601Q64.403 6.808 64.403 7.097M69.872 7.929L67.892 7.929L67.892 7.632Q68.161 7.632 68.329 7.587Q68.497 7.542 68.497 7.370L68.497 5.234Q68.497 5.019 68.435 4.923Q68.372 4.827 68.255 4.806Q68.138 4.784 67.892 4.784L67.892 4.488L69.060 4.402L69.060 5.187Q69.138 4.976 69.290 4.790Q69.443 4.605 69.642 4.503Q69.841 4.402 70.068 4.402Q70.314 4.402 70.505 4.546Q70.696 4.691 70.696 4.921Q70.696 5.077 70.591 5.187Q70.486 5.296 70.329 5.296Q70.173 5.296 70.064 5.187Q69.954 5.077 69.954 4.921Q69.954 4.761 70.060 4.656Q69.736 4.656 69.521 4.884Q69.306 5.113 69.210 5.452Q69.114 5.792 69.114 6.097L69.114 7.370Q69.114 7.538 69.341 7.585Q69.568 7.632 69.872 7.632L69.872 7.929M73.107 7.929L71.251 7.929L71.251 7.632Q71.525 7.632 71.693 7.585Q71.861 7.538 71.861 7.370L71.861 5.234Q71.861 5.019 71.798 4.923Q71.736 4.827 71.616 4.806Q71.497 4.784 71.251 4.784L71.251 4.488L72.443 4.402L72.443 5.136Q72.556 4.921 72.749 4.753Q72.943 4.585 73.181 4.493Q73.419 4.402 73.673 4.402Q74.841 4.402 74.841 5.480L74.841 7.370Q74.841 7.538 75.011 7.585Q75.181 7.632 75.450 7.632L75.450 7.929L73.595 7.929L73.595 7.632Q73.868 7.632 74.036 7.585Q74.204 7.538 74.204 7.370L74.204 5.495Q74.204 5.113 74.083 4.884Q73.962 4.656 73.611 4.656Q73.298 4.656 73.044 4.818Q72.790 4.980 72.644 5.249Q72.497 5.519 72.497 5.816L72.497 7.370Q72.497 7.538 72.667 7.585Q72.837 7.632 73.107 7.632L73.107 7.929M77.755 7.929L75.978 7.929L75.978 7.632Q76.251 7.632 76.419 7.585Q76.587 7.538 76.587 7.370L76.587 5.234Q76.587 5.019 76.530 4.923Q76.474 4.827 76.361 4.806Q76.247 4.784 76.001 4.784L76.001 4.488L77.200 4.402L77.200 7.370Q77.200 7.538 77.347 7.585Q77.493 7.632 77.755 7.632L77.755 7.929M76.314 3.007Q76.314 2.816 76.448 2.685Q76.583 2.554 76.778 2.554Q76.900 2.554 77.003 2.617Q77.107 2.679 77.169 2.783Q77.232 2.886 77.232 3.007Q77.232 3.202 77.101 3.337Q76.970 3.472 76.778 3.472Q76.579 3.472 76.446 3.339Q76.314 3.206 76.314 3.007M80.185 7.929L78.329 7.929L78.329 7.632Q78.603 7.632 78.771 7.585Q78.939 7.538 78.939 7.370L78.939 5.234Q78.939 5.019 78.876 4.923Q78.814 4.827 78.694 4.806Q78.575 4.784 78.329 4.784L78.329 4.488L79.521 4.402L79.521 5.136Q79.634 4.921 79.827 4.753Q80.021 4.585 80.259 4.493Q80.497 4.402 80.751 4.402Q81.919 4.402 81.919 5.480L81.919 7.370Q81.919 7.538 82.089 7.585Q82.259 7.632 82.528 7.632L82.528 7.929L80.673 7.929L80.673 7.632Q80.946 7.632 81.114 7.585Q81.282 7.538 81.282 7.370L81.282 5.495Q81.282 5.113 81.161 4.884Q81.040 4.656 80.689 4.656Q80.376 4.656 80.122 4.818Q79.868 4.980 79.722 5.249Q79.575 5.519 79.575 5.816L79.575 7.370Q79.575 7.538 79.745 7.585Q79.915 7.632 80.185 7.632L80.185 7.929M82.974 8.538Q82.974 8.257 83.185 8.046Q83.396 7.835 83.681 7.745Q83.525 7.620 83.446 7.431Q83.368 7.242 83.368 7.042Q83.368 6.687 83.599 6.394Q83.232 6.054 83.232 5.585Q83.232 5.234 83.435 4.964Q83.638 4.695 83.958 4.548Q84.278 4.402 84.622 4.402Q85.142 4.402 85.513 4.683Q85.876 4.312 86.423 4.312Q86.603 4.312 86.730 4.439Q86.857 4.566 86.857 4.745Q86.857 4.851 86.778 4.929Q86.700 5.007 86.591 5.007Q86.482 5.007 86.405 4.931Q86.329 4.855 86.329 4.745Q86.329 4.644 86.368 4.593Q86.376 4.585 86.380 4.579Q86.384 4.574 86.384 4.570Q86.009 4.570 85.689 4.824Q86.009 5.163 86.009 5.585Q86.009 5.855 85.892 6.072Q85.775 6.288 85.569 6.447Q85.364 6.605 85.122 6.687Q84.880 6.769 84.622 6.769Q84.403 6.769 84.191 6.710Q83.978 6.652 83.782 6.531Q83.689 6.671 83.689 6.851Q83.689 7.058 83.825 7.210Q83.962 7.363 84.169 7.363L84.864 7.363Q85.353 7.363 85.765 7.447Q86.177 7.531 86.456 7.788Q86.736 8.046 86.736 8.538Q86.736 8.902 86.415 9.134Q86.095 9.367 85.653 9.468Q85.212 9.570 84.857 9.570Q84.501 9.570 84.058 9.468Q83.614 9.367 83.294 9.134Q82.974 8.902 82.974 8.538M83.478 8.538Q83.478 8.734 83.622 8.882Q83.767 9.031 83.980 9.120Q84.193 9.210 84.433 9.257Q84.673 9.304 84.857 9.304Q85.099 9.304 85.429 9.226Q85.759 9.148 85.995 8.974Q86.232 8.800 86.232 8.538Q86.232 8.132 85.821 8.023Q85.411 7.913 84.849 7.913L84.169 7.913Q83.900 7.913 83.689 8.091Q83.478 8.269 83.478 8.538M84.622 6.503Q85.345 6.503 85.345 5.585Q85.345 4.663 84.622 4.663Q83.896 4.663 83.896 5.585Q83.896 6.503 84.622 6.503\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-73.258 20.287)\">\u003Cpath d=\"M56.604 15.675Q56.604 15.195 56.837 14.779Q57.069 14.363 57.479 14.113Q57.889 13.863 58.366 13.863Q59.096 13.863 59.495 14.304Q59.893 14.745 59.893 15.476Q59.893 15.581 59.800 15.605L57.350 15.605L57.350 15.675Q57.350 16.085 57.471 16.441Q57.593 16.796 57.864 17.013Q58.136 17.230 58.565 17.230Q58.928 17.230 59.225 17.001Q59.522 16.773 59.624 16.421Q59.632 16.374 59.718 16.359L59.800 16.359Q59.893 16.386 59.893 16.468Q59.893 16.476 59.886 16.507Q59.823 16.734 59.684 16.917Q59.546 17.101 59.354 17.234Q59.163 17.366 58.944 17.437Q58.725 17.507 58.487 17.507Q58.116 17.507 57.778 17.370Q57.440 17.234 57.173 16.982Q56.905 16.730 56.755 16.390Q56.604 16.050 56.604 15.675M57.358 15.366L59.319 15.366Q59.319 15.062 59.218 14.771Q59.116 14.480 58.899 14.298Q58.682 14.116 58.366 14.116Q58.065 14.116 57.835 14.304Q57.604 14.491 57.481 14.783Q57.358 15.074 57.358 15.366M62.296 17.429L60.464 17.429L60.464 17.132Q60.737 17.132 60.905 17.085Q61.073 17.038 61.073 16.870L61.073 12.710Q61.073 12.495 61.011 12.400Q60.948 12.304 60.829 12.283Q60.710 12.261 60.464 12.261L60.464 11.964L61.686 11.878L61.686 16.870Q61.686 17.038 61.854 17.085Q62.022 17.132 62.296 17.132L62.296 17.429M62.741 15.675Q62.741 15.195 62.973 14.779Q63.206 14.363 63.616 14.113Q64.026 13.863 64.503 13.863Q65.233 13.863 65.632 14.304Q66.030 14.745 66.030 15.476Q66.030 15.581 65.936 15.605L63.487 15.605L63.487 15.675Q63.487 16.085 63.608 16.441Q63.729 16.796 64.001 17.013Q64.272 17.230 64.702 17.230Q65.065 17.230 65.362 17.001Q65.659 16.773 65.761 16.421Q65.768 16.374 65.854 16.359L65.936 16.359Q66.030 16.386 66.030 16.468Q66.030 16.476 66.022 16.507Q65.960 16.734 65.821 16.917Q65.682 17.101 65.491 17.234Q65.300 17.366 65.081 17.437Q64.862 17.507 64.624 17.507Q64.253 17.507 63.915 17.370Q63.577 17.234 63.309 16.982Q63.042 16.730 62.891 16.390Q62.741 16.050 62.741 15.675M63.495 15.366L65.456 15.366Q65.456 15.062 65.354 14.771Q65.253 14.480 65.036 14.298Q64.819 14.116 64.503 14.116Q64.202 14.116 63.971 14.304Q63.741 14.491 63.618 14.783Q63.495 15.074 63.495 15.366M68.448 17.429L66.593 17.429L66.593 17.132Q66.866 17.132 67.034 17.085Q67.202 17.038 67.202 16.870L67.202 14.734Q67.202 14.519 67.139 14.423Q67.077 14.327 66.958 14.306Q66.839 14.284 66.593 14.284L66.593 13.988L67.784 13.902L67.784 14.636Q67.897 14.421 68.091 14.253Q68.284 14.085 68.522 13.993Q68.761 13.902 69.014 13.902Q69.975 13.902 70.151 14.613Q70.335 14.284 70.663 14.093Q70.991 13.902 71.370 13.902Q72.546 13.902 72.546 14.980L72.546 16.870Q72.546 17.038 72.714 17.085Q72.882 17.132 73.151 17.132L73.151 17.429L71.296 17.429L71.296 17.132Q71.569 17.132 71.737 17.087Q71.905 17.042 71.905 16.870L71.905 14.995Q71.905 14.609 71.780 14.382Q71.655 14.156 71.303 14.156Q70.999 14.156 70.743 14.318Q70.487 14.480 70.339 14.749Q70.190 15.019 70.190 15.316L70.190 16.870Q70.190 17.038 70.360 17.085Q70.530 17.132 70.800 17.132L70.800 17.429L68.944 17.429L68.944 17.132Q69.218 17.132 69.386 17.085Q69.553 17.038 69.553 16.870L69.553 14.995Q69.553 14.609 69.428 14.382Q69.303 14.156 68.952 14.156Q68.647 14.156 68.391 14.318Q68.136 14.480 67.987 14.749Q67.839 15.019 67.839 15.316L67.839 16.870Q67.839 17.038 68.009 17.085Q68.178 17.132 68.448 17.132L68.448 17.429M73.596 15.675Q73.596 15.195 73.829 14.779Q74.061 14.363 74.471 14.113Q74.882 13.863 75.358 13.863Q76.089 13.863 76.487 14.304Q76.886 14.745 76.886 15.476Q76.886 15.581 76.792 15.605L74.343 15.605L74.343 15.675Q74.343 16.085 74.464 16.441Q74.585 16.796 74.856 17.013Q75.128 17.230 75.557 17.230Q75.921 17.230 76.218 17.001Q76.514 16.773 76.616 16.421Q76.624 16.374 76.710 16.359L76.792 16.359Q76.886 16.386 76.886 16.468Q76.886 16.476 76.878 16.507Q76.815 16.734 76.677 16.917Q76.538 17.101 76.346 17.234Q76.155 17.366 75.936 17.437Q75.718 17.507 75.479 17.507Q75.108 17.507 74.770 17.370Q74.432 17.234 74.165 16.982Q73.897 16.730 73.747 16.390Q73.596 16.050 73.596 15.675M74.350 15.366L76.311 15.366Q76.311 15.062 76.210 14.771Q76.108 14.480 75.891 14.298Q75.675 14.116 75.358 14.116Q75.057 14.116 74.827 14.304Q74.596 14.491 74.473 14.783Q74.350 15.074 74.350 15.366M79.303 17.429L77.448 17.429L77.448 17.132Q77.721 17.132 77.889 17.085Q78.057 17.038 78.057 16.870L78.057 14.734Q78.057 14.519 77.995 14.423Q77.932 14.327 77.813 14.306Q77.694 14.284 77.448 14.284L77.448 13.988L78.639 13.902L78.639 14.636Q78.753 14.421 78.946 14.253Q79.139 14.085 79.378 13.993Q79.616 13.902 79.870 13.902Q81.038 13.902 81.038 14.980L81.038 16.870Q81.038 17.038 81.208 17.085Q81.378 17.132 81.647 17.132L81.647 17.429L79.792 17.429L79.792 17.132Q80.065 17.132 80.233 17.085Q80.401 17.038 80.401 16.870L80.401 14.995Q80.401 14.613 80.280 14.384Q80.159 14.156 79.807 14.156Q79.495 14.156 79.241 14.318Q78.987 14.480 78.841 14.749Q78.694 15.019 78.694 15.316L78.694 16.870Q78.694 17.038 78.864 17.085Q79.034 17.132 79.303 17.132\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-73.258 20.287)\">\u003Cpath d=\"M82.493 16.468L82.493 14.277L81.790 14.277L81.790 14.023Q82.146 14.023 82.388 13.790Q82.630 13.558 82.741 13.210Q82.853 12.863 82.853 12.507L83.134 12.507L83.134 13.980L84.310 13.980L84.310 14.277L83.134 14.277L83.134 16.452Q83.134 16.773 83.253 17.001Q83.372 17.230 83.653 17.230Q83.833 17.230 83.950 17.107Q84.067 16.984 84.120 16.804Q84.173 16.624 84.173 16.452L84.173 15.980L84.454 15.980L84.454 16.468Q84.454 16.722 84.349 16.962Q84.243 17.202 84.046 17.355Q83.849 17.507 83.591 17.507Q83.275 17.507 83.023 17.384Q82.771 17.261 82.632 17.027Q82.493 16.792 82.493 16.468\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M65.68 45.882h68.286V14.584H65.68Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(22.321 20.331)\">\u003Cpath d=\"M57.032 7.929L54.650 7.929L54.650 7.632Q54.974 7.632 55.216 7.585Q55.458 7.538 55.458 7.370L55.458 3.027Q55.458 2.855 55.216 2.808Q54.974 2.761 54.650 2.761L54.650 2.464L57.595 2.464Q57.939 2.464 58.294 2.564Q58.650 2.663 58.944 2.855Q59.239 3.046 59.421 3.331Q59.603 3.617 59.603 3.976Q59.603 4.449 59.292 4.784Q58.982 5.120 58.517 5.292Q58.052 5.464 57.595 5.464L56.228 5.464L56.228 7.370Q56.228 7.538 56.470 7.585Q56.712 7.632 57.032 7.632L57.032 7.929M56.200 3.027L56.200 5.195L57.376 5.195Q58.064 5.195 58.402 4.919Q58.739 4.644 58.739 3.976Q58.739 3.312 58.402 3.036Q58.064 2.761 57.376 2.761L56.603 2.761Q56.384 2.761 56.292 2.804Q56.200 2.847 56.200 3.027\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(22.321 20.331)\">\u003Cpath d=\"M60.081 6.175Q60.081 5.695 60.314 5.279Q60.546 4.863 60.956 4.613Q61.366 4.363 61.843 4.363Q62.573 4.363 62.972 4.804Q63.370 5.245 63.370 5.976Q63.370 6.081 63.277 6.105L60.827 6.105L60.827 6.175Q60.827 6.585 60.948 6.941Q61.070 7.296 61.341 7.513Q61.613 7.730 62.042 7.730Q62.406 7.730 62.702 7.501Q62.999 7.273 63.101 6.921Q63.109 6.874 63.195 6.859L63.277 6.859Q63.370 6.886 63.370 6.968Q63.370 6.976 63.363 7.007Q63.300 7.234 63.161 7.417Q63.023 7.601 62.831 7.734Q62.640 7.867 62.421 7.937Q62.202 8.007 61.964 8.007Q61.593 8.007 61.255 7.870Q60.917 7.734 60.650 7.482Q60.382 7.230 60.232 6.890Q60.081 6.550 60.081 6.175M60.835 5.867L62.796 5.867Q62.796 5.562 62.695 5.271Q62.593 4.980 62.376 4.798Q62.159 4.617 61.843 4.617Q61.542 4.617 61.312 4.804Q61.081 4.992 60.958 5.283Q60.835 5.574 60.835 5.867M65.866 7.929L63.886 7.929L63.886 7.632Q64.156 7.632 64.323 7.587Q64.491 7.542 64.491 7.370L64.491 5.234Q64.491 5.019 64.429 4.923Q64.366 4.827 64.249 4.806Q64.132 4.784 63.886 4.784L63.886 4.488L65.054 4.402L65.054 5.187Q65.132 4.976 65.284 4.790Q65.437 4.605 65.636 4.503Q65.835 4.402 66.062 4.402Q66.308 4.402 66.499 4.546Q66.691 4.691 66.691 4.921Q66.691 5.077 66.585 5.187Q66.480 5.296 66.323 5.296Q66.167 5.296 66.058 5.187Q65.948 5.077 65.948 4.921Q65.948 4.761 66.054 4.656Q65.730 4.656 65.515 4.884Q65.300 5.113 65.204 5.452Q65.109 5.792 65.109 6.097L65.109 7.370Q65.109 7.538 65.335 7.585Q65.562 7.632 65.866 7.632L65.866 7.929M69.238 7.929L67.253 7.929L67.253 7.632Q67.527 7.632 67.695 7.585Q67.863 7.538 67.863 7.370L67.863 4.777L67.222 4.777L67.222 4.480L67.863 4.480L67.863 3.546Q67.863 3.281 67.980 3.044Q68.097 2.808 68.290 2.644Q68.484 2.480 68.732 2.388Q68.980 2.296 69.245 2.296Q69.531 2.296 69.755 2.454Q69.980 2.613 69.980 2.890Q69.980 3.046 69.874 3.156Q69.769 3.265 69.605 3.265Q69.448 3.265 69.339 3.156Q69.230 3.046 69.230 2.890Q69.230 2.683 69.390 2.577Q69.292 2.554 69.198 2.554Q68.968 2.554 68.796 2.710Q68.624 2.867 68.538 3.103Q68.452 3.339 68.452 3.562L68.452 4.480L69.421 4.480L69.421 4.777L68.476 4.777L68.476 7.370Q68.476 7.538 68.702 7.585Q68.929 7.632 69.238 7.632L69.238 7.929M69.765 6.234Q69.765 5.730 70.021 5.298Q70.277 4.867 70.712 4.615Q71.148 4.363 71.648 4.363Q72.034 4.363 72.376 4.507Q72.718 4.652 72.980 4.913Q73.241 5.175 73.384 5.511Q73.527 5.847 73.527 6.234Q73.527 6.726 73.263 7.136Q72.999 7.546 72.570 7.777Q72.140 8.007 71.648 8.007Q71.156 8.007 70.722 7.775Q70.288 7.542 70.027 7.134Q69.765 6.726 69.765 6.234M71.648 7.730Q72.105 7.730 72.357 7.507Q72.609 7.284 72.697 6.933Q72.784 6.581 72.784 6.136Q72.784 5.706 72.691 5.368Q72.597 5.031 72.343 4.824Q72.089 4.617 71.648 4.617Q70.999 4.617 70.755 5.033Q70.511 5.449 70.511 6.136Q70.511 6.581 70.599 6.933Q70.687 7.284 70.939 7.507Q71.191 7.730 71.648 7.730M76.019 7.929L74.038 7.929L74.038 7.632Q74.308 7.632 74.476 7.587Q74.644 7.542 74.644 7.370L74.644 5.234Q74.644 5.019 74.581 4.923Q74.519 4.827 74.402 4.806Q74.284 4.784 74.038 4.784L74.038 4.488L75.206 4.402L75.206 5.187Q75.284 4.976 75.437 4.790Q75.589 4.605 75.788 4.503Q75.988 4.402 76.214 4.402Q76.460 4.402 76.652 4.546Q76.843 4.691 76.843 4.921Q76.843 5.077 76.738 5.187Q76.632 5.296 76.476 5.296Q76.320 5.296 76.210 5.187Q76.101 5.077 76.101 4.921Q76.101 4.761 76.206 4.656Q75.882 4.656 75.667 4.884Q75.452 5.113 75.357 5.452Q75.261 5.792 75.261 6.097L75.261 7.370Q75.261 7.538 75.488 7.585Q75.714 7.632 76.019 7.632L76.019 7.929M79.253 7.929L77.398 7.929L77.398 7.632Q77.671 7.632 77.839 7.585Q78.007 7.538 78.007 7.370L78.007 5.234Q78.007 5.019 77.945 4.923Q77.882 4.827 77.763 4.806Q77.644 4.784 77.398 4.784L77.398 4.488L78.589 4.402L78.589 5.136Q78.702 4.921 78.896 4.753Q79.089 4.585 79.327 4.493Q79.566 4.402 79.820 4.402Q80.781 4.402 80.956 5.113Q81.140 4.784 81.468 4.593Q81.796 4.402 82.175 4.402Q83.351 4.402 83.351 5.480L83.351 7.370Q83.351 7.538 83.519 7.585Q83.687 7.632 83.956 7.632L83.956 7.929L82.101 7.929L82.101 7.632Q82.374 7.632 82.542 7.587Q82.710 7.542 82.710 7.370L82.710 5.495Q82.710 5.109 82.585 4.882Q82.460 4.656 82.109 4.656Q81.804 4.656 81.548 4.818Q81.292 4.980 81.144 5.249Q80.995 5.519 80.995 5.816L80.995 7.370Q80.995 7.538 81.165 7.585Q81.335 7.632 81.605 7.632L81.605 7.929L79.749 7.929L79.749 7.632Q80.023 7.632 80.191 7.585Q80.359 7.538 80.359 7.370L80.359 5.495Q80.359 5.109 80.234 4.882Q80.109 4.656 79.757 4.656Q79.452 4.656 79.197 4.818Q78.941 4.980 78.792 5.249Q78.644 5.519 78.644 5.816L78.644 7.370Q78.644 7.538 78.814 7.585Q78.984 7.632 79.253 7.632L79.253 7.929M84.499 7.097Q84.499 6.613 84.902 6.318Q85.304 6.023 85.855 5.904Q86.406 5.784 86.898 5.784L86.898 5.495Q86.898 5.269 86.782 5.062Q86.667 4.855 86.470 4.736Q86.273 4.617 86.042 4.617Q85.616 4.617 85.331 4.722Q85.402 4.749 85.448 4.804Q85.495 4.859 85.521 4.929Q85.546 4.999 85.546 5.074Q85.546 5.179 85.495 5.271Q85.445 5.363 85.353 5.413Q85.261 5.464 85.156 5.464Q85.050 5.464 84.958 5.413Q84.866 5.363 84.816 5.271Q84.765 5.179 84.765 5.074Q84.765 4.656 85.154 4.509Q85.542 4.363 86.042 4.363Q86.374 4.363 86.728 4.493Q87.081 4.624 87.310 4.878Q87.538 5.132 87.538 5.480L87.538 7.281Q87.538 7.413 87.611 7.523Q87.683 7.632 87.812 7.632Q87.937 7.632 88.005 7.527Q88.073 7.421 88.073 7.281L88.073 6.769L88.355 6.769L88.355 7.281Q88.355 7.484 88.238 7.642Q88.120 7.800 87.939 7.884Q87.757 7.968 87.554 7.968Q87.323 7.968 87.171 7.796Q87.019 7.624 86.988 7.394Q86.827 7.675 86.519 7.841Q86.210 8.007 85.859 8.007Q85.347 8.007 84.923 7.784Q84.499 7.562 84.499 7.097M85.187 7.097Q85.187 7.382 85.413 7.568Q85.640 7.753 85.933 7.753Q86.179 7.753 86.404 7.636Q86.628 7.519 86.763 7.316Q86.898 7.113 86.898 6.859L86.898 6.027Q86.632 6.027 86.347 6.081Q86.062 6.136 85.790 6.265Q85.519 6.394 85.353 6.601Q85.187 6.808 85.187 7.097M90.577 7.929L88.722 7.929L88.722 7.632Q88.995 7.632 89.163 7.585Q89.331 7.538 89.331 7.370L89.331 5.234Q89.331 5.019 89.269 4.923Q89.206 4.827 89.087 4.806Q88.968 4.784 88.722 4.784L88.722 4.488L89.913 4.402L89.913 5.136Q90.027 4.921 90.220 4.753Q90.413 4.585 90.652 4.493Q90.890 4.402 91.144 4.402Q92.312 4.402 92.312 5.480L92.312 7.370Q92.312 7.538 92.482 7.585Q92.652 7.632 92.921 7.632L92.921 7.929L91.066 7.929L91.066 7.632Q91.339 7.632 91.507 7.585Q91.675 7.538 91.675 7.370L91.675 5.495Q91.675 5.113 91.554 4.884Q91.433 4.656 91.081 4.656Q90.769 4.656 90.515 4.818Q90.261 4.980 90.114 5.249Q89.968 5.519 89.968 5.816L89.968 7.370Q89.968 7.538 90.138 7.585Q90.308 7.632 90.577 7.632L90.577 7.929M93.409 6.202Q93.409 5.706 93.659 5.281Q93.909 4.855 94.329 4.609Q94.749 4.363 95.249 4.363Q95.788 4.363 96.179 4.488Q96.570 4.613 96.570 5.027Q96.570 5.132 96.519 5.224Q96.468 5.316 96.376 5.367Q96.284 5.417 96.175 5.417Q96.070 5.417 95.978 5.367Q95.886 5.316 95.835 5.224Q95.784 5.132 95.784 5.027Q95.784 4.804 95.952 4.699Q95.730 4.640 95.257 4.640Q94.960 4.640 94.745 4.779Q94.531 4.917 94.400 5.148Q94.269 5.378 94.210 5.648Q94.152 5.917 94.152 6.202Q94.152 6.597 94.284 6.947Q94.417 7.296 94.689 7.513Q94.960 7.730 95.359 7.730Q95.734 7.730 96.009 7.513Q96.284 7.296 96.386 6.937Q96.402 6.874 96.464 6.874L96.570 6.874Q96.605 6.874 96.630 6.902Q96.656 6.929 96.656 6.968L96.656 6.992Q96.523 7.472 96.138 7.740Q95.753 8.007 95.249 8.007Q94.886 8.007 94.552 7.870Q94.218 7.734 93.958 7.484Q93.698 7.234 93.554 6.898Q93.409 6.562 93.409 6.202M97.144 6.175Q97.144 5.695 97.376 5.279Q97.609 4.863 98.019 4.613Q98.429 4.363 98.906 4.363Q99.636 4.363 100.034 4.804Q100.433 5.245 100.433 5.976Q100.433 6.081 100.339 6.105L97.890 6.105L97.890 6.175Q97.890 6.585 98.011 6.941Q98.132 7.296 98.404 7.513Q98.675 7.730 99.105 7.730Q99.468 7.730 99.765 7.501Q100.062 7.273 100.163 6.921Q100.171 6.874 100.257 6.859L100.339 6.859Q100.433 6.886 100.433 6.968Q100.433 6.976 100.425 7.007Q100.363 7.234 100.224 7.417Q100.085 7.601 99.894 7.734Q99.702 7.867 99.484 7.937Q99.265 8.007 99.027 8.007Q98.656 8.007 98.318 7.870Q97.980 7.734 97.712 7.482Q97.445 7.230 97.294 6.890Q97.144 6.550 97.144 6.175M97.898 5.867L99.859 5.867Q99.859 5.562 99.757 5.271Q99.656 4.980 99.439 4.798Q99.222 4.617 98.906 4.617Q98.605 4.617 98.374 4.804Q98.144 4.992 98.021 5.283Q97.898 5.574 97.898 5.867\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(22.321 20.331)\">\u003Cpath d=\"M63.454 15.675Q63.454 15.195 63.687 14.779Q63.919 14.363 64.329 14.113Q64.739 13.863 65.216 13.863Q65.946 13.863 66.345 14.304Q66.743 14.745 66.743 15.476Q66.743 15.581 66.650 15.605L64.200 15.605L64.200 15.675Q64.200 16.085 64.321 16.441Q64.443 16.796 64.714 17.013Q64.986 17.230 65.415 17.230Q65.779 17.230 66.075 17.001Q66.372 16.773 66.474 16.421Q66.482 16.374 66.568 16.359L66.650 16.359Q66.743 16.386 66.743 16.468Q66.743 16.476 66.736 16.507Q66.673 16.734 66.534 16.917Q66.396 17.101 66.204 17.234Q66.013 17.366 65.794 17.437Q65.575 17.507 65.337 17.507Q64.966 17.507 64.628 17.370Q64.290 17.234 64.023 16.982Q63.755 16.730 63.605 16.390Q63.454 16.050 63.454 15.675M64.208 15.366L66.169 15.366Q66.169 15.062 66.068 14.771Q65.966 14.480 65.749 14.298Q65.532 14.116 65.216 14.116Q64.915 14.116 64.685 14.304Q64.454 14.491 64.331 14.783Q64.208 15.074 64.208 15.366M69.146 17.429L67.314 17.429L67.314 17.132Q67.587 17.132 67.755 17.085Q67.923 17.038 67.923 16.870L67.923 12.710Q67.923 12.495 67.861 12.400Q67.798 12.304 67.679 12.283Q67.560 12.261 67.314 12.261L67.314 11.964L68.536 11.878L68.536 16.870Q68.536 17.038 68.704 17.085Q68.872 17.132 69.146 17.132L69.146 17.429M69.591 15.675Q69.591 15.195 69.823 14.779Q70.056 14.363 70.466 14.113Q70.876 13.863 71.353 13.863Q72.083 13.863 72.482 14.304Q72.880 14.745 72.880 15.476Q72.880 15.581 72.786 15.605L70.337 15.605L70.337 15.675Q70.337 16.085 70.458 16.441Q70.579 16.796 70.851 17.013Q71.122 17.230 71.552 17.230Q71.915 17.230 72.212 17.001Q72.509 16.773 72.611 16.421Q72.618 16.374 72.704 16.359L72.786 16.359Q72.880 16.386 72.880 16.468Q72.880 16.476 72.872 16.507Q72.810 16.734 72.671 16.917Q72.532 17.101 72.341 17.234Q72.150 17.366 71.931 17.437Q71.712 17.507 71.474 17.507Q71.103 17.507 70.765 17.370Q70.427 17.234 70.159 16.982Q69.892 16.730 69.741 16.390Q69.591 16.050 69.591 15.675M70.345 15.366L72.306 15.366Q72.306 15.062 72.204 14.771Q72.103 14.480 71.886 14.298Q71.669 14.116 71.353 14.116Q71.052 14.116 70.821 14.304Q70.591 14.491 70.468 14.783Q70.345 15.074 70.345 15.366M75.298 17.429L73.443 17.429L73.443 17.132Q73.716 17.132 73.884 17.085Q74.052 17.038 74.052 16.870L74.052 14.734Q74.052 14.519 73.989 14.423Q73.927 14.327 73.808 14.306Q73.689 14.284 73.443 14.284L73.443 13.988L74.634 13.902L74.634 14.636Q74.747 14.421 74.941 14.253Q75.134 14.085 75.372 13.993Q75.611 13.902 75.864 13.902Q76.825 13.902 77.001 14.613Q77.185 14.284 77.513 14.093Q77.841 13.902 78.220 13.902Q79.396 13.902 79.396 14.980L79.396 16.870Q79.396 17.038 79.564 17.085Q79.732 17.132 80.001 17.132L80.001 17.429L78.146 17.429L78.146 17.132Q78.419 17.132 78.587 17.087Q78.755 17.042 78.755 16.870L78.755 14.995Q78.755 14.609 78.630 14.382Q78.505 14.156 78.154 14.156Q77.849 14.156 77.593 14.318Q77.337 14.480 77.189 14.749Q77.040 15.019 77.040 15.316L77.040 16.870Q77.040 17.038 77.210 17.085Q77.380 17.132 77.650 17.132L77.650 17.429L75.794 17.429L75.794 17.132Q76.068 17.132 76.236 17.085Q76.404 17.038 76.404 16.870L76.404 14.995Q76.404 14.609 76.279 14.382Q76.154 14.156 75.802 14.156Q75.497 14.156 75.241 14.318Q74.986 14.480 74.837 14.749Q74.689 15.019 74.689 15.316L74.689 16.870Q74.689 17.038 74.859 17.085Q75.029 17.132 75.298 17.132L75.298 17.429M80.446 15.675Q80.446 15.195 80.679 14.779Q80.911 14.363 81.321 14.113Q81.732 13.863 82.208 13.863Q82.939 13.863 83.337 14.304Q83.736 14.745 83.736 15.476Q83.736 15.581 83.642 15.605L81.193 15.605L81.193 15.675Q81.193 16.085 81.314 16.441Q81.435 16.796 81.706 17.013Q81.978 17.230 82.407 17.230Q82.771 17.230 83.068 17.001Q83.364 16.773 83.466 16.421Q83.474 16.374 83.560 16.359L83.642 16.359Q83.736 16.386 83.736 16.468Q83.736 16.476 83.728 16.507Q83.665 16.734 83.527 16.917Q83.388 17.101 83.196 17.234Q83.005 17.366 82.786 17.437Q82.568 17.507 82.329 17.507Q81.958 17.507 81.620 17.370Q81.282 17.234 81.015 16.982Q80.747 16.730 80.597 16.390Q80.446 16.050 80.446 15.675M81.200 15.366L83.161 15.366Q83.161 15.062 83.060 14.771Q82.958 14.480 82.741 14.298Q82.525 14.116 82.208 14.116Q81.907 14.116 81.677 14.304Q81.446 14.491 81.323 14.783Q81.200 15.074 81.200 15.366M86.154 17.429L84.298 17.429L84.298 17.132Q84.571 17.132 84.739 17.085Q84.907 17.038 84.907 16.870L84.907 14.734Q84.907 14.519 84.845 14.423Q84.782 14.327 84.663 14.306Q84.544 14.284 84.298 14.284L84.298 13.988L85.489 13.902L85.489 14.636Q85.603 14.421 85.796 14.253Q85.989 14.085 86.228 13.993Q86.466 13.902 86.720 13.902Q87.888 13.902 87.888 14.980L87.888 16.870Q87.888 17.038 88.058 17.085Q88.228 17.132 88.497 17.132L88.497 17.429L86.642 17.429L86.642 17.132Q86.915 17.132 87.083 17.085Q87.251 17.038 87.251 16.870L87.251 14.995Q87.251 14.613 87.130 14.384Q87.009 14.156 86.657 14.156Q86.345 14.156 86.091 14.318Q85.837 14.480 85.691 14.749Q85.544 15.019 85.544 15.316L85.544 16.870Q85.544 17.038 85.714 17.085Q85.884 17.132 86.154 17.132\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(22.321 20.331)\">\u003Cpath d=\"M89.344 16.468L89.344 14.277L88.641 14.277L88.641 14.023Q88.997 14.023 89.239 13.790Q89.481 13.558 89.592 13.210Q89.704 12.863 89.704 12.507L89.985 12.507L89.985 13.980L91.161 13.980L91.161 14.277L89.985 14.277L89.985 16.452Q89.985 16.773 90.104 17.001Q90.223 17.230 90.504 17.230Q90.684 17.230 90.801 17.107Q90.918 16.984 90.971 16.804Q91.024 16.624 91.024 16.452L91.024 15.980L91.305 15.980L91.305 16.468Q91.305 16.722 91.200 16.962Q91.094 17.202 90.897 17.355Q90.700 17.507 90.442 17.507Q90.126 17.507 89.874 17.384Q89.622 17.261 89.483 17.027Q89.344 16.792 89.344 16.468\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-36.75 89.984h68.286V58.686h-68.287Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-74.385 63.655)\">\u003Cpath d=\"M58.868 7.929L56.486 7.929L56.486 7.632Q56.810 7.632 57.052 7.585Q57.294 7.538 57.294 7.370L57.294 3.027Q57.294 2.855 57.052 2.808Q56.810 2.761 56.486 2.761L56.486 2.464L59.431 2.464Q59.775 2.464 60.130 2.564Q60.486 2.663 60.780 2.855Q61.075 3.046 61.257 3.331Q61.439 3.617 61.439 3.976Q61.439 4.449 61.128 4.784Q60.818 5.120 60.353 5.292Q59.888 5.464 59.431 5.464L58.064 5.464L58.064 7.370Q58.064 7.538 58.306 7.585Q58.548 7.632 58.868 7.632L58.868 7.929M58.036 3.027L58.036 5.195L59.212 5.195Q59.900 5.195 60.238 4.919Q60.575 4.644 60.575 3.976Q60.575 3.312 60.238 3.036Q59.900 2.761 59.212 2.761L58.439 2.761Q58.220 2.761 58.128 2.804Q58.036 2.847 58.036 3.027M64.157 7.929L62.177 7.929L62.177 7.632Q62.447 7.632 62.614 7.587Q62.782 7.542 62.782 7.370L62.782 5.234Q62.782 5.019 62.720 4.923Q62.657 4.827 62.540 4.806Q62.423 4.784 62.177 4.784L62.177 4.488L63.345 4.402L63.345 5.187Q63.423 4.976 63.575 4.790Q63.728 4.605 63.927 4.503Q64.126 4.402 64.353 4.402Q64.599 4.402 64.790 4.546Q64.982 4.691 64.982 4.921Q64.982 5.077 64.876 5.187Q64.771 5.296 64.614 5.296Q64.458 5.296 64.349 5.187Q64.239 5.077 64.239 4.921Q64.239 4.761 64.345 4.656Q64.021 4.656 63.806 4.884Q63.591 5.113 63.495 5.452Q63.400 5.792 63.400 6.097L63.400 7.370Q63.400 7.538 63.626 7.585Q63.853 7.632 64.157 7.632L64.157 7.929M65.462 6.234Q65.462 5.730 65.718 5.298Q65.974 4.867 66.409 4.615Q66.845 4.363 67.345 4.363Q67.732 4.363 68.073 4.507Q68.415 4.652 68.677 4.913Q68.939 5.175 69.081 5.511Q69.224 5.847 69.224 6.234Q69.224 6.726 68.960 7.136Q68.697 7.546 68.267 7.777Q67.837 8.007 67.345 8.007Q66.853 8.007 66.419 7.775Q65.986 7.542 65.724 7.134Q65.462 6.726 65.462 6.234M67.345 7.730Q67.802 7.730 68.054 7.507Q68.306 7.284 68.394 6.933Q68.482 6.581 68.482 6.136Q68.482 5.706 68.388 5.368Q68.294 5.031 68.040 4.824Q67.786 4.617 67.345 4.617Q66.697 4.617 66.452 5.033Q66.208 5.449 66.208 6.136Q66.208 6.581 66.296 6.933Q66.384 7.284 66.636 7.507Q66.888 7.730 67.345 7.730M70.622 7.929L70.341 7.929L70.341 3.210Q70.341 2.995 70.279 2.900Q70.216 2.804 70.099 2.783Q69.982 2.761 69.736 2.761L69.736 2.464L70.958 2.378L70.958 4.867Q71.435 4.402 72.134 4.402Q72.614 4.402 73.023 4.646Q73.431 4.890 73.667 5.304Q73.904 5.718 73.904 6.202Q73.904 6.577 73.755 6.906Q73.607 7.234 73.337 7.486Q73.068 7.738 72.724 7.872Q72.380 8.007 72.021 8.007Q71.700 8.007 71.402 7.859Q71.103 7.710 70.896 7.449L70.622 7.929M70.982 5.257L70.982 7.097Q71.134 7.394 71.394 7.574Q71.654 7.753 71.966 7.753Q72.392 7.753 72.659 7.534Q72.927 7.316 73.042 6.970Q73.157 6.624 73.157 6.202Q73.157 5.554 72.909 5.105Q72.661 4.656 72.064 4.656Q71.728 4.656 71.439 4.814Q71.150 4.972 70.982 5.257M76.341 7.929L74.509 7.929L74.509 7.632Q74.782 7.632 74.950 7.585Q75.118 7.538 75.118 7.370L75.118 3.210Q75.118 2.995 75.056 2.900Q74.993 2.804 74.874 2.783Q74.755 2.761 74.509 2.761L74.509 2.464L75.732 2.378L75.732 7.370Q75.732 7.538 75.900 7.585Q76.068 7.632 76.341 7.632L76.341 7.929M76.786 6.175Q76.786 5.695 77.019 5.279Q77.251 4.863 77.661 4.613Q78.072 4.363 78.548 4.363Q79.279 4.363 79.677 4.804Q80.075 5.245 80.075 5.976Q80.075 6.081 79.982 6.105L77.532 6.105L77.532 6.175Q77.532 6.585 77.654 6.941Q77.775 7.296 78.046 7.513Q78.318 7.730 78.747 7.730Q79.111 7.730 79.407 7.501Q79.704 7.273 79.806 6.921Q79.814 6.874 79.900 6.859L79.982 6.859Q80.075 6.886 80.075 6.968Q80.075 6.976 80.068 7.007Q80.005 7.234 79.866 7.417Q79.728 7.601 79.536 7.734Q79.345 7.867 79.126 7.937Q78.907 8.007 78.669 8.007Q78.298 8.007 77.960 7.870Q77.622 7.734 77.355 7.482Q77.087 7.230 76.937 6.890Q76.786 6.550 76.786 6.175M77.540 5.867L79.501 5.867Q79.501 5.562 79.400 5.271Q79.298 4.980 79.081 4.798Q78.864 4.617 78.548 4.617Q78.247 4.617 78.017 4.804Q77.786 4.992 77.663 5.283Q77.540 5.574 77.540 5.867M82.493 7.929L80.638 7.929L80.638 7.632Q80.911 7.632 81.079 7.585Q81.247 7.538 81.247 7.370L81.247 5.234Q81.247 5.019 81.185 4.923Q81.122 4.827 81.003 4.806Q80.884 4.784 80.638 4.784L80.638 4.488L81.829 4.402L81.829 5.136Q81.943 4.921 82.136 4.753Q82.329 4.585 82.568 4.493Q82.806 4.402 83.060 4.402Q84.021 4.402 84.197 5.113Q84.380 4.784 84.708 4.593Q85.036 4.402 85.415 4.402Q86.591 4.402 86.591 5.480L86.591 7.370Q86.591 7.538 86.759 7.585Q86.927 7.632 87.197 7.632L87.197 7.929L85.341 7.929L85.341 7.632Q85.614 7.632 85.782 7.587Q85.950 7.542 85.950 7.370L85.950 5.495Q85.950 5.109 85.825 4.882Q85.700 4.656 85.349 4.656Q85.044 4.656 84.788 4.818Q84.532 4.980 84.384 5.249Q84.236 5.519 84.236 5.816L84.236 7.370Q84.236 7.538 84.405 7.585Q84.575 7.632 84.845 7.632L84.845 7.929L82.989 7.929L82.989 7.632Q83.263 7.632 83.431 7.585Q83.599 7.538 83.599 7.370L83.599 5.495Q83.599 5.109 83.474 4.882Q83.349 4.656 82.997 4.656Q82.693 4.656 82.437 4.818Q82.181 4.980 82.032 5.249Q81.884 5.519 81.884 5.816L81.884 7.370Q81.884 7.538 82.054 7.585Q82.224 7.632 82.493 7.632\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-74.385 63.655)\">\u003Cpath d=\"M54.536 18.038Q54.536 17.757 54.747 17.546Q54.958 17.335 55.243 17.245Q55.087 17.120 55.009 16.931Q54.931 16.741 54.931 16.542Q54.931 16.187 55.161 15.894Q54.794 15.554 54.794 15.085Q54.794 14.734 54.997 14.464Q55.200 14.195 55.521 14.048Q55.841 13.902 56.185 13.902Q56.704 13.902 57.075 14.183Q57.439 13.812 57.986 13.812Q58.165 13.812 58.292 13.939Q58.419 14.066 58.419 14.245Q58.419 14.351 58.341 14.429Q58.263 14.507 58.153 14.507Q58.044 14.507 57.968 14.431Q57.892 14.355 57.892 14.245Q57.892 14.144 57.931 14.093Q57.939 14.085 57.943 14.079Q57.946 14.074 57.946 14.070Q57.571 14.070 57.251 14.324Q57.571 14.663 57.571 15.085Q57.571 15.355 57.454 15.572Q57.337 15.788 57.132 15.947Q56.927 16.105 56.685 16.187Q56.443 16.269 56.185 16.269Q55.966 16.269 55.753 16.210Q55.540 16.152 55.345 16.031Q55.251 16.171 55.251 16.351Q55.251 16.558 55.388 16.710Q55.525 16.863 55.732 16.863L56.427 16.863Q56.915 16.863 57.327 16.947Q57.739 17.031 58.019 17.288Q58.298 17.546 58.298 18.038Q58.298 18.402 57.978 18.634Q57.657 18.866 57.216 18.968Q56.775 19.070 56.419 19.070Q56.064 19.070 55.620 18.968Q55.177 18.866 54.857 18.634Q54.536 18.402 54.536 18.038M55.040 18.038Q55.040 18.234 55.185 18.382Q55.329 18.531 55.542 18.620Q55.755 18.710 55.995 18.757Q56.236 18.804 56.419 18.804Q56.661 18.804 56.991 18.726Q57.321 18.648 57.558 18.474Q57.794 18.300 57.794 18.038Q57.794 17.632 57.384 17.523Q56.974 17.413 56.411 17.413L55.732 17.413Q55.462 17.413 55.251 17.591Q55.040 17.769 55.040 18.038M56.185 16.003Q56.907 16.003 56.907 15.085Q56.907 14.163 56.185 14.163Q55.458 14.163 55.458 15.085Q55.458 16.003 56.185 16.003M58.782 15.675Q58.782 15.195 59.015 14.779Q59.247 14.363 59.657 14.113Q60.068 13.863 60.544 13.863Q61.275 13.863 61.673 14.304Q62.071 14.745 62.071 15.476Q62.071 15.581 61.978 15.605L59.528 15.605L59.528 15.675Q59.528 16.085 59.650 16.441Q59.771 16.796 60.042 17.013Q60.314 17.230 60.743 17.230Q61.107 17.230 61.403 17.001Q61.700 16.773 61.802 16.421Q61.810 16.374 61.896 16.359L61.978 16.359Q62.071 16.386 62.071 16.468Q62.071 16.476 62.064 16.507Q62.001 16.734 61.862 16.917Q61.724 17.101 61.532 17.234Q61.341 17.366 61.122 17.437Q60.903 17.507 60.665 17.507Q60.294 17.507 59.956 17.370Q59.618 17.234 59.351 16.982Q59.083 16.730 58.933 16.390Q58.782 16.050 58.782 15.675M59.536 15.366L61.497 15.366Q61.497 15.062 61.396 14.771Q61.294 14.480 61.077 14.298Q60.861 14.116 60.544 14.116Q60.243 14.116 60.013 14.304Q59.782 14.491 59.659 14.783Q59.536 15.074 59.536 15.366M64.489 17.429L62.634 17.429L62.634 17.132Q62.907 17.132 63.075 17.085Q63.243 17.038 63.243 16.870L63.243 14.734Q63.243 14.519 63.181 14.423Q63.118 14.327 62.999 14.306Q62.880 14.284 62.634 14.284L62.634 13.988L63.825 13.902L63.825 14.636Q63.939 14.421 64.132 14.253Q64.325 14.085 64.564 13.993Q64.802 13.902 65.056 13.902Q66.224 13.902 66.224 14.980L66.224 16.870Q66.224 17.038 66.394 17.085Q66.564 17.132 66.833 17.132L66.833 17.429L64.978 17.429L64.978 17.132Q65.251 17.132 65.419 17.085Q65.587 17.038 65.587 16.870L65.587 14.995Q65.587 14.613 65.466 14.384Q65.345 14.156 64.993 14.156Q64.681 14.156 64.427 14.318Q64.173 14.480 64.027 14.749Q63.880 15.019 63.880 15.316L63.880 16.870Q63.880 17.038 64.050 17.085Q64.220 17.132 64.489 17.132L64.489 17.429M67.278 15.675Q67.278 15.195 67.511 14.779Q67.743 14.363 68.153 14.113Q68.564 13.863 69.040 13.863Q69.771 13.863 70.169 14.304Q70.568 14.745 70.568 15.476Q70.568 15.581 70.474 15.605L68.025 15.605L68.025 15.675Q68.025 16.085 68.146 16.441Q68.267 16.796 68.538 17.013Q68.810 17.230 69.239 17.230Q69.603 17.230 69.900 17.001Q70.196 16.773 70.298 16.421Q70.306 16.374 70.392 16.359L70.474 16.359Q70.568 16.386 70.568 16.468Q70.568 16.476 70.560 16.507Q70.497 16.734 70.359 16.917Q70.220 17.101 70.028 17.234Q69.837 17.366 69.618 17.437Q69.400 17.507 69.161 17.507Q68.790 17.507 68.452 17.370Q68.114 17.234 67.847 16.982Q67.579 16.730 67.429 16.390Q67.278 16.050 67.278 15.675M68.032 15.366L69.993 15.366Q69.993 15.062 69.892 14.771Q69.790 14.480 69.573 14.298Q69.357 14.116 69.040 14.116Q68.739 14.116 68.509 14.304Q68.278 14.491 68.155 14.783Q68.032 15.074 68.032 15.366M73.064 17.429L71.083 17.429L71.083 17.132Q71.353 17.132 71.521 17.087Q71.689 17.042 71.689 16.870L71.689 14.734Q71.689 14.519 71.626 14.423Q71.564 14.327 71.446 14.306Q71.329 14.284 71.083 14.284L71.083 13.988L72.251 13.902L72.251 14.687Q72.329 14.476 72.482 14.290Q72.634 14.105 72.833 14.003Q73.032 13.902 73.259 13.902Q73.505 13.902 73.696 14.046Q73.888 14.191 73.888 14.421Q73.888 14.577 73.782 14.687Q73.677 14.796 73.521 14.796Q73.364 14.796 73.255 14.687Q73.146 14.577 73.146 14.421Q73.146 14.261 73.251 14.156Q72.927 14.156 72.712 14.384Q72.497 14.613 72.402 14.952Q72.306 15.292 72.306 15.597L72.306 16.870Q72.306 17.038 72.532 17.085Q72.759 17.132 73.064 17.132L73.064 17.429M74.466 16.597Q74.466 16.113 74.868 15.818Q75.271 15.523 75.821 15.404Q76.372 15.284 76.864 15.284L76.864 14.995Q76.864 14.769 76.749 14.562Q76.634 14.355 76.437 14.236Q76.239 14.116 76.009 14.116Q75.583 14.116 75.298 14.222Q75.368 14.249 75.415 14.304Q75.462 14.359 75.487 14.429Q75.513 14.499 75.513 14.574Q75.513 14.679 75.462 14.771Q75.411 14.863 75.319 14.913Q75.228 14.964 75.122 14.964Q75.017 14.964 74.925 14.913Q74.833 14.863 74.782 14.771Q74.732 14.679 74.732 14.574Q74.732 14.156 75.120 14.009Q75.509 13.863 76.009 13.863Q76.341 13.863 76.694 13.993Q77.048 14.124 77.277 14.378Q77.505 14.632 77.505 14.980L77.505 16.781Q77.505 16.913 77.577 17.023Q77.650 17.132 77.778 17.132Q77.903 17.132 77.972 17.027Q78.040 16.921 78.040 16.781L78.040 16.269L78.321 16.269L78.321 16.781Q78.321 16.984 78.204 17.142Q78.087 17.300 77.905 17.384Q77.724 17.468 77.521 17.468Q77.290 17.468 77.138 17.296Q76.986 17.124 76.954 16.894Q76.794 17.175 76.486 17.341Q76.177 17.507 75.825 17.507Q75.314 17.507 74.890 17.284Q74.466 17.062 74.466 16.597M75.153 16.597Q75.153 16.882 75.380 17.068Q75.607 17.253 75.900 17.253Q76.146 17.253 76.370 17.136Q76.595 17.019 76.730 16.816Q76.864 16.613 76.864 16.359L76.864 15.527Q76.599 15.527 76.314 15.581Q76.028 15.636 75.757 15.765Q75.486 15.894 75.319 16.101Q75.153 16.308 75.153 16.597M79.239 16.468L79.239 14.277L78.536 14.277L78.536 14.023Q78.892 14.023 79.134 13.790Q79.376 13.558 79.487 13.210Q79.599 12.863 79.599 12.507L79.880 12.507L79.880 13.980L81.056 13.980L81.056 14.277L79.880 14.277L79.880 16.452Q79.880 16.773 79.999 17.001Q80.118 17.230 80.400 17.230Q80.579 17.230 80.696 17.107Q80.814 16.984 80.866 16.804Q80.919 16.624 80.919 16.452L80.919 15.980L81.200 15.980L81.200 16.468Q81.200 16.722 81.095 16.962Q80.989 17.202 80.792 17.355Q80.595 17.507 80.337 17.507Q80.021 17.507 79.769 17.384Q79.517 17.261 79.378 17.027Q79.239 16.792 79.239 16.468M81.919 15.734Q81.919 15.230 82.175 14.798Q82.431 14.366 82.866 14.115Q83.302 13.863 83.802 13.863Q84.189 13.863 84.530 14.007Q84.872 14.152 85.134 14.413Q85.396 14.675 85.538 15.011Q85.681 15.347 85.681 15.734Q85.681 16.226 85.417 16.636Q85.153 17.046 84.724 17.277Q84.294 17.507 83.802 17.507Q83.310 17.507 82.876 17.275Q82.443 17.042 82.181 16.634Q81.919 16.226 81.919 15.734M83.802 17.230Q84.259 17.230 84.511 17.007Q84.763 16.784 84.851 16.433Q84.939 16.081 84.939 15.636Q84.939 15.206 84.845 14.868Q84.751 14.531 84.497 14.324Q84.243 14.116 83.802 14.116Q83.153 14.116 82.909 14.533Q82.665 14.949 82.665 15.636Q82.665 16.081 82.753 16.433Q82.841 16.784 83.093 17.007Q83.345 17.230 83.802 17.230M88.173 17.429L86.193 17.429L86.193 17.132Q86.462 17.132 86.630 17.087Q86.798 17.042 86.798 16.870L86.798 14.734Q86.798 14.519 86.736 14.423Q86.673 14.327 86.556 14.306Q86.439 14.284 86.193 14.284L86.193 13.988L87.361 13.902L87.361 14.687Q87.439 14.476 87.591 14.290Q87.743 14.105 87.943 14.003Q88.142 13.902 88.368 13.902Q88.614 13.902 88.806 14.046Q88.997 14.191 88.997 14.421Q88.997 14.577 88.892 14.687Q88.786 14.796 88.630 14.796Q88.474 14.796 88.364 14.687Q88.255 14.577 88.255 14.421Q88.255 14.261 88.361 14.156Q88.036 14.156 87.821 14.384Q87.607 14.613 87.511 14.952Q87.415 15.292 87.415 15.597L87.415 16.870Q87.415 17.038 87.642 17.085Q87.868 17.132 88.173 17.132\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M201.016-48.212 76.973-25.714\"\u002F>\u003Cpath stroke=\"none\" d=\"m74.415-25.25 4.464 1.304-1.906-1.768 1.164-2.325\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M40.072-59.393V-43.7\"\u002F>\u003Cpath stroke=\"none\" d=\"m40.072-41.1 2.08-4.159-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M27.884-9.401 11.168 12.323\"\u002F>\u003Cpath stroke=\"none\" d=\"m9.582 14.384 4.185-2.029-2.6-.032-.697-2.504\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-31.832 -12.507)\">\u003Cpath d=\"M56.410 17.429L54.677 17.429L54.677 17.149Q54.903 17.149 55.052 17.115Q55.200 17.080 55.200 16.940L55.200 14.691L54.612 14.691L54.612 14.411L55.200 14.411L55.200 13.594Q55.200 13.276 55.378 13.028Q55.556 12.781 55.846 12.640Q56.137 12.500 56.448 12.500Q56.704 12.500 56.908 12.642Q57.111 12.784 57.111 13.027Q57.111 13.163 57.012 13.262Q56.913 13.362 56.776 13.362Q56.639 13.362 56.540 13.262Q56.441 13.163 56.441 13.027Q56.441 12.846 56.581 12.753Q56.503 12.726 56.403 12.726Q56.195 12.726 56.041 12.859Q55.887 12.992 55.807 13.196Q55.727 13.399 55.727 13.608L55.727 14.411L56.615 14.411L56.615 14.691L55.754 14.691L55.754 16.940Q55.754 17.149 56.410 17.149L56.410 17.429M57.049 15.894Q57.049 15.573 57.174 15.284Q57.299 14.995 57.525 14.772Q57.750 14.548 58.046 14.428Q58.341 14.308 58.659 14.308Q58.987 14.308 59.249 14.408Q59.510 14.507 59.686 14.689Q59.862 14.872 59.956 15.130Q60.050 15.388 60.050 15.720Q60.050 15.812 59.968 15.833L57.713 15.833L57.713 15.894Q57.713 16.482 57.996 16.865Q58.280 17.248 58.847 17.248Q59.169 17.248 59.437 17.055Q59.705 16.862 59.794 16.547Q59.801 16.506 59.876 16.492L59.968 16.492Q60.050 16.516 60.050 16.588Q60.050 16.595 60.044 16.622Q59.931 17.019 59.560 17.258Q59.189 17.497 58.765 17.497Q58.328 17.497 57.928 17.289Q57.528 17.080 57.289 16.713Q57.049 16.346 57.049 15.894M57.719 15.624L59.534 15.624Q59.534 15.347 59.437 15.095Q59.340 14.842 59.141 14.686Q58.943 14.531 58.659 14.531Q58.382 14.531 58.169 14.689Q57.955 14.848 57.837 15.103Q57.719 15.358 57.719 15.624M60.597 15.894Q60.597 15.573 60.722 15.284Q60.847 14.995 61.072 14.772Q61.298 14.548 61.594 14.428Q61.889 14.308 62.207 14.308Q62.535 14.308 62.797 14.408Q63.058 14.507 63.234 14.689Q63.410 14.872 63.504 15.130Q63.598 15.388 63.598 15.720Q63.598 15.812 63.516 15.833L61.260 15.833L61.260 15.894Q61.260 16.482 61.544 16.865Q61.828 17.248 62.395 17.248Q62.716 17.248 62.985 17.055Q63.253 16.862 63.342 16.547Q63.349 16.506 63.424 16.492L63.516 16.492Q63.598 16.516 63.598 16.588Q63.598 16.595 63.591 16.622Q63.479 17.019 63.108 17.258Q62.737 17.497 62.313 17.497Q61.876 17.497 61.476 17.289Q61.076 17.080 60.837 16.713Q60.597 16.346 60.597 15.894M61.267 15.624L63.082 15.624Q63.082 15.347 62.985 15.095Q62.887 14.842 62.689 14.686Q62.491 14.531 62.207 14.531Q61.930 14.531 61.717 14.689Q61.503 14.848 61.385 15.103Q61.267 15.358 61.267 15.624M64.186 15.918Q64.186 15.580 64.326 15.289Q64.466 14.999 64.711 14.785Q64.955 14.572 65.259 14.457Q65.564 14.343 65.888 14.343Q66.158 14.343 66.422 14.442Q66.685 14.541 66.876 14.719L66.876 13.321Q66.876 13.051 66.768 12.989Q66.661 12.928 66.350 12.928L66.350 12.647L67.426 12.572L67.426 16.756Q67.426 16.944 67.481 17.027Q67.536 17.111 67.637 17.130Q67.737 17.149 67.953 17.149L67.953 17.429L66.845 17.497L66.845 17.080Q66.428 17.497 65.803 17.497Q65.372 17.497 65 17.285Q64.627 17.074 64.407 16.713Q64.186 16.352 64.186 15.918M65.861 17.275Q66.069 17.275 66.256 17.203Q66.442 17.132 66.596 16.995Q66.750 16.858 66.845 16.680L66.845 15.071Q66.760 14.924 66.615 14.804Q66.469 14.684 66.300 14.625Q66.131 14.565 65.950 14.565Q65.389 14.565 65.121 14.954Q64.853 15.344 64.853 15.925Q64.853 16.496 65.087 16.886Q65.321 17.275 65.861 17.275M69.409 17.429L69.142 17.429L69.142 13.321Q69.142 13.051 69.035 12.989Q68.927 12.928 68.616 12.928L68.616 12.647L69.696 12.572L69.696 14.742Q69.904 14.551 70.190 14.447Q70.475 14.343 70.773 14.343Q71.090 14.343 71.388 14.464Q71.685 14.585 71.907 14.801Q72.130 15.016 72.256 15.301Q72.382 15.587 72.382 15.918Q72.382 16.363 72.143 16.727Q71.904 17.091 71.511 17.294Q71.118 17.497 70.673 17.497Q70.479 17.497 70.289 17.441Q70.099 17.385 69.939 17.280Q69.778 17.176 69.638 17.015L69.409 17.429M69.723 15.084L69.723 16.701Q69.860 16.961 70.101 17.118Q70.342 17.275 70.619 17.275Q70.913 17.275 71.125 17.168Q71.337 17.060 71.470 16.868Q71.603 16.677 71.661 16.438Q71.719 16.199 71.719 15.918Q71.719 15.559 71.625 15.255Q71.531 14.951 71.304 14.758Q71.077 14.565 70.711 14.565Q70.410 14.565 70.144 14.701Q69.877 14.838 69.723 15.084M73.076 16.701Q73.076 16.369 73.300 16.142Q73.524 15.915 73.868 15.787Q74.211 15.658 74.584 15.606Q74.956 15.553 75.260 15.553L75.260 15.300Q75.260 15.095 75.153 14.915Q75.045 14.736 74.864 14.633Q74.683 14.531 74.474 14.531Q74.068 14.531 73.832 14.623Q73.921 14.660 73.967 14.744Q74.013 14.828 74.013 14.930Q74.013 15.026 73.967 15.105Q73.921 15.183 73.840 15.228Q73.760 15.272 73.671 15.272Q73.521 15.272 73.420 15.175Q73.319 15.077 73.319 14.930Q73.319 14.308 74.474 14.308Q74.686 14.308 74.936 14.372Q75.185 14.435 75.387 14.554Q75.589 14.674 75.715 14.859Q75.841 15.043 75.841 15.286L75.841 16.862Q75.841 16.978 75.903 17.074Q75.965 17.169 76.077 17.169Q76.187 17.169 76.252 17.075Q76.317 16.981 76.317 16.862L76.317 16.414L76.583 16.414L76.583 16.862Q76.583 17.132 76.356 17.297Q76.129 17.463 75.848 17.463Q75.640 17.463 75.503 17.309Q75.366 17.156 75.342 16.940Q75.195 17.207 74.913 17.352Q74.631 17.497 74.307 17.497Q74.030 17.497 73.746 17.422Q73.463 17.347 73.269 17.168Q73.076 16.988 73.076 16.701M73.692 16.701Q73.692 16.875 73.792 17.005Q73.893 17.135 74.049 17.205Q74.204 17.275 74.368 17.275Q74.587 17.275 74.796 17.178Q75.004 17.080 75.132 16.899Q75.260 16.718 75.260 16.492L75.260 15.764Q74.936 15.764 74.570 15.855Q74.204 15.946 73.948 16.158Q73.692 16.369 73.692 16.701M77 15.918Q77 15.590 77.135 15.289Q77.270 14.989 77.506 14.768Q77.742 14.548 78.046 14.428Q78.350 14.308 78.675 14.308Q79.181 14.308 79.529 14.411Q79.878 14.513 79.878 14.889Q79.878 15.036 79.781 15.137Q79.683 15.238 79.536 15.238Q79.382 15.238 79.283 15.139Q79.184 15.040 79.184 14.889Q79.184 14.701 79.324 14.609Q79.123 14.558 78.682 14.558Q78.326 14.558 78.097 14.754Q77.868 14.951 77.767 15.260Q77.667 15.570 77.667 15.918Q77.667 16.267 77.793 16.573Q77.920 16.879 78.174 17.063Q78.429 17.248 78.784 17.248Q79.006 17.248 79.191 17.164Q79.376 17.080 79.511 16.925Q79.646 16.769 79.704 16.561Q79.717 16.506 79.772 16.506L79.885 16.506Q79.916 16.506 79.938 16.530Q79.960 16.554 79.960 16.588L79.960 16.609Q79.875 16.896 79.687 17.094Q79.499 17.292 79.234 17.395Q78.969 17.497 78.675 17.497Q78.244 17.497 77.856 17.291Q77.468 17.084 77.234 16.721Q77 16.359 77 15.918\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.832 -12.507)\">\u003Cpath d=\"M81.959 17.429L80.376 17.429L80.376 17.149Q80.605 17.149 80.754 17.115Q80.902 17.080 80.902 16.940L80.902 13.321Q80.902 13.051 80.795 12.989Q80.687 12.928 80.376 12.928L80.376 12.647L81.456 12.572L81.456 15.860L82.441 15.091Q82.646 14.954 82.646 14.804Q82.646 14.760 82.605 14.725Q82.564 14.691 82.519 14.691L82.519 14.411L83.883 14.411L83.883 14.691Q83.394 14.691 82.875 15.091L82.318 15.525L83.295 16.749Q83.497 16.995 83.630 17.072Q83.763 17.149 84.050 17.149L84.050 17.429L82.618 17.429L82.618 17.149Q82.806 17.149 82.806 17.036Q82.806 16.940 82.652 16.749L81.918 15.840L81.436 16.219L81.436 16.940Q81.436 17.077 81.584 17.113Q81.733 17.149 81.959 17.149\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M31.736 30.233H62.88\"\u002F>\u003Cpath stroke=\"none\" d=\"m65.48 30.233-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-19.125 7.71)\">\u003Cpath d=\"M54.612 15.918Q54.612 15.590 54.747 15.289Q54.882 14.989 55.118 14.768Q55.354 14.548 55.658 14.428Q55.963 14.308 56.287 14.308Q56.793 14.308 57.142 14.411Q57.490 14.513 57.490 14.889Q57.490 15.036 57.393 15.137Q57.296 15.238 57.149 15.238Q56.995 15.238 56.896 15.139Q56.797 15.040 56.797 14.889Q56.797 14.701 56.937 14.609Q56.735 14.558 56.294 14.558Q55.939 14.558 55.710 14.754Q55.481 14.951 55.380 15.260Q55.279 15.570 55.279 15.918Q55.279 16.267 55.405 16.573Q55.532 16.879 55.787 17.063Q56.041 17.248 56.397 17.248Q56.619 17.248 56.803 17.164Q56.988 17.080 57.123 16.925Q57.258 16.769 57.316 16.561Q57.330 16.506 57.384 16.506L57.497 16.506Q57.528 16.506 57.550 16.530Q57.572 16.554 57.572 16.588L57.572 16.609Q57.487 16.896 57.299 17.094Q57.111 17.292 56.846 17.395Q56.581 17.497 56.287 17.497Q55.857 17.497 55.469 17.291Q55.081 17.084 54.847 16.721Q54.612 16.359 54.612 15.918\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-19.125 7.71)\">\u003Cpath d=\"M59.635 17.429L58.001 17.429L58.001 17.149Q58.230 17.149 58.379 17.115Q58.528 17.080 58.528 16.940L58.528 13.321Q58.528 13.051 58.420 12.989Q58.312 12.928 58.001 12.928L58.001 12.647L59.081 12.572L59.081 14.958Q59.187 14.773 59.365 14.631Q59.543 14.490 59.751 14.416Q59.960 14.343 60.185 14.343Q60.691 14.343 60.975 14.566Q61.259 14.790 61.259 15.286L61.259 16.940Q61.259 17.077 61.407 17.113Q61.556 17.149 61.782 17.149L61.782 17.429L60.151 17.429L60.151 17.149Q60.380 17.149 60.529 17.115Q60.678 17.080 60.678 16.940L60.678 15.300Q60.678 14.965 60.558 14.765Q60.438 14.565 60.124 14.565Q59.854 14.565 59.620 14.701Q59.386 14.838 59.247 15.072Q59.109 15.306 59.109 15.580L59.109 16.940Q59.109 17.077 59.259 17.113Q59.410 17.149 59.635 17.149L59.635 17.429M62.428 16.701Q62.428 16.369 62.651 16.142Q62.875 15.915 63.219 15.787Q63.562 15.658 63.935 15.606Q64.307 15.553 64.612 15.553L64.612 15.300Q64.612 15.095 64.504 14.915Q64.396 14.736 64.215 14.633Q64.034 14.531 63.826 14.531Q63.419 14.531 63.183 14.623Q63.272 14.660 63.318 14.744Q63.364 14.828 63.364 14.930Q63.364 15.026 63.318 15.105Q63.272 15.183 63.191 15.228Q63.111 15.272 63.022 15.272Q62.872 15.272 62.771 15.175Q62.670 15.077 62.670 14.930Q62.670 14.308 63.826 14.308Q64.037 14.308 64.287 14.372Q64.536 14.435 64.738 14.554Q64.940 14.674 65.066 14.859Q65.193 15.043 65.193 15.286L65.193 16.862Q65.193 16.978 65.254 17.074Q65.316 17.169 65.429 17.169Q65.538 17.169 65.603 17.075Q65.668 16.981 65.668 16.862L65.668 16.414L65.934 16.414L65.934 16.862Q65.934 17.132 65.707 17.297Q65.480 17.463 65.200 17.463Q64.991 17.463 64.854 17.309Q64.718 17.156 64.694 16.940Q64.547 17.207 64.265 17.352Q63.983 17.497 63.658 17.497Q63.381 17.497 63.097 17.422Q62.814 17.347 62.621 17.168Q62.428 16.988 62.428 16.701M63.043 16.701Q63.043 16.875 63.144 17.005Q63.244 17.135 63.400 17.205Q63.556 17.275 63.720 17.275Q63.938 17.275 64.147 17.178Q64.355 17.080 64.483 16.899Q64.612 16.718 64.612 16.492L64.612 15.764Q64.287 15.764 63.921 15.855Q63.556 15.946 63.299 16.158Q63.043 16.369 63.043 16.701M68.033 17.429L66.399 17.429L66.399 17.149Q66.628 17.149 66.777 17.115Q66.926 17.080 66.926 16.940L66.926 15.091Q66.926 14.821 66.818 14.760Q66.710 14.698 66.399 14.698L66.399 14.418L67.459 14.343L67.459 14.992Q67.630 14.684 67.934 14.513Q68.238 14.343 68.583 14.343Q69.089 14.343 69.373 14.566Q69.657 14.790 69.657 15.286L69.657 16.940Q69.657 17.077 69.805 17.113Q69.954 17.149 70.180 17.149L70.180 17.429L68.549 17.429L68.549 17.149Q68.778 17.149 68.927 17.115Q69.076 17.080 69.076 16.940L69.076 15.300Q69.076 14.965 68.956 14.765Q68.836 14.565 68.522 14.565Q68.252 14.565 68.018 14.701Q67.784 14.838 67.645 15.072Q67.507 15.306 67.507 15.580L67.507 16.940Q67.507 17.077 67.657 17.113Q67.807 17.149 68.033 17.149L68.033 17.429M70.726 17.962Q70.726 17.716 70.923 17.532Q71.119 17.347 71.376 17.268Q71.239 17.156 71.167 16.995Q71.096 16.834 71.096 16.653Q71.096 16.332 71.307 16.086Q70.972 15.788 70.972 15.378Q70.972 14.917 71.362 14.630Q71.752 14.343 72.230 14.343Q72.702 14.343 73.037 14.589Q73.211 14.435 73.421 14.353Q73.632 14.271 73.861 14.271Q74.025 14.271 74.146 14.378Q74.267 14.486 74.267 14.650Q74.267 14.746 74.196 14.818Q74.124 14.889 74.032 14.889Q73.932 14.889 73.862 14.816Q73.792 14.742 73.792 14.643Q73.792 14.589 73.806 14.558L73.813 14.544Q73.820 14.524 73.828 14.513Q73.837 14.503 73.840 14.496Q73.485 14.496 73.198 14.719Q73.485 15.012 73.485 15.378Q73.485 15.693 73.300 15.925Q73.116 16.158 72.827 16.286Q72.538 16.414 72.230 16.414Q72.029 16.414 71.837 16.364Q71.646 16.315 71.468 16.205Q71.376 16.332 71.376 16.475Q71.376 16.657 71.504 16.792Q71.632 16.927 71.817 16.927L72.449 16.927Q72.897 16.927 73.266 16.998Q73.635 17.070 73.895 17.299Q74.155 17.528 74.155 17.962Q74.155 18.283 73.859 18.485Q73.563 18.687 73.160 18.776Q72.757 18.865 72.442 18.865Q72.124 18.865 71.721 18.776Q71.318 18.687 71.022 18.485Q70.726 18.283 70.726 17.962M71.181 17.962Q71.181 18.191 71.400 18.340Q71.618 18.489 71.911 18.557Q72.203 18.625 72.442 18.625Q72.606 18.625 72.815 18.589Q73.023 18.554 73.230 18.473Q73.437 18.393 73.568 18.265Q73.700 18.137 73.700 17.962Q73.700 17.610 73.319 17.516Q72.938 17.422 72.435 17.422L71.817 17.422Q71.577 17.422 71.379 17.573Q71.181 17.723 71.181 17.962M72.230 16.175Q72.897 16.175 72.897 15.378Q72.897 14.578 72.230 14.578Q71.560 14.578 71.560 15.378Q71.560 16.175 72.230 16.175M74.708 15.894Q74.708 15.573 74.833 15.284Q74.958 14.995 75.183 14.772Q75.409 14.548 75.705 14.428Q76 14.308 76.318 14.308Q76.646 14.308 76.908 14.408Q77.169 14.507 77.345 14.689Q77.521 14.872 77.615 15.130Q77.709 15.388 77.709 15.720Q77.709 15.812 77.627 15.833L75.371 15.833L75.371 15.894Q75.371 16.482 75.655 16.865Q75.939 17.248 76.506 17.248Q76.827 17.248 77.096 17.055Q77.364 16.862 77.453 16.547Q77.460 16.506 77.535 16.492L77.627 16.492Q77.709 16.516 77.709 16.588Q77.709 16.595 77.702 16.622Q77.590 17.019 77.219 17.258Q76.848 17.497 76.424 17.497Q75.987 17.497 75.587 17.289Q75.187 17.080 74.948 16.713Q74.708 16.346 74.708 15.894M75.378 15.624L77.193 15.624Q77.193 15.347 77.096 15.095Q76.998 14.842 76.800 14.686Q76.602 14.531 76.318 14.531Q76.041 14.531 75.828 14.689Q75.614 14.848 75.496 15.103Q75.378 15.358 75.378 15.624M78.297 17.422L78.297 16.359Q78.297 16.335 78.325 16.308Q78.352 16.281 78.376 16.281L78.485 16.281Q78.550 16.281 78.564 16.339Q78.660 16.773 78.906 17.024Q79.152 17.275 79.565 17.275Q79.907 17.275 80.160 17.142Q80.413 17.009 80.413 16.701Q80.413 16.544 80.319 16.429Q80.225 16.315 80.087 16.246Q79.948 16.178 79.781 16.140L79.200 16.041Q78.844 15.973 78.571 15.752Q78.297 15.532 78.297 15.190Q78.297 14.941 78.408 14.766Q78.519 14.592 78.706 14.493Q78.892 14.394 79.107 14.351Q79.323 14.308 79.565 14.308Q79.979 14.308 80.259 14.490L80.474 14.315Q80.485 14.312 80.492 14.310Q80.498 14.308 80.509 14.308L80.560 14.308Q80.587 14.308 80.611 14.332Q80.635 14.356 80.635 14.384L80.635 15.231Q80.635 15.252 80.611 15.279Q80.587 15.306 80.560 15.306L80.447 15.306Q80.420 15.306 80.394 15.281Q80.368 15.255 80.368 15.231Q80.368 14.995 80.263 14.831Q80.157 14.667 79.974 14.585Q79.791 14.503 79.558 14.503Q79.230 14.503 78.974 14.606Q78.718 14.708 78.718 14.985Q78.718 15.180 78.900 15.289Q79.083 15.399 79.312 15.440L79.887 15.546Q80.133 15.594 80.346 15.722Q80.560 15.850 80.697 16.053Q80.833 16.257 80.833 16.506Q80.833 17.019 80.468 17.258Q80.102 17.497 79.565 17.497Q79.070 17.497 78.738 17.203L78.472 17.477Q78.451 17.497 78.424 17.497L78.376 17.497Q78.352 17.497 78.325 17.470Q78.297 17.443 78.297 17.422\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M65.48 30.233H34.335\"\u002F>\u003Cpath stroke=\"none\" d=\"m31.736 30.233 4.16 2.08-1.56-2.08 1.56-2.08\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-23.628 21.398)\">\u003Cpath d=\"M56.209 17.429L54.626 17.429L54.626 17.149Q54.855 17.149 55.004 17.115Q55.152 17.080 55.152 16.940L55.152 13.321Q55.152 13.051 55.045 12.989Q54.937 12.928 54.626 12.928L54.626 12.647L55.706 12.572L55.706 15.860L56.691 15.091Q56.896 14.954 56.896 14.804Q56.896 14.760 56.855 14.725Q56.814 14.691 56.769 14.691L56.769 14.411L58.133 14.411L58.133 14.691Q57.644 14.691 57.125 15.091L56.568 15.525L57.545 16.749Q57.747 16.995 57.880 17.072Q58.013 17.149 58.300 17.149L58.300 17.429L56.868 17.429L56.868 17.149Q57.056 17.149 57.056 17.036Q57.056 16.940 56.902 16.749L56.168 15.840L55.686 16.219L55.686 16.940Q55.686 17.077 55.834 17.113Q55.983 17.149 56.209 17.149L56.209 17.429M60.495 17.429L58.861 17.429L58.861 17.149Q59.090 17.149 59.239 17.115Q59.387 17.080 59.387 16.940L59.387 15.091Q59.387 14.821 59.280 14.760Q59.172 14.698 58.861 14.698L58.861 14.418L59.921 14.343L59.921 14.992Q60.091 14.684 60.396 14.513Q60.700 14.343 61.045 14.343Q61.551 14.343 61.835 14.566Q62.118 14.790 62.118 15.286L62.118 16.940Q62.118 17.077 62.267 17.113Q62.416 17.149 62.641 17.149L62.641 17.429L61.011 17.429L61.011 17.149Q61.240 17.149 61.389 17.115Q61.537 17.080 61.537 16.940L61.537 15.300Q61.537 14.965 61.418 14.765Q61.298 14.565 60.984 14.565Q60.714 14.565 60.479 14.701Q60.245 14.838 60.107 15.072Q59.968 15.306 59.968 15.580L59.968 16.940Q59.968 17.077 60.119 17.113Q60.269 17.149 60.495 17.149L60.495 17.429M63.188 15.946Q63.188 15.604 63.323 15.305Q63.458 15.006 63.697 14.782Q63.937 14.558 64.255 14.433Q64.572 14.308 64.904 14.308Q65.348 14.308 65.748 14.524Q66.148 14.739 66.382 15.117Q66.616 15.494 66.616 15.946Q66.616 16.287 66.475 16.571Q66.333 16.855 66.088 17.062Q65.844 17.268 65.535 17.383Q65.225 17.497 64.904 17.497Q64.473 17.497 64.072 17.296Q63.670 17.094 63.429 16.742Q63.188 16.390 63.188 15.946M64.904 17.248Q65.506 17.248 65.729 16.870Q65.953 16.492 65.953 15.860Q65.953 15.248 65.719 14.889Q65.485 14.531 64.904 14.531Q63.851 14.531 63.851 15.860Q63.851 16.492 64.077 16.870Q64.302 17.248 64.904 17.248\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-23.628 21.398)\">\u003Cpath d=\"M68.389 17.402L67.408 14.903Q67.347 14.760 67.229 14.725Q67.111 14.691 66.895 14.691L66.895 14.411L68.375 14.411L68.375 14.691Q67.996 14.691 67.996 14.852Q67.996 14.862 68.010 14.903L68.724 16.735L69.397 15.030Q69.367 14.958 69.367 14.930Q69.367 14.903 69.339 14.903Q69.278 14.756 69.160 14.724Q69.042 14.691 68.830 14.691L68.830 14.411L70.228 14.411L70.228 14.691Q69.852 14.691 69.852 14.852Q69.852 14.883 69.859 14.903L70.614 16.841L71.301 15.091Q71.322 15.040 71.322 14.985Q71.322 14.845 71.209 14.768Q71.096 14.691 70.956 14.691L70.956 14.411L72.176 14.411L72.176 14.691Q71.971 14.691 71.816 14.797Q71.660 14.903 71.588 15.091L70.683 17.402Q70.648 17.497 70.536 17.497L70.467 17.497Q70.358 17.497 70.320 17.402L69.538 15.399L68.751 17.402Q68.717 17.497 68.604 17.497L68.536 17.497Q68.427 17.497 68.389 17.402M74.374 17.429L72.771 17.429L72.771 17.149Q72.997 17.149 73.145 17.115Q73.294 17.080 73.294 16.940L73.294 13.321Q73.294 13.051 73.186 12.989Q73.079 12.928 72.771 12.928L72.771 12.647L73.848 12.572L73.848 16.940Q73.848 17.077 73.998 17.113Q74.148 17.149 74.374 17.149L74.374 17.429M74.928 15.894Q74.928 15.573 75.052 15.284Q75.177 14.995 75.403 14.772Q75.628 14.548 75.924 14.428Q76.220 14.308 76.538 14.308Q76.866 14.308 77.127 14.408Q77.389 14.507 77.565 14.689Q77.741 14.872 77.835 15.130Q77.929 15.388 77.929 15.720Q77.929 15.812 77.847 15.833L75.591 15.833L75.591 15.894Q75.591 16.482 75.874 16.865Q76.158 17.248 76.726 17.248Q77.047 17.248 77.315 17.055Q77.583 16.862 77.672 16.547Q77.679 16.506 77.754 16.492L77.847 16.492Q77.929 16.516 77.929 16.588Q77.929 16.595 77.922 16.622Q77.809 17.019 77.438 17.258Q77.067 17.497 76.644 17.497Q76.206 17.497 75.806 17.289Q75.406 17.080 75.167 16.713Q74.928 16.346 74.928 15.894M75.598 15.624L77.413 15.624Q77.413 15.347 77.315 15.095Q77.218 14.842 77.020 14.686Q76.821 14.531 76.538 14.531Q76.261 14.531 76.047 14.689Q75.833 14.848 75.716 15.103Q75.598 15.358 75.598 15.624M78.517 15.918Q78.517 15.580 78.657 15.289Q78.797 14.999 79.041 14.785Q79.286 14.572 79.590 14.457Q79.894 14.343 80.219 14.343Q80.489 14.343 80.752 14.442Q81.015 14.541 81.207 14.719L81.207 13.321Q81.207 13.051 81.099 12.989Q80.991 12.928 80.680 12.928L80.680 12.647L81.757 12.572L81.757 16.756Q81.757 16.944 81.812 17.027Q81.866 17.111 81.967 17.130Q82.068 17.149 82.283 17.149L82.283 17.429L81.176 17.497L81.176 17.080Q80.759 17.497 80.133 17.497Q79.703 17.497 79.330 17.285Q78.958 17.074 78.737 16.713Q78.517 16.352 78.517 15.918M80.191 17.275Q80.400 17.275 80.586 17.203Q80.772 17.132 80.926 16.995Q81.080 16.858 81.176 16.680L81.176 15.071Q81.090 14.924 80.945 14.804Q80.800 14.684 80.631 14.625Q80.461 14.565 80.280 14.565Q79.720 14.565 79.451 14.954Q79.183 15.344 79.183 15.925Q79.183 16.496 79.417 16.886Q79.651 17.275 80.191 17.275M82.892 17.962Q82.892 17.716 83.088 17.532Q83.285 17.347 83.541 17.268Q83.404 17.156 83.333 16.995Q83.261 16.834 83.261 16.653Q83.261 16.332 83.473 16.086Q83.138 15.788 83.138 15.378Q83.138 14.917 83.527 14.630Q83.917 14.343 84.395 14.343Q84.867 14.343 85.202 14.589Q85.376 14.435 85.587 14.353Q85.797 14.271 86.026 14.271Q86.190 14.271 86.311 14.378Q86.433 14.486 86.433 14.650Q86.433 14.746 86.361 14.818Q86.289 14.889 86.197 14.889Q86.098 14.889 86.028 14.816Q85.958 14.742 85.958 14.643Q85.958 14.589 85.971 14.558L85.978 14.544Q85.985 14.524 85.993 14.513Q86.002 14.503 86.005 14.496Q85.650 14.496 85.363 14.719Q85.650 15.012 85.650 15.378Q85.650 15.693 85.465 15.925Q85.281 16.158 84.992 16.286Q84.703 16.414 84.395 16.414Q84.194 16.414 84.002 16.364Q83.811 16.315 83.633 16.205Q83.541 16.332 83.541 16.475Q83.541 16.657 83.669 16.792Q83.797 16.927 83.982 16.927L84.614 16.927Q85.062 16.927 85.431 16.998Q85.800 17.070 86.060 17.299Q86.320 17.528 86.320 17.962Q86.320 18.283 86.024 18.485Q85.729 18.687 85.325 18.776Q84.922 18.865 84.607 18.865Q84.290 18.865 83.886 18.776Q83.483 18.687 83.187 18.485Q82.892 18.283 82.892 17.962M83.346 17.962Q83.346 18.191 83.565 18.340Q83.784 18.489 84.076 18.557Q84.368 18.625 84.607 18.625Q84.771 18.625 84.980 18.589Q85.188 18.554 85.395 18.473Q85.602 18.393 85.734 18.265Q85.865 18.137 85.865 17.962Q85.865 17.610 85.484 17.516Q85.103 17.422 84.601 17.422L83.982 17.422Q83.743 17.422 83.544 17.573Q83.346 17.723 83.346 17.962M84.395 16.175Q85.062 16.175 85.062 15.378Q85.062 14.578 84.395 14.578Q83.726 14.578 83.726 15.378Q83.726 16.175 84.395 16.175M86.874 15.894Q86.874 15.573 86.998 15.284Q87.123 14.995 87.349 14.772Q87.574 14.548 87.870 14.428Q88.166 14.308 88.483 14.308Q88.812 14.308 89.073 14.408Q89.334 14.507 89.510 14.689Q89.687 14.872 89.781 15.130Q89.874 15.388 89.874 15.720Q89.874 15.812 89.792 15.833L87.537 15.833L87.537 15.894Q87.537 16.482 87.820 16.865Q88.104 17.248 88.671 17.248Q88.993 17.248 89.261 17.055Q89.529 16.862 89.618 16.547Q89.625 16.506 89.700 16.492L89.792 16.492Q89.874 16.516 89.874 16.588Q89.874 16.595 89.868 16.622Q89.755 17.019 89.384 17.258Q89.013 17.497 88.589 17.497Q88.152 17.497 87.752 17.289Q87.352 17.080 87.113 16.713Q86.874 16.346 86.874 15.894M87.543 15.624L89.358 15.624Q89.358 15.347 89.261 15.095Q89.164 14.842 88.965 14.686Q88.767 14.531 88.483 14.531Q88.207 14.531 87.993 14.689Q87.779 14.848 87.661 15.103Q87.543 15.358 87.543 15.624\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-2.607 46.082v9.804\"\u002F>\u003Cpath stroke=\"none\" d=\"m-2.607 58.486 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003Cg transform=\"translate(-78.029 36.605)\">\u003Cpath d=\"M54.571 17.962Q54.571 17.716 54.768 17.532Q54.965 17.347 55.221 17.268Q55.084 17.156 55.012 16.995Q54.941 16.834 54.941 16.653Q54.941 16.332 55.152 16.086Q54.818 15.788 54.818 15.378Q54.818 14.917 55.207 14.630Q55.597 14.343 56.075 14.343Q56.547 14.343 56.882 14.589Q57.056 14.435 57.267 14.353Q57.477 14.271 57.706 14.271Q57.870 14.271 57.991 14.378Q58.112 14.486 58.112 14.650Q58.112 14.746 58.041 14.818Q57.969 14.889 57.877 14.889Q57.777 14.889 57.707 14.816Q57.637 14.742 57.637 14.643Q57.637 14.589 57.651 14.558L57.658 14.544Q57.665 14.524 57.673 14.513Q57.682 14.503 57.685 14.496Q57.330 14.496 57.043 14.719Q57.330 15.012 57.330 15.378Q57.330 15.693 57.145 15.925Q56.961 16.158 56.672 16.286Q56.383 16.414 56.075 16.414Q55.874 16.414 55.682 16.364Q55.491 16.315 55.313 16.205Q55.221 16.332 55.221 16.475Q55.221 16.657 55.349 16.792Q55.477 16.927 55.662 16.927L56.294 16.927Q56.742 16.927 57.111 16.998Q57.480 17.070 57.740 17.299Q58 17.528 58 17.962Q58 18.283 57.704 18.485Q57.408 18.687 57.005 18.776Q56.602 18.865 56.287 18.865Q55.969 18.865 55.566 18.776Q55.163 18.687 54.867 18.485Q54.571 18.283 54.571 17.962M55.026 17.962Q55.026 18.191 55.245 18.340Q55.464 18.489 55.756 18.557Q56.048 18.625 56.287 18.625Q56.451 18.625 56.660 18.589Q56.868 18.554 57.075 18.473Q57.282 18.393 57.413 18.265Q57.545 18.137 57.545 17.962Q57.545 17.610 57.164 17.516Q56.783 17.422 56.280 17.422L55.662 17.422Q55.423 17.422 55.224 17.573Q55.026 17.723 55.026 17.962M56.075 16.175Q56.742 16.175 56.742 15.378Q56.742 14.578 56.075 14.578Q55.405 14.578 55.405 15.378Q55.405 16.175 56.075 16.175M58.553 15.946Q58.553 15.604 58.688 15.305Q58.823 15.006 59.063 14.782Q59.302 14.558 59.620 14.433Q59.938 14.308 60.269 14.308Q60.714 14.308 61.113 14.524Q61.513 14.739 61.747 15.117Q61.982 15.494 61.982 15.946Q61.982 16.287 61.840 16.571Q61.698 16.855 61.454 17.062Q61.209 17.268 60.900 17.383Q60.590 17.497 60.269 17.497Q59.839 17.497 59.437 17.296Q59.035 17.094 58.794 16.742Q58.553 16.390 58.553 15.946M60.269 17.248Q60.871 17.248 61.095 16.870Q61.319 16.492 61.319 15.860Q61.319 15.248 61.084 14.889Q60.850 14.531 60.269 14.531Q59.216 14.531 59.216 15.860Q59.216 16.492 59.442 16.870Q59.668 17.248 60.269 17.248M62.634 16.701Q62.634 16.369 62.858 16.142Q63.082 15.915 63.426 15.787Q63.769 15.658 64.142 15.606Q64.514 15.553 64.819 15.553L64.819 15.300Q64.819 15.095 64.711 14.915Q64.603 14.736 64.422 14.633Q64.241 14.531 64.032 14.531Q63.626 14.531 63.390 14.623Q63.479 14.660 63.525 14.744Q63.571 14.828 63.571 14.930Q63.571 15.026 63.525 15.105Q63.479 15.183 63.398 15.228Q63.318 15.272 63.229 15.272Q63.079 15.272 62.978 15.175Q62.877 15.077 62.877 14.930Q62.877 14.308 64.032 14.308Q64.244 14.308 64.494 14.372Q64.743 14.435 64.945 14.554Q65.147 14.674 65.273 14.859Q65.400 15.043 65.400 15.286L65.400 16.862Q65.400 16.978 65.461 17.074Q65.523 17.169 65.635 17.169Q65.745 17.169 65.810 17.075Q65.875 16.981 65.875 16.862L65.875 16.414L66.141 16.414L66.141 16.862Q66.141 17.132 65.914 17.297Q65.687 17.463 65.406 17.463Q65.198 17.463 65.061 17.309Q64.924 17.156 64.901 16.940Q64.754 17.207 64.472 17.352Q64.190 17.497 63.865 17.497Q63.588 17.497 63.304 17.422Q63.021 17.347 62.828 17.168Q62.634 16.988 62.634 16.701M63.250 16.701Q63.250 16.875 63.350 17.005Q63.451 17.135 63.607 17.205Q63.762 17.275 63.926 17.275Q64.145 17.275 64.354 17.178Q64.562 17.080 64.690 16.899Q64.819 16.718 64.819 16.492L64.819 15.764Q64.494 15.764 64.128 15.855Q63.762 15.946 63.506 16.158Q63.250 16.369 63.250 16.701M68.226 17.429L66.623 17.429L66.623 17.149Q66.849 17.149 66.997 17.115Q67.146 17.080 67.146 16.940L67.146 13.321Q67.146 13.051 67.038 12.989Q66.931 12.928 66.623 12.928L66.623 12.647L67.700 12.572L67.700 16.940Q67.700 17.077 67.850 17.113Q68.001 17.149 68.226 17.149L68.226 17.429M68.821 17.422L68.821 16.359Q68.821 16.335 68.848 16.308Q68.876 16.281 68.900 16.281L69.009 16.281Q69.074 16.281 69.088 16.339Q69.183 16.773 69.429 17.024Q69.675 17.275 70.089 17.275Q70.431 17.275 70.684 17.142Q70.937 17.009 70.937 16.701Q70.937 16.544 70.843 16.429Q70.749 16.315 70.610 16.246Q70.472 16.178 70.304 16.140L69.723 16.041Q69.368 15.973 69.094 15.752Q68.821 15.532 68.821 15.190Q68.821 14.941 68.932 14.766Q69.043 14.592 69.229 14.493Q69.416 14.394 69.631 14.351Q69.846 14.308 70.089 14.308Q70.503 14.308 70.783 14.490L70.998 14.315Q71.008 14.312 71.015 14.310Q71.022 14.308 71.032 14.308L71.084 14.308Q71.111 14.308 71.135 14.332Q71.159 14.356 71.159 14.384L71.159 15.231Q71.159 15.252 71.135 15.279Q71.111 15.306 71.084 15.306L70.971 15.306Q70.944 15.306 70.918 15.281Q70.892 15.255 70.892 15.231Q70.892 14.995 70.786 14.831Q70.680 14.667 70.497 14.585Q70.315 14.503 70.082 14.503Q69.754 14.503 69.498 14.606Q69.241 14.708 69.241 14.985Q69.241 15.180 69.424 15.289Q69.607 15.399 69.836 15.440L70.410 15.546Q70.656 15.594 70.870 15.722Q71.084 15.850 71.220 16.053Q71.357 16.257 71.357 16.506Q71.357 17.019 70.991 17.258Q70.626 17.497 70.089 17.497Q69.593 17.497 69.262 17.203L68.995 17.477Q68.975 17.497 68.947 17.497L68.900 17.497Q68.876 17.497 68.848 17.470Q68.821 17.443 68.821 17.422\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"m31.736 74.335 31.75-26.584\"\u002F>\u003Cpath stroke=\"none\" d=\"m65.48 46.082-4.525 1.075 2.531.594.14 2.596\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M99.823 46.082v17.071h101.193v31.544\"\u002F>\u003Cpath stroke=\"none\" d=\"m201.016 97.297 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">A general learning agent. The performance element (a whole agent of one of the earlier kinds) selects actions; the critic judges results against a fixed performance standard; the learning element uses that feedback to improve the performance element; the problem generator suggests exploratory actions.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:411.967px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 308.975 80.523\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cpath fill=\"none\" d=\"M-65.403-33.659h22.762V-56.42h-22.762Z\"\u002F>\u003Cg transform=\"translate(-3.008 2.733)\">\u003Cpath d=\"M-50.374-45.040L-53.655-45.040L-53.655-45.337Q-53.331-45.337-53.088-45.384Q-52.846-45.431-52.846-45.599L-52.846-49.942Q-52.846-50.114-53.088-50.161Q-53.331-50.208-53.655-50.208L-53.655-50.505L-50.608-50.505Q-50.182-50.505-49.749-50.351Q-49.315-50.196-49.020-49.888Q-48.725-49.579-48.725-49.145Q-48.725-48.892-48.850-48.675Q-48.975-48.458-49.176-48.302Q-49.377-48.145-49.610-48.046Q-49.842-47.946-50.100-47.895Q-49.725-47.860-49.346-47.683Q-48.967-47.505-48.727-47.206Q-48.487-46.907-48.487-46.513Q-48.487-46.060-48.770-45.726Q-49.053-45.392-49.489-45.216Q-49.924-45.040-50.374-45.040M-52.135-47.751L-52.135-45.599Q-52.135-45.427-52.043-45.382Q-51.952-45.337-51.733-45.337L-50.608-45.337Q-50.370-45.337-50.135-45.425Q-49.901-45.513-49.715-45.673Q-49.530-45.833-49.428-46.046Q-49.327-46.259-49.327-46.513Q-49.327-46.833-49.479-47.118Q-49.631-47.403-49.901-47.577Q-50.170-47.751-50.487-47.751L-52.135-47.751M-52.135-49.942L-52.135-48.009L-50.846-48.009Q-50.604-48.009-50.366-48.091Q-50.127-48.173-49.944-48.319Q-49.760-48.466-49.647-48.683Q-49.534-48.899-49.534-49.145Q-49.534-49.356-49.620-49.558Q-49.706-49.759-49.852-49.901Q-49.999-50.044-50.194-50.126Q-50.389-50.208-50.608-50.208L-51.733-50.208Q-51.952-50.208-52.043-50.165Q-52.135-50.122-52.135-49.942\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-25.57-33.659h22.762V-56.42H-25.57Z\"\u002F>\u003Cg transform=\"translate(36.764 2.733)\">\u003Cpath d=\"M-53.549-47.774Q-53.549-48.368-53.317-48.899Q-53.084-49.431-52.668-49.831Q-52.252-50.231-51.719-50.452Q-51.186-50.673-50.581-50.673Q-50.143-50.673-49.745-50.491Q-49.346-50.310-49.038-49.977L-48.565-50.642Q-48.534-50.673-48.502-50.673L-48.456-50.673Q-48.428-50.673-48.397-50.642Q-48.366-50.610-48.366-50.583L-48.366-48.446Q-48.366-48.423-48.397-48.392Q-48.428-48.360-48.456-48.360L-48.573-48.360Q-48.600-48.360-48.631-48.392Q-48.663-48.423-48.663-48.446Q-48.663-48.712-48.805-49.065Q-48.948-49.419-49.127-49.657Q-49.381-49.989-49.731-50.183Q-50.081-50.376-50.487-50.376Q-50.991-50.376-51.444-50.157Q-51.897-49.938-52.190-49.544Q-52.686-48.876-52.686-47.774Q-52.686-47.243-52.549-46.776Q-52.413-46.310-52.137-45.944Q-51.862-45.579-51.442-45.374Q-51.022-45.169-50.479-45.169Q-49.991-45.169-49.567-45.413Q-49.143-45.657-48.895-46.077Q-48.647-46.497-48.647-46.993Q-48.647-47.028-48.618-47.054Q-48.588-47.079-48.557-47.079L-48.456-47.079Q-48.413-47.079-48.389-47.050Q-48.366-47.020-48.366-46.977Q-48.366-46.540-48.542-46.151Q-48.717-45.763-49.028-45.479Q-49.338-45.196-49.749-45.034Q-50.159-44.872-50.581-44.872Q-51.170-44.872-51.711-45.093Q-52.252-45.313-52.668-45.718Q-53.084-46.122-53.317-46.651Q-53.549-47.181-53.549-47.774\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-42.441-45.04h14.071\"\u002F>\u003Cpath stroke=\"none\" d=\"m-25.77-45.04-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(8.174 33.849)\">\u003Cpath d=\"M-53.649-45.768Q-53.649-46.100-53.426-46.327Q-53.202-46.554-52.858-46.682Q-52.515-46.811-52.142-46.863Q-51.770-46.916-51.465-46.916L-51.465-47.169Q-51.465-47.374-51.573-47.554Q-51.681-47.733-51.862-47.836Q-52.043-47.938-52.251-47.938Q-52.658-47.938-52.894-47.846Q-52.805-47.809-52.759-47.725Q-52.713-47.641-52.713-47.539Q-52.713-47.443-52.759-47.364Q-52.805-47.286-52.886-47.241Q-52.966-47.197-53.055-47.197Q-53.205-47.197-53.306-47.294Q-53.407-47.392-53.407-47.539Q-53.407-48.161-52.251-48.161Q-52.040-48.161-51.790-48.097Q-51.541-48.034-51.339-47.915Q-51.137-47.795-51.011-47.610Q-50.884-47.426-50.884-47.183L-50.884-45.607Q-50.884-45.491-50.823-45.395Q-50.761-45.300-50.648-45.300Q-50.539-45.300-50.474-45.394Q-50.409-45.488-50.409-45.607L-50.409-46.055L-50.143-46.055L-50.143-45.607Q-50.143-45.337-50.370-45.172Q-50.597-45.006-50.877-45.006Q-51.086-45.006-51.223-45.160Q-51.359-45.313-51.383-45.529Q-51.530-45.262-51.812-45.117Q-52.094-44.972-52.419-44.972Q-52.696-44.972-52.980-45.047Q-53.263-45.122-53.456-45.301Q-53.649-45.481-53.649-45.768M-53.034-45.768Q-53.034-45.594-52.933-45.464Q-52.833-45.334-52.677-45.264Q-52.522-45.194-52.357-45.194Q-52.139-45.194-51.930-45.291Q-51.722-45.389-51.594-45.570Q-51.465-45.751-51.465-45.977L-51.465-46.705Q-51.790-46.705-52.156-46.614Q-52.522-46.523-52.778-46.311Q-53.034-46.100-53.034-45.768M-49.199-45.881L-49.199-47.778L-49.838-47.778L-49.838-48Q-49.521-48-49.303-48.210Q-49.086-48.420-48.986-48.730Q-48.885-49.039-48.885-49.347L-48.618-49.347L-48.618-48.058L-47.542-48.058L-47.542-47.778L-48.618-47.778L-48.618-45.894Q-48.618-45.618-48.514-45.419Q-48.410-45.221-48.150-45.221Q-47.993-45.221-47.887-45.325Q-47.781-45.430-47.731-45.583Q-47.682-45.737-47.682-45.894L-47.682-46.308L-47.415-46.308L-47.415-45.881Q-47.415-45.655-47.514-45.445Q-47.613-45.235-47.798-45.103Q-47.982-44.972-48.211-44.972Q-48.649-44.972-48.924-45.209Q-49.199-45.447-49.199-45.881M-46.646-46.523Q-46.646-46.865-46.511-47.164Q-46.376-47.463-46.137-47.687Q-45.897-47.911-45.580-48.036Q-45.262-48.161-44.930-48.161Q-44.486-48.161-44.086-47.945Q-43.686-47.730-43.452-47.352Q-43.218-46.975-43.218-46.523Q-43.218-46.182-43.360-45.898Q-43.501-45.614-43.746-45.407Q-43.990-45.201-44.300-45.086Q-44.609-44.972-44.930-44.972Q-45.361-44.972-45.762-45.173Q-46.164-45.375-46.405-45.727Q-46.646-46.079-46.646-46.523M-44.930-45.221Q-44.329-45.221-44.105-45.599Q-43.881-45.977-43.881-46.609Q-43.881-47.221-44.115-47.580Q-44.349-47.938-44.930-47.938Q-45.983-47.938-45.983-46.609Q-45.983-45.977-45.757-45.599Q-45.532-45.221-44.930-45.221M-40.941-45.040L-42.575-45.040L-42.575-45.320Q-42.346-45.320-42.198-45.354Q-42.049-45.389-42.049-45.529L-42.049-47.378Q-42.049-47.648-42.157-47.709Q-42.264-47.771-42.575-47.771L-42.575-48.051L-41.516-48.126L-41.516-47.477Q-41.345-47.785-41.041-47.956Q-40.736-48.126-40.391-48.126Q-39.991-48.126-39.714-47.986Q-39.438-47.846-39.352-47.498Q-39.185-47.791-38.886-47.959Q-38.586-48.126-38.241-48.126Q-37.735-48.126-37.452-47.903Q-37.168-47.679-37.168-47.183L-37.168-45.529Q-37.168-45.392-37.019-45.356Q-36.871-45.320-36.645-45.320L-36.645-45.040L-38.275-45.040L-38.275-45.320Q-38.050-45.320-37.899-45.356Q-37.749-45.392-37.749-45.529L-37.749-47.169Q-37.749-47.504-37.869-47.704Q-37.988-47.904-38.303-47.904Q-38.573-47.904-38.807-47.768Q-39.041-47.631-39.179-47.397Q-39.318-47.163-39.318-46.889L-39.318-45.529Q-39.318-45.392-39.169-45.356Q-39.021-45.320-38.795-45.320L-38.795-45.040L-40.425-45.040L-40.425-45.320Q-40.196-45.320-40.048-45.354Q-39.899-45.389-39.899-45.529L-39.899-47.169Q-39.899-47.504-40.019-47.704Q-40.138-47.904-40.453-47.904Q-40.723-47.904-40.957-47.768Q-41.191-47.631-41.329-47.397Q-41.468-47.163-41.468-46.889L-41.468-45.529Q-41.468-45.392-41.317-45.356Q-41.167-45.320-40.941-45.320L-40.941-45.040M-34.440-45.040L-35.992-45.040L-35.992-45.320Q-35.767-45.320-35.618-45.354Q-35.469-45.389-35.469-45.529L-35.469-47.378Q-35.469-47.566-35.517-47.650Q-35.565-47.733-35.662-47.752Q-35.760-47.771-35.972-47.771L-35.972-48.051L-34.916-48.126L-34.916-45.529Q-34.916-45.389-34.784-45.354Q-34.652-45.320-34.440-45.320L-34.440-45.040M-35.712-49.347Q-35.712-49.518-35.589-49.637Q-35.466-49.757-35.295-49.757Q-35.127-49.757-35.004-49.637Q-34.881-49.518-34.881-49.347Q-34.881-49.172-35.004-49.049Q-35.127-48.926-35.295-48.926Q-35.466-48.926-35.589-49.049Q-35.712-49.172-35.712-49.347M-33.794-46.551Q-33.794-46.879-33.659-47.180Q-33.524-47.480-33.289-47.701Q-33.053-47.921-32.749-48.041Q-32.444-48.161-32.120-48.161Q-31.614-48.161-31.265-48.058Q-30.917-47.956-30.917-47.580Q-30.917-47.433-31.014-47.332Q-31.111-47.231-31.258-47.231Q-31.412-47.231-31.511-47.330Q-31.610-47.429-31.610-47.580Q-31.610-47.768-31.470-47.860Q-31.672-47.911-32.113-47.911Q-32.468-47.911-32.697-47.715Q-32.926-47.518-33.027-47.209Q-33.128-46.899-33.128-46.551Q-33.128-46.202-33.001-45.896Q-32.875-45.590-32.620-45.406Q-32.366-45.221-32.010-45.221Q-31.788-45.221-31.604-45.305Q-31.419-45.389-31.284-45.544Q-31.149-45.700-31.091-45.908Q-31.077-45.963-31.022-45.963L-30.910-45.963Q-30.879-45.963-30.857-45.939Q-30.834-45.915-30.834-45.881L-30.834-45.860Q-30.920-45.573-31.108-45.375Q-31.296-45.177-31.561-45.074Q-31.826-44.972-32.120-44.972Q-32.550-44.972-32.938-45.178Q-33.326-45.385-33.560-45.748Q-33.794-46.110-33.794-46.551\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M65.48-29.39v-42.68h42.678v42.68Zm42.678-42.68\"\u002F>\u003Cg transform=\"translate(125.203 -16.064)\">\u003Cpath d=\"M-53.749-46.523Q-53.749-46.865-53.614-47.164Q-53.479-47.463-53.239-47.687Q-53-47.911-52.682-48.036Q-52.364-48.161-52.033-48.161Q-51.588-48.161-51.189-47.945Q-50.789-47.730-50.554-47.352Q-50.320-46.975-50.320-46.523Q-50.320-46.182-50.462-45.898Q-50.604-45.614-50.848-45.407Q-51.093-45.201-51.402-45.086Q-51.711-44.972-52.033-44.972Q-52.463-44.972-52.865-45.173Q-53.267-45.375-53.508-45.727Q-53.749-46.079-53.749-46.523M-52.033-45.221Q-51.431-45.221-51.207-45.599Q-50.983-45.977-50.983-46.609Q-50.983-47.221-51.218-47.580Q-51.452-47.938-52.033-47.938Q-53.085-47.938-53.085-46.609Q-53.085-45.977-52.860-45.599Q-52.634-45.221-52.033-45.221M-48.109-45.040L-49.661-45.040L-49.661-45.320Q-49.435-45.320-49.286-45.354Q-49.138-45.389-49.138-45.529L-49.138-47.378Q-49.138-47.566-49.186-47.650Q-49.233-47.733-49.331-47.752Q-49.428-47.771-49.640-47.771L-49.640-48.051L-48.584-48.126L-48.584-45.529Q-48.584-45.389-48.452-45.354Q-48.321-45.320-48.109-45.320L-48.109-45.040M-49.380-49.347Q-49.380-49.518-49.257-49.637Q-49.134-49.757-48.963-49.757Q-48.796-49.757-48.673-49.637Q-48.550-49.518-48.550-49.347Q-48.550-49.172-48.673-49.049Q-48.796-48.926-48.963-48.926Q-49.134-48.926-49.257-49.049Q-49.380-49.172-49.380-49.347M-45.795-45.040L-47.398-45.040L-47.398-45.320Q-47.172-45.320-47.024-45.354Q-46.875-45.389-46.875-45.529L-46.875-49.148Q-46.875-49.418-46.983-49.480Q-47.090-49.541-47.398-49.541L-47.398-49.822L-46.321-49.897L-46.321-45.529Q-46.321-45.392-46.171-45.356Q-46.021-45.320-45.795-45.320\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(125.312 -6.287)\">\u003Cpath d=\"M-53.749-44.507Q-53.749-44.753-53.552-44.937Q-53.355-45.122-53.099-45.201Q-53.236-45.313-53.308-45.474Q-53.379-45.635-53.379-45.816Q-53.379-46.137-53.168-46.383Q-53.502-46.681-53.502-47.091Q-53.502-47.552-53.113-47.839Q-52.723-48.126-52.245-48.126Q-51.773-48.126-51.438-47.880Q-51.264-48.034-51.053-48.116Q-50.843-48.198-50.614-48.198Q-50.450-48.198-50.329-48.091Q-50.208-47.983-50.208-47.819Q-50.208-47.723-50.279-47.651Q-50.351-47.580-50.443-47.580Q-50.543-47.580-50.613-47.653Q-50.683-47.727-50.683-47.826Q-50.683-47.880-50.669-47.911L-50.662-47.925Q-50.655-47.945-50.647-47.956Q-50.638-47.966-50.635-47.973Q-50.990-47.973-51.277-47.750Q-50.990-47.457-50.990-47.091Q-50.990-46.776-51.175-46.544Q-51.359-46.311-51.648-46.183Q-51.937-46.055-52.245-46.055Q-52.446-46.055-52.638-46.105Q-52.829-46.154-53.007-46.264Q-53.099-46.137-53.099-45.994Q-53.099-45.812-52.971-45.677Q-52.843-45.542-52.658-45.542L-52.026-45.542Q-51.578-45.542-51.209-45.471Q-50.840-45.399-50.580-45.170Q-50.320-44.941-50.320-44.507Q-50.320-44.186-50.616-43.984Q-50.912-43.782-51.315-43.693Q-51.718-43.604-52.033-43.604Q-52.351-43.604-52.754-43.693Q-53.157-43.782-53.453-43.984Q-53.749-44.186-53.749-44.507M-53.294-44.507Q-53.294-44.278-53.075-44.129Q-52.856-43.980-52.564-43.912Q-52.272-43.844-52.033-43.844Q-51.869-43.844-51.660-43.880Q-51.452-43.915-51.245-43.996Q-51.038-44.076-50.907-44.204Q-50.775-44.332-50.775-44.507Q-50.775-44.859-51.156-44.953Q-51.537-45.047-52.040-45.047L-52.658-45.047Q-52.897-45.047-53.096-44.896Q-53.294-44.746-53.294-44.507M-52.245-46.294Q-51.578-46.294-51.578-47.091Q-51.578-47.891-52.245-47.891Q-52.915-47.891-52.915-47.091Q-52.915-46.294-52.245-46.294M-49.668-45.768Q-49.668-46.100-49.444-46.327Q-49.220-46.554-48.876-46.682Q-48.533-46.811-48.160-46.863Q-47.788-46.916-47.483-46.916L-47.483-47.169Q-47.483-47.374-47.591-47.554Q-47.699-47.733-47.880-47.836Q-48.061-47.938-48.270-47.938Q-48.676-47.938-48.912-47.846Q-48.823-47.809-48.777-47.725Q-48.731-47.641-48.731-47.539Q-48.731-47.443-48.777-47.364Q-48.823-47.286-48.904-47.241Q-48.984-47.197-49.073-47.197Q-49.223-47.197-49.324-47.294Q-49.425-47.392-49.425-47.539Q-49.425-48.161-48.270-48.161Q-48.058-48.161-47.808-48.097Q-47.559-48.034-47.357-47.915Q-47.155-47.795-47.029-47.610Q-46.902-47.426-46.902-47.183L-46.902-45.607Q-46.902-45.491-46.841-45.395Q-46.779-45.300-46.667-45.300Q-46.557-45.300-46.492-45.394Q-46.427-45.488-46.427-45.607L-46.427-46.055L-46.161-46.055L-46.161-45.607Q-46.161-45.337-46.388-45.172Q-46.615-45.006-46.896-45.006Q-47.104-45.006-47.241-45.160Q-47.377-45.313-47.401-45.529Q-47.548-45.262-47.830-45.117Q-48.112-44.972-48.437-44.972Q-48.714-44.972-48.998-45.047Q-49.281-45.122-49.474-45.301Q-49.668-45.481-49.668-45.768M-49.052-45.768Q-49.052-45.594-48.951-45.464Q-48.851-45.334-48.695-45.264Q-48.540-45.194-48.376-45.194Q-48.157-45.194-47.948-45.291Q-47.740-45.389-47.612-45.570Q-47.483-45.751-47.483-45.977L-47.483-46.705Q-47.808-46.705-48.174-46.614Q-48.540-46.523-48.796-46.311Q-49.052-46.100-49.052-45.768M-45.744-45.047L-45.744-46.110Q-45.744-46.134-45.716-46.161Q-45.689-46.188-45.665-46.188L-45.556-46.188Q-45.491-46.188-45.477-46.130Q-45.381-45.696-45.135-45.445Q-44.889-45.194-44.476-45.194Q-44.134-45.194-43.881-45.327Q-43.628-45.460-43.628-45.768Q-43.628-45.925-43.722-46.040Q-43.816-46.154-43.954-46.223Q-44.093-46.291-44.260-46.329L-44.841-46.428Q-45.197-46.496-45.470-46.717Q-45.744-46.937-45.744-47.279Q-45.744-47.528-45.633-47.703Q-45.522-47.877-45.335-47.976Q-45.149-48.075-44.934-48.118Q-44.718-48.161-44.476-48.161Q-44.062-48.161-43.782-47.979L-43.566-48.154Q-43.556-48.157-43.549-48.159Q-43.543-48.161-43.532-48.161L-43.481-48.161Q-43.454-48.161-43.430-48.137Q-43.406-48.113-43.406-48.085L-43.406-47.238Q-43.406-47.217-43.430-47.190Q-43.454-47.163-43.481-47.163L-43.594-47.163Q-43.621-47.163-43.647-47.188Q-43.672-47.214-43.672-47.238Q-43.672-47.474-43.778-47.638Q-43.884-47.802-44.067-47.884Q-44.250-47.966-44.482-47.966Q-44.811-47.966-45.067-47.863Q-45.323-47.761-45.323-47.484Q-45.323-47.289-45.140-47.180Q-44.958-47.070-44.729-47.029L-44.154-46.923Q-43.908-46.875-43.695-46.747Q-43.481-46.619-43.344-46.416Q-43.208-46.212-43.208-45.963Q-43.208-45.450-43.573-45.211Q-43.939-44.972-44.476-44.972Q-44.971-44.972-45.303-45.266L-45.569-44.992Q-45.590-44.972-45.617-44.972L-45.665-44.972Q-45.689-44.972-45.716-44.999Q-45.744-45.026-45.744-45.047\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(127.263 5.941)\">\u003Cpath d=\"M-53.708-46.551Q-53.708-46.879-53.573-47.180Q-53.438-47.480-53.202-47.701Q-52.966-47.921-52.662-48.041Q-52.357-48.161-52.033-48.161Q-51.527-48.161-51.178-48.058Q-50.830-47.956-50.830-47.580Q-50.830-47.433-50.927-47.332Q-51.024-47.231-51.171-47.231Q-51.325-47.231-51.424-47.330Q-51.523-47.429-51.523-47.580Q-51.523-47.768-51.383-47.860Q-51.585-47.911-52.026-47.911Q-52.381-47.911-52.610-47.715Q-52.839-47.518-52.940-47.209Q-53.041-46.899-53.041-46.551Q-53.041-46.202-52.915-45.896Q-52.788-45.590-52.533-45.406Q-52.279-45.221-51.923-45.221Q-51.701-45.221-51.517-45.305Q-51.332-45.389-51.197-45.544Q-51.062-45.700-51.004-45.908Q-50.990-45.963-50.936-45.963L-50.823-45.963Q-50.792-45.963-50.770-45.939Q-50.748-45.915-50.748-45.881L-50.748-45.860Q-50.833-45.573-51.021-45.375Q-51.209-45.177-51.474-45.074Q-51.739-44.972-52.033-44.972Q-52.463-44.972-52.851-45.178Q-53.239-45.385-53.473-45.748Q-53.708-46.110-53.708-46.551M-48.543-45.040L-50.095-45.040L-50.095-45.320Q-49.869-45.320-49.720-45.354Q-49.572-45.389-49.572-45.529L-49.572-47.378Q-49.572-47.566-49.620-47.650Q-49.668-47.733-49.765-47.752Q-49.862-47.771-50.074-47.771L-50.074-48.051L-49.018-48.126L-49.018-45.529Q-49.018-45.389-48.887-45.354Q-48.755-45.320-48.543-45.320L-48.543-45.040M-49.814-49.347Q-49.814-49.518-49.691-49.637Q-49.568-49.757-49.397-49.757Q-49.230-49.757-49.107-49.637Q-48.984-49.518-48.984-49.347Q-48.984-49.172-49.107-49.049Q-49.230-48.926-49.397-48.926Q-49.568-48.926-49.691-49.049Q-49.814-49.172-49.814-49.347M-47.371-45.881L-47.371-47.778L-48.010-47.778L-48.010-48Q-47.692-48-47.475-48.210Q-47.258-48.420-47.157-48.730Q-47.056-49.039-47.056-49.347L-46.790-49.347L-46.790-48.058L-45.713-48.058L-45.713-47.778L-46.790-47.778L-46.790-45.894Q-46.790-45.618-46.685-45.419Q-46.581-45.221-46.321-45.221Q-46.164-45.221-46.058-45.325Q-45.952-45.430-45.903-45.583Q-45.853-45.737-45.853-45.894L-45.853-46.308L-45.586-46.308L-45.586-45.881Q-45.586-45.655-45.686-45.445Q-45.785-45.235-45.969-45.103Q-46.154-44.972-46.383-44.972Q-46.820-44.972-47.095-45.209Q-47.371-45.447-47.371-45.881\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(127.263 5.941)\">\u003Cpath d=\"M-44.644-43.905Q-44.514-43.837-44.377-43.837Q-44.206-43.837-44.056-43.926Q-43.905-44.015-43.794-44.160Q-43.683-44.305-43.605-44.473L-43.341-45.040L-44.510-47.566Q-44.585-47.713-44.715-47.745Q-44.845-47.778-45.078-47.778L-45.078-48.058L-43.557-48.058L-43.557-47.778Q-43.905-47.778-43.905-47.631Q-43.902-47.610-43.900-47.593Q-43.898-47.576-43.898-47.566L-43.041-45.707L-42.268-47.378Q-42.234-47.446-42.234-47.525Q-42.234-47.638-42.318-47.708Q-42.401-47.778-42.514-47.778L-42.514-48.058L-41.318-48.058L-41.318-47.778Q-41.537-47.778-41.709-47.674Q-41.882-47.569-41.974-47.378L-43.311-44.473Q-43.481-44.103-43.751-43.857Q-44.022-43.611-44.377-43.611Q-44.647-43.611-44.866-43.777Q-45.085-43.943-45.085-44.206Q-45.085-44.343-44.992-44.432Q-44.900-44.520-44.760-44.520Q-44.623-44.520-44.534-44.432Q-44.445-44.343-44.445-44.206Q-44.445-44.103-44.498-44.025Q-44.551-43.946-44.644-43.905\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M87.019-35.74h17.071v-10.065H87.02Z\"\u002F>\u003Cg transform=\"translate(147.24 5.967)\">\u003Cpath d=\"M-51.227-45.040L-53.597-45.040L-53.597-45.279Q-53.043-45.279-53.043-45.399L-53.043-48.094Q-53.043-48.214-53.597-48.214L-53.597-48.456L-51.402-48.456Q-51.122-48.456-50.794-48.363Q-50.467-48.270-50.240-48.076Q-50.013-47.882-50.013-47.596Q-50.013-47.281-50.324-47.086Q-50.636-46.891-51.002-46.825Q-50.777-46.825-50.500-46.714Q-50.223-46.602-50.030-46.405Q-49.837-46.207-49.837-45.970Q-49.837-45.743-49.970-45.564Q-50.104-45.384-50.318-45.268Q-50.533-45.152-50.770-45.096Q-51.007-45.040-51.227-45.040M-52.533-46.725L-52.533-45.399Q-52.533-45.318-52.456-45.299Q-52.379-45.279-52.252-45.279L-51.402-45.279Q-51.192-45.279-50.962-45.356Q-50.731-45.433-50.576-45.589Q-50.421-45.746-50.421-45.970Q-50.421-46.190-50.552-46.363Q-50.682-46.537-50.888-46.631Q-51.095-46.725-51.312-46.725L-52.533-46.725M-52.533-48.094L-52.533-46.910L-51.571-46.910Q-51.422-46.910-51.249-46.952Q-51.075-46.993-50.919-47.080Q-50.763-47.166-50.670-47.297Q-50.577-47.428-50.577-47.596Q-50.577-47.789-50.703-47.928Q-50.829-48.067-51.020-48.141Q-51.212-48.214-51.402-48.214L-52.252-48.214Q-52.379-48.214-52.456-48.194Q-52.533-48.175-52.533-48.094\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.150\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(126.726 34.001)\">\u003Cpath d=\"M-51.910-45.040L-53.643-45.040L-53.643-45.320Q-53.417-45.320-53.268-45.354Q-53.120-45.389-53.120-45.529L-53.120-47.778L-53.708-47.778L-53.708-48.058L-53.120-48.058L-53.120-48.875Q-53.120-49.193-52.942-49.441Q-52.764-49.688-52.474-49.829Q-52.183-49.969-51.872-49.969Q-51.616-49.969-51.412-49.827Q-51.209-49.685-51.209-49.442Q-51.209-49.306-51.308-49.207Q-51.407-49.107-51.544-49.107Q-51.681-49.107-51.780-49.207Q-51.879-49.306-51.879-49.442Q-51.879-49.623-51.739-49.716Q-51.817-49.743-51.917-49.743Q-52.125-49.743-52.279-49.610Q-52.433-49.477-52.513-49.273Q-52.593-49.070-52.593-48.861L-52.593-48.058L-51.705-48.058L-51.705-47.778L-52.566-47.778L-52.566-45.529Q-52.566-45.320-51.910-45.320L-51.910-45.040M-51.171-45.768Q-51.171-46.100-50.948-46.327Q-50.724-46.554-50.380-46.682Q-50.037-46.811-49.664-46.863Q-49.292-46.916-48.987-46.916L-48.987-47.169Q-48.987-47.374-49.095-47.554Q-49.203-47.733-49.384-47.836Q-49.565-47.938-49.773-47.938Q-50.180-47.938-50.416-47.846Q-50.327-47.809-50.281-47.725Q-50.235-47.641-50.235-47.539Q-50.235-47.443-50.281-47.364Q-50.327-47.286-50.407-47.241Q-50.488-47.197-50.577-47.197Q-50.727-47.197-50.828-47.294Q-50.929-47.392-50.929-47.539Q-50.929-48.161-49.773-48.161Q-49.562-48.161-49.312-48.097Q-49.063-48.034-48.861-47.915Q-48.659-47.795-48.533-47.610Q-48.406-47.426-48.406-47.183L-48.406-45.607Q-48.406-45.491-48.345-45.395Q-48.283-45.300-48.170-45.300Q-48.061-45.300-47.996-45.394Q-47.931-45.488-47.931-45.607L-47.931-46.055L-47.665-46.055L-47.665-45.607Q-47.665-45.337-47.892-45.172Q-48.119-45.006-48.399-45.006Q-48.608-45.006-48.745-45.160Q-48.881-45.313-48.905-45.529Q-49.052-45.262-49.334-45.117Q-49.616-44.972-49.941-44.972Q-50.218-44.972-50.501-45.047Q-50.785-45.122-50.978-45.301Q-51.171-45.481-51.171-45.768M-50.556-45.768Q-50.556-45.594-50.455-45.464Q-50.355-45.334-50.199-45.264Q-50.043-45.194-49.879-45.194Q-49.661-45.194-49.452-45.291Q-49.244-45.389-49.116-45.570Q-48.987-45.751-48.987-45.977L-48.987-46.705Q-49.312-46.705-49.678-46.614Q-50.043-46.523-50.300-46.311Q-50.556-46.100-50.556-45.768M-47.248-46.551Q-47.248-46.879-47.113-47.180Q-46.978-47.480-46.742-47.701Q-46.506-47.921-46.202-48.041Q-45.897-48.161-45.573-48.161Q-45.067-48.161-44.718-48.058Q-44.370-47.956-44.370-47.580Q-44.370-47.433-44.467-47.332Q-44.564-47.231-44.711-47.231Q-44.865-47.231-44.964-47.330Q-45.064-47.429-45.064-47.580Q-45.064-47.768-44.923-47.860Q-45.125-47.911-45.566-47.911Q-45.921-47.911-46.150-47.715Q-46.379-47.518-46.480-47.209Q-46.581-46.899-46.581-46.551Q-46.581-46.202-46.455-45.896Q-46.328-45.590-46.074-45.406Q-45.819-45.221-45.463-45.221Q-45.241-45.221-45.057-45.305Q-44.872-45.389-44.737-45.544Q-44.602-45.700-44.544-45.908Q-44.530-45.963-44.476-45.963L-44.363-45.963Q-44.332-45.963-44.310-45.939Q-44.288-45.915-44.288-45.881L-44.288-45.860Q-44.373-45.573-44.561-45.375Q-44.749-45.177-45.014-45.074Q-45.279-44.972-45.573-44.972Q-46.003-44.972-46.391-45.178Q-46.779-45.385-47.013-45.748Q-47.248-46.110-47.248-46.551M-43.173-45.881L-43.173-47.778L-43.813-47.778L-43.813-48Q-43.495-48-43.278-48.210Q-43.061-48.420-42.960-48.730Q-42.859-49.039-42.859-49.347L-42.592-49.347L-42.592-48.058L-41.516-48.058L-41.516-47.778L-42.592-47.778L-42.592-45.894Q-42.592-45.618-42.488-45.419Q-42.384-45.221-42.124-45.221Q-41.967-45.221-41.861-45.325Q-41.755-45.430-41.705-45.583Q-41.656-45.737-41.656-45.894L-41.656-46.308L-41.389-46.308L-41.389-45.881Q-41.389-45.655-41.488-45.445Q-41.587-45.235-41.772-45.103Q-41.957-44.972-42.186-44.972Q-42.623-44.972-42.898-45.209Q-43.173-45.447-43.173-45.881M-40.620-46.523Q-40.620-46.865-40.485-47.164Q-40.350-47.463-40.111-47.687Q-39.872-47.911-39.554-48.036Q-39.236-48.161-38.904-48.161Q-38.460-48.161-38.060-47.945Q-37.660-47.730-37.426-47.352Q-37.192-46.975-37.192-46.523Q-37.192-46.182-37.334-45.898Q-37.476-45.614-37.720-45.407Q-37.964-45.201-38.274-45.086Q-38.583-44.972-38.904-44.972Q-39.335-44.972-39.737-45.173Q-40.138-45.375-40.379-45.727Q-40.620-46.079-40.620-46.523M-38.904-45.221Q-38.303-45.221-38.079-45.599Q-37.855-45.977-37.855-46.609Q-37.855-47.221-38.089-47.580Q-38.323-47.938-38.904-47.938Q-39.957-47.938-39.957-46.609Q-39.957-45.977-39.731-45.599Q-39.506-45.221-38.904-45.221M-34.847-45.040L-36.584-45.040L-36.584-45.320Q-36.355-45.320-36.206-45.354Q-36.057-45.389-36.057-45.529L-36.057-47.378Q-36.057-47.648-36.165-47.709Q-36.272-47.771-36.584-47.771L-36.584-48.051L-35.555-48.126L-35.555-47.419Q-35.425-47.727-35.182-47.926Q-34.939-48.126-34.622-48.126Q-34.403-48.126-34.232-48.002Q-34.061-47.877-34.061-47.665Q-34.061-47.528-34.160-47.429Q-34.259-47.330-34.393-47.330Q-34.529-47.330-34.628-47.429Q-34.728-47.528-34.728-47.665Q-34.728-47.805-34.628-47.904Q-34.919-47.904-35.119-47.708Q-35.319-47.511-35.411-47.217Q-35.503-46.923-35.503-46.643L-35.503-45.529Q-35.503-45.320-34.847-45.320L-34.847-45.040M-33.518-46.575Q-33.518-46.896-33.393-47.185Q-33.268-47.474-33.043-47.697Q-32.817-47.921-32.521-48.041Q-32.226-48.161-31.908-48.161Q-31.580-48.161-31.318-48.061Q-31.057-47.962-30.881-47.780Q-30.705-47.597-30.611-47.339Q-30.517-47.081-30.517-46.749Q-30.517-46.657-30.599-46.636L-32.855-46.636L-32.855-46.575Q-32.855-45.987-32.571-45.604Q-32.287-45.221-31.720-45.221Q-31.398-45.221-31.130-45.414Q-30.862-45.607-30.773-45.922Q-30.766-45.963-30.691-45.977L-30.599-45.977Q-30.517-45.953-30.517-45.881Q-30.517-45.874-30.523-45.847Q-30.636-45.450-31.007-45.211Q-31.378-44.972-31.802-44.972Q-32.239-44.972-32.639-45.180Q-33.039-45.389-33.278-45.756Q-33.518-46.123-33.518-46.575M-32.848-46.845L-31.033-46.845Q-31.033-47.122-31.130-47.374Q-31.228-47.627-31.426-47.783Q-31.624-47.938-31.908-47.938Q-32.185-47.938-32.398-47.780Q-32.612-47.621-32.730-47.366Q-32.848-47.111-32.848-46.845M-29.929-46.551Q-29.929-46.889-29.789-47.180Q-29.648-47.470-29.404-47.684Q-29.160-47.897-28.855-48.012Q-28.551-48.126-28.227-48.126Q-27.957-48.126-27.693-48.027Q-27.430-47.928-27.239-47.750L-27.239-49.148Q-27.239-49.418-27.346-49.480Q-27.454-49.541-27.765-49.541L-27.765-49.822L-26.689-49.897L-26.689-45.713Q-26.689-45.525-26.634-45.442Q-26.579-45.358-26.478-45.339Q-26.377-45.320-26.162-45.320L-26.162-45.040L-27.270-44.972L-27.270-45.389Q-27.687-44.972-28.312-44.972Q-28.743-44.972-29.115-45.184Q-29.488-45.395-29.708-45.756Q-29.929-46.117-29.929-46.551M-28.254-45.194Q-28.045-45.194-27.859-45.266Q-27.673-45.337-27.519-45.474Q-27.365-45.611-27.270-45.789L-27.270-47.398Q-27.355-47.545-27.500-47.665Q-27.646-47.785-27.815-47.844Q-27.984-47.904-28.165-47.904Q-28.726-47.904-28.994-47.515Q-29.262-47.125-29.262-46.544Q-29.262-45.973-29.028-45.583Q-28.794-45.194-28.254-45.194\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M170.755-46.463h17.071v-17.071h-17.071ZM213.434-46.463h17.071v-17.071h-17.071ZM192.094-22.278h17.072v-17.071h-17.072Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M188.026-54.999h23.208\"\u002F>\u003Cpath stroke=\"none\" d=\"m213.234-54.999-3.2-1.6 1.2 1.6-1.2 1.6\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"m187-46.263 4.6 5.214\"\u002F>\u003Cpath stroke=\"none\" d=\"m192.924-39.55-.917-3.457-.406 1.958-1.994.16\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"m208.339-39.55 4.601-5.213\"\u002F>\u003Cpath stroke=\"none\" d=\"m214.264-46.263-3.317 1.34 1.993.16.406 1.958\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(236.637 43.96)\">\u003Cpath d=\"M-53.708-45.047L-53.708-46.110Q-53.708-46.134-53.680-46.161Q-53.653-46.188-53.629-46.188L-53.520-46.188Q-53.455-46.188-53.441-46.130Q-53.345-45.696-53.099-45.445Q-52.853-45.194-52.439-45.194Q-52.098-45.194-51.845-45.327Q-51.592-45.460-51.592-45.768Q-51.592-45.925-51.686-46.040Q-51.780-46.154-51.918-46.223Q-52.057-46.291-52.224-46.329L-52.805-46.428Q-53.161-46.496-53.434-46.717Q-53.708-46.937-53.708-47.279Q-53.708-47.528-53.596-47.703Q-53.485-47.877-53.299-47.976Q-53.113-48.075-52.897-48.118Q-52.682-48.161-52.439-48.161Q-52.026-48.161-51.746-47.979L-51.530-48.154Q-51.520-48.157-51.513-48.159Q-51.506-48.161-51.496-48.161L-51.445-48.161Q-51.418-48.161-51.394-48.137Q-51.370-48.113-51.370-48.085L-51.370-47.238Q-51.370-47.217-51.394-47.190Q-51.418-47.163-51.445-47.163L-51.558-47.163Q-51.585-47.163-51.611-47.188Q-51.636-47.214-51.636-47.238Q-51.636-47.474-51.742-47.638Q-51.848-47.802-52.031-47.884Q-52.214-47.966-52.446-47.966Q-52.774-47.966-53.031-47.863Q-53.287-47.761-53.287-47.484Q-53.287-47.289-53.104-47.180Q-52.921-47.070-52.692-47.029L-52.118-46.923Q-51.872-46.875-51.658-46.747Q-51.445-46.619-51.308-46.416Q-51.171-46.212-51.171-45.963Q-51.171-45.450-51.537-45.211Q-51.903-44.972-52.439-44.972Q-52.935-44.972-53.267-45.266L-53.533-44.992Q-53.554-44.972-53.581-44.972L-53.629-44.972Q-53.653-44.972-53.680-44.999Q-53.708-45.026-53.708-45.047M-50.016-45.881L-50.016-47.778L-50.655-47.778L-50.655-48Q-50.337-48-50.120-48.210Q-49.903-48.420-49.803-48.730Q-49.702-49.039-49.702-49.347L-49.435-49.347L-49.435-48.058L-48.358-48.058L-48.358-47.778L-49.435-47.778L-49.435-45.894Q-49.435-45.618-49.331-45.419Q-49.227-45.221-48.967-45.221Q-48.810-45.221-48.704-45.325Q-48.598-45.430-48.548-45.583Q-48.499-45.737-48.499-45.894L-48.499-46.308L-48.232-46.308L-48.232-45.881Q-48.232-45.655-48.331-45.445Q-48.430-45.235-48.615-45.103Q-48.799-44.972-49.028-44.972Q-49.466-44.972-49.741-45.209Q-50.016-45.447-50.016-45.881M-45.672-45.040L-47.408-45.040L-47.408-45.320Q-47.179-45.320-47.031-45.354Q-46.882-45.389-46.882-45.529L-46.882-47.378Q-46.882-47.648-46.990-47.709Q-47.097-47.771-47.408-47.771L-47.408-48.051L-46.379-48.126L-46.379-47.419Q-46.250-47.727-46.007-47.926Q-45.764-48.126-45.446-48.126Q-45.228-48.126-45.057-48.002Q-44.886-47.877-44.886-47.665Q-44.886-47.528-44.985-47.429Q-45.084-47.330-45.217-47.330Q-45.354-47.330-45.453-47.429Q-45.552-47.528-45.552-47.665Q-45.552-47.805-45.453-47.904Q-45.744-47.904-45.944-47.708Q-46.144-47.511-46.236-47.217Q-46.328-46.923-46.328-46.643L-46.328-45.529Q-46.328-45.320-45.672-45.320L-45.672-45.040M-43.727-45.874L-43.727-47.378Q-43.727-47.648-43.835-47.709Q-43.942-47.771-44.253-47.771L-44.253-48.051L-43.146-48.126L-43.146-45.894L-43.146-45.874Q-43.146-45.594-43.095-45.450Q-43.043-45.307-42.902-45.250Q-42.760-45.194-42.473-45.194Q-42.220-45.194-42.015-45.334Q-41.810-45.474-41.693-45.700Q-41.577-45.925-41.577-46.175L-41.577-47.378Q-41.577-47.648-41.685-47.709Q-41.793-47.771-42.104-47.771L-42.104-48.051L-40.996-48.126L-40.996-45.713Q-40.996-45.522-40.943-45.440Q-40.890-45.358-40.789-45.339Q-40.689-45.320-40.473-45.320L-40.473-45.040L-41.550-44.972L-41.550-45.536Q-41.659-45.354-41.804-45.231Q-41.950-45.108-42.136-45.040Q-42.322-44.972-42.524-44.972Q-43.727-44.972-43.727-45.874M-39.885-46.551Q-39.885-46.879-39.750-47.180Q-39.615-47.480-39.379-47.701Q-39.144-47.921-38.839-48.041Q-38.535-48.161-38.210-48.161Q-37.705-48.161-37.356-48.058Q-37.007-47.956-37.007-47.580Q-37.007-47.433-37.105-47.332Q-37.202-47.231-37.349-47.231Q-37.503-47.231-37.602-47.330Q-37.701-47.429-37.701-47.580Q-37.701-47.768-37.561-47.860Q-37.763-47.911-38.204-47.911Q-38.559-47.911-38.788-47.715Q-39.017-47.518-39.118-47.209Q-39.219-46.899-39.219-46.551Q-39.219-46.202-39.092-45.896Q-38.966-45.590-38.711-45.406Q-38.457-45.221-38.101-45.221Q-37.879-45.221-37.694-45.305Q-37.510-45.389-37.375-45.544Q-37.240-45.700-37.182-45.908Q-37.168-45.963-37.113-45.963L-37.001-45.963Q-36.970-45.963-36.948-45.939Q-36.925-45.915-36.925-45.881L-36.925-45.860Q-37.011-45.573-37.199-45.375Q-37.387-45.177-37.652-45.074Q-37.917-44.972-38.210-44.972Q-38.641-44.972-39.029-45.178Q-39.417-45.385-39.651-45.748Q-39.885-46.110-39.885-46.551M-35.811-45.881L-35.811-47.778L-36.450-47.778L-36.450-48Q-36.132-48-35.915-48.210Q-35.698-48.420-35.597-48.730Q-35.497-49.039-35.497-49.347L-35.230-49.347L-35.230-48.058L-34.153-48.058L-34.153-47.778L-35.230-47.778L-35.230-45.894Q-35.230-45.618-35.126-45.419Q-35.022-45.221-34.762-45.221Q-34.605-45.221-34.499-45.325Q-34.393-45.430-34.343-45.583Q-34.293-45.737-34.293-45.894L-34.293-46.308L-34.027-46.308L-34.027-45.881Q-34.027-45.655-34.126-45.445Q-34.225-45.235-34.410-45.103Q-34.594-44.972-34.823-44.972Q-35.261-44.972-35.536-45.209Q-35.811-45.447-35.811-45.881M-32.643-45.874L-32.643-47.378Q-32.643-47.648-32.750-47.709Q-32.858-47.771-33.169-47.771L-33.169-48.051L-32.062-48.126L-32.062-45.894L-32.062-45.874Q-32.062-45.594-32.010-45.450Q-31.959-45.307-31.817-45.250Q-31.675-45.194-31.388-45.194Q-31.135-45.194-30.930-45.334Q-30.725-45.474-30.609-45.700Q-30.493-45.925-30.493-46.175L-30.493-47.378Q-30.493-47.648-30.600-47.709Q-30.708-47.771-31.019-47.771L-31.019-48.051L-29.912-48.126L-29.912-45.713Q-29.912-45.522-29.859-45.440Q-29.806-45.358-29.705-45.339Q-29.604-45.320-29.389-45.320L-29.389-45.040L-30.465-44.972L-30.465-45.536Q-30.575-45.354-30.720-45.231Q-30.865-45.108-31.052-45.040Q-31.238-44.972-31.439-44.972Q-32.643-44.972-32.643-45.874M-27.051-45.040L-28.787-45.040L-28.787-45.320Q-28.558-45.320-28.409-45.354Q-28.261-45.389-28.261-45.529L-28.261-47.378Q-28.261-47.648-28.368-47.709Q-28.476-47.771-28.787-47.771L-28.787-48.051L-27.758-48.126L-27.758-47.419Q-27.628-47.727-27.386-47.926Q-27.143-48.126-26.825-48.126Q-26.606-48.126-26.436-48.002Q-26.265-47.877-26.265-47.665Q-26.265-47.528-26.364-47.429Q-26.463-47.330-26.596-47.330Q-26.733-47.330-26.832-47.429Q-26.931-47.528-26.931-47.665Q-26.931-47.805-26.832-47.904Q-27.123-47.904-27.323-47.708Q-27.522-47.511-27.615-47.217Q-27.707-46.923-27.707-46.643L-27.707-45.529Q-27.707-45.320-27.051-45.320L-27.051-45.040M-25.721-46.575Q-25.721-46.896-25.596-47.185Q-25.472-47.474-25.246-47.697Q-25.021-47.921-24.725-48.041Q-24.429-48.161-24.111-48.161Q-23.783-48.161-23.522-48.061Q-23.260-47.962-23.084-47.780Q-22.908-47.597-22.814-47.339Q-22.720-47.081-22.720-46.749Q-22.720-46.657-22.802-46.636L-25.058-46.636L-25.058-46.575Q-25.058-45.987-24.774-45.604Q-24.491-45.221-23.923-45.221Q-23.602-45.221-23.334-45.414Q-23.065-45.607-22.977-45.922Q-22.970-45.963-22.895-45.977L-22.802-45.977Q-22.720-45.953-22.720-45.881Q-22.720-45.874-22.727-45.847Q-22.840-45.450-23.211-45.211Q-23.582-44.972-24.005-44.972Q-24.443-44.972-24.843-45.180Q-25.243-45.389-25.482-45.756Q-25.721-46.123-25.721-46.575M-25.051-46.845L-23.236-46.845Q-23.236-47.122-23.334-47.374Q-23.431-47.627-23.629-47.783Q-23.828-47.938-24.111-47.938Q-24.388-47.938-24.602-47.780Q-24.815-47.621-24.933-47.366Q-25.051-47.111-25.051-46.845M-22.132-46.551Q-22.132-46.889-21.992-47.180Q-21.852-47.470-21.608-47.684Q-21.363-47.897-21.059-48.012Q-20.755-48.126-20.430-48.126Q-20.160-48.126-19.897-48.027Q-19.634-47.928-19.442-47.750L-19.442-49.148Q-19.442-49.418-19.550-49.480Q-19.658-49.541-19.969-49.541L-19.969-49.822L-18.892-49.897L-18.892-45.713Q-18.892-45.525-18.837-45.442Q-18.783-45.358-18.682-45.339Q-18.581-45.320-18.366-45.320L-18.366-45.040L-19.473-44.972L-19.473-45.389Q-19.890-44.972-20.516-44.972Q-20.946-44.972-21.319-45.184Q-21.691-45.395-21.912-45.756Q-22.132-46.117-22.132-46.551M-20.458-45.194Q-20.249-45.194-20.063-45.266Q-19.876-45.337-19.723-45.474Q-19.569-45.611-19.473-45.789L-19.473-47.398Q-19.559-47.545-19.704-47.665Q-19.849-47.785-20.018-47.844Q-20.188-47.904-20.369-47.904Q-20.929-47.904-21.198-47.515Q-21.466-47.125-21.466-46.544Q-21.466-45.973-21.232-45.583Q-20.998-45.194-20.458-45.194\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">Three ways to represent a state, in order of increasing expressive power: atomic (an indivisible label), factored (a vector of attribute values), and structured (objects with attributes and relations among them).\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:400.835px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 300.626 86.467\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-64.414-43.417H9.563V-71.87h-73.977Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-31.076 -37.834)\">\u003Cpath d=\"M-25.179-17.810L-27.159-17.810L-27.159-18.107Q-26.890-18.107-26.722-18.152Q-26.554-18.197-26.554-18.369L-26.554-20.505Q-26.554-20.720-26.616-20.816Q-26.679-20.912-26.796-20.933Q-26.913-20.955-27.159-20.955L-27.159-21.251L-25.991-21.337L-25.991-20.552Q-25.913-20.763-25.761-20.949Q-25.609-21.134-25.409-21.236Q-25.210-21.337-24.984-21.337Q-24.738-21.337-24.546-21.193Q-24.355-21.048-24.355-20.818Q-24.355-20.662-24.460-20.552Q-24.566-20.443-24.722-20.443Q-24.878-20.443-24.988-20.552Q-25.097-20.662-25.097-20.818Q-25.097-20.978-24.991-21.083Q-25.316-21.083-25.530-20.855Q-25.745-20.626-25.841-20.287Q-25.937-19.947-25.937-19.642L-25.937-18.369Q-25.937-18.201-25.710-18.154Q-25.484-18.107-25.179-18.107L-25.179-17.810M-23.874-19.564Q-23.874-20.044-23.642-20.460Q-23.409-20.876-22.999-21.126Q-22.589-21.376-22.113-21.376Q-21.382-21.376-20.984-20.935Q-20.585-20.494-20.585-19.763Q-20.585-19.658-20.679-19.634L-23.128-19.634L-23.128-19.564Q-23.128-19.154-23.007-18.798Q-22.886-18.443-22.614-18.226Q-22.343-18.009-21.913-18.009Q-21.550-18.009-21.253-18.238Q-20.956-18.466-20.855-18.818Q-20.847-18.865-20.761-18.880L-20.679-18.880Q-20.585-18.853-20.585-18.771Q-20.585-18.763-20.593-18.732Q-20.655-18.505-20.794-18.322Q-20.933-18.138-21.124-18.005Q-21.316-17.872-21.534-17.802Q-21.753-17.732-21.991-17.732Q-22.363-17.732-22.700-17.869Q-23.038-18.005-23.306-18.257Q-23.573-18.509-23.724-18.849Q-23.874-19.189-23.874-19.564M-23.120-19.872L-21.159-19.872Q-21.159-20.177-21.261-20.468Q-21.363-20.759-21.579-20.941Q-21.796-21.122-22.113-21.122Q-22.413-21.122-22.644-20.935Q-22.874-20.747-22.997-20.456Q-23.120-20.165-23.120-19.872M-19.999-18.642Q-19.999-19.126-19.597-19.421Q-19.195-19.716-18.644-19.835Q-18.093-19.955-17.601-19.955L-17.601-20.244Q-17.601-20.470-17.716-20.677Q-17.831-20.884-18.029-21.003Q-18.226-21.122-18.456-21.122Q-18.882-21.122-19.167-21.017Q-19.097-20.990-19.050-20.935Q-19.003-20.880-18.978-20.810Q-18.952-20.740-18.952-20.665Q-18.952-20.560-19.003-20.468Q-19.054-20.376-19.146-20.326Q-19.238-20.275-19.343-20.275Q-19.448-20.275-19.540-20.326Q-19.632-20.376-19.683-20.468Q-19.734-20.560-19.734-20.665Q-19.734-21.083-19.345-21.230Q-18.956-21.376-18.456-21.376Q-18.124-21.376-17.771-21.246Q-17.417-21.115-17.189-20.861Q-16.960-20.607-16.960-20.259L-16.960-18.458Q-16.960-18.326-16.888-18.216Q-16.816-18.107-16.687-18.107Q-16.562-18.107-16.493-18.212Q-16.425-18.318-16.425-18.458L-16.425-18.970L-16.144-18.970L-16.144-18.458Q-16.144-18.255-16.261-18.097Q-16.378-17.939-16.560-17.855Q-16.741-17.771-16.945-17.771Q-17.175-17.771-17.327-17.943Q-17.480-18.115-17.511-18.345Q-17.671-18.064-17.980-17.898Q-18.288-17.732-18.640-17.732Q-19.152-17.732-19.575-17.955Q-19.999-18.177-19.999-18.642M-19.312-18.642Q-19.312-18.357-19.085-18.171Q-18.859-17.986-18.566-17.986Q-18.320-17.986-18.095-18.103Q-17.870-18.220-17.736-18.423Q-17.601-18.626-17.601-18.880L-17.601-19.712Q-17.866-19.712-18.152-19.658Q-18.437-19.603-18.708-19.474Q-18.980-19.345-19.146-19.138Q-19.312-18.931-19.312-18.642M-15.808-17.818L-15.808-19.040Q-15.808-19.068-15.777-19.099Q-15.745-19.130-15.722-19.130L-15.616-19.130Q-15.546-19.130-15.530-19.068Q-15.468-18.747-15.329-18.507Q-15.191-18.267-14.958-18.126Q-14.726-17.986-14.417-17.986Q-14.179-17.986-13.970-18.046Q-13.761-18.107-13.624-18.255Q-13.488-18.404-13.488-18.650Q-13.488-18.904-13.698-19.070Q-13.909-19.236-14.179-19.290L-14.800-19.404Q-15.206-19.482-15.507-19.738Q-15.808-19.994-15.808-20.369Q-15.808-20.736-15.607-20.958Q-15.405-21.181-15.081-21.279Q-14.757-21.376-14.417-21.376Q-13.952-21.376-13.655-21.169L-13.433-21.353Q-13.409-21.376-13.378-21.376L-13.327-21.376Q-13.296-21.376-13.269-21.349Q-13.241-21.322-13.241-21.290L-13.241-20.306Q-13.241-20.275-13.267-20.246Q-13.292-20.216-13.327-20.216L-13.433-20.216Q-13.468-20.216-13.495-20.244Q-13.523-20.271-13.523-20.306Q-13.523-20.705-13.775-20.925Q-14.027-21.146-14.425-21.146Q-14.780-21.146-15.064-21.023Q-15.347-20.900-15.347-20.595Q-15.347-20.376-15.146-20.244Q-14.945-20.111-14.698-20.068L-14.073-19.955Q-13.644-19.865-13.335-19.568Q-13.027-19.271-13.027-18.857Q-13.027-18.287-13.425-18.009Q-13.823-17.732-14.417-17.732Q-14.968-17.732-15.320-18.068L-15.616-17.755Q-15.640-17.732-15.675-17.732L-15.722-17.732Q-15.745-17.732-15.777-17.763Q-15.808-17.794-15.808-17.818M-12.499-19.505Q-12.499-20.009-12.243-20.441Q-11.988-20.872-11.552-21.124Q-11.116-21.376-10.616-21.376Q-10.230-21.376-9.888-21.232Q-9.546-21.087-9.284-20.826Q-9.023-20.564-8.880-20.228Q-8.738-19.892-8.738-19.505Q-8.738-19.013-9.001-18.603Q-9.265-18.193-9.695-17.962Q-10.124-17.732-10.616-17.732Q-11.109-17.732-11.542-17.964Q-11.976-18.197-12.238-18.605Q-12.499-19.013-12.499-19.505M-10.616-18.009Q-10.159-18.009-9.907-18.232Q-9.655-18.455-9.568-18.806Q-9.480-19.158-9.480-19.603Q-9.480-20.033-9.573-20.371Q-9.667-20.708-9.921-20.915Q-10.175-21.122-10.616-21.122Q-11.265-21.122-11.509-20.706Q-11.753-20.290-11.753-19.603Q-11.753-19.158-11.665-18.806Q-11.577-18.455-11.325-18.232Q-11.073-18.009-10.616-18.009M-6.323-17.810L-8.179-17.810L-8.179-18.107Q-7.905-18.107-7.738-18.154Q-7.570-18.201-7.570-18.369L-7.570-20.505Q-7.570-20.720-7.632-20.816Q-7.695-20.912-7.814-20.933Q-7.933-20.955-8.179-20.955L-8.179-21.251L-6.988-21.337L-6.988-20.603Q-6.874-20.818-6.681-20.986Q-6.488-21.154-6.249-21.246Q-6.011-21.337-5.757-21.337Q-4.589-21.337-4.589-20.259L-4.589-18.369Q-4.589-18.201-4.419-18.154Q-4.249-18.107-3.980-18.107L-3.980-17.810L-5.835-17.810L-5.835-18.107Q-5.562-18.107-5.394-18.154Q-5.226-18.201-5.226-18.369L-5.226-20.244Q-5.226-20.626-5.347-20.855Q-5.468-21.083-5.820-21.083Q-6.132-21.083-6.386-20.921Q-6.640-20.759-6.786-20.490Q-6.933-20.220-6.933-19.923L-6.933-18.369Q-6.933-18.201-6.763-18.154Q-6.593-18.107-6.323-18.107\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.076 -37.834)\">\u003Cpath d=\"M1.691-15.818Q1.078-16.275 0.676-16.910Q0.273-17.544 0.078-18.290Q-0.117-19.037-0.117-19.810Q-0.117-20.583 0.078-21.330Q0.273-22.076 0.676-22.710Q1.078-23.345 1.691-23.802Q1.703-23.806 1.711-23.808Q1.719-23.810 1.730-23.810L1.808-23.810Q1.847-23.810 1.873-23.783Q1.898-23.755 1.898-23.712Q1.898-23.662 1.867-23.642Q1.359-23.189 1.037-22.566Q0.715-21.943 0.574-21.247Q0.433-20.552 0.433-19.810Q0.433-19.076 0.572-18.376Q0.711-17.677 1.035-17.052Q1.359-16.427 1.867-15.978Q1.898-15.958 1.898-15.908Q1.898-15.865 1.873-15.837Q1.847-15.810 1.808-15.810L1.730-15.810Q1.722-15.814 1.713-15.816Q1.703-15.818 1.691-15.818M3.242-18.771L3.242-20.962L2.539-20.962L2.539-21.216Q2.894-21.216 3.136-21.449Q3.379-21.681 3.490-22.029Q3.601-22.376 3.601-22.732L3.883-22.732L3.883-21.259L5.058-21.259L5.058-20.962L3.883-20.962L3.883-18.787Q3.883-18.466 4.002-18.238Q4.121-18.009 4.402-18.009Q4.582-18.009 4.699-18.132Q4.816-18.255 4.869-18.435Q4.922-18.615 4.922-18.787L4.922-19.259L5.203-19.259L5.203-18.771Q5.203-18.517 5.097-18.277Q4.992-18.037 4.795-17.884Q4.597-17.732 4.340-17.732Q4.023-17.732 3.771-17.855Q3.519-17.978 3.381-18.212Q3.242-18.447 3.242-18.771M7.851-17.810L5.996-17.810L5.996-18.107Q6.269-18.107 6.437-18.154Q6.605-18.201 6.605-18.369L6.605-22.529Q6.605-22.744 6.543-22.839Q6.480-22.935 6.361-22.956Q6.242-22.978 5.996-22.978L5.996-23.275L7.219-23.361L7.219-20.658Q7.344-20.869 7.531-21.019Q7.719-21.169 7.945-21.253Q8.172-21.337 8.418-21.337Q9.586-21.337 9.586-20.259L9.586-18.369Q9.586-18.201 9.756-18.154Q9.926-18.107 10.195-18.107L10.195-17.810L8.340-17.810L8.340-18.107Q8.613-18.107 8.781-18.154Q8.949-18.201 8.949-18.369L8.949-20.244Q8.949-20.626 8.828-20.855Q8.707-21.083 8.355-21.083Q8.043-21.083 7.789-20.921Q7.535-20.759 7.388-20.490Q7.242-20.220 7.242-19.923L7.242-18.369Q7.242-18.201 7.412-18.154Q7.582-18.107 7.851-18.107L7.851-17.810M10.640-19.505Q10.640-20.009 10.896-20.441Q11.152-20.872 11.588-21.124Q12.023-21.376 12.523-21.376Q12.910-21.376 13.252-21.232Q13.594-21.087 13.855-20.826Q14.117-20.564 14.260-20.228Q14.402-19.892 14.402-19.505Q14.402-19.013 14.138-18.603Q13.875-18.193 13.445-17.962Q13.015-17.732 12.523-17.732Q12.031-17.732 11.597-17.964Q11.164-18.197 10.902-18.605Q10.640-19.013 10.640-19.505M12.523-18.009Q12.980-18.009 13.232-18.232Q13.484-18.455 13.572-18.806Q13.660-19.158 13.660-19.603Q13.660-20.033 13.566-20.371Q13.472-20.708 13.219-20.915Q12.965-21.122 12.523-21.122Q11.875-21.122 11.631-20.706Q11.386-20.290 11.386-19.603Q11.386-19.158 11.474-18.806Q11.562-18.455 11.814-18.232Q12.066-18.009 12.523-18.009M15.570-18.763L15.570-20.505Q15.570-20.720 15.508-20.816Q15.445-20.912 15.326-20.933Q15.207-20.955 14.961-20.955L14.961-21.251L16.207-21.337L16.207-18.787L16.207-18.763Q16.207-18.451 16.261-18.289Q16.316-18.126 16.467-18.056Q16.617-17.986 16.937-17.986Q17.367-17.986 17.640-18.324Q17.914-18.662 17.914-19.107L17.914-20.505Q17.914-20.720 17.851-20.816Q17.789-20.912 17.670-20.933Q17.551-20.955 17.304-20.955L17.304-21.251L18.551-21.337L18.551-18.552Q18.551-18.341 18.613-18.246Q18.676-18.150 18.795-18.128Q18.914-18.107 19.160-18.107L19.160-17.810L17.937-17.732L17.937-18.353Q17.769-18.064 17.488-17.898Q17.207-17.732 16.886-17.732Q15.570-17.732 15.570-18.763M19.605-17.201Q19.605-17.482 19.816-17.693Q20.027-17.904 20.312-17.994Q20.156-18.119 20.078-18.308Q20-18.497 20-18.697Q20-19.052 20.230-19.345Q19.863-19.685 19.863-20.154Q19.863-20.505 20.066-20.775Q20.269-21.044 20.590-21.191Q20.910-21.337 21.254-21.337Q21.773-21.337 22.144-21.056Q22.508-21.427 23.054-21.427Q23.234-21.427 23.361-21.300Q23.488-21.173 23.488-20.994Q23.488-20.888 23.410-20.810Q23.332-20.732 23.222-20.732Q23.113-20.732 23.037-20.808Q22.961-20.884 22.961-20.994Q22.961-21.095 23-21.146Q23.008-21.154 23.011-21.160Q23.015-21.165 23.015-21.169Q22.640-21.169 22.320-20.915Q22.640-20.576 22.640-20.154Q22.640-19.884 22.523-19.667Q22.406-19.451 22.201-19.292Q21.996-19.134 21.754-19.052Q21.511-18.970 21.254-18.970Q21.035-18.970 20.822-19.029Q20.609-19.087 20.414-19.208Q20.320-19.068 20.320-18.888Q20.320-18.681 20.457-18.529Q20.594-18.376 20.801-18.376L21.496-18.376Q21.984-18.376 22.396-18.292Q22.808-18.208 23.088-17.951Q23.367-17.693 23.367-17.201Q23.367-16.837 23.047-16.605Q22.726-16.372 22.285-16.271Q21.844-16.169 21.488-16.169Q21.133-16.169 20.689-16.271Q20.246-16.372 19.926-16.605Q19.605-16.837 19.605-17.201M20.109-17.201Q20.109-17.005 20.254-16.857Q20.398-16.708 20.611-16.619Q20.824-16.529 21.064-16.482Q21.304-16.435 21.488-16.435Q21.730-16.435 22.060-16.513Q22.390-16.591 22.627-16.765Q22.863-16.939 22.863-17.201Q22.863-17.607 22.453-17.716Q22.043-17.826 21.480-17.826L20.801-17.826Q20.531-17.826 20.320-17.648Q20.109-17.470 20.109-17.201M21.254-19.236Q21.976-19.236 21.976-20.154Q21.976-21.076 21.254-21.076Q20.527-21.076 20.527-20.154Q20.527-19.236 21.254-19.236M25.781-17.810L23.926-17.810L23.926-18.107Q24.199-18.107 24.367-18.154Q24.535-18.201 24.535-18.369L24.535-22.529Q24.535-22.744 24.472-22.839Q24.410-22.935 24.291-22.956Q24.172-22.978 23.926-22.978L23.926-23.275L25.148-23.361L25.148-20.658Q25.273-20.869 25.461-21.019Q25.648-21.169 25.875-21.253Q26.101-21.337 26.347-21.337Q27.515-21.337 27.515-20.259L27.515-18.369Q27.515-18.201 27.685-18.154Q27.855-18.107 28.125-18.107L28.125-17.810L26.269-17.810L26.269-18.107Q26.543-18.107 26.711-18.154Q26.879-18.201 26.879-18.369L26.879-20.244Q26.879-20.626 26.758-20.855Q26.636-21.083 26.285-21.083Q25.972-21.083 25.719-20.921Q25.465-20.759 25.318-20.490Q25.172-20.220 25.172-19.923L25.172-18.369Q25.172-18.201 25.342-18.154Q25.511-18.107 25.781-18.107\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.076 -37.834)\">\u003Cpath d=\"M28.979-18.771L28.979-20.962L28.276-20.962L28.276-21.216Q28.632-21.216 28.874-21.449Q29.116-21.681 29.227-22.029Q29.339-22.376 29.339-22.732L29.620-22.732L29.620-21.259L30.796-21.259L30.796-20.962L29.620-20.962L29.620-18.787Q29.620-18.466 29.739-18.238Q29.858-18.009 30.139-18.009Q30.319-18.009 30.436-18.132Q30.553-18.255 30.606-18.435Q30.659-18.615 30.659-18.787L30.659-19.259L30.940-19.259L30.940-18.771Q30.940-18.517 30.835-18.277Q30.729-18.037 30.532-17.884Q30.335-17.732 30.077-17.732Q29.761-17.732 29.509-17.855Q29.257-17.978 29.118-18.212Q28.979-18.447 28.979-18.771M32.061-15.810L31.979-15.810Q31.944-15.810 31.919-15.839Q31.893-15.869 31.893-15.908Q31.893-15.958 31.925-15.978Q32.311-16.314 32.595-16.763Q32.878-17.212 33.044-17.712Q33.210-18.212 33.284-18.730Q33.358-19.247 33.358-19.810Q33.358-20.380 33.284-20.896Q33.210-21.412 33.044-21.908Q32.878-22.404 32.598-22.851Q32.319-23.298 31.925-23.642Q31.893-23.662 31.893-23.712Q31.893-23.751 31.919-23.781Q31.944-23.810 31.979-23.810L32.061-23.810Q32.073-23.810 32.083-23.808Q32.093-23.806 32.100-23.802Q32.714-23.345 33.116-22.710Q33.518-22.076 33.714-21.330Q33.909-20.583 33.909-19.810Q33.909-19.037 33.714-18.290Q33.518-17.544 33.116-16.910Q32.714-16.275 32.100-15.818Q32.089-15.818 32.081-15.816Q32.073-15.814 32.061-15.810\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-68.537 7.797h82.223v-28.452h-82.223Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-37.778 13.38)\">\u003Cpath d=\"M-27.089-18.642Q-27.089-19.126-26.687-19.421Q-26.284-19.716-25.734-19.835Q-25.183-19.955-24.691-19.955L-24.691-20.244Q-24.691-20.470-24.806-20.677Q-24.921-20.884-25.118-21.003Q-25.316-21.122-25.546-21.122Q-25.972-21.122-26.257-21.017Q-26.187-20.990-26.140-20.935Q-26.093-20.880-26.068-20.810Q-26.042-20.740-26.042-20.665Q-26.042-20.560-26.093-20.468Q-26.144-20.376-26.236-20.326Q-26.327-20.275-26.433-20.275Q-26.538-20.275-26.630-20.326Q-26.722-20.376-26.773-20.468Q-26.823-20.560-26.823-20.665Q-26.823-21.083-26.435-21.230Q-26.046-21.376-25.546-21.376Q-25.214-21.376-24.861-21.246Q-24.507-21.115-24.279-20.861Q-24.050-20.607-24.050-20.259L-24.050-18.458Q-24.050-18.326-23.978-18.216Q-23.905-18.107-23.777-18.107Q-23.652-18.107-23.583-18.212Q-23.515-18.318-23.515-18.458L-23.515-18.970L-23.234-18.970L-23.234-18.458Q-23.234-18.255-23.351-18.097Q-23.468-17.939-23.650-17.855Q-23.831-17.771-24.034-17.771Q-24.265-17.771-24.417-17.943Q-24.570-18.115-24.601-18.345Q-24.761-18.064-25.070-17.898Q-25.378-17.732-25.730-17.732Q-26.241-17.732-26.665-17.955Q-27.089-18.177-27.089-18.642M-26.402-18.642Q-26.402-18.357-26.175-18.171Q-25.948-17.986-25.655-17.986Q-25.409-17.986-25.185-18.103Q-24.960-18.220-24.825-18.423Q-24.691-18.626-24.691-18.880L-24.691-19.712Q-24.956-19.712-25.241-19.658Q-25.527-19.603-25.798-19.474Q-26.070-19.345-26.236-19.138Q-26.402-18.931-26.402-18.642M-22.898-19.537Q-22.898-20.033-22.648-20.458Q-22.398-20.884-21.978-21.130Q-21.558-21.376-21.058-21.376Q-20.519-21.376-20.128-21.251Q-19.738-21.126-19.738-20.712Q-19.738-20.607-19.788-20.515Q-19.839-20.423-19.931-20.372Q-20.023-20.322-20.132-20.322Q-20.238-20.322-20.329-20.372Q-20.421-20.423-20.472-20.515Q-20.523-20.607-20.523-20.712Q-20.523-20.935-20.355-21.040Q-20.577-21.099-21.050-21.099Q-21.347-21.099-21.562-20.960Q-21.777-20.822-21.907-20.591Q-22.038-20.361-22.097-20.091Q-22.155-19.822-22.155-19.537Q-22.155-19.142-22.023-18.792Q-21.890-18.443-21.618-18.226Q-21.347-18.009-20.948-18.009Q-20.573-18.009-20.298-18.226Q-20.023-18.443-19.921-18.802Q-19.905-18.865-19.843-18.865L-19.738-18.865Q-19.702-18.865-19.677-18.837Q-19.652-18.810-19.652-18.771L-19.652-18.747Q-19.784-18.267-20.169-17.999Q-20.554-17.732-21.058-17.732Q-21.421-17.732-21.755-17.869Q-22.089-18.005-22.349-18.255Q-22.609-18.505-22.753-18.841Q-22.898-19.177-22.898-19.537M-18.538-18.771L-18.538-20.962L-19.241-20.962L-19.241-21.216Q-18.886-21.216-18.644-21.449Q-18.402-21.681-18.290-22.029Q-18.179-22.376-18.179-22.732L-17.898-22.732L-17.898-21.259L-16.722-21.259L-16.722-20.962L-17.898-20.962L-17.898-18.787Q-17.898-18.466-17.779-18.238Q-17.659-18.009-17.378-18.009Q-17.198-18.009-17.081-18.132Q-16.964-18.255-16.911-18.435Q-16.859-18.615-16.859-18.787L-16.859-19.259L-16.577-19.259L-16.577-18.771Q-16.577-18.517-16.683-18.277Q-16.788-18.037-16.986-17.884Q-17.183-17.732-17.441-17.732Q-17.757-17.732-18.009-17.855Q-18.261-17.978-18.400-18.212Q-18.538-18.447-18.538-18.771\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-37.778 13.38)\">\u003Cpath d=\"M-10.642-15.818Q-11.255-16.275-11.657-16.910Q-12.060-17.544-12.255-18.290Q-12.450-19.037-12.450-19.810Q-12.450-20.583-12.255-21.330Q-12.060-22.076-11.657-22.710Q-11.255-23.345-10.642-23.802Q-10.630-23.806-10.622-23.808Q-10.614-23.810-10.603-23.810L-10.525-23.810Q-10.486-23.810-10.460-23.783Q-10.435-23.755-10.435-23.712Q-10.435-23.662-10.466-23.642Q-10.974-23.189-11.296-22.566Q-11.618-21.943-11.759-21.247Q-11.900-20.552-11.900-19.810Q-11.900-19.076-11.761-18.376Q-11.622-17.677-11.298-17.052Q-10.974-16.427-10.466-15.978Q-10.435-15.958-10.435-15.908Q-10.435-15.865-10.460-15.837Q-10.486-15.810-10.525-15.810L-10.603-15.810Q-10.611-15.814-10.620-15.816Q-10.630-15.818-10.642-15.818M-9.091-18.771L-9.091-20.962L-9.794-20.962L-9.794-21.216Q-9.439-21.216-9.197-21.449Q-8.954-21.681-8.843-22.029Q-8.732-22.376-8.732-22.732L-8.450-22.732L-8.450-21.259L-7.275-21.259L-7.275-20.962L-8.450-20.962L-8.450-18.787Q-8.450-18.466-8.331-18.238Q-8.212-18.009-7.931-18.009Q-7.751-18.009-7.634-18.132Q-7.517-18.255-7.464-18.435Q-7.411-18.615-7.411-18.787L-7.411-19.259L-7.130-19.259L-7.130-18.771Q-7.130-18.517-7.236-18.277Q-7.341-18.037-7.538-17.884Q-7.736-17.732-7.993-17.732Q-8.310-17.732-8.562-17.855Q-8.814-17.978-8.952-18.212Q-9.091-18.447-9.091-18.771M-6.411-19.564Q-6.411-20.044-6.179-20.460Q-5.947-20.876-5.536-21.126Q-5.126-21.376-4.650-21.376Q-3.919-21.376-3.521-20.935Q-3.122-20.494-3.122-19.763Q-3.122-19.658-3.216-19.634L-5.665-19.634L-5.665-19.564Q-5.665-19.154-5.544-18.798Q-5.423-18.443-5.152-18.226Q-4.880-18.009-4.450-18.009Q-4.087-18.009-3.790-18.238Q-3.493-18.466-3.392-18.818Q-3.384-18.865-3.298-18.880L-3.216-18.880Q-3.122-18.853-3.122-18.771Q-3.122-18.763-3.130-18.732Q-3.193-18.505-3.331-18.322Q-3.470-18.138-3.661-18.005Q-3.853-17.872-4.072-17.802Q-4.290-17.732-4.529-17.732Q-4.900-17.732-5.238-17.869Q-5.575-18.005-5.843-18.257Q-6.111-18.509-6.261-18.849Q-6.411-19.189-6.411-19.564M-5.657-19.872L-3.697-19.872Q-3.697-20.177-3.798-20.468Q-3.900-20.759-4.116-20.941Q-4.333-21.122-4.650-21.122Q-4.950-21.122-5.181-20.935Q-5.411-20.747-5.534-20.456Q-5.657-20.165-5.657-19.872M-1.247-17.810L-2.743-17.810L-2.743-18.107Q-2.111-18.107-1.689-18.587L-0.919-19.497L-1.911-20.697Q-2.068-20.876-2.230-20.919Q-2.392-20.962-2.697-20.962L-2.697-21.259L-1.009-21.259L-1.009-20.962Q-1.103-20.962-1.179-20.919Q-1.255-20.876-1.255-20.787Q-1.255-20.744-1.224-20.697L-0.568-19.908L-0.087-20.482Q0.030-20.619 0.030-20.755Q0.030-20.845-0.021-20.904Q-0.072-20.962-0.154-20.962L-0.154-21.259L1.335-21.259L1.335-20.962Q0.698-20.962 0.288-20.482L-0.392-19.681L0.694-18.369Q0.854-18.193 1.014-18.150Q1.175-18.107 1.479-18.107L1.479-17.810L-0.208-17.810L-0.208-18.107Q-0.118-18.107-0.040-18.150Q0.038-18.193 0.038-18.283Q0.038-18.306 0.007-18.369L-0.736-19.275L-1.322-18.587Q-1.439-18.451-1.439-18.314Q-1.439-18.228-1.388-18.167Q-1.337-18.107-1.247-18.107L-1.247-17.810M2.471-18.771L2.471-20.962L1.768-20.962L1.768-21.216Q2.124-21.216 2.366-21.449Q2.608-21.681 2.720-22.029Q2.831-22.376 2.831-22.732L3.112-22.732L3.112-21.259L4.288-21.259L4.288-20.962L3.112-20.962L3.112-18.787Q3.112-18.466 3.231-18.238Q3.350-18.009 3.632-18.009Q3.811-18.009 3.928-18.132Q4.046-18.255 4.098-18.435Q4.151-18.615 4.151-18.787L4.151-19.259L4.432-19.259L4.432-18.771Q4.432-18.517 4.327-18.277Q4.221-18.037 4.024-17.884Q3.827-17.732 3.569-17.732Q3.253-17.732 3.001-17.855Q2.749-17.978 2.610-18.212Q2.471-18.447 2.471-18.771\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-37.778 13.38)\">\u003Cpath d=\"M8.229-15.994Q8.229-16.013 8.244-16.068L11.170-23.705Q11.236-23.810 11.342-23.810Q11.420-23.810 11.473-23.757Q11.526-23.705 11.526-23.626Q11.526-23.607 11.510-23.552L8.580-15.915Q8.518-15.810 8.412-15.810Q8.338-15.810 8.283-15.865Q8.229-15.919 8.229-15.994\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-37.778 13.38)\">\u003Cpath d=\"M15.702-18.771L15.702-20.962L14.999-20.962L14.999-21.216Q15.355-21.216 15.597-21.449Q15.839-21.681 15.950-22.029Q16.062-22.376 16.062-22.732L16.343-22.732L16.343-21.259L17.519-21.259L17.519-20.962L16.343-20.962L16.343-18.787Q16.343-18.466 16.462-18.238Q16.581-18.009 16.862-18.009Q17.042-18.009 17.159-18.132Q17.276-18.255 17.329-18.435Q17.382-18.615 17.382-18.787L17.382-19.259L17.663-19.259L17.663-18.771Q17.663-18.517 17.558-18.277Q17.452-18.037 17.255-17.884Q17.058-17.732 16.800-17.732Q16.484-17.732 16.232-17.855Q15.980-17.978 15.841-18.212Q15.702-18.447 15.702-18.771M18.382-19.505Q18.382-20.009 18.638-20.441Q18.894-20.872 19.329-21.124Q19.765-21.376 20.265-21.376Q20.651-21.376 20.993-21.232Q21.335-21.087 21.597-20.826Q21.859-20.564 22.001-20.228Q22.144-19.892 22.144-19.505Q22.144-19.013 21.880-18.603Q21.616-18.193 21.187-17.962Q20.757-17.732 20.265-17.732Q19.773-17.732 19.339-17.964Q18.905-18.197 18.644-18.605Q18.382-19.013 18.382-19.505M20.265-18.009Q20.722-18.009 20.974-18.232Q21.226-18.455 21.314-18.806Q21.401-19.158 21.401-19.603Q21.401-20.033 21.308-20.371Q21.214-20.708 20.960-20.915Q20.706-21.122 20.265-21.122Q19.616-21.122 19.372-20.706Q19.128-20.290 19.128-19.603Q19.128-19.158 19.216-18.806Q19.304-18.455 19.556-18.232Q19.808-18.009 20.265-18.009\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-37.778 13.38)\">\u003Cpath d=\"M22.869-19.505Q22.869-20.009 23.125-20.441Q23.381-20.872 23.817-21.124Q24.252-21.376 24.752-21.376Q25.139-21.376 25.481-21.232Q25.822-21.087 26.084-20.826Q26.346-20.564 26.488-20.228Q26.631-19.892 26.631-19.505Q26.631-19.013 26.367-18.603Q26.104-18.193 25.674-17.962Q25.244-17.732 24.752-17.732Q24.260-17.732 23.826-17.964Q23.393-18.197 23.131-18.605Q22.869-19.013 22.869-19.505M24.752-18.009Q25.209-18.009 25.461-18.232Q25.713-18.455 25.801-18.806Q25.889-19.158 25.889-19.603Q25.889-20.033 25.795-20.371Q25.701-20.708 25.447-20.915Q25.194-21.122 24.752-21.122Q24.104-21.122 23.860-20.706Q23.615-20.290 23.615-19.603Q23.615-19.158 23.703-18.806Q23.791-18.455 24.043-18.232Q24.295-18.009 24.752-18.009M29.029-17.810L27.197-17.810L27.197-18.107Q27.471-18.107 27.639-18.154Q27.807-18.201 27.807-18.369L27.807-22.529Q27.807-22.744 27.744-22.839Q27.682-22.935 27.563-22.956Q27.444-22.978 27.197-22.978L27.197-23.275L28.420-23.361L28.420-18.369Q28.420-18.201 28.588-18.154Q28.756-18.107 29.029-18.107\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-37.778 13.38)\">\u003Cpath d=\"M32.356-19.537Q32.356-20.033 32.606-20.458Q32.856-20.884 33.276-21.130Q33.696-21.376 34.196-21.376Q34.735-21.376 35.126-21.251Q35.516-21.126 35.516-20.712Q35.516-20.607 35.466-20.515Q35.415-20.423 35.323-20.372Q35.231-20.322 35.122-20.322Q35.016-20.322 34.925-20.372Q34.833-20.423 34.782-20.515Q34.731-20.607 34.731-20.712Q34.731-20.935 34.899-21.040Q34.677-21.099 34.204-21.099Q33.907-21.099 33.692-20.960Q33.477-20.822 33.346-20.591Q33.216-20.361 33.157-20.091Q33.098-19.822 33.098-19.537Q33.098-19.142 33.231-18.792Q33.364-18.443 33.636-18.226Q33.907-18.009 34.305-18.009Q34.680-18.009 34.956-18.226Q35.231-18.443 35.333-18.802Q35.348-18.865 35.411-18.865L35.516-18.865Q35.552-18.865 35.577-18.837Q35.602-18.810 35.602-18.771L35.602-18.747Q35.470-18.267 35.085-17.999Q34.700-17.732 34.196-17.732Q33.833-17.732 33.499-17.869Q33.165-18.005 32.905-18.255Q32.645-18.505 32.501-18.841Q32.356-19.177 32.356-19.537M36.188-18.642Q36.188-19.126 36.591-19.421Q36.993-19.716 37.544-19.835Q38.095-19.955 38.587-19.955L38.587-20.244Q38.587-20.470 38.471-20.677Q38.356-20.884 38.159-21.003Q37.962-21.122 37.731-21.122Q37.305-21.122 37.020-21.017Q37.091-20.990 37.138-20.935Q37.184-20.880 37.210-20.810Q37.235-20.740 37.235-20.665Q37.235-20.560 37.184-20.468Q37.134-20.376 37.042-20.326Q36.950-20.275 36.845-20.275Q36.739-20.275 36.647-20.326Q36.555-20.376 36.505-20.468Q36.454-20.560 36.454-20.665Q36.454-21.083 36.843-21.230Q37.231-21.376 37.731-21.376Q38.063-21.376 38.417-21.246Q38.770-21.115 38.999-20.861Q39.227-20.607 39.227-20.259L39.227-18.458Q39.227-18.326 39.300-18.216Q39.372-18.107 39.501-18.107Q39.626-18.107 39.694-18.212Q39.763-18.318 39.763-18.458L39.763-18.970L40.044-18.970L40.044-18.458Q40.044-18.255 39.927-18.097Q39.809-17.939 39.628-17.855Q39.446-17.771 39.243-17.771Q39.013-17.771 38.860-17.943Q38.708-18.115 38.677-18.345Q38.516-18.064 38.208-17.898Q37.899-17.732 37.548-17.732Q37.036-17.732 36.612-17.955Q36.188-18.177 36.188-18.642M36.876-18.642Q36.876-18.357 37.102-18.171Q37.329-17.986 37.622-17.986Q37.868-17.986 38.093-18.103Q38.317-18.220 38.452-18.423Q38.587-18.626 38.587-18.880L38.587-19.712Q38.321-19.712 38.036-19.658Q37.751-19.603 37.479-19.474Q37.208-19.345 37.042-19.138Q36.876-18.931 36.876-18.642M42.251-17.810L40.419-17.810L40.419-18.107Q40.692-18.107 40.860-18.154Q41.028-18.201 41.028-18.369L41.028-22.529Q41.028-22.744 40.966-22.839Q40.903-22.935 40.784-22.956Q40.665-22.978 40.419-22.978L40.419-23.275L41.641-23.361L41.641-18.369Q41.641-18.201 41.809-18.154Q41.977-18.107 42.251-18.107L42.251-17.810M44.610-17.810L42.778-17.810L42.778-18.107Q43.052-18.107 43.220-18.154Q43.388-18.201 43.388-18.369L43.388-22.529Q43.388-22.744 43.325-22.839Q43.263-22.935 43.143-22.956Q43.024-22.978 42.778-22.978L42.778-23.275L44.001-23.361L44.001-18.369Q44.001-18.201 44.169-18.154Q44.337-18.107 44.610-18.107L44.610-17.810M45.458-15.810L45.376-15.810Q45.341-15.810 45.315-15.839Q45.290-15.869 45.290-15.908Q45.290-15.958 45.321-15.978Q45.708-16.314 45.991-16.763Q46.274-17.212 46.440-17.712Q46.606-18.212 46.680-18.730Q46.755-19.247 46.755-19.810Q46.755-20.380 46.680-20.896Q46.606-21.412 46.440-21.908Q46.274-22.404 45.995-22.851Q45.716-23.298 45.321-23.642Q45.290-23.662 45.290-23.712Q45.290-23.751 45.315-23.781Q45.341-23.810 45.376-23.810L45.458-23.810Q45.470-23.810 45.479-23.808Q45.489-23.806 45.497-23.802Q46.110-23.345 46.513-22.710Q46.915-22.076 47.110-21.330Q47.305-20.583 47.305-19.810Q47.305-19.037 47.110-18.290Q46.915-17.544 46.513-16.910Q46.110-16.275 45.497-15.818Q45.485-15.818 45.477-15.816Q45.470-15.814 45.458-15.810\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M94.922 7.797h73.977v-28.452H94.922Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(133.781 14.159)\">\u003Cpath d=\"M-27.187-19.505Q-27.187-20.009-26.931-20.441Q-26.675-20.872-26.239-21.124Q-25.804-21.376-25.304-21.376Q-24.917-21.376-24.575-21.232Q-24.234-21.087-23.972-20.826Q-23.710-20.564-23.568-20.228Q-23.425-19.892-23.425-19.505Q-23.425-19.013-23.689-18.603Q-23.952-18.193-24.382-17.962Q-24.812-17.732-25.304-17.732Q-25.796-17.732-26.230-17.964Q-26.663-18.197-26.925-18.605Q-27.187-19.013-27.187-19.505M-25.304-18.009Q-24.847-18.009-24.595-18.232Q-24.343-18.455-24.255-18.806Q-24.167-19.158-24.167-19.603Q-24.167-20.033-24.261-20.371Q-24.355-20.708-24.609-20.915Q-24.863-21.122-25.304-21.122Q-25.952-21.122-26.196-20.706Q-26.441-20.290-26.441-19.603Q-26.441-19.158-26.353-18.806Q-26.265-18.455-26.013-18.232Q-25.761-18.009-25.304-18.009M-22.027-17.810L-22.308-17.810L-22.308-22.529Q-22.308-22.744-22.370-22.839Q-22.433-22.935-22.550-22.956Q-22.667-22.978-22.913-22.978L-22.913-23.275L-21.691-23.361L-21.691-20.872Q-21.214-21.337-20.515-21.337Q-20.034-21.337-19.626-21.093Q-19.218-20.849-18.982-20.435Q-18.745-20.021-18.745-19.537Q-18.745-19.162-18.894-18.833Q-19.042-18.505-19.312-18.253Q-19.581-18.001-19.925-17.867Q-20.269-17.732-20.628-17.732Q-20.948-17.732-21.247-17.880Q-21.546-18.029-21.753-18.290L-22.027-17.810M-21.667-20.482L-21.667-18.642Q-21.515-18.345-21.255-18.165Q-20.995-17.986-20.683-17.986Q-20.257-17.986-19.989-18.205Q-19.722-18.423-19.607-18.769Q-19.491-19.115-19.491-19.537Q-19.491-20.185-19.739-20.634Q-19.988-21.083-20.585-21.083Q-20.921-21.083-21.210-20.925Q-21.499-20.767-21.667-20.482M-18.179-17.818L-18.179-19.040Q-18.179-19.068-18.148-19.099Q-18.116-19.130-18.093-19.130L-17.988-19.130Q-17.917-19.130-17.902-19.068Q-17.839-18.747-17.700-18.507Q-17.562-18.267-17.329-18.126Q-17.097-17.986-16.788-17.986Q-16.550-17.986-16.341-18.046Q-16.132-18.107-15.995-18.255Q-15.859-18.404-15.859-18.650Q-15.859-18.904-16.070-19.070Q-16.280-19.236-16.550-19.290L-17.171-19.404Q-17.577-19.482-17.878-19.738Q-18.179-19.994-18.179-20.369Q-18.179-20.736-17.978-20.958Q-17.777-21.181-17.452-21.279Q-17.128-21.376-16.788-21.376Q-16.323-21.376-16.027-21.169L-15.804-21.353Q-15.780-21.376-15.749-21.376L-15.698-21.376Q-15.667-21.376-15.640-21.349Q-15.613-21.322-15.613-21.290L-15.613-20.306Q-15.613-20.275-15.638-20.246Q-15.663-20.216-15.698-20.216L-15.804-20.216Q-15.839-20.216-15.866-20.244Q-15.894-20.271-15.894-20.306Q-15.894-20.705-16.146-20.925Q-16.398-21.146-16.796-21.146Q-17.152-21.146-17.435-21.023Q-17.718-20.900-17.718-20.595Q-17.718-20.376-17.517-20.244Q-17.316-20.111-17.070-20.068L-16.445-19.955Q-16.015-19.865-15.706-19.568Q-15.398-19.271-15.398-18.857Q-15.398-18.287-15.796-18.009Q-16.195-17.732-16.788-17.732Q-17.339-17.732-17.691-18.068L-17.988-17.755Q-18.011-17.732-18.046-17.732L-18.093-17.732Q-18.116-17.732-18.148-17.763Q-18.179-17.794-18.179-17.818M-14.870-19.564Q-14.870-20.044-14.638-20.460Q-14.405-20.876-13.995-21.126Q-13.585-21.376-13.109-21.376Q-12.378-21.376-11.980-20.935Q-11.581-20.494-11.581-19.763Q-11.581-19.658-11.675-19.634L-14.124-19.634L-14.124-19.564Q-14.124-19.154-14.003-18.798Q-13.882-18.443-13.611-18.226Q-13.339-18.009-12.909-18.009Q-12.546-18.009-12.249-18.238Q-11.952-18.466-11.851-18.818Q-11.843-18.865-11.757-18.880L-11.675-18.880Q-11.581-18.853-11.581-18.771Q-11.581-18.763-11.589-18.732Q-11.652-18.505-11.790-18.322Q-11.929-18.138-12.120-18.005Q-12.312-17.872-12.530-17.802Q-12.749-17.732-12.988-17.732Q-13.359-17.732-13.696-17.869Q-14.034-18.005-14.302-18.257Q-14.570-18.509-14.720-18.849Q-14.870-19.189-14.870-19.564M-14.116-19.872L-12.155-19.872Q-12.155-20.177-12.257-20.468Q-12.359-20.759-12.575-20.941Q-12.792-21.122-13.109-21.122Q-13.409-21.122-13.640-20.935Q-13.870-20.747-13.993-20.456Q-14.116-20.165-14.116-19.872M-9.085-17.810L-11.066-17.810L-11.066-18.107Q-10.796-18.107-10.628-18.152Q-10.460-18.197-10.460-18.369L-10.460-20.505Q-10.460-20.720-10.523-20.816Q-10.585-20.912-10.702-20.933Q-10.820-20.955-11.066-20.955L-11.066-21.251L-9.898-21.337L-9.898-20.552Q-9.820-20.763-9.667-20.949Q-9.515-21.134-9.316-21.236Q-9.116-21.337-8.890-21.337Q-8.644-21.337-8.452-21.193Q-8.261-21.048-8.261-20.818Q-8.261-20.662-8.366-20.552Q-8.472-20.443-8.628-20.443Q-8.784-20.443-8.894-20.552Q-9.003-20.662-9.003-20.818Q-9.003-20.978-8.898-21.083Q-9.222-21.083-9.437-20.855Q-9.652-20.626-9.747-20.287Q-9.843-19.947-9.843-19.642L-9.843-18.369Q-9.843-18.201-9.616-18.154Q-9.390-18.107-9.085-18.107L-9.085-17.810M-5.980-17.841L-7.202-20.697Q-7.284-20.872-7.429-20.917Q-7.573-20.962-7.843-20.962L-7.843-21.259L-6.132-21.259L-6.132-20.962Q-6.554-20.962-6.554-20.779Q-6.554-20.744-6.538-20.697L-5.593-18.505L-4.753-20.482Q-4.714-20.560-4.714-20.650Q-4.714-20.790-4.820-20.876Q-4.925-20.962-5.066-20.962L-5.066-21.259L-3.714-21.259L-3.714-20.962Q-4.238-20.962-4.452-20.482L-5.577-17.841Q-5.640-17.732-5.745-17.732L-5.812-17.732Q-5.925-17.732-5.980-17.841\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(133.781 14.159)\">\u003Cpath d=\"M-3.522-19.564Q-3.522-20.044-3.289-20.460Q-3.057-20.876-2.647-21.126Q-2.237-21.376-1.760-21.376Q-1.030-21.376-0.631-20.935Q-0.233-20.494-0.233-19.763Q-0.233-19.658-0.326-19.634L-2.776-19.634L-2.776-19.564Q-2.776-19.154-2.655-18.798Q-2.533-18.443-2.262-18.226Q-1.990-18.009-1.561-18.009Q-1.197-18.009-0.901-18.238Q-0.604-18.466-0.502-18.818Q-0.494-18.865-0.408-18.880L-0.326-18.880Q-0.233-18.853-0.233-18.771Q-0.233-18.763-0.240-18.732Q-0.303-18.505-0.442-18.322Q-0.580-18.138-0.772-18.005Q-0.963-17.872-1.182-17.802Q-1.401-17.732-1.639-17.732Q-2.010-17.732-2.348-17.869Q-2.686-18.005-2.953-18.257Q-3.221-18.509-3.371-18.849Q-3.522-19.189-3.522-19.564M-2.768-19.872L-0.807-19.872Q-0.807-20.177-0.908-20.468Q-1.010-20.759-1.227-20.941Q-1.444-21.122-1.760-21.122Q-2.061-21.122-2.291-20.935Q-2.522-20.747-2.645-20.456Q-2.768-20.165-2.768-19.872\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(133.781 14.159)\">\u003Cpath d=\"M5.097-17.810L3.117-17.810L3.117-18.107Q3.386-18.107 3.554-18.152Q3.722-18.197 3.722-18.369L3.722-20.505Q3.722-20.720 3.660-20.816Q3.597-20.912 3.480-20.933Q3.363-20.955 3.117-20.955L3.117-21.251L4.285-21.337L4.285-20.552Q4.363-20.763 4.515-20.949Q4.667-21.134 4.867-21.236Q5.066-21.337 5.292-21.337Q5.539-21.337 5.730-21.193Q5.921-21.048 5.921-20.818Q5.921-20.662 5.816-20.552Q5.710-20.443 5.554-20.443Q5.398-20.443 5.289-20.552Q5.179-20.662 5.179-20.818Q5.179-20.978 5.285-21.083Q4.960-21.083 4.746-20.855Q4.531-20.626 4.435-20.287Q4.339-19.947 4.339-19.642L4.339-18.369Q4.339-18.201 4.566-18.154Q4.792-18.107 5.097-18.107L5.097-17.810M6.402-19.564Q6.402-20.044 6.634-20.460Q6.867-20.876 7.277-21.126Q7.687-21.376 8.163-21.376Q8.894-21.376 9.292-20.935Q9.691-20.494 9.691-19.763Q9.691-19.658 9.597-19.634L7.148-19.634L7.148-19.564Q7.148-19.154 7.269-18.798Q7.390-18.443 7.662-18.226Q7.933-18.009 8.363-18.009Q8.726-18.009 9.023-18.238Q9.320-18.466 9.421-18.818Q9.429-18.865 9.515-18.880L9.597-18.880Q9.691-18.853 9.691-18.771Q9.691-18.763 9.683-18.732Q9.621-18.505 9.482-18.322Q9.343-18.138 9.152-18.005Q8.960-17.872 8.742-17.802Q8.523-17.732 8.285-17.732Q7.914-17.732 7.576-17.869Q7.238-18.005 6.970-18.257Q6.703-18.509 6.552-18.849Q6.402-19.189 6.402-19.564M7.156-19.872L9.117-19.872Q9.117-20.177 9.015-20.468Q8.913-20.759 8.697-20.941Q8.480-21.122 8.163-21.122Q7.863-21.122 7.632-20.935Q7.402-20.747 7.279-20.456Q7.156-20.165 7.156-19.872M10.222-17.818L10.222-19.040Q10.222-19.068 10.253-19.099Q10.285-19.130 10.308-19.130L10.413-19.130Q10.484-19.130 10.499-19.068Q10.562-18.747 10.701-18.507Q10.839-18.267 11.072-18.126Q11.304-17.986 11.613-17.986Q11.851-17.986 12.060-18.046Q12.269-18.107 12.406-18.255Q12.542-18.404 12.542-18.650Q12.542-18.904 12.331-19.070Q12.121-19.236 11.851-19.290L11.230-19.404Q10.824-19.482 10.523-19.738Q10.222-19.994 10.222-20.369Q10.222-20.736 10.423-20.958Q10.624-21.181 10.949-21.279Q11.273-21.376 11.613-21.376Q12.078-21.376 12.374-21.169L12.597-21.353Q12.621-21.376 12.652-21.376L12.703-21.376Q12.734-21.376 12.761-21.349Q12.788-21.322 12.788-21.290L12.788-20.306Q12.788-20.275 12.763-20.246Q12.738-20.216 12.703-20.216L12.597-20.216Q12.562-20.216 12.535-20.244Q12.507-20.271 12.507-20.306Q12.507-20.705 12.255-20.925Q12.003-21.146 11.605-21.146Q11.249-21.146 10.966-21.023Q10.683-20.900 10.683-20.595Q10.683-20.376 10.884-20.244Q11.085-20.111 11.331-20.068L11.956-19.955Q12.386-19.865 12.695-19.568Q13.003-19.271 13.003-18.857Q13.003-18.287 12.605-18.009Q12.206-17.732 11.613-17.732Q11.062-17.732 10.710-18.068L10.413-17.755Q10.390-17.732 10.355-17.732L10.308-17.732Q10.285-17.732 10.253-17.763Q10.222-17.794 10.222-17.818M14.214-18.763L14.214-20.505Q14.214-20.720 14.152-20.816Q14.089-20.912 13.970-20.933Q13.851-20.955 13.605-20.955L13.605-21.251L14.851-21.337L14.851-18.787L14.851-18.763Q14.851-18.451 14.906-18.289Q14.960-18.126 15.111-18.056Q15.261-17.986 15.581-17.986Q16.011-17.986 16.285-18.324Q16.558-18.662 16.558-19.107L16.558-20.505Q16.558-20.720 16.496-20.816Q16.433-20.912 16.314-20.933Q16.195-20.955 15.949-20.955L15.949-21.251L17.195-21.337L17.195-18.552Q17.195-18.341 17.257-18.246Q17.320-18.150 17.439-18.128Q17.558-18.107 17.804-18.107L17.804-17.810L16.581-17.732L16.581-18.353Q16.413-18.064 16.132-17.898Q15.851-17.732 15.531-17.732Q14.214-17.732 14.214-18.763M20.163-17.810L18.331-17.810L18.331-18.107Q18.605-18.107 18.773-18.154Q18.941-18.201 18.941-18.369L18.941-22.529Q18.941-22.744 18.878-22.839Q18.816-22.935 18.697-22.956Q18.578-22.978 18.331-22.978L18.331-23.275L19.554-23.361L19.554-18.369Q19.554-18.201 19.722-18.154Q19.890-18.107 20.163-18.107L20.163-17.810M21.234-18.771L21.234-20.962L20.531-20.962L20.531-21.216Q20.886-21.216 21.128-21.449Q21.371-21.681 21.482-22.029Q21.593-22.376 21.593-22.732L21.874-22.732L21.874-21.259L23.050-21.259L23.050-20.962L21.874-20.962L21.874-18.787Q21.874-18.466 21.994-18.238Q22.113-18.009 22.394-18.009Q22.574-18.009 22.691-18.132Q22.808-18.255 22.861-18.435Q22.913-18.615 22.913-18.787L22.913-19.259L23.195-19.259L23.195-18.771Q23.195-18.517 23.089-18.277Q22.984-18.037 22.787-17.884Q22.589-17.732 22.331-17.732Q22.015-17.732 21.763-17.855Q21.511-17.978 21.372-18.212Q21.234-18.447 21.234-18.771\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M94.922-43.417h73.977V-71.87H94.922Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(133.923 -38.151)\">\u003Cpath d=\"M-25.257-17.810L-27.113-17.810L-27.113-18.107Q-26.839-18.107-26.671-18.154Q-26.503-18.201-26.503-18.369L-26.503-20.505Q-26.503-20.720-26.566-20.816Q-26.628-20.912-26.747-20.933Q-26.866-20.955-27.113-20.955L-27.113-21.251L-25.921-21.337L-25.921-20.603Q-25.808-20.818-25.614-20.986Q-25.421-21.154-25.183-21.246Q-24.945-21.337-24.691-21.337Q-23.730-21.337-23.554-20.626Q-23.370-20.955-23.042-21.146Q-22.714-21.337-22.335-21.337Q-21.159-21.337-21.159-20.259L-21.159-18.369Q-21.159-18.201-20.991-18.154Q-20.823-18.107-20.554-18.107L-20.554-17.810L-22.409-17.810L-22.409-18.107Q-22.136-18.107-21.968-18.152Q-21.800-18.197-21.800-18.369L-21.800-20.244Q-21.800-20.630-21.925-20.857Q-22.050-21.083-22.402-21.083Q-22.706-21.083-22.962-20.921Q-23.218-20.759-23.366-20.490Q-23.515-20.220-23.515-19.923L-23.515-18.369Q-23.515-18.201-23.345-18.154Q-23.175-18.107-22.905-18.107L-22.905-17.810L-24.761-17.810L-24.761-18.107Q-24.488-18.107-24.320-18.154Q-24.152-18.201-24.152-18.369L-24.152-20.244Q-24.152-20.630-24.277-20.857Q-24.402-21.083-24.753-21.083Q-25.058-21.083-25.314-20.921Q-25.570-20.759-25.718-20.490Q-25.866-20.220-25.866-19.923L-25.866-18.369Q-25.866-18.201-25.696-18.154Q-25.527-18.107-25.257-18.107L-25.257-17.810M-20.109-19.564Q-20.109-20.044-19.876-20.460Q-19.644-20.876-19.234-21.126Q-18.823-21.376-18.347-21.376Q-17.616-21.376-17.218-20.935Q-16.820-20.494-16.820-19.763Q-16.820-19.658-16.913-19.634L-19.363-19.634L-19.363-19.564Q-19.363-19.154-19.241-18.798Q-19.120-18.443-18.849-18.226Q-18.577-18.009-18.148-18.009Q-17.784-18.009-17.488-18.238Q-17.191-18.466-17.089-18.818Q-17.081-18.865-16.995-18.880L-16.913-18.880Q-16.820-18.853-16.820-18.771Q-16.820-18.763-16.827-18.732Q-16.890-18.505-17.029-18.322Q-17.167-18.138-17.359-18.005Q-17.550-17.872-17.769-17.802Q-17.988-17.732-18.226-17.732Q-18.597-17.732-18.935-17.869Q-19.273-18.005-19.540-18.257Q-19.808-18.509-19.958-18.849Q-20.109-19.189-20.109-19.564M-19.355-19.872L-17.394-19.872Q-17.394-20.177-17.495-20.468Q-17.597-20.759-17.814-20.941Q-18.030-21.122-18.347-21.122Q-18.648-21.122-18.878-20.935Q-19.109-20.747-19.232-20.456Q-19.355-20.165-19.355-19.872M-14.402-17.810L-16.257-17.810L-16.257-18.107Q-15.984-18.107-15.816-18.154Q-15.648-18.201-15.648-18.369L-15.648-20.505Q-15.648-20.720-15.710-20.816Q-15.773-20.912-15.892-20.933Q-16.011-20.955-16.257-20.955L-16.257-21.251L-15.066-21.337L-15.066-20.603Q-14.952-20.818-14.759-20.986Q-14.566-21.154-14.327-21.246Q-14.089-21.337-13.835-21.337Q-12.874-21.337-12.698-20.626Q-12.515-20.955-12.187-21.146Q-11.859-21.337-11.480-21.337Q-10.304-21.337-10.304-20.259L-10.304-18.369Q-10.304-18.201-10.136-18.154Q-9.968-18.107-9.698-18.107L-9.698-17.810L-11.554-17.810L-11.554-18.107Q-11.280-18.107-11.113-18.152Q-10.945-18.197-10.945-18.369L-10.945-20.244Q-10.945-20.630-11.070-20.857Q-11.195-21.083-11.546-21.083Q-11.851-21.083-12.107-20.921Q-12.363-20.759-12.511-20.490Q-12.659-20.220-12.659-19.923L-12.659-18.369Q-12.659-18.201-12.489-18.154Q-12.320-18.107-12.050-18.107L-12.050-17.810L-13.905-17.810L-13.905-18.107Q-13.632-18.107-13.464-18.154Q-13.296-18.201-13.296-18.369L-13.296-20.244Q-13.296-20.630-13.421-20.857Q-13.546-21.083-13.898-21.083Q-14.202-21.083-14.458-20.921Q-14.714-20.759-14.863-20.490Q-15.011-20.220-15.011-19.923L-15.011-18.369Q-15.011-18.201-14.841-18.154Q-14.671-18.107-14.402-18.107L-14.402-17.810M-9.253-19.505Q-9.253-20.009-8.997-20.441Q-8.741-20.872-8.306-21.124Q-7.870-21.376-7.370-21.376Q-6.984-21.376-6.642-21.232Q-6.300-21.087-6.038-20.826Q-5.777-20.564-5.634-20.228Q-5.491-19.892-5.491-19.505Q-5.491-19.013-5.755-18.603Q-6.019-18.193-6.448-17.962Q-6.878-17.732-7.370-17.732Q-7.863-17.732-8.296-17.964Q-8.730-18.197-8.991-18.605Q-9.253-19.013-9.253-19.505M-7.370-18.009Q-6.913-18.009-6.661-18.232Q-6.409-18.455-6.321-18.806Q-6.234-19.158-6.234-19.603Q-6.234-20.033-6.327-20.371Q-6.421-20.708-6.675-20.915Q-6.929-21.122-7.370-21.122Q-8.019-21.122-8.263-20.706Q-8.507-20.290-8.507-19.603Q-8.507-19.158-8.419-18.806Q-8.331-18.455-8.079-18.232Q-7.827-18.009-7.370-18.009M-2.999-17.810L-4.980-17.810L-4.980-18.107Q-4.710-18.107-4.542-18.152Q-4.374-18.197-4.374-18.369L-4.374-20.505Q-4.374-20.720-4.437-20.816Q-4.499-20.912-4.616-20.933Q-4.734-20.955-4.980-20.955L-4.980-21.251L-3.812-21.337L-3.812-20.552Q-3.734-20.763-3.581-20.949Q-3.429-21.134-3.230-21.236Q-3.030-21.337-2.804-21.337Q-2.558-21.337-2.366-21.193Q-2.175-21.048-2.175-20.818Q-2.175-20.662-2.280-20.552Q-2.386-20.443-2.542-20.443Q-2.698-20.443-2.808-20.552Q-2.917-20.662-2.917-20.818Q-2.917-20.978-2.812-21.083Q-3.136-21.083-3.351-20.855Q-3.566-20.626-3.661-20.287Q-3.757-19.947-3.757-19.642L-3.757-18.369Q-3.757-18.201-3.530-18.154Q-3.304-18.107-2.999-18.107L-2.999-17.810M-1.277-16.513Q-1.163-16.435-0.988-16.435Q-0.698-16.435-0.478-16.648Q-0.257-16.861-0.132-17.162L0.157-17.810L-1.116-20.697Q-1.198-20.872-1.343-20.917Q-1.488-20.962-1.757-20.962L-1.757-21.259L-0.038-21.259L-0.038-20.962Q-0.460-20.962-0.460-20.779Q-0.460-20.767-0.445-20.697L0.493-18.572L1.325-20.482Q1.364-20.572 1.364-20.650Q1.364-20.790 1.262-20.876Q1.161-20.962 1.020-20.962L1.020-21.259L2.372-21.259L2.372-20.962Q2.118-20.962 1.925-20.837Q1.731-20.712 1.626-20.482L0.180-17.162Q0.067-16.908-0.099-16.685Q-0.265-16.462-0.493-16.320Q-0.722-16.177-0.988-16.177Q-1.284-16.177-1.525-16.369Q-1.765-16.560-1.765-16.849Q-1.765-17.005-1.659-17.107Q-1.554-17.208-1.405-17.208Q-1.300-17.208-1.220-17.162Q-1.140-17.115-1.093-17.037Q-1.046-16.958-1.046-16.849Q-1.046-16.728-1.107-16.640Q-1.167-16.552-1.277-16.513\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(133.923 -38.151)\">\u003Cpath d=\"M5.682-17.818L5.682-19.040Q5.682-19.068 5.713-19.099Q5.745-19.130 5.768-19.130L5.874-19.130Q5.944-19.130 5.960-19.068Q6.022-18.747 6.161-18.507Q6.299-18.267 6.532-18.126Q6.764-17.986 7.073-17.986Q7.311-17.986 7.520-18.046Q7.729-18.107 7.866-18.255Q8.003-18.404 8.003-18.650Q8.003-18.904 7.792-19.070Q7.581-19.236 7.311-19.290L6.690-19.404Q6.284-19.482 5.983-19.738Q5.682-19.994 5.682-20.369Q5.682-20.736 5.883-20.958Q6.085-21.181 6.409-21.279Q6.733-21.376 7.073-21.376Q7.538-21.376 7.835-21.169L8.057-21.353Q8.081-21.376 8.112-21.376L8.163-21.376Q8.194-21.376 8.221-21.349Q8.249-21.322 8.249-21.290L8.249-20.306Q8.249-20.275 8.223-20.246Q8.198-20.216 8.163-20.216L8.057-20.216Q8.022-20.216 7.995-20.244Q7.967-20.271 7.967-20.306Q7.967-20.705 7.715-20.925Q7.463-21.146 7.065-21.146Q6.710-21.146 6.426-21.023Q6.143-20.900 6.143-20.595Q6.143-20.376 6.344-20.244Q6.546-20.111 6.792-20.068L7.417-19.955Q7.846-19.865 8.155-19.568Q8.463-19.271 8.463-18.857Q8.463-18.287 8.065-18.009Q7.667-17.732 7.073-17.732Q6.522-17.732 6.171-18.068L5.874-17.755Q5.850-17.732 5.815-17.732L5.768-17.732Q5.745-17.732 5.713-17.763Q5.682-17.794 5.682-17.818M9.616-18.771L9.616-20.962L8.913-20.962L8.913-21.216Q9.268-21.216 9.510-21.449Q9.753-21.681 9.864-22.029Q9.975-22.376 9.975-22.732L10.256-22.732L10.256-21.259L11.432-21.259L11.432-20.962L10.256-20.962L10.256-18.787Q10.256-18.466 10.376-18.238Q10.495-18.009 10.776-18.009Q10.956-18.009 11.073-18.132Q11.190-18.255 11.243-18.435Q11.296-18.615 11.296-18.787L11.296-19.259L11.577-19.259L11.577-18.771Q11.577-18.517 11.471-18.277Q11.366-18.037 11.169-17.884Q10.971-17.732 10.713-17.732Q10.397-17.732 10.145-17.855Q9.893-17.978 9.755-18.212Q9.616-18.447 9.616-18.771M12.296-19.505Q12.296-20.009 12.551-20.441Q12.807-20.872 13.243-21.124Q13.678-21.376 14.178-21.376Q14.565-21.376 14.907-21.232Q15.249-21.087 15.510-20.826Q15.772-20.564 15.915-20.228Q16.057-19.892 16.057-19.505Q16.057-19.013 15.794-18.603Q15.530-18.193 15.100-17.962Q14.671-17.732 14.178-17.732Q13.686-17.732 13.253-17.964Q12.819-18.197 12.557-18.605Q12.296-19.013 12.296-19.505M14.178-18.009Q14.635-18.009 14.887-18.232Q15.139-18.455 15.227-18.806Q15.315-19.158 15.315-19.603Q15.315-20.033 15.221-20.371Q15.128-20.708 14.874-20.915Q14.620-21.122 14.178-21.122Q13.530-21.122 13.286-20.706Q13.042-20.290 13.042-19.603Q13.042-19.158 13.130-18.806Q13.217-18.455 13.469-18.232Q13.721-18.009 14.178-18.009M18.549-17.810L16.569-17.810L16.569-18.107Q16.838-18.107 17.006-18.152Q17.174-18.197 17.174-18.369L17.174-20.505Q17.174-20.720 17.112-20.816Q17.049-20.912 16.932-20.933Q16.815-20.955 16.569-20.955L16.569-21.251L17.737-21.337L17.737-20.552Q17.815-20.763 17.967-20.949Q18.120-21.134 18.319-21.236Q18.518-21.337 18.745-21.337Q18.991-21.337 19.182-21.193Q19.374-21.048 19.374-20.818Q19.374-20.662 19.268-20.552Q19.163-20.443 19.006-20.443Q18.850-20.443 18.741-20.552Q18.631-20.662 18.631-20.818Q18.631-20.978 18.737-21.083Q18.413-21.083 18.198-20.855Q17.983-20.626 17.887-20.287Q17.792-19.947 17.792-19.642L17.792-18.369Q17.792-18.201 18.018-18.154Q18.245-18.107 18.549-18.107L18.549-17.810M19.854-19.564Q19.854-20.044 20.087-20.460Q20.319-20.876 20.729-21.126Q21.139-21.376 21.616-21.376Q22.346-21.376 22.745-20.935Q23.143-20.494 23.143-19.763Q23.143-19.658 23.049-19.634L20.600-19.634L20.600-19.564Q20.600-19.154 20.721-18.798Q20.842-18.443 21.114-18.226Q21.385-18.009 21.815-18.009Q22.178-18.009 22.475-18.238Q22.772-18.466 22.874-18.818Q22.881-18.865 22.967-18.880L23.049-18.880Q23.143-18.853 23.143-18.771Q23.143-18.763 23.135-18.732Q23.073-18.505 22.934-18.322Q22.796-18.138 22.604-18.005Q22.413-17.872 22.194-17.802Q21.975-17.732 21.737-17.732Q21.366-17.732 21.028-17.869Q20.690-18.005 20.422-18.257Q20.155-18.509 20.005-18.849Q19.854-19.189 19.854-19.564M20.608-19.872L22.569-19.872Q22.569-20.177 22.467-20.468Q22.366-20.759 22.149-20.941Q21.932-21.122 21.616-21.122Q21.315-21.122 21.085-20.935Q20.854-20.747 20.731-20.456Q20.608-20.165 20.608-19.872\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-27.425-43.017v19.362\"\u002F>\u003Cpath stroke=\"none\" d=\"m-27.425-21.055 2.08-4.16-2.08 1.56-2.08-1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M14.086-6.43h78.036\"\u002F>\u003Cpath stroke=\"none\" d=\"m94.722-6.43-4.16-2.079 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M131.91-20.855v-14.027H9.963v-20.162\"\u002F>\u003Cpath stroke=\"none\" d=\"m9.963-57.644-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(52.463 6.426)\">\u003Cpath d=\"M-26.584-18.651L-26.584-20.548L-27.223-20.548L-27.223-20.770Q-26.905-20.770-26.688-20.980Q-26.471-21.190-26.371-21.500Q-26.270-21.809-26.270-22.117L-26.003-22.117L-26.003-20.828L-24.926-20.828L-24.926-20.548L-26.003-20.548L-26.003-18.664Q-26.003-18.388-25.899-18.189Q-25.795-17.991-25.535-17.991Q-25.378-17.991-25.272-18.095Q-25.166-18.200-25.116-18.353Q-25.067-18.507-25.067-18.664L-25.067-19.078L-24.800-19.078L-24.800-18.651Q-24.800-18.425-24.899-18.215Q-24.998-18.005-25.183-17.873Q-25.367-17.742-25.596-17.742Q-26.034-17.742-26.309-17.979Q-26.584-18.217-26.584-18.651M-24.031-19.293Q-24.031-19.635-23.896-19.934Q-23.761-20.233-23.522-20.457Q-23.282-20.681-22.965-20.806Q-22.647-20.931-22.315-20.931Q-21.871-20.931-21.471-20.715Q-21.071-20.500-20.837-20.122Q-20.603-19.745-20.603-19.293Q-20.603-18.952-20.745-18.668Q-20.886-18.384-21.131-18.177Q-21.375-17.971-21.685-17.856Q-21.994-17.742-22.315-17.742Q-22.746-17.742-23.147-17.943Q-23.549-18.145-23.790-18.497Q-24.031-18.849-24.031-19.293M-22.315-17.991Q-21.714-17.991-21.490-18.369Q-21.266-18.747-21.266-19.379Q-21.266-19.991-21.500-20.350Q-21.734-20.708-22.315-20.708Q-23.368-20.708-23.368-19.379Q-23.368-18.747-23.142-18.369Q-22.917-17.991-22.315-17.991\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(52.463 6.426)\">\u003Cpath d=\"M-19.826-19.293Q-19.826-19.635-19.691-19.934Q-19.556-20.233-19.316-20.457Q-19.077-20.681-18.759-20.806Q-18.441-20.931-18.110-20.931Q-17.665-20.931-17.266-20.715Q-16.866-20.500-16.631-20.122Q-16.397-19.745-16.397-19.293Q-16.397-18.952-16.539-18.668Q-16.681-18.384-16.925-18.177Q-17.170-17.971-17.479-17.856Q-17.788-17.742-18.110-17.742Q-18.540-17.742-18.942-17.943Q-19.344-18.145-19.585-18.497Q-19.826-18.849-19.826-19.293M-18.110-17.991Q-17.508-17.991-17.284-18.369Q-17.060-18.747-17.060-19.379Q-17.060-19.991-17.295-20.350Q-17.529-20.708-18.110-20.708Q-19.162-20.708-19.162-19.379Q-19.162-18.747-18.937-18.369Q-18.711-17.991-18.110-17.991M-14.135-17.810L-15.738-17.810L-15.738-18.090Q-15.512-18.090-15.363-18.124Q-15.215-18.159-15.215-18.299L-15.215-21.918Q-15.215-22.188-15.322-22.250Q-15.430-22.311-15.738-22.311L-15.738-22.592L-14.661-22.667L-14.661-18.299Q-14.661-18.162-14.511-18.126Q-14.360-18.090-14.135-18.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(52.463 6.426)\">\u003Cpath d=\"M-5.672-18.617L-10.505-18.617Q-10.573-18.627-10.619-18.673Q-10.665-18.719-10.665-18.791Q-10.665-18.856-10.619-18.902Q-10.573-18.948-10.505-18.958L-5.672-18.958Q-5.603-18.948-5.557-18.902Q-5.511-18.856-5.511-18.791Q-5.511-18.719-5.557-18.673Q-5.603-18.627-5.672-18.617M-5.672-20.155L-10.505-20.155Q-10.573-20.165-10.619-20.211Q-10.665-20.257-10.665-20.329Q-10.665-20.473-10.505-20.497L-5.672-20.497Q-5.511-20.473-5.511-20.329Q-5.511-20.257-5.557-20.211Q-5.603-20.165-5.672-20.155\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(52.463 6.426)\">\u003Cpath d=\"M-1.948-18.538Q-1.948-18.870-1.725-19.097Q-1.501-19.324-1.157-19.452Q-0.814-19.581-0.441-19.633Q-0.069-19.686 0.236-19.686L0.236-19.939Q0.236-20.144 0.128-20.324Q0.020-20.503-0.161-20.606Q-0.342-20.708-0.550-20.708Q-0.957-20.708-1.193-20.616Q-1.104-20.579-1.058-20.495Q-1.012-20.411-1.012-20.309Q-1.012-20.213-1.058-20.134Q-1.104-20.056-1.185-20.011Q-1.265-19.967-1.354-19.967Q-1.504-19.967-1.605-20.064Q-1.706-20.162-1.706-20.309Q-1.706-20.931-0.550-20.931Q-0.339-20.931-0.089-20.867Q0.160-20.804 0.362-20.685Q0.564-20.565 0.690-20.380Q0.817-20.196 0.817-19.953L0.817-18.377Q0.817-18.261 0.878-18.165Q0.940-18.070 1.053-18.070Q1.162-18.070 1.227-18.164Q1.292-18.258 1.292-18.377L1.292-18.825L1.558-18.825L1.558-18.377Q1.558-18.107 1.331-17.942Q1.104-17.776 0.824-17.776Q0.615-17.776 0.478-17.930Q0.342-18.083 0.318-18.299Q0.171-18.032-0.111-17.887Q-0.393-17.742-0.718-17.742Q-0.995-17.742-1.279-17.817Q-1.562-17.892-1.755-18.071Q-1.948-18.251-1.948-18.538M-1.333-18.538Q-1.333-18.364-1.232-18.234Q-1.132-18.104-0.976-18.034Q-0.821-17.964-0.656-17.964Q-0.438-17.964-0.229-18.061Q-0.021-18.159 0.107-18.340Q0.236-18.521 0.236-18.747L0.236-19.475Q-0.089-19.475-0.455-19.384Q-0.821-19.293-1.077-19.081Q-1.333-18.870-1.333-18.538M1.975-19.321Q1.975-19.649 2.110-19.950Q2.245-20.250 2.481-20.471Q2.717-20.691 3.021-20.811Q3.325-20.931 3.650-20.931Q4.156-20.931 4.505-20.828Q4.853-20.726 4.853-20.350Q4.853-20.203 4.756-20.102Q4.658-20.001 4.512-20.001Q4.358-20.001 4.259-20.100Q4.159-20.199 4.159-20.350Q4.159-20.538 4.300-20.630Q4.098-20.681 3.657-20.681Q3.302-20.681 3.073-20.485Q2.844-20.288 2.743-19.979Q2.642-19.669 2.642-19.321Q2.642-18.972 2.768-18.666Q2.895-18.360 3.149-18.176Q3.404-17.991 3.760-17.991Q3.982-17.991 4.166-18.075Q4.351-18.159 4.486-18.314Q4.621-18.470 4.679-18.678Q4.693-18.733 4.747-18.733L4.860-18.733Q4.891-18.733 4.913-18.709Q4.935-18.685 4.935-18.651L4.935-18.630Q4.850-18.343 4.662-18.145Q4.474-17.947 4.209-17.844Q3.944-17.742 3.650-17.742Q3.220-17.742 2.832-17.948Q2.444-18.155 2.210-18.518Q1.975-18.880 1.975-19.321M6.050-18.651L6.050-20.548L5.410-20.548L5.410-20.770Q5.728-20.770 5.945-20.980Q6.162-21.190 6.263-21.500Q6.364-21.809 6.364-22.117L6.631-22.117L6.631-20.828L7.707-20.828L7.707-20.548L6.631-20.548L6.631-18.664Q6.631-18.388 6.735-18.189Q6.839-17.991 7.099-17.991Q7.256-17.991 7.362-18.095Q7.468-18.200 7.518-18.353Q7.567-18.507 7.567-18.664L7.567-19.078L7.834-19.078L7.834-18.651Q7.834-18.425 7.735-18.215Q7.636-18.005 7.451-17.873Q7.266-17.742 7.037-17.742Q6.600-17.742 6.325-17.979Q6.050-18.217 6.050-18.651M9.218-18.644L9.218-20.148Q9.218-20.418 9.110-20.479Q9.003-20.541 8.692-20.541L8.692-20.821L9.799-20.896L9.799-18.664L9.799-18.644Q9.799-18.364 9.850-18.220Q9.902-18.077 10.044-18.020Q10.185-17.964 10.472-17.964Q10.725-17.964 10.930-18.104Q11.136-18.244 11.252-18.470Q11.368-18.695 11.368-18.945L11.368-20.148Q11.368-20.418 11.260-20.479Q11.153-20.541 10.842-20.541L10.842-20.821L11.949-20.896L11.949-18.483Q11.949-18.292 12.002-18.210Q12.055-18.128 12.156-18.109Q12.257-18.090 12.472-18.090L12.472-17.810L11.395-17.742L11.395-18.306Q11.286-18.124 11.141-18.001Q10.995-17.878 10.809-17.810Q10.623-17.742 10.421-17.742Q9.218-17.742 9.218-18.644M13.118-18.538Q13.118-18.870 13.342-19.097Q13.566-19.324 13.909-19.452Q14.253-19.581 14.625-19.633Q14.998-19.686 15.302-19.686L15.302-19.939Q15.302-20.144 15.194-20.324Q15.087-20.503 14.906-20.606Q14.724-20.708 14.516-20.708Q14.109-20.708 13.873-20.616Q13.962-20.579 14.008-20.495Q14.054-20.411 14.054-20.309Q14.054-20.213 14.008-20.134Q13.962-20.056 13.882-20.011Q13.802-19.967 13.713-19.967Q13.562-19.967 13.461-20.064Q13.361-20.162 13.361-20.309Q13.361-20.931 14.516-20.931Q14.728-20.931 14.977-20.867Q15.227-20.804 15.429-20.685Q15.630-20.565 15.757-20.380Q15.883-20.196 15.883-19.953L15.883-18.377Q15.883-18.261 15.945-18.165Q16.006-18.070 16.119-18.070Q16.228-18.070 16.293-18.164Q16.358-18.258 16.358-18.377L16.358-18.825L16.625-18.825L16.625-18.377Q16.625-18.107 16.398-17.942Q16.170-17.776 15.890-17.776Q15.681-17.776 15.545-17.930Q15.408-18.083 15.384-18.299Q15.237-18.032 14.955-17.887Q14.673-17.742 14.348-17.742Q14.072-17.742 13.788-17.817Q13.504-17.892 13.311-18.071Q13.118-18.251 13.118-18.538M13.733-18.538Q13.733-18.364 13.834-18.234Q13.935-18.104 14.090-18.034Q14.246-17.964 14.410-17.964Q14.629-17.964 14.837-18.061Q15.046-18.159 15.174-18.340Q15.302-18.521 15.302-18.747L15.302-19.475Q14.977-19.475 14.612-19.384Q14.246-19.293 13.990-19.081Q13.733-18.870 13.733-18.538M17.568-18.651L17.568-20.548L16.929-20.548L16.929-20.770Q17.247-20.770 17.464-20.980Q17.681-21.190 17.782-21.500Q17.883-21.809 17.883-22.117L18.149-22.117L18.149-20.828L19.226-20.828L19.226-20.548L18.149-20.548L18.149-18.664Q18.149-18.388 18.253-18.189Q18.358-17.991 18.617-17.991Q18.775-17.991 18.881-18.095Q18.987-18.200 19.036-18.353Q19.086-18.507 19.086-18.664L19.086-19.078L19.352-19.078L19.352-18.651Q19.352-18.425 19.253-18.215Q19.154-18.005 18.970-17.873Q18.785-17.742 18.556-17.742Q18.118-17.742 17.843-17.979Q17.568-18.217 17.568-18.651M20.121-19.293Q20.121-19.635 20.256-19.934Q20.391-20.233 20.631-20.457Q20.870-20.681 21.188-20.806Q21.506-20.931 21.837-20.931Q22.282-20.931 22.681-20.715Q23.081-20.500 23.315-20.122Q23.550-19.745 23.550-19.293Q23.550-18.952 23.408-18.668Q23.266-18.384 23.022-18.177Q22.777-17.971 22.468-17.856Q22.158-17.742 21.837-17.742Q21.407-17.742 21.005-17.943Q20.603-18.145 20.362-18.497Q20.121-18.849 20.121-19.293M21.837-17.991Q22.439-17.991 22.663-18.369Q22.887-18.747 22.887-19.379Q22.887-19.991 22.652-20.350Q22.418-20.708 21.837-20.708Q20.784-20.708 20.784-19.379Q20.784-18.747 21.010-18.369Q21.236-17.991 21.837-17.991M25.894-17.810L24.158-17.810L24.158-18.090Q24.387-18.090 24.536-18.124Q24.684-18.159 24.684-18.299L24.684-20.148Q24.684-20.418 24.577-20.479Q24.469-20.541 24.158-20.541L24.158-20.821L25.187-20.896L25.187-20.189Q25.317-20.497 25.559-20.696Q25.802-20.896 26.120-20.896Q26.339-20.896 26.510-20.772Q26.680-20.647 26.680-20.435Q26.680-20.298 26.581-20.199Q26.482-20.100 26.349-20.100Q26.212-20.100 26.113-20.199Q26.014-20.298 26.014-20.435Q26.014-20.575 26.113-20.674Q25.823-20.674 25.623-20.478Q25.423-20.281 25.330-19.987Q25.238-19.693 25.238-19.413L25.238-18.299Q25.238-18.090 25.894-18.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M94.722-57.644H11.963\"\u002F>\u003Cpath stroke=\"none\" d=\"m9.963-57.644 3.2 1.6-1.2-1.6 1.2-1.6\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(199.857 -37.403)\">\u003Cpath d=\"M-25.494-17.810L-27.046-17.810L-27.046-18.090Q-26.820-18.090-26.671-18.124Q-26.523-18.159-26.523-18.299L-26.523-20.148Q-26.523-20.336-26.571-20.420Q-26.618-20.503-26.716-20.522Q-26.813-20.541-27.025-20.541L-27.025-20.821L-25.969-20.896L-25.969-18.299Q-25.969-18.159-25.837-18.124Q-25.706-18.090-25.494-18.090L-25.494-17.810M-26.765-22.117Q-26.765-22.288-26.642-22.407Q-26.519-22.527-26.348-22.527Q-26.181-22.527-26.058-22.407Q-25.935-22.288-25.935-22.117Q-25.935-21.942-26.058-21.819Q-26.181-21.696-26.348-21.696Q-26.519-21.696-26.642-21.819Q-26.765-21.942-26.765-22.117M-23.166-17.810L-24.800-17.810L-24.800-18.090Q-24.571-18.090-24.422-18.124Q-24.274-18.159-24.274-18.299L-24.274-20.148Q-24.274-20.418-24.381-20.479Q-24.489-20.541-24.800-20.541L-24.800-20.821L-23.740-20.896L-23.740-20.247Q-23.570-20.555-23.265-20.726Q-22.961-20.896-22.616-20.896Q-22.110-20.896-21.826-20.673Q-21.543-20.449-21.543-19.953L-21.543-18.299Q-21.543-18.162-21.394-18.126Q-21.245-18.090-21.020-18.090L-21.020-17.810L-22.650-17.810L-22.650-18.090Q-22.421-18.090-22.272-18.124Q-22.124-18.159-22.124-18.299L-22.124-19.939Q-22.124-20.274-22.243-20.474Q-22.363-20.674-22.677-20.674Q-22.947-20.674-23.182-20.538Q-23.416-20.401-23.554-20.167Q-23.693-19.933-23.693-19.659L-23.693-18.299Q-23.693-18.162-23.542-18.126Q-23.392-18.090-23.166-18.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(199.857 -37.403)\">\u003Cpath d=\"M-20.119-18.651L-20.119-20.548L-20.758-20.548L-20.758-20.770Q-20.440-20.770-20.223-20.980Q-20.006-21.190-19.906-21.500Q-19.805-21.809-19.805-22.117L-19.538-22.117L-19.538-20.828L-18.461-20.828L-18.461-20.548L-19.538-20.548L-19.538-18.664Q-19.538-18.388-19.434-18.189Q-19.330-17.991-19.070-17.991Q-18.913-17.991-18.807-18.095Q-18.701-18.200-18.651-18.353Q-18.602-18.507-18.602-18.664L-18.602-19.078L-18.335-19.078L-18.335-18.651Q-18.335-18.425-18.434-18.215Q-18.533-18.005-18.718-17.873Q-18.902-17.742-19.131-17.742Q-19.569-17.742-19.844-17.979Q-20.119-18.217-20.119-18.651M-17.566-19.345Q-17.566-19.666-17.441-19.955Q-17.316-20.244-17.091-20.467Q-16.865-20.691-16.570-20.811Q-16.274-20.931-15.956-20.931Q-15.628-20.931-15.366-20.831Q-15.105-20.732-14.929-20.550Q-14.753-20.367-14.659-20.109Q-14.565-19.851-14.565-19.519Q-14.565-19.427-14.647-19.406L-16.903-19.406L-16.903-19.345Q-16.903-18.757-16.619-18.374Q-16.335-17.991-15.768-17.991Q-15.447-17.991-15.179-18.184Q-14.910-18.377-14.821-18.692Q-14.814-18.733-14.739-18.747L-14.647-18.747Q-14.565-18.723-14.565-18.651Q-14.565-18.644-14.572-18.617Q-14.685-18.220-15.055-17.981Q-15.426-17.742-15.850-17.742Q-16.288-17.742-16.688-17.950Q-17.087-18.159-17.327-18.526Q-17.566-18.893-17.566-19.345M-16.896-19.615L-15.081-19.615Q-15.081-19.892-15.179-20.144Q-15.276-20.397-15.474-20.553Q-15.672-20.708-15.956-20.708Q-16.233-20.708-16.447-20.550Q-16.660-20.391-16.778-20.136Q-16.896-19.881-16.896-19.615M-12.227-17.810L-13.963-17.810L-13.963-18.090Q-13.734-18.090-13.586-18.124Q-13.437-18.159-13.437-18.299L-13.437-20.148Q-13.437-20.418-13.545-20.479Q-13.652-20.541-13.963-20.541L-13.963-20.821L-12.935-20.896L-12.935-20.189Q-12.805-20.497-12.562-20.696Q-12.319-20.896-12.002-20.896Q-11.783-20.896-11.612-20.772Q-11.441-20.647-11.441-20.435Q-11.441-20.298-11.540-20.199Q-11.639-20.100-11.773-20.100Q-11.909-20.100-12.008-20.199Q-12.107-20.298-12.107-20.435Q-12.107-20.575-12.008-20.674Q-12.299-20.674-12.499-20.478Q-12.699-20.281-12.791-19.987Q-12.883-19.693-12.883-19.413L-12.883-18.299Q-12.883-18.090-12.227-18.090L-12.227-17.810M-9.175-17.810L-10.809-17.810L-10.809-18.090Q-10.580-18.090-10.431-18.124Q-10.282-18.159-10.282-18.299L-10.282-20.148Q-10.282-20.418-10.390-20.479Q-10.498-20.541-10.809-20.541L-10.809-20.821L-9.749-20.896L-9.749-20.247Q-9.578-20.555-9.274-20.726Q-8.970-20.896-8.625-20.896Q-8.119-20.896-7.835-20.673Q-7.551-20.449-7.551-19.953L-7.551-18.299Q-7.551-18.162-7.403-18.126Q-7.254-18.090-7.028-18.090L-7.028-17.810L-8.659-17.810L-8.659-18.090Q-8.430-18.090-8.281-18.124Q-8.132-18.159-8.132-18.299L-8.132-19.939Q-8.132-20.274-8.252-20.474Q-8.372-20.674-8.686-20.674Q-8.956-20.674-9.190-20.538Q-9.424-20.401-9.563-20.167Q-9.701-19.933-9.701-19.659L-9.701-18.299Q-9.701-18.162-9.551-18.126Q-9.400-18.090-9.175-18.090L-9.175-17.810M-6.382-18.538Q-6.382-18.870-6.158-19.097Q-5.935-19.324-5.591-19.452Q-5.248-19.581-4.875-19.633Q-4.502-19.686-4.198-19.686L-4.198-19.939Q-4.198-20.144-4.306-20.324Q-4.414-20.503-4.595-20.606Q-4.776-20.708-4.984-20.708Q-5.391-20.708-5.627-20.616Q-5.538-20.579-5.492-20.495Q-5.446-20.411-5.446-20.309Q-5.446-20.213-5.492-20.134Q-5.538-20.056-5.618-20.011Q-5.699-19.967-5.788-19.967Q-5.938-19.967-6.039-20.064Q-6.140-20.162-6.140-20.309Q-6.140-20.931-4.984-20.931Q-4.773-20.931-4.523-20.867Q-4.273-20.804-4.072-20.685Q-3.870-20.565-3.744-20.380Q-3.617-20.196-3.617-19.953L-3.617-18.377Q-3.617-18.261-3.556-18.165Q-3.494-18.070-3.381-18.070Q-3.272-18.070-3.207-18.164Q-3.142-18.258-3.142-18.377L-3.142-18.825L-2.876-18.825L-2.876-18.377Q-2.876-18.107-3.103-17.942Q-3.330-17.776-3.610-17.776Q-3.819-17.776-3.956-17.930Q-4.092-18.083-4.116-18.299Q-4.263-18.032-4.545-17.887Q-4.827-17.742-5.152-17.742Q-5.429-17.742-5.712-17.817Q-5.996-17.892-6.189-18.071Q-6.382-18.251-6.382-18.538M-5.767-18.538Q-5.767-18.364-5.666-18.234Q-5.565-18.104-5.410-18.034Q-5.254-17.964-5.090-17.964Q-4.872-17.964-4.663-18.061Q-4.455-18.159-4.326-18.340Q-4.198-18.521-4.198-18.747L-4.198-19.475Q-4.523-19.475-4.889-19.384Q-5.254-19.293-5.511-19.081Q-5.767-18.870-5.767-18.538M-0.791-17.810L-2.394-17.810L-2.394-18.090Q-2.168-18.090-2.019-18.124Q-1.871-18.159-1.871-18.299L-1.871-21.918Q-1.871-22.188-1.978-22.250Q-2.086-22.311-2.394-22.311L-2.394-22.592L-1.317-22.667L-1.317-18.299Q-1.317-18.162-1.167-18.126Q-1.016-18.090-0.791-18.090\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(199.857 -37.403)\">\u003Cpath d=\"M2.521-17.817L2.521-18.880Q2.521-18.904 2.549-18.931Q2.576-18.958 2.600-18.958L2.709-18.958Q2.774-18.958 2.788-18.900Q2.884-18.466 3.130-18.215Q3.376-17.964 3.790-17.964Q4.131-17.964 4.384-18.097Q4.637-18.230 4.637-18.538Q4.637-18.695 4.543-18.810Q4.449-18.924 4.311-18.993Q4.172-19.061 4.005-19.099L3.424-19.198Q3.068-19.266 2.795-19.487Q2.521-19.707 2.521-20.049Q2.521-20.298 2.633-20.473Q2.744-20.647 2.930-20.746Q3.116-20.845 3.332-20.888Q3.547-20.931 3.790-20.931Q4.203-20.931 4.483-20.749L4.699-20.924Q4.709-20.927 4.716-20.929Q4.723-20.931 4.733-20.931L4.784-20.931Q4.811-20.931 4.835-20.907Q4.859-20.883 4.859-20.855L4.859-20.008Q4.859-19.987 4.835-19.960Q4.811-19.933 4.784-19.933L4.671-19.933Q4.644-19.933 4.618-19.958Q4.593-19.984 4.593-20.008Q4.593-20.244 4.487-20.408Q4.381-20.572 4.198-20.654Q4.015-20.736 3.783-20.736Q3.455-20.736 3.198-20.633Q2.942-20.531 2.942-20.254Q2.942-20.059 3.125-19.950Q3.308-19.840 3.537-19.799L4.111-19.693Q4.357-19.645 4.571-19.517Q4.784-19.389 4.921-19.186Q5.058-18.982 5.058-18.733Q5.058-18.220 4.692-17.981Q4.326-17.742 3.790-17.742Q3.294-17.742 2.962-18.036L2.696-17.762Q2.675-17.742 2.648-17.742L2.600-17.742Q2.576-17.742 2.549-17.769Q2.521-17.796 2.521-17.817M6.213-18.651L6.213-20.548L5.574-20.548L5.574-20.770Q5.892-20.770 6.109-20.980Q6.326-21.190 6.426-21.500Q6.527-21.809 6.527-22.117L6.794-22.117L6.794-20.828L7.871-20.828L7.871-20.548L6.794-20.548L6.794-18.664Q6.794-18.388 6.898-18.189Q7.002-17.991 7.262-17.991Q7.419-17.991 7.525-18.095Q7.631-18.200 7.681-18.353Q7.730-18.507 7.730-18.664L7.730-19.078L7.997-19.078L7.997-18.651Q7.997-18.425 7.898-18.215Q7.799-18.005 7.614-17.873Q7.430-17.742 7.201-17.742Q6.763-17.742 6.488-17.979Q6.213-18.217 6.213-18.651M8.865-18.538Q8.865-18.870 9.089-19.097Q9.313-19.324 9.656-19.452Q10-19.581 10.373-19.633Q10.745-19.686 11.049-19.686L11.049-19.939Q11.049-20.144 10.942-20.324Q10.834-20.503 10.653-20.606Q10.472-20.708 10.263-20.708Q9.856-20.708 9.621-20.616Q9.709-20.579 9.756-20.495Q9.802-20.411 9.802-20.309Q9.802-20.213 9.756-20.134Q9.709-20.056 9.629-20.011Q9.549-19.967 9.460-19.967Q9.310-19.967 9.209-20.064Q9.108-20.162 9.108-20.309Q9.108-20.931 10.263-20.931Q10.475-20.931 10.725-20.867Q10.974-20.804 11.176-20.685Q11.377-20.565 11.504-20.380Q11.630-20.196 11.630-19.953L11.630-18.377Q11.630-18.261 11.692-18.165Q11.753-18.070 11.866-18.070Q11.976-18.070 12.040-18.164Q12.105-18.258 12.105-18.377L12.105-18.825L12.372-18.825L12.372-18.377Q12.372-18.107 12.145-17.942Q11.917-17.776 11.637-17.776Q11.429-17.776 11.292-17.930Q11.155-18.083 11.131-18.299Q10.984-18.032 10.702-17.887Q10.420-17.742 10.096-17.742Q9.819-17.742 9.535-17.817Q9.251-17.892 9.058-18.071Q8.865-18.251 8.865-18.538M9.480-18.538Q9.480-18.364 9.581-18.234Q9.682-18.104 9.838-18.034Q9.993-17.964 10.157-17.964Q10.376-17.964 10.584-18.061Q10.793-18.159 10.921-18.340Q11.049-18.521 11.049-18.747L11.049-19.475Q10.725-19.475 10.359-19.384Q9.993-19.293 9.737-19.081Q9.480-18.870 9.480-18.538M13.315-18.651L13.315-20.548L12.676-20.548L12.676-20.770Q12.994-20.770 13.211-20.980Q13.428-21.190 13.529-21.500Q13.630-21.809 13.630-22.117L13.896-22.117L13.896-20.828L14.973-20.828L14.973-20.548L13.896-20.548L13.896-18.664Q13.896-18.388 14.001-18.189Q14.105-17.991 14.365-17.991Q14.522-17.991 14.628-18.095Q14.734-18.200 14.783-18.353Q14.833-18.507 14.833-18.664L14.833-19.078L15.100-19.078L15.100-18.651Q15.100-18.425 15-18.215Q14.901-18.005 14.717-17.873Q14.532-17.742 14.303-17.742Q13.866-17.742 13.591-17.979Q13.315-18.217 13.315-18.651M15.869-19.345Q15.869-19.666 15.993-19.955Q16.118-20.244 16.344-20.467Q16.569-20.691 16.865-20.811Q17.161-20.931 17.478-20.931Q17.807-20.931 18.068-20.831Q18.330-20.732 18.506-20.550Q18.682-20.367 18.776-20.109Q18.870-19.851 18.870-19.519Q18.870-19.427 18.788-19.406L16.532-19.406L16.532-19.345Q16.532-18.757 16.815-18.374Q17.099-17.991 17.666-17.991Q17.988-17.991 18.256-18.184Q18.524-18.377 18.613-18.692Q18.620-18.733 18.695-18.747L18.788-18.747Q18.870-18.723 18.870-18.651Q18.870-18.644 18.863-18.617Q18.750-18.220 18.379-17.981Q18.008-17.742 17.584-17.742Q17.147-17.742 16.747-17.950Q16.347-18.159 16.108-18.526Q15.869-18.893 15.869-19.345M16.539-19.615L18.353-19.615Q18.353-19.892 18.256-20.144Q18.159-20.397 17.960-20.553Q17.762-20.708 17.478-20.708Q17.202-20.708 16.988-20.550Q16.774-20.391 16.656-20.136Q16.539-19.881 16.539-19.615\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">A language-model agent in the ReAct loop, mapped onto the goal-based skeleton. The model reasons (predicts an outcome), acts (emits text or a tool call), and observes the result, which becomes the next percept. Tools are actuators and sensors; a memory store supplies internal state.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:244.660px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 183.495 154.354\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cpath fill=\"none\" d=\"M-68.537 71.616H56.655V43.164H-68.537Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M2.383 47.882L2.383 46.660Q2.383 46.632 2.414 46.601Q2.446 46.570 2.469 46.570L2.575 46.570Q2.645 46.570 2.661 46.632Q2.723 46.953 2.862 47.193Q3 47.433 3.233 47.574Q3.465 47.714 3.774 47.714Q4.012 47.714 4.221 47.654Q4.430 47.593 4.567 47.445Q4.704 47.296 4.704 47.050Q4.704 46.796 4.493 46.630Q4.282 46.464 4.012 46.410L3.391 46.296Q2.985 46.218 2.684 45.962Q2.383 45.706 2.383 45.331Q2.383 44.964 2.584 44.742Q2.786 44.519 3.110 44.421Q3.434 44.324 3.774 44.324Q4.239 44.324 4.536 44.531L4.758 44.347Q4.782 44.324 4.813 44.324L4.864 44.324Q4.895 44.324 4.922 44.351Q4.950 44.378 4.950 44.410L4.950 45.394Q4.950 45.425 4.924 45.454Q4.899 45.484 4.864 45.484L4.758 45.484Q4.723 45.484 4.696 45.456Q4.668 45.429 4.668 45.394Q4.668 44.995 4.416 44.775Q4.165 44.554 3.766 44.554Q3.411 44.554 3.127 44.677Q2.844 44.800 2.844 45.105Q2.844 45.324 3.045 45.456Q3.247 45.589 3.493 45.632L4.118 45.745Q4.547 45.835 4.856 46.132Q5.165 46.429 5.165 46.843Q5.165 47.413 4.766 47.691Q4.368 47.968 3.774 47.968Q3.223 47.968 2.872 47.632L2.575 47.945Q2.551 47.968 2.516 47.968L2.469 47.968Q2.446 47.968 2.414 47.937Q2.383 47.906 2.383 47.882M7.551 47.890L5.774 47.890L5.774 47.593Q6.047 47.593 6.215 47.546Q6.383 47.499 6.383 47.331L6.383 45.195Q6.383 44.980 6.327 44.884Q6.270 44.788 6.157 44.767Q6.043 44.745 5.797 44.745L5.797 44.449L6.997 44.363L6.997 47.331Q6.997 47.499 7.143 47.546Q7.290 47.593 7.551 47.593L7.551 47.890M6.110 42.968Q6.110 42.777 6.245 42.646Q6.379 42.515 6.575 42.515Q6.696 42.515 6.799 42.578Q6.903 42.640 6.965 42.744Q7.028 42.847 7.028 42.968Q7.028 43.163 6.897 43.298Q6.766 43.433 6.575 43.433Q6.375 43.433 6.243 43.300Q6.110 43.167 6.110 42.968M9.981 47.890L8.125 47.890L8.125 47.593Q8.399 47.593 8.567 47.546Q8.735 47.499 8.735 47.331L8.735 45.195Q8.735 44.980 8.672 44.884Q8.610 44.788 8.491 44.767Q8.372 44.745 8.125 44.745L8.125 44.449L9.317 44.363L9.317 45.097Q9.430 44.882 9.623 44.714Q9.817 44.546 10.055 44.454Q10.293 44.363 10.547 44.363Q11.508 44.363 11.684 45.074Q11.868 44.745 12.196 44.554Q12.524 44.363 12.903 44.363Q14.079 44.363 14.079 45.441L14.079 47.331Q14.079 47.499 14.247 47.546Q14.415 47.593 14.684 47.593L14.684 47.890L12.829 47.890L12.829 47.593Q13.102 47.593 13.270 47.548Q13.438 47.503 13.438 47.331L13.438 45.456Q13.438 45.070 13.313 44.843Q13.188 44.617 12.836 44.617Q12.532 44.617 12.276 44.779Q12.020 44.941 11.872 45.210Q11.723 45.480 11.723 45.777L11.723 47.331Q11.723 47.499 11.893 47.546Q12.063 47.593 12.332 47.593L12.332 47.890L10.477 47.890L10.477 47.593Q10.750 47.593 10.918 47.546Q11.086 47.499 11.086 47.331L11.086 45.456Q11.086 45.070 10.961 44.843Q10.836 44.617 10.485 44.617Q10.180 44.617 9.924 44.779Q9.668 44.941 9.520 45.210Q9.372 45.480 9.372 45.777L9.372 47.331Q9.372 47.499 9.541 47.546Q9.711 47.593 9.981 47.593L9.981 47.890M17.012 49.441L15.157 49.441L15.157 49.148Q15.426 49.148 15.594 49.103Q15.762 49.058 15.762 48.882L15.762 45.058Q15.762 44.851 15.606 44.798Q15.450 44.745 15.157 44.745L15.157 44.449L16.379 44.363L16.379 44.828Q16.610 44.605 16.924 44.484Q17.239 44.363 17.579 44.363Q18.051 44.363 18.456 44.609Q18.860 44.855 19.092 45.271Q19.325 45.687 19.325 46.163Q19.325 46.538 19.176 46.867Q19.028 47.195 18.758 47.447Q18.489 47.699 18.145 47.833Q17.801 47.968 17.442 47.968Q17.153 47.968 16.881 47.847Q16.610 47.726 16.403 47.515L16.403 48.882Q16.403 49.058 16.571 49.103Q16.739 49.148 17.012 49.148L17.012 49.441M16.403 45.226L16.403 47.066Q16.555 47.355 16.817 47.535Q17.079 47.714 17.387 47.714Q17.672 47.714 17.895 47.576Q18.118 47.437 18.270 47.206Q18.422 46.976 18.500 46.704Q18.579 46.433 18.579 46.163Q18.579 45.831 18.454 45.474Q18.329 45.117 18.081 44.880Q17.832 44.644 17.485 44.644Q17.161 44.644 16.866 44.800Q16.571 44.956 16.403 45.226M21.762 47.890L19.930 47.890L19.930 47.593Q20.204 47.593 20.372 47.546Q20.540 47.499 20.540 47.331L20.540 43.171Q20.540 42.956 20.477 42.861Q20.415 42.765 20.295 42.744Q20.176 42.722 19.930 42.722L19.930 42.425L21.153 42.339L21.153 47.331Q21.153 47.499 21.321 47.546Q21.489 47.593 21.762 47.593L21.762 47.890M22.207 46.136Q22.207 45.656 22.440 45.240Q22.672 44.824 23.082 44.574Q23.493 44.324 23.969 44.324Q24.700 44.324 25.098 44.765Q25.497 45.206 25.497 45.937Q25.497 46.042 25.403 46.066L22.954 46.066L22.954 46.136Q22.954 46.546 23.075 46.902Q23.196 47.257 23.467 47.474Q23.739 47.691 24.168 47.691Q24.532 47.691 24.829 47.462Q25.125 47.234 25.227 46.882Q25.235 46.835 25.321 46.820L25.403 46.820Q25.497 46.847 25.497 46.929Q25.497 46.937 25.489 46.968Q25.426 47.195 25.288 47.378Q25.149 47.562 24.957 47.695Q24.766 47.828 24.547 47.898Q24.329 47.968 24.090 47.968Q23.719 47.968 23.381 47.831Q23.043 47.695 22.776 47.443Q22.508 47.191 22.358 46.851Q22.207 46.511 22.207 46.136M22.961 45.828L24.922 45.828Q24.922 45.523 24.821 45.232Q24.719 44.941 24.502 44.759Q24.286 44.578 23.969 44.578Q23.668 44.578 23.438 44.765Q23.207 44.953 23.084 45.244Q22.961 45.535 22.961 45.828\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M30.840 47.890L28.860 47.890L28.860 47.593Q29.129 47.593 29.297 47.548Q29.465 47.503 29.465 47.331L29.465 45.195Q29.465 44.980 29.403 44.884Q29.340 44.788 29.223 44.767Q29.106 44.745 28.860 44.745L28.860 44.449L30.028 44.363L30.028 45.148Q30.106 44.937 30.258 44.751Q30.410 44.566 30.610 44.464Q30.809 44.363 31.035 44.363Q31.282 44.363 31.473 44.507Q31.664 44.652 31.664 44.882Q31.664 45.038 31.559 45.148Q31.453 45.257 31.297 45.257Q31.141 45.257 31.032 45.148Q30.922 45.038 30.922 44.882Q30.922 44.722 31.028 44.617Q30.703 44.617 30.489 44.845Q30.274 45.074 30.178 45.413Q30.082 45.753 30.082 46.058L30.082 47.331Q30.082 47.499 30.309 47.546Q30.535 47.593 30.840 47.593L30.840 47.890M32.145 46.136Q32.145 45.656 32.377 45.240Q32.610 44.824 33.020 44.574Q33.430 44.324 33.907 44.324Q34.637 44.324 35.035 44.765Q35.434 45.206 35.434 45.937Q35.434 46.042 35.340 46.066L32.891 46.066L32.891 46.136Q32.891 46.546 33.012 46.902Q33.133 47.257 33.405 47.474Q33.676 47.691 34.106 47.691Q34.469 47.691 34.766 47.462Q35.063 47.234 35.164 46.882Q35.172 46.835 35.258 46.820L35.340 46.820Q35.434 46.847 35.434 46.929Q35.434 46.937 35.426 46.968Q35.364 47.195 35.225 47.378Q35.086 47.562 34.895 47.695Q34.703 47.828 34.485 47.898Q34.266 47.968 34.028 47.968Q33.657 47.968 33.319 47.831Q32.981 47.695 32.713 47.443Q32.446 47.191 32.295 46.851Q32.145 46.511 32.145 46.136M32.899 45.828L34.860 45.828Q34.860 45.523 34.758 45.232Q34.657 44.941 34.440 44.759Q34.223 44.578 33.907 44.578Q33.606 44.578 33.375 44.765Q33.145 44.953 33.022 45.244Q32.899 45.535 32.899 45.828M37.989 47.890L36.004 47.890L36.004 47.593Q36.278 47.593 36.446 47.546Q36.614 47.499 36.614 47.331L36.614 44.738L35.973 44.738L35.973 44.441L36.614 44.441L36.614 43.507Q36.614 43.242 36.731 43.005Q36.848 42.769 37.041 42.605Q37.235 42.441 37.483 42.349Q37.731 42.257 37.996 42.257Q38.282 42.257 38.506 42.415Q38.731 42.574 38.731 42.851Q38.731 43.007 38.625 43.117Q38.520 43.226 38.356 43.226Q38.199 43.226 38.090 43.117Q37.981 43.007 37.981 42.851Q37.981 42.644 38.141 42.538Q38.043 42.515 37.949 42.515Q37.719 42.515 37.547 42.671Q37.375 42.828 37.289 43.064Q37.203 43.300 37.203 43.523L37.203 44.441L38.172 44.441L38.172 44.738L37.227 44.738L37.227 47.331Q37.227 47.499 37.453 47.546Q37.680 47.593 37.989 47.593\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M41.065 47.890L39.233 47.890L39.233 47.593Q39.507 47.593 39.675 47.546Q39.843 47.499 39.843 47.331L39.843 43.171Q39.843 42.956 39.780 42.861Q39.718 42.765 39.599 42.744Q39.479 42.722 39.233 42.722L39.233 42.425L40.456 42.339L40.456 47.331Q40.456 47.499 40.624 47.546Q40.792 47.593 41.065 47.593L41.065 47.890M41.511 46.136Q41.511 45.656 41.743 45.240Q41.975 44.824 42.386 44.574Q42.796 44.324 43.272 44.324Q44.003 44.324 44.401 44.765Q44.800 45.206 44.800 45.937Q44.800 46.042 44.706 46.066L42.257 46.066L42.257 46.136Q42.257 46.546 42.378 46.902Q42.499 47.257 42.770 47.474Q43.042 47.691 43.472 47.691Q43.835 47.691 44.132 47.462Q44.429 47.234 44.530 46.882Q44.538 46.835 44.624 46.820L44.706 46.820Q44.800 46.847 44.800 46.929Q44.800 46.937 44.792 46.968Q44.729 47.195 44.591 47.378Q44.452 47.562 44.261 47.695Q44.069 47.828 43.850 47.898Q43.632 47.968 43.393 47.968Q43.022 47.968 42.684 47.831Q42.347 47.695 42.079 47.443Q41.811 47.191 41.661 46.851Q41.511 46.511 41.511 46.136M42.265 45.828L44.225 45.828Q44.225 45.523 44.124 45.232Q44.022 44.941 43.806 44.759Q43.589 44.578 43.272 44.578Q42.972 44.578 42.741 44.765Q42.511 44.953 42.388 45.244Q42.265 45.535 42.265 45.828M46.675 47.890L45.179 47.890L45.179 47.593Q45.811 47.593 46.233 47.113L47.003 46.203L46.011 45.003Q45.854 44.824 45.692 44.781Q45.530 44.738 45.225 44.738L45.225 44.441L46.913 44.441L46.913 44.738Q46.819 44.738 46.743 44.781Q46.667 44.824 46.667 44.913Q46.667 44.956 46.698 45.003L47.354 45.792L47.835 45.218Q47.952 45.081 47.952 44.945Q47.952 44.855 47.901 44.796Q47.850 44.738 47.768 44.738L47.768 44.441L49.257 44.441L49.257 44.738Q48.620 44.738 48.210 45.218L47.530 46.019L48.616 47.331Q48.776 47.507 48.936 47.550Q49.097 47.593 49.401 47.593L49.401 47.890L47.714 47.890L47.714 47.593Q47.804 47.593 47.882 47.550Q47.960 47.507 47.960 47.417Q47.960 47.394 47.929 47.331L47.186 46.425L46.600 47.113Q46.483 47.249 46.483 47.386Q46.483 47.472 46.534 47.533Q46.585 47.593 46.675 47.593\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M-3.820 58.941L-5.675 58.941L-5.675 58.648Q-5.406 58.648-5.238 58.603Q-5.070 58.558-5.070 58.382L-5.070 54.558Q-5.070 54.351-5.226 54.298Q-5.382 54.245-5.675 54.245L-5.675 53.949L-4.453 53.863L-4.453 54.328Q-4.222 54.105-3.908 53.984Q-3.593 53.863-3.253 53.863Q-2.781 53.863-2.377 54.109Q-1.972 54.355-1.740 54.771Q-1.507 55.187-1.507 55.663Q-1.507 56.038-1.656 56.367Q-1.804 56.695-2.074 56.947Q-2.343 57.199-2.687 57.333Q-3.031 57.468-3.390 57.468Q-3.679 57.468-3.951 57.347Q-4.222 57.226-4.429 57.015L-4.429 58.382Q-4.429 58.558-4.261 58.603Q-4.093 58.648-3.820 58.648L-3.820 58.941M-4.429 54.726L-4.429 56.566Q-4.277 56.855-4.015 57.035Q-3.753 57.214-3.445 57.214Q-3.160 57.214-2.937 57.076Q-2.714 56.937-2.562 56.706Q-2.410 56.476-2.332 56.204Q-2.253 55.933-2.253 55.663Q-2.253 55.331-2.378 54.974Q-2.503 54.617-2.752 54.380Q-3 54.144-3.347 54.144Q-3.671 54.144-3.966 54.300Q-4.261 54.456-4.429 54.726\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M-0.744 55.636Q-0.744 55.156-0.511 54.740Q-0.279 54.324 0.131 54.074Q0.541 53.824 1.018 53.824Q1.748 53.824 2.147 54.265Q2.545 54.706 2.545 55.437Q2.545 55.542 2.452 55.566L0.002 55.566L0.002 55.636Q0.002 56.046 0.123 56.402Q0.245 56.757 0.516 56.974Q0.788 57.191 1.217 57.191Q1.581 57.191 1.877 56.962Q2.174 56.734 2.276 56.382Q2.284 56.335 2.370 56.320L2.452 56.320Q2.545 56.347 2.545 56.429Q2.545 56.437 2.538 56.468Q2.475 56.695 2.336 56.878Q2.198 57.062 2.006 57.195Q1.815 57.328 1.596 57.398Q1.377 57.468 1.139 57.468Q0.768 57.468 0.430 57.331Q0.092 57.195-0.175 56.943Q-0.443 56.691-0.593 56.351Q-0.744 56.011-0.744 55.636M0.010 55.328L1.971 55.328Q1.971 55.023 1.870 54.732Q1.768 54.441 1.551 54.259Q1.334 54.078 1.018 54.078Q0.717 54.078 0.487 54.265Q0.256 54.453 0.133 54.744Q0.010 55.035 0.010 55.328M5.041 57.390L3.061 57.390L3.061 57.093Q3.330 57.093 3.498 57.048Q3.666 57.003 3.666 56.831L3.666 54.695Q3.666 54.480 3.604 54.384Q3.541 54.288 3.424 54.267Q3.307 54.245 3.061 54.245L3.061 53.949L4.229 53.863L4.229 54.648Q4.307 54.437 4.459 54.251Q4.612 54.066 4.811 53.964Q5.010 53.863 5.237 53.863Q5.483 53.863 5.674 54.007Q5.866 54.152 5.866 54.382Q5.866 54.538 5.760 54.648Q5.655 54.757 5.498 54.757Q5.342 54.757 5.233 54.648Q5.123 54.538 5.123 54.382Q5.123 54.222 5.229 54.117Q4.905 54.117 4.690 54.345Q4.475 54.574 4.379 54.913Q4.284 55.253 4.284 55.558L4.284 56.831Q4.284 56.999 4.510 57.046Q4.737 57.093 5.041 57.093L5.041 57.390M6.389 55.663Q6.389 55.167 6.639 54.742Q6.889 54.316 7.309 54.070Q7.729 53.824 8.229 53.824Q8.768 53.824 9.159 53.949Q9.549 54.074 9.549 54.488Q9.549 54.593 9.498 54.685Q9.448 54.777 9.356 54.828Q9.264 54.878 9.155 54.878Q9.049 54.878 8.957 54.828Q8.866 54.777 8.815 54.685Q8.764 54.593 8.764 54.488Q8.764 54.265 8.932 54.160Q8.709 54.101 8.237 54.101Q7.940 54.101 7.725 54.240Q7.510 54.378 7.379 54.609Q7.248 54.839 7.190 55.109Q7.131 55.378 7.131 55.663Q7.131 56.058 7.264 56.408Q7.397 56.757 7.668 56.974Q7.940 57.191 8.338 57.191Q8.713 57.191 8.989 56.974Q9.264 56.757 9.366 56.398Q9.381 56.335 9.444 56.335L9.549 56.335Q9.584 56.335 9.610 56.363Q9.635 56.390 9.635 56.429L9.635 56.453Q9.502 56.933 9.118 57.201Q8.733 57.468 8.229 57.468Q7.866 57.468 7.532 57.331Q7.198 57.195 6.938 56.945Q6.678 56.695 6.534 56.359Q6.389 56.023 6.389 55.663M10.123 55.636Q10.123 55.156 10.356 54.740Q10.588 54.324 10.998 54.074Q11.409 53.824 11.885 53.824Q12.616 53.824 13.014 54.265Q13.413 54.706 13.413 55.437Q13.413 55.542 13.319 55.566L10.870 55.566L10.870 55.636Q10.870 56.046 10.991 56.402Q11.112 56.757 11.383 56.974Q11.655 57.191 12.084 57.191Q12.448 57.191 12.745 56.962Q13.041 56.734 13.143 56.382Q13.151 56.335 13.237 56.320L13.319 56.320Q13.413 56.347 13.413 56.429Q13.413 56.437 13.405 56.468Q13.342 56.695 13.204 56.878Q13.065 57.062 12.873 57.195Q12.682 57.328 12.463 57.398Q12.245 57.468 12.006 57.468Q11.635 57.468 11.297 57.331Q10.959 57.195 10.692 56.943Q10.424 56.691 10.274 56.351Q10.123 56.011 10.123 55.636M10.877 55.328L12.838 55.328Q12.838 55.023 12.737 54.732Q12.635 54.441 12.418 54.259Q12.202 54.078 11.885 54.078Q11.584 54.078 11.354 54.265Q11.123 54.453 11 54.744Q10.877 55.035 10.877 55.328M15.784 58.941L13.928 58.941L13.928 58.648Q14.198 58.648 14.366 58.603Q14.534 58.558 14.534 58.382L14.534 54.558Q14.534 54.351 14.377 54.298Q14.221 54.245 13.928 54.245L13.928 53.949L15.151 53.863L15.151 54.328Q15.381 54.105 15.696 53.984Q16.010 53.863 16.350 53.863Q16.823 53.863 17.227 54.109Q17.631 54.355 17.864 54.771Q18.096 55.187 18.096 55.663Q18.096 56.038 17.948 56.367Q17.799 56.695 17.530 56.947Q17.260 57.199 16.916 57.333Q16.573 57.468 16.213 57.468Q15.924 57.468 15.653 57.347Q15.381 57.226 15.174 57.015L15.174 58.382Q15.174 58.558 15.342 58.603Q15.510 58.648 15.784 58.648L15.784 58.941M15.174 54.726L15.174 56.566Q15.327 56.855 15.588 57.035Q15.850 57.214 16.159 57.214Q16.444 57.214 16.666 57.076Q16.889 56.937 17.041 56.706Q17.194 56.476 17.272 56.204Q17.350 55.933 17.350 55.663Q17.350 55.331 17.225 54.974Q17.100 54.617 16.852 54.380Q16.604 54.144 16.256 54.144Q15.932 54.144 15.637 54.300Q15.342 54.456 15.174 54.726M19.245 56.429L19.245 54.238L18.541 54.238L18.541 53.984Q18.897 53.984 19.139 53.751Q19.381 53.519 19.493 53.171Q19.604 52.824 19.604 52.468L19.885 52.468L19.885 53.941L21.061 53.941L21.061 54.238L19.885 54.238L19.885 56.413Q19.885 56.734 20.004 56.962Q20.123 57.191 20.405 57.191Q20.584 57.191 20.702 57.068Q20.819 56.945 20.872 56.765Q20.924 56.585 20.924 56.413L20.924 55.941L21.206 55.941L21.206 56.429Q21.206 56.683 21.100 56.923Q20.995 57.163 20.797 57.316Q20.600 57.468 20.342 57.468Q20.026 57.468 19.774 57.345Q19.522 57.222 19.383 56.988Q19.245 56.753 19.245 56.429\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M25.388 56.429L25.388 54.238L24.685 54.238L24.685 53.984Q25.041 53.984 25.283 53.751Q25.525 53.519 25.636 53.171Q25.748 52.824 25.748 52.468L26.029 52.468L26.029 53.941L27.205 53.941L27.205 54.238L26.029 54.238L26.029 56.413Q26.029 56.734 26.148 56.962Q26.267 57.191 26.548 57.191Q26.728 57.191 26.845 57.068Q26.962 56.945 27.015 56.765Q27.068 56.585 27.068 56.413L27.068 55.941L27.349 55.941L27.349 56.429Q27.349 56.683 27.244 56.923Q27.138 57.163 26.941 57.316Q26.744 57.468 26.486 57.468Q26.170 57.468 25.918 57.345Q25.666 57.222 25.527 56.988Q25.388 56.753 25.388 56.429M28.068 55.695Q28.068 55.191 28.324 54.759Q28.580 54.328 29.015 54.076Q29.451 53.824 29.951 53.824Q30.337 53.824 30.679 53.968Q31.021 54.113 31.283 54.374Q31.545 54.636 31.687 54.972Q31.830 55.308 31.830 55.695Q31.830 56.187 31.566 56.597Q31.302 57.007 30.873 57.238Q30.443 57.468 29.951 57.468Q29.459 57.468 29.025 57.236Q28.591 57.003 28.330 56.595Q28.068 56.187 28.068 55.695M29.951 57.191Q30.408 57.191 30.660 56.968Q30.912 56.745 31 56.394Q31.087 56.042 31.087 55.597Q31.087 55.167 30.994 54.829Q30.900 54.492 30.646 54.285Q30.392 54.078 29.951 54.078Q29.302 54.078 29.058 54.494Q28.814 54.910 28.814 55.597Q28.814 56.042 28.902 56.394Q28.990 56.745 29.242 56.968Q29.494 57.191 29.951 57.191\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-31.76 6.75)\">\u003Cpath d=\"M35.250 56.558Q35.250 56.074 35.652 55.779Q36.055 55.484 36.605 55.365Q37.156 55.245 37.648 55.245L37.648 54.956Q37.648 54.730 37.533 54.523Q37.418 54.316 37.221 54.197Q37.023 54.078 36.793 54.078Q36.367 54.078 36.082 54.183Q36.152 54.210 36.199 54.265Q36.246 54.320 36.271 54.390Q36.297 54.460 36.297 54.535Q36.297 54.640 36.246 54.732Q36.195 54.824 36.103 54.874Q36.012 54.925 35.906 54.925Q35.801 54.925 35.709 54.874Q35.617 54.824 35.566 54.732Q35.516 54.640 35.516 54.535Q35.516 54.117 35.904 53.970Q36.293 53.824 36.793 53.824Q37.125 53.824 37.478 53.954Q37.832 54.085 38.060 54.339Q38.289 54.593 38.289 54.941L38.289 56.742Q38.289 56.874 38.361 56.984Q38.434 57.093 38.562 57.093Q38.687 57.093 38.756 56.988Q38.824 56.882 38.824 56.742L38.824 56.230L39.105 56.230L39.105 56.742Q39.105 56.945 38.988 57.103Q38.871 57.261 38.689 57.345Q38.508 57.429 38.305 57.429Q38.074 57.429 37.922 57.257Q37.769 57.085 37.738 56.855Q37.578 57.136 37.269 57.302Q36.961 57.468 36.609 57.468Q36.098 57.468 35.674 57.245Q35.250 57.023 35.250 56.558M35.937 56.558Q35.937 56.843 36.164 57.029Q36.391 57.214 36.684 57.214Q36.930 57.214 37.154 57.097Q37.379 56.980 37.514 56.777Q37.648 56.574 37.648 56.320L37.648 55.488Q37.383 55.488 37.098 55.542Q36.812 55.597 36.541 55.726Q36.269 55.855 36.103 56.062Q35.937 56.269 35.937 56.558M39.441 55.663Q39.441 55.167 39.691 54.742Q39.941 54.316 40.361 54.070Q40.781 53.824 41.281 53.824Q41.820 53.824 42.211 53.949Q42.602 54.074 42.602 54.488Q42.602 54.593 42.551 54.685Q42.500 54.777 42.408 54.828Q42.316 54.878 42.207 54.878Q42.102 54.878 42.010 54.828Q41.918 54.777 41.867 54.685Q41.816 54.593 41.816 54.488Q41.816 54.265 41.984 54.160Q41.762 54.101 41.289 54.101Q40.992 54.101 40.777 54.240Q40.562 54.378 40.432 54.609Q40.301 54.839 40.242 55.109Q40.184 55.378 40.184 55.663Q40.184 56.058 40.316 56.408Q40.449 56.757 40.721 56.974Q40.992 57.191 41.391 57.191Q41.766 57.191 42.041 56.974Q42.316 56.757 42.418 56.398Q42.434 56.335 42.496 56.335L42.602 56.335Q42.637 56.335 42.662 56.363Q42.687 56.390 42.687 56.429L42.687 56.453Q42.555 56.933 42.170 57.201Q41.785 57.468 41.281 57.468Q40.918 57.468 40.584 57.331Q40.250 57.195 39.990 56.945Q39.730 56.695 39.586 56.359Q39.441 56.023 39.441 55.663M43.801 56.429L43.801 54.238L43.098 54.238L43.098 53.984Q43.453 53.984 43.695 53.751Q43.937 53.519 44.049 53.171Q44.160 52.824 44.160 52.468L44.441 52.468L44.441 53.941L45.617 53.941L45.617 54.238L44.441 54.238L44.441 56.413Q44.441 56.734 44.560 56.962Q44.680 57.191 44.961 57.191Q45.141 57.191 45.258 57.068Q45.375 56.945 45.428 56.765Q45.480 56.585 45.480 56.413L45.480 55.941L45.762 55.941L45.762 56.429Q45.762 56.683 45.656 56.923Q45.551 57.163 45.353 57.316Q45.156 57.468 44.898 57.468Q44.582 57.468 44.330 57.345Q44.078 57.222 43.939 56.988Q43.801 56.753 43.801 56.429M48.340 57.390L46.562 57.390L46.562 57.093Q46.836 57.093 47.004 57.046Q47.172 56.999 47.172 56.831L47.172 54.695Q47.172 54.480 47.115 54.384Q47.059 54.288 46.945 54.267Q46.832 54.245 46.586 54.245L46.586 53.949L47.785 53.863L47.785 56.831Q47.785 56.999 47.932 57.046Q48.078 57.093 48.340 57.093L48.340 57.390M46.898 52.468Q46.898 52.277 47.033 52.146Q47.168 52.015 47.363 52.015Q47.484 52.015 47.588 52.078Q47.691 52.140 47.754 52.244Q47.816 52.347 47.816 52.468Q47.816 52.663 47.685 52.798Q47.555 52.933 47.363 52.933Q47.164 52.933 47.031 52.800Q46.898 52.667 46.898 52.468M48.840 55.695Q48.840 55.191 49.096 54.759Q49.352 54.328 49.787 54.076Q50.223 53.824 50.723 53.824Q51.109 53.824 51.451 53.968Q51.793 54.113 52.055 54.374Q52.316 54.636 52.459 54.972Q52.602 55.308 52.602 55.695Q52.602 56.187 52.338 56.597Q52.074 57.007 51.644 57.238Q51.215 57.468 50.723 57.468Q50.230 57.468 49.797 57.236Q49.363 57.003 49.102 56.595Q48.840 56.187 48.840 55.695M50.723 57.191Q51.180 57.191 51.432 56.968Q51.684 56.745 51.771 56.394Q51.859 56.042 51.859 55.597Q51.859 55.167 51.766 54.829Q51.672 54.492 51.418 54.285Q51.164 54.078 50.723 54.078Q50.074 54.078 49.830 54.494Q49.586 54.910 49.586 55.597Q49.586 56.042 49.674 56.394Q49.762 56.745 50.014 56.968Q50.266 57.191 50.723 57.191M55.016 57.390L53.160 57.390L53.160 57.093Q53.434 57.093 53.602 57.046Q53.769 56.999 53.769 56.831L53.769 54.695Q53.769 54.480 53.707 54.384Q53.644 54.288 53.525 54.267Q53.406 54.245 53.160 54.245L53.160 53.949L54.352 53.863L54.352 54.597Q54.465 54.382 54.658 54.214Q54.852 54.046 55.090 53.954Q55.328 53.863 55.582 53.863Q56.750 53.863 56.750 54.941L56.750 56.831Q56.750 56.999 56.920 57.046Q57.090 57.093 57.359 57.093L57.359 57.390L55.504 57.390L55.504 57.093Q55.777 57.093 55.945 57.046Q56.113 56.999 56.113 56.831L56.113 54.956Q56.113 54.574 55.992 54.345Q55.871 54.117 55.519 54.117Q55.207 54.117 54.953 54.279Q54.699 54.441 54.553 54.710Q54.406 54.980 54.406 55.277L54.406 56.831Q54.406 56.999 54.576 57.046Q54.746 57.093 55.016 57.093\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-68.537 34.628H56.655V6.175H-68.537Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-32.965 -29.46)\">\u003Cpath d=\"M6.148 47.890L4.293 47.890L4.293 47.593Q4.566 47.593 4.734 47.546Q4.902 47.499 4.902 47.331L4.902 45.195Q4.902 44.980 4.839 44.884Q4.777 44.788 4.658 44.767Q4.539 44.745 4.293 44.745L4.293 44.449L5.484 44.363L5.484 45.097Q5.597 44.882 5.791 44.714Q5.984 44.546 6.222 44.454Q6.460 44.363 6.714 44.363Q7.675 44.363 7.851 45.074Q8.035 44.745 8.363 44.554Q8.691 44.363 9.070 44.363Q10.246 44.363 10.246 45.441L10.246 47.331Q10.246 47.499 10.414 47.546Q10.582 47.593 10.851 47.593L10.851 47.890L8.996 47.890L8.996 47.593Q9.269 47.593 9.437 47.548Q9.605 47.503 9.605 47.331L9.605 45.456Q9.605 45.070 9.480 44.843Q9.355 44.617 9.003 44.617Q8.699 44.617 8.443 44.779Q8.187 44.941 8.039 45.210Q7.890 45.480 7.890 45.777L7.890 47.331Q7.890 47.499 8.060 47.546Q8.230 47.593 8.500 47.593L8.500 47.890L6.644 47.890L6.644 47.593Q6.918 47.593 7.085 47.546Q7.253 47.499 7.253 47.331L7.253 45.456Q7.253 45.070 7.128 44.843Q7.003 44.617 6.652 44.617Q6.347 44.617 6.091 44.779Q5.835 44.941 5.687 45.210Q5.539 45.480 5.539 45.777L5.539 47.331Q5.539 47.499 5.709 47.546Q5.878 47.593 6.148 47.593L6.148 47.890M11.296 46.195Q11.296 45.691 11.552 45.259Q11.808 44.828 12.244 44.576Q12.679 44.324 13.179 44.324Q13.566 44.324 13.908 44.468Q14.250 44.613 14.511 44.874Q14.773 45.136 14.916 45.472Q15.058 45.808 15.058 46.195Q15.058 46.687 14.794 47.097Q14.531 47.507 14.101 47.738Q13.671 47.968 13.179 47.968Q12.687 47.968 12.253 47.736Q11.820 47.503 11.558 47.095Q11.296 46.687 11.296 46.195M13.179 47.691Q13.636 47.691 13.888 47.468Q14.140 47.245 14.228 46.894Q14.316 46.542 14.316 46.097Q14.316 45.667 14.222 45.329Q14.128 44.992 13.875 44.785Q13.621 44.578 13.179 44.578Q12.531 44.578 12.287 44.994Q12.043 45.410 12.043 46.097Q12.043 46.542 12.130 46.894Q12.218 47.245 12.470 47.468Q12.722 47.691 13.179 47.691\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.965 -29.46)\">\u003Cpath d=\"M17.604 47.968Q17.123 47.968 16.715 47.724Q16.307 47.480 16.069 47.066Q15.830 46.652 15.830 46.163Q15.830 45.671 16.088 45.255Q16.346 44.839 16.778 44.601Q17.209 44.363 17.701 44.363Q18.322 44.363 18.772 44.800L18.772 43.171Q18.772 42.956 18.709 42.861Q18.647 42.765 18.529 42.744Q18.412 42.722 18.166 42.722L18.166 42.425L19.389 42.339L19.389 47.148Q19.389 47.359 19.451 47.454Q19.514 47.550 19.631 47.572Q19.748 47.593 19.998 47.593L19.998 47.890L18.748 47.968L18.748 47.484Q18.283 47.968 17.604 47.968M17.670 47.714Q18.010 47.714 18.303 47.523Q18.596 47.331 18.748 47.035L18.748 45.203Q18.600 44.929 18.338 44.773Q18.076 44.617 17.764 44.617Q17.139 44.617 16.856 45.064Q16.572 45.511 16.572 46.171Q16.572 46.816 16.824 47.265Q17.076 47.714 17.670 47.714M20.506 46.136Q20.506 45.656 20.738 45.240Q20.971 44.824 21.381 44.574Q21.791 44.324 22.268 44.324Q22.998 44.324 23.397 44.765Q23.795 45.206 23.795 45.937Q23.795 46.042 23.701 46.066L21.252 46.066L21.252 46.136Q21.252 46.546 21.373 46.902Q21.494 47.257 21.766 47.474Q22.037 47.691 22.467 47.691Q22.830 47.691 23.127 47.462Q23.424 47.234 23.526 46.882Q23.533 46.835 23.619 46.820L23.701 46.820Q23.795 46.847 23.795 46.929Q23.795 46.937 23.787 46.968Q23.725 47.195 23.586 47.378Q23.447 47.562 23.256 47.695Q23.065 47.828 22.846 47.898Q22.627 47.968 22.389 47.968Q22.018 47.968 21.680 47.831Q21.342 47.695 21.074 47.443Q20.807 47.191 20.656 46.851Q20.506 46.511 20.506 46.136M21.260 45.828L23.221 45.828Q23.221 45.523 23.119 45.232Q23.018 44.941 22.801 44.759Q22.584 44.578 22.268 44.578Q21.967 44.578 21.736 44.765Q21.506 44.953 21.383 45.244Q21.260 45.535 21.260 45.828M26.197 47.890L24.365 47.890L24.365 47.593Q24.639 47.593 24.807 47.546Q24.975 47.499 24.975 47.331L24.975 43.171Q24.975 42.956 24.912 42.861Q24.850 42.765 24.731 42.744Q24.611 42.722 24.365 42.722L24.365 42.425L25.588 42.339L25.588 47.331Q25.588 47.499 25.756 47.546Q25.924 47.593 26.197 47.593L26.197 47.890M28.756 46.441L26.502 46.441L26.502 45.890L28.756 45.890L28.756 46.441M30.389 47.890L30.108 47.890L30.108 43.171Q30.108 42.956 30.045 42.861Q29.983 42.765 29.865 42.744Q29.748 42.722 29.502 42.722L29.502 42.425L30.725 42.339L30.725 44.828Q31.201 44.363 31.901 44.363Q32.381 44.363 32.789 44.607Q33.197 44.851 33.434 45.265Q33.670 45.679 33.670 46.163Q33.670 46.538 33.522 46.867Q33.373 47.195 33.104 47.447Q32.834 47.699 32.490 47.833Q32.147 47.968 31.787 47.968Q31.467 47.968 31.168 47.820Q30.869 47.671 30.662 47.410L30.389 47.890M30.748 45.218L30.748 47.058Q30.901 47.355 31.160 47.535Q31.420 47.714 31.733 47.714Q32.158 47.714 32.426 47.495Q32.694 47.277 32.809 46.931Q32.924 46.585 32.924 46.163Q32.924 45.515 32.676 45.066Q32.428 44.617 31.830 44.617Q31.494 44.617 31.205 44.775Q30.916 44.933 30.748 45.218M34.291 47.058Q34.291 46.574 34.694 46.279Q35.096 45.984 35.647 45.865Q36.197 45.745 36.690 45.745L36.690 45.456Q36.690 45.230 36.574 45.023Q36.459 44.816 36.262 44.697Q36.065 44.578 35.834 44.578Q35.408 44.578 35.123 44.683Q35.194 44.710 35.240 44.765Q35.287 44.820 35.313 44.890Q35.338 44.960 35.338 45.035Q35.338 45.140 35.287 45.232Q35.236 45.324 35.145 45.374Q35.053 45.425 34.947 45.425Q34.842 45.425 34.750 45.374Q34.658 45.324 34.608 45.232Q34.557 45.140 34.557 45.035Q34.557 44.617 34.945 44.470Q35.334 44.324 35.834 44.324Q36.166 44.324 36.520 44.454Q36.873 44.585 37.102 44.839Q37.330 45.093 37.330 45.441L37.330 47.242Q37.330 47.374 37.403 47.484Q37.475 47.593 37.604 47.593Q37.729 47.593 37.797 47.488Q37.865 47.382 37.865 47.242L37.865 46.730L38.147 46.730L38.147 47.242Q38.147 47.445 38.029 47.603Q37.912 47.761 37.731 47.845Q37.549 47.929 37.346 47.929Q37.115 47.929 36.963 47.757Q36.811 47.585 36.779 47.355Q36.619 47.636 36.311 47.802Q36.002 47.968 35.651 47.968Q35.139 47.968 34.715 47.745Q34.291 47.523 34.291 47.058M34.979 47.058Q34.979 47.343 35.205 47.529Q35.432 47.714 35.725 47.714Q35.971 47.714 36.195 47.597Q36.420 47.480 36.555 47.277Q36.690 47.074 36.690 46.820L36.690 45.988Q36.424 45.988 36.139 46.042Q35.854 46.097 35.582 46.226Q35.311 46.355 35.145 46.562Q34.979 46.769 34.979 47.058M38.483 47.882L38.483 46.660Q38.483 46.632 38.514 46.601Q38.545 46.570 38.569 46.570L38.674 46.570Q38.744 46.570 38.760 46.632Q38.822 46.953 38.961 47.193Q39.100 47.433 39.332 47.574Q39.565 47.714 39.873 47.714Q40.111 47.714 40.320 47.654Q40.529 47.593 40.666 47.445Q40.803 47.296 40.803 47.050Q40.803 46.796 40.592 46.630Q40.381 46.464 40.111 46.410L39.490 46.296Q39.084 46.218 38.783 45.962Q38.483 45.706 38.483 45.331Q38.483 44.964 38.684 44.742Q38.885 44.519 39.209 44.421Q39.533 44.324 39.873 44.324Q40.338 44.324 40.635 44.531L40.858 44.347Q40.881 44.324 40.912 44.324L40.963 44.324Q40.994 44.324 41.022 44.351Q41.049 44.378 41.049 44.410L41.049 45.394Q41.049 45.425 41.024 45.454Q40.998 45.484 40.963 45.484L40.858 45.484Q40.822 45.484 40.795 45.456Q40.768 45.429 40.768 45.394Q40.768 44.995 40.516 44.775Q40.264 44.554 39.865 44.554Q39.510 44.554 39.227 44.677Q38.944 44.800 38.944 45.105Q38.944 45.324 39.145 45.456Q39.346 45.589 39.592 45.632L40.217 45.745Q40.647 45.835 40.955 46.132Q41.264 46.429 41.264 46.843Q41.264 47.413 40.865 47.691Q40.467 47.968 39.873 47.968Q39.322 47.968 38.971 47.632L38.674 47.945Q38.651 47.968 38.615 47.968L38.569 47.968Q38.545 47.968 38.514 47.937Q38.483 47.906 38.483 47.882M41.791 46.136Q41.791 45.656 42.024 45.240Q42.256 44.824 42.666 44.574Q43.076 44.324 43.553 44.324Q44.283 44.324 44.682 44.765Q45.080 45.206 45.080 45.937Q45.080 46.042 44.986 46.066L42.537 46.066L42.537 46.136Q42.537 46.546 42.658 46.902Q42.779 47.257 43.051 47.474Q43.322 47.691 43.752 47.691Q44.115 47.691 44.412 47.462Q44.709 47.234 44.811 46.882Q44.819 46.835 44.904 46.820L44.986 46.820Q45.080 46.847 45.080 46.929Q45.080 46.937 45.072 46.968Q45.010 47.195 44.871 47.378Q44.733 47.562 44.541 47.695Q44.350 47.828 44.131 47.898Q43.912 47.968 43.674 47.968Q43.303 47.968 42.965 47.831Q42.627 47.695 42.360 47.443Q42.092 47.191 41.942 46.851Q41.791 46.511 41.791 46.136M42.545 45.828L44.506 45.828Q44.506 45.523 44.404 45.232Q44.303 44.941 44.086 44.759Q43.869 44.578 43.553 44.578Q43.252 44.578 43.022 44.765Q42.791 44.953 42.668 45.244Q42.545 45.535 42.545 45.828M47.385 47.968Q46.904 47.968 46.496 47.724Q46.088 47.480 45.850 47.066Q45.611 46.652 45.611 46.163Q45.611 45.671 45.869 45.255Q46.127 44.839 46.559 44.601Q46.990 44.363 47.483 44.363Q48.104 44.363 48.553 44.800L48.553 43.171Q48.553 42.956 48.490 42.861Q48.428 42.765 48.311 42.744Q48.194 42.722 47.947 42.722L47.947 42.425L49.170 42.339L49.170 47.148Q49.170 47.359 49.233 47.454Q49.295 47.550 49.412 47.572Q49.529 47.593 49.779 47.593L49.779 47.890L48.529 47.968L48.529 47.484Q48.065 47.968 47.385 47.968M47.451 47.714Q47.791 47.714 48.084 47.523Q48.377 47.331 48.529 47.035L48.529 45.203Q48.381 44.929 48.119 44.773Q47.858 44.617 47.545 44.617Q46.920 44.617 46.637 45.064Q46.354 45.511 46.354 46.171Q46.354 46.816 46.606 47.265Q46.858 47.714 47.451 47.714\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.965 -29.46)\">\u003Cpath d=\"M-5.605 56.558Q-5.605 56.074-5.203 55.779Q-4.800 55.484-4.250 55.365Q-3.699 55.245-3.207 55.245L-3.207 54.956Q-3.207 54.730-3.322 54.523Q-3.437 54.316-3.634 54.197Q-3.832 54.078-4.062 54.078Q-4.488 54.078-4.773 54.183Q-4.703 54.210-4.656 54.265Q-4.609 54.320-4.584 54.390Q-4.558 54.460-4.558 54.535Q-4.558 54.640-4.609 54.732Q-4.660 54.824-4.752 54.874Q-4.843 54.925-4.949 54.925Q-5.054 54.925-5.146 54.874Q-5.238 54.824-5.289 54.732Q-5.339 54.640-5.339 54.535Q-5.339 54.117-4.951 53.970Q-4.562 53.824-4.062 53.824Q-3.730 53.824-3.377 53.954Q-3.023 54.085-2.795 54.339Q-2.566 54.593-2.566 54.941L-2.566 56.742Q-2.566 56.874-2.494 56.984Q-2.421 57.093-2.293 57.093Q-2.168 57.093-2.099 56.988Q-2.031 56.882-2.031 56.742L-2.031 56.230L-1.750 56.230L-1.750 56.742Q-1.750 56.945-1.867 57.103Q-1.984 57.261-2.166 57.345Q-2.347 57.429-2.550 57.429Q-2.781 57.429-2.933 57.257Q-3.086 57.085-3.117 56.855Q-3.277 57.136-3.586 57.302Q-3.894 57.468-4.246 57.468Q-4.757 57.468-5.181 57.245Q-5.605 57.023-5.605 56.558M-4.918 56.558Q-4.918 56.843-4.691 57.029Q-4.464 57.214-4.171 57.214Q-3.925 57.214-3.701 57.097Q-3.476 56.980-3.341 56.777Q-3.207 56.574-3.207 56.320L-3.207 55.488Q-3.472 55.488-3.757 55.542Q-4.043 55.597-4.314 55.726Q-4.586 55.855-4.752 56.062Q-4.918 56.269-4.918 56.558M0.360 57.468Q-0.121 57.468-0.529 57.224Q-0.937 56.980-1.175 56.566Q-1.414 56.152-1.414 55.663Q-1.414 55.171-1.156 54.755Q-0.898 54.339-0.466 54.101Q-0.035 53.863 0.457 53.863Q1.079 53.863 1.528 54.300L1.528 52.671Q1.528 52.456 1.465 52.361Q1.403 52.265 1.286 52.244Q1.168 52.222 0.922 52.222L0.922 51.925L2.145 51.839L2.145 56.648Q2.145 56.859 2.207 56.954Q2.270 57.050 2.387 57.072Q2.504 57.093 2.754 57.093L2.754 57.390L1.504 57.468L1.504 56.984Q1.039 57.468 0.360 57.468M0.426 57.214Q0.766 57.214 1.059 57.023Q1.352 56.831 1.504 56.535L1.504 54.703Q1.356 54.429 1.094 54.273Q0.832 54.117 0.520 54.117Q-0.105 54.117-0.388 54.564Q-0.671 55.011-0.671 55.671Q-0.671 56.316-0.420 56.765Q-0.168 57.214 0.426 57.214M5.079 57.468Q4.598 57.468 4.190 57.224Q3.782 56.980 3.543 56.566Q3.305 56.152 3.305 55.663Q3.305 55.171 3.563 54.755Q3.821 54.339 4.252 54.101Q4.684 53.863 5.176 53.863Q5.797 53.863 6.247 54.300L6.247 52.671Q6.247 52.456 6.184 52.361Q6.122 52.265 6.004 52.244Q5.887 52.222 5.641 52.222L5.641 51.925L6.864 51.839L6.864 56.648Q6.864 56.859 6.926 56.954Q6.989 57.050 7.106 57.072Q7.223 57.093 7.473 57.093L7.473 57.390L6.223 57.468L6.223 56.984Q5.758 57.468 5.079 57.468M5.145 57.214Q5.485 57.214 5.778 57.023Q6.071 56.831 6.223 56.535L6.223 54.703Q6.075 54.429 5.813 54.273Q5.551 54.117 5.239 54.117Q4.614 54.117 4.330 54.564Q4.047 55.011 4.047 55.671Q4.047 56.316 4.299 56.765Q4.551 57.214 5.145 57.214\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.965 -29.46)\">\u003Cpath d=\"M12.685 57.390L10.907 57.390L10.907 57.093Q11.181 57.093 11.349 57.046Q11.517 56.999 11.517 56.831L11.517 54.695Q11.517 54.480 11.460 54.384Q11.403 54.288 11.290 54.267Q11.177 54.245 10.931 54.245L10.931 53.949L12.130 53.863L12.130 56.831Q12.130 56.999 12.276 57.046Q12.423 57.093 12.685 57.093L12.685 57.390M11.243 52.468Q11.243 52.277 11.378 52.146Q11.513 52.015 11.708 52.015Q11.829 52.015 11.933 52.078Q12.036 52.140 12.099 52.244Q12.161 52.347 12.161 52.468Q12.161 52.663 12.030 52.798Q11.899 52.933 11.708 52.933Q11.509 52.933 11.376 52.800Q11.243 52.667 11.243 52.468M15.114 57.390L13.259 57.390L13.259 57.093Q13.532 57.093 13.700 57.046Q13.868 56.999 13.868 56.831L13.868 54.695Q13.868 54.480 13.806 54.384Q13.743 54.288 13.624 54.267Q13.505 54.245 13.259 54.245L13.259 53.949L14.450 53.863L14.450 54.597Q14.564 54.382 14.757 54.214Q14.950 54.046 15.189 53.954Q15.427 53.863 15.681 53.863Q16.849 53.863 16.849 54.941L16.849 56.831Q16.849 56.999 17.019 57.046Q17.189 57.093 17.458 57.093L17.458 57.390L15.603 57.390L15.603 57.093Q15.876 57.093 16.044 57.046Q16.212 56.999 16.212 56.831L16.212 54.956Q16.212 54.574 16.091 54.345Q15.970 54.117 15.618 54.117Q15.306 54.117 15.052 54.279Q14.798 54.441 14.651 54.710Q14.505 54.980 14.505 55.277L14.505 56.831Q14.505 56.999 14.675 57.046Q14.845 57.093 15.114 57.093\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.965 -29.46)\">\u003Cpath d=\"M18.298 56.429L18.298 54.238L17.595 54.238L17.595 53.984Q17.951 53.984 18.193 53.751Q18.435 53.519 18.546 53.171Q18.658 52.824 18.658 52.468L18.939 52.468L18.939 53.941L20.115 53.941L20.115 54.238L18.939 54.238L18.939 56.413Q18.939 56.734 19.058 56.962Q19.177 57.191 19.458 57.191Q19.638 57.191 19.755 57.068Q19.872 56.945 19.925 56.765Q19.978 56.585 19.978 56.413L19.978 55.941L20.259 55.941L20.259 56.429Q20.259 56.683 20.154 56.923Q20.048 57.163 19.851 57.316Q19.654 57.468 19.396 57.468Q19.080 57.468 18.828 57.345Q18.576 57.222 18.437 56.988Q18.298 56.753 18.298 56.429M20.978 55.636Q20.978 55.156 21.210 54.740Q21.443 54.324 21.853 54.074Q22.263 53.824 22.740 53.824Q23.470 53.824 23.869 54.265Q24.267 54.706 24.267 55.437Q24.267 55.542 24.173 55.566L21.724 55.566L21.724 55.636Q21.724 56.046 21.845 56.402Q21.966 56.757 22.238 56.974Q22.509 57.191 22.939 57.191Q23.302 57.191 23.599 56.962Q23.896 56.734 23.997 56.382Q24.005 56.335 24.091 56.320L24.173 56.320Q24.267 56.347 24.267 56.429Q24.267 56.437 24.259 56.468Q24.197 56.695 24.058 56.878Q23.919 57.062 23.728 57.195Q23.537 57.328 23.318 57.398Q23.099 57.468 22.861 57.468Q22.490 57.468 22.152 57.331Q21.814 57.195 21.546 56.943Q21.279 56.691 21.128 56.351Q20.978 56.011 20.978 55.636M21.732 55.328L23.693 55.328Q23.693 55.023 23.591 54.732Q23.490 54.441 23.273 54.259Q23.056 54.078 22.740 54.078Q22.439 54.078 22.208 54.265Q21.978 54.453 21.855 54.744Q21.732 55.035 21.732 55.328M26.763 57.390L24.783 57.390L24.783 57.093Q25.052 57.093 25.220 57.048Q25.388 57.003 25.388 56.831L25.388 54.695Q25.388 54.480 25.326 54.384Q25.263 54.288 25.146 54.267Q25.029 54.245 24.783 54.245L24.783 53.949L25.951 53.863L25.951 54.648Q26.029 54.437 26.181 54.251Q26.333 54.066 26.533 53.964Q26.732 53.863 26.958 53.863Q27.205 53.863 27.396 54.007Q27.587 54.152 27.587 54.382Q27.587 54.538 27.482 54.648Q27.376 54.757 27.220 54.757Q27.064 54.757 26.955 54.648Q26.845 54.538 26.845 54.382Q26.845 54.222 26.951 54.117Q26.626 54.117 26.412 54.345Q26.197 54.574 26.101 54.913Q26.005 55.253 26.005 55.558L26.005 56.831Q26.005 56.999 26.232 57.046Q26.458 57.093 26.763 57.093L26.763 57.390M29.997 57.390L28.142 57.390L28.142 57.093Q28.415 57.093 28.583 57.046Q28.751 56.999 28.751 56.831L28.751 54.695Q28.751 54.480 28.689 54.384Q28.626 54.288 28.507 54.267Q28.388 54.245 28.142 54.245L28.142 53.949L29.333 53.863L29.333 54.597Q29.447 54.382 29.640 54.214Q29.833 54.046 30.072 53.954Q30.310 53.863 30.564 53.863Q31.732 53.863 31.732 54.941L31.732 56.831Q31.732 56.999 31.902 57.046Q32.072 57.093 32.341 57.093L32.341 57.390L30.486 57.390L30.486 57.093Q30.759 57.093 30.927 57.046Q31.095 56.999 31.095 56.831L31.095 54.956Q31.095 54.574 30.974 54.345Q30.853 54.117 30.501 54.117Q30.189 54.117 29.935 54.279Q29.681 54.441 29.535 54.710Q29.388 54.980 29.388 55.277L29.388 56.831Q29.388 56.999 29.558 57.046Q29.728 57.093 29.997 57.093L29.997 57.390M32.884 56.558Q32.884 56.074 33.287 55.779Q33.689 55.484 34.240 55.365Q34.790 55.245 35.283 55.245L35.283 54.956Q35.283 54.730 35.167 54.523Q35.052 54.316 34.855 54.197Q34.658 54.078 34.427 54.078Q34.001 54.078 33.716 54.183Q33.787 54.210 33.833 54.265Q33.880 54.320 33.906 54.390Q33.931 54.460 33.931 54.535Q33.931 54.640 33.880 54.732Q33.830 54.824 33.738 54.874Q33.646 54.925 33.540 54.925Q33.435 54.925 33.343 54.874Q33.251 54.824 33.201 54.732Q33.150 54.640 33.150 54.535Q33.150 54.117 33.539 53.970Q33.927 53.824 34.427 53.824Q34.759 53.824 35.113 53.954Q35.466 54.085 35.695 54.339Q35.923 54.593 35.923 54.941L35.923 56.742Q35.923 56.874 35.996 56.984Q36.068 57.093 36.197 57.093Q36.322 57.093 36.390 56.988Q36.458 56.882 36.458 56.742L36.458 56.230L36.740 56.230L36.740 56.742Q36.740 56.945 36.623 57.103Q36.505 57.261 36.324 57.345Q36.142 57.429 35.939 57.429Q35.708 57.429 35.556 57.257Q35.404 57.085 35.373 56.855Q35.212 57.136 34.904 57.302Q34.595 57.468 34.244 57.468Q33.732 57.468 33.308 57.245Q32.884 57.023 32.884 56.558M33.572 56.558Q33.572 56.843 33.798 57.029Q34.025 57.214 34.318 57.214Q34.564 57.214 34.789 57.097Q35.013 56.980 35.148 56.777Q35.283 56.574 35.283 56.320L35.283 55.488Q35.017 55.488 34.732 55.542Q34.447 55.597 34.175 55.726Q33.904 55.855 33.738 56.062Q33.572 56.269 33.572 56.558M38.947 57.390L37.115 57.390L37.115 57.093Q37.388 57.093 37.556 57.046Q37.724 56.999 37.724 56.831L37.724 52.671Q37.724 52.456 37.662 52.361Q37.599 52.265 37.480 52.244Q37.361 52.222 37.115 52.222L37.115 51.925L38.337 51.839L38.337 56.831Q38.337 56.999 38.505 57.046Q38.673 57.093 38.947 57.093\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.965 -29.46)\">\u003Cpath d=\"M42.279 57.382L42.279 56.160Q42.279 56.132 42.310 56.101Q42.342 56.070 42.365 56.070L42.471 56.070Q42.541 56.070 42.557 56.132Q42.619 56.453 42.758 56.693Q42.896 56.933 43.129 57.074Q43.361 57.214 43.670 57.214Q43.908 57.214 44.117 57.154Q44.326 57.093 44.463 56.945Q44.600 56.796 44.600 56.550Q44.600 56.296 44.389 56.130Q44.178 55.964 43.908 55.910L43.287 55.796Q42.881 55.718 42.580 55.462Q42.279 55.206 42.279 54.831Q42.279 54.464 42.480 54.242Q42.682 54.019 43.006 53.921Q43.330 53.824 43.670 53.824Q44.135 53.824 44.432 54.031L44.654 53.847Q44.678 53.824 44.709 53.824L44.760 53.824Q44.791 53.824 44.818 53.851Q44.846 53.878 44.846 53.910L44.846 54.894Q44.846 54.925 44.820 54.954Q44.795 54.984 44.760 54.984L44.654 54.984Q44.619 54.984 44.592 54.956Q44.564 54.929 44.564 54.894Q44.564 54.495 44.312 54.275Q44.060 54.054 43.662 54.054Q43.307 54.054 43.023 54.177Q42.740 54.300 42.740 54.605Q42.740 54.824 42.941 54.956Q43.143 55.089 43.389 55.132L44.014 55.245Q44.443 55.335 44.752 55.632Q45.060 55.929 45.060 56.343Q45.060 56.913 44.662 57.191Q44.264 57.468 43.670 57.468Q43.119 57.468 42.768 57.132L42.471 57.445Q42.447 57.468 42.412 57.468L42.365 57.468Q42.342 57.468 42.310 57.437Q42.279 57.406 42.279 57.382M46.213 56.429L46.213 54.238L45.510 54.238L45.510 53.984Q45.865 53.984 46.107 53.751Q46.350 53.519 46.461 53.171Q46.572 52.824 46.572 52.468L46.853 52.468L46.853 53.941L48.029 53.941L48.029 54.238L46.853 54.238L46.853 56.413Q46.853 56.734 46.973 56.962Q47.092 57.191 47.373 57.191Q47.553 57.191 47.670 57.068Q47.787 56.945 47.840 56.765Q47.893 56.585 47.893 56.413L47.893 55.941L48.174 55.941L48.174 56.429Q48.174 56.683 48.068 56.923Q47.963 57.163 47.766 57.316Q47.568 57.468 47.310 57.468Q46.994 57.468 46.742 57.345Q46.490 57.222 46.352 56.988Q46.213 56.753 46.213 56.429M48.990 56.558Q48.990 56.074 49.393 55.779Q49.795 55.484 50.346 55.365Q50.896 55.245 51.389 55.245L51.389 54.956Q51.389 54.730 51.273 54.523Q51.158 54.316 50.961 54.197Q50.764 54.078 50.533 54.078Q50.107 54.078 49.822 54.183Q49.893 54.210 49.939 54.265Q49.986 54.320 50.012 54.390Q50.037 54.460 50.037 54.535Q50.037 54.640 49.986 54.732Q49.935 54.824 49.844 54.874Q49.752 54.925 49.646 54.925Q49.541 54.925 49.449 54.874Q49.357 54.824 49.307 54.732Q49.256 54.640 49.256 54.535Q49.256 54.117 49.644 53.970Q50.033 53.824 50.533 53.824Q50.865 53.824 51.219 53.954Q51.572 54.085 51.801 54.339Q52.029 54.593 52.029 54.941L52.029 56.742Q52.029 56.874 52.102 56.984Q52.174 57.093 52.303 57.093Q52.428 57.093 52.496 56.988Q52.564 56.882 52.564 56.742L52.564 56.230L52.846 56.230L52.846 56.742Q52.846 56.945 52.728 57.103Q52.611 57.261 52.430 57.345Q52.248 57.429 52.045 57.429Q51.814 57.429 51.662 57.257Q51.510 57.085 51.478 56.855Q51.318 57.136 51.010 57.302Q50.701 57.468 50.350 57.468Q49.838 57.468 49.414 57.245Q48.990 57.023 48.990 56.558M49.678 56.558Q49.678 56.843 49.904 57.029Q50.131 57.214 50.424 57.214Q50.670 57.214 50.894 57.097Q51.119 56.980 51.254 56.777Q51.389 56.574 51.389 56.320L51.389 55.488Q51.123 55.488 50.838 55.542Q50.553 55.597 50.281 55.726Q50.010 55.855 49.844 56.062Q49.678 56.269 49.678 56.558M53.764 56.429L53.764 54.238L53.060 54.238L53.060 53.984Q53.416 53.984 53.658 53.751Q53.900 53.519 54.012 53.171Q54.123 52.824 54.123 52.468L54.404 52.468L54.404 53.941L55.580 53.941L55.580 54.238L54.404 54.238L54.404 56.413Q54.404 56.734 54.523 56.962Q54.643 57.191 54.924 57.191Q55.103 57.191 55.221 57.068Q55.338 56.945 55.391 56.765Q55.443 56.585 55.443 56.413L55.443 55.941L55.725 55.941L55.725 56.429Q55.725 56.683 55.619 56.923Q55.514 57.163 55.316 57.316Q55.119 57.468 54.861 57.468Q54.545 57.468 54.293 57.345Q54.041 57.222 53.902 56.988Q53.764 56.753 53.764 56.429M56.443 55.636Q56.443 55.156 56.676 54.740Q56.908 54.324 57.318 54.074Q57.728 53.824 58.205 53.824Q58.935 53.824 59.334 54.265Q59.732 54.706 59.732 55.437Q59.732 55.542 59.639 55.566L57.189 55.566L57.189 55.636Q57.189 56.046 57.310 56.402Q57.432 56.757 57.703 56.974Q57.975 57.191 58.404 57.191Q58.768 57.191 59.064 56.962Q59.361 56.734 59.463 56.382Q59.471 56.335 59.557 56.320L59.639 56.320Q59.732 56.347 59.732 56.429Q59.732 56.437 59.725 56.468Q59.662 56.695 59.523 56.878Q59.385 57.062 59.193 57.195Q59.002 57.328 58.783 57.398Q58.564 57.468 58.326 57.468Q57.955 57.468 57.617 57.331Q57.279 57.195 57.012 56.943Q56.744 56.691 56.594 56.351Q56.443 56.011 56.443 55.636M57.197 55.328L59.158 55.328Q59.158 55.023 59.057 54.732Q58.955 54.441 58.738 54.259Q58.521 54.078 58.205 54.078Q57.904 54.078 57.674 54.265Q57.443 54.453 57.320 54.744Q57.197 55.035 57.197 55.328\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-68.537-2.361H56.655v-28.453H-68.537Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M16.732 48.499Q16.732 48.218 16.943 48.007Q17.154 47.796 17.439 47.706Q17.283 47.581 17.205 47.392Q17.127 47.203 17.127 47.003Q17.127 46.648 17.357 46.355Q16.990 46.015 16.990 45.546Q16.990 45.195 17.193 44.925Q17.396 44.656 17.717 44.509Q18.037 44.363 18.381 44.363Q18.900 44.363 19.271 44.644Q19.635 44.273 20.181 44.273Q20.361 44.273 20.488 44.400Q20.615 44.527 20.615 44.706Q20.615 44.812 20.537 44.890Q20.459 44.968 20.349 44.968Q20.240 44.968 20.164 44.892Q20.088 44.816 20.088 44.706Q20.088 44.605 20.127 44.554Q20.135 44.546 20.139 44.540Q20.142 44.535 20.142 44.531Q19.767 44.531 19.447 44.785Q19.767 45.124 19.767 45.546Q19.767 45.816 19.650 46.033Q19.533 46.249 19.328 46.408Q19.123 46.566 18.881 46.648Q18.639 46.730 18.381 46.730Q18.162 46.730 17.949 46.671Q17.736 46.613 17.541 46.492Q17.447 46.632 17.447 46.812Q17.447 47.019 17.584 47.171Q17.721 47.324 17.928 47.324L18.623 47.324Q19.111 47.324 19.523 47.408Q19.935 47.492 20.215 47.749Q20.494 48.007 20.494 48.499Q20.494 48.863 20.174 49.095Q19.853 49.328 19.412 49.429Q18.971 49.531 18.615 49.531Q18.260 49.531 17.816 49.429Q17.373 49.328 17.053 49.095Q16.732 48.863 16.732 48.499M17.236 48.499Q17.236 48.695 17.381 48.843Q17.525 48.992 17.738 49.081Q17.951 49.171 18.191 49.218Q18.431 49.265 18.615 49.265Q18.857 49.265 19.187 49.187Q19.517 49.109 19.754 48.935Q19.990 48.761 19.990 48.499Q19.990 48.093 19.580 47.984Q19.170 47.874 18.607 47.874L17.928 47.874Q17.658 47.874 17.447 48.052Q17.236 48.230 17.236 48.499M18.381 46.464Q19.103 46.464 19.103 45.546Q19.103 44.624 18.381 44.624Q17.654 44.624 17.654 45.546Q17.654 46.464 18.381 46.464M20.978 46.195Q20.978 45.691 21.234 45.259Q21.490 44.828 21.926 44.576Q22.361 44.324 22.861 44.324Q23.248 44.324 23.590 44.468Q23.931 44.613 24.193 44.874Q24.455 45.136 24.598 45.472Q24.740 45.808 24.740 46.195Q24.740 46.687 24.476 47.097Q24.213 47.507 23.783 47.738Q23.353 47.968 22.861 47.968Q22.369 47.968 21.935 47.736Q21.502 47.503 21.240 47.095Q20.978 46.687 20.978 46.195M22.861 47.691Q23.318 47.691 23.570 47.468Q23.822 47.245 23.910 46.894Q23.998 46.542 23.998 46.097Q23.998 45.667 23.904 45.329Q23.810 44.992 23.556 44.785Q23.303 44.578 22.861 44.578Q22.213 44.578 21.969 44.994Q21.724 45.410 21.724 46.097Q21.724 46.542 21.812 46.894Q21.900 47.245 22.152 47.468Q22.404 47.691 22.861 47.691M25.322 47.058Q25.322 46.574 25.724 46.279Q26.127 45.984 26.678 45.865Q27.228 45.745 27.721 45.745L27.721 45.456Q27.721 45.230 27.605 45.023Q27.490 44.816 27.293 44.697Q27.096 44.578 26.865 44.578Q26.439 44.578 26.154 44.683Q26.224 44.710 26.271 44.765Q26.318 44.820 26.344 44.890Q26.369 44.960 26.369 45.035Q26.369 45.140 26.318 45.232Q26.267 45.324 26.176 45.374Q26.084 45.425 25.978 45.425Q25.873 45.425 25.781 45.374Q25.689 45.324 25.639 45.232Q25.588 45.140 25.588 45.035Q25.588 44.617 25.976 44.470Q26.365 44.324 26.865 44.324Q27.197 44.324 27.551 44.454Q27.904 44.585 28.133 44.839Q28.361 45.093 28.361 45.441L28.361 47.242Q28.361 47.374 28.433 47.484Q28.506 47.593 28.635 47.593Q28.760 47.593 28.828 47.488Q28.896 47.382 28.896 47.242L28.896 46.730L29.178 46.730L29.178 47.242Q29.178 47.445 29.060 47.603Q28.943 47.761 28.762 47.845Q28.580 47.929 28.377 47.929Q28.146 47.929 27.994 47.757Q27.842 47.585 27.810 47.355Q27.650 47.636 27.342 47.802Q27.033 47.968 26.681 47.968Q26.170 47.968 25.746 47.745Q25.322 47.523 25.322 47.058M26.010 47.058Q26.010 47.343 26.236 47.529Q26.463 47.714 26.756 47.714Q27.002 47.714 27.226 47.597Q27.451 47.480 27.586 47.277Q27.721 47.074 27.721 46.820L27.721 45.988Q27.455 45.988 27.170 46.042Q26.885 46.097 26.613 46.226Q26.342 46.355 26.176 46.562Q26.010 46.769 26.010 47.058M31.385 47.890L29.553 47.890L29.553 47.593Q29.826 47.593 29.994 47.546Q30.162 47.499 30.162 47.331L30.162 43.171Q30.162 42.956 30.099 42.861Q30.037 42.765 29.918 42.744Q29.799 42.722 29.553 42.722L29.553 42.425L30.775 42.339L30.775 47.331Q30.775 47.499 30.943 47.546Q31.111 47.593 31.385 47.593L31.385 47.890M33.943 46.441L31.689 46.441L31.689 45.890L33.943 45.890L33.943 46.441M35.576 47.890L35.295 47.890L35.295 43.171Q35.295 42.956 35.232 42.861Q35.170 42.765 35.053 42.744Q34.935 42.722 34.689 42.722L34.689 42.425L35.912 42.339L35.912 44.828Q36.389 44.363 37.088 44.363Q37.568 44.363 37.976 44.607Q38.385 44.851 38.621 45.265Q38.857 45.679 38.857 46.163Q38.857 46.538 38.709 46.867Q38.560 47.195 38.291 47.447Q38.021 47.699 37.678 47.833Q37.334 47.968 36.974 47.968Q36.654 47.968 36.355 47.820Q36.056 47.671 35.849 47.410L35.576 47.890M35.935 45.218L35.935 47.058Q36.088 47.355 36.348 47.535Q36.607 47.714 36.920 47.714Q37.346 47.714 37.613 47.495Q37.881 47.277 37.996 46.931Q38.111 46.585 38.111 46.163Q38.111 45.515 37.863 45.066Q37.615 44.617 37.017 44.617Q36.681 44.617 36.392 44.775Q36.103 44.933 35.935 45.218M39.478 47.058Q39.478 46.574 39.881 46.279Q40.283 45.984 40.834 45.865Q41.385 45.745 41.877 45.745L41.877 45.456Q41.877 45.230 41.762 45.023Q41.646 44.816 41.449 44.697Q41.252 44.578 41.021 44.578Q40.596 44.578 40.310 44.683Q40.381 44.710 40.428 44.765Q40.474 44.820 40.500 44.890Q40.525 44.960 40.525 45.035Q40.525 45.140 40.474 45.232Q40.424 45.324 40.332 45.374Q40.240 45.425 40.135 45.425Q40.029 45.425 39.937 45.374Q39.846 45.324 39.795 45.232Q39.744 45.140 39.744 45.035Q39.744 44.617 40.133 44.470Q40.521 44.324 41.021 44.324Q41.353 44.324 41.707 44.454Q42.060 44.585 42.289 44.839Q42.517 45.093 42.517 45.441L42.517 47.242Q42.517 47.374 42.590 47.484Q42.662 47.593 42.791 47.593Q42.916 47.593 42.984 47.488Q43.053 47.382 43.053 47.242L43.053 46.730L43.334 46.730L43.334 47.242Q43.334 47.445 43.217 47.603Q43.099 47.761 42.918 47.845Q42.736 47.929 42.533 47.929Q42.303 47.929 42.150 47.757Q41.998 47.585 41.967 47.355Q41.806 47.636 41.498 47.802Q41.189 47.968 40.838 47.968Q40.326 47.968 39.902 47.745Q39.478 47.523 39.478 47.058M40.166 47.058Q40.166 47.343 40.392 47.529Q40.619 47.714 40.912 47.714Q41.158 47.714 41.383 47.597Q41.607 47.480 41.742 47.277Q41.877 47.074 41.877 46.820L41.877 45.988Q41.611 45.988 41.326 46.042Q41.041 46.097 40.769 46.226Q40.498 46.355 40.332 46.562Q40.166 46.769 40.166 47.058M43.670 47.882L43.670 46.660Q43.670 46.632 43.701 46.601Q43.732 46.570 43.756 46.570L43.861 46.570Q43.931 46.570 43.947 46.632Q44.010 46.953 44.148 47.193Q44.287 47.433 44.519 47.574Q44.752 47.714 45.060 47.714Q45.299 47.714 45.508 47.654Q45.717 47.593 45.853 47.445Q45.990 47.296 45.990 47.050Q45.990 46.796 45.779 46.630Q45.568 46.464 45.299 46.410L44.678 46.296Q44.271 46.218 43.971 45.962Q43.670 45.706 43.670 45.331Q43.670 44.964 43.871 44.742Q44.072 44.519 44.396 44.421Q44.721 44.324 45.060 44.324Q45.525 44.324 45.822 44.531L46.045 44.347Q46.068 44.324 46.099 44.324L46.150 44.324Q46.181 44.324 46.209 44.351Q46.236 44.378 46.236 44.410L46.236 45.394Q46.236 45.425 46.211 45.454Q46.185 45.484 46.150 45.484L46.045 45.484Q46.010 45.484 45.982 45.456Q45.955 45.429 45.955 45.394Q45.955 44.995 45.703 44.775Q45.451 44.554 45.053 44.554Q44.697 44.554 44.414 44.677Q44.131 44.800 44.131 45.105Q44.131 45.324 44.332 45.456Q44.533 45.589 44.779 45.632L45.404 45.745Q45.834 45.835 46.142 46.132Q46.451 46.429 46.451 46.843Q46.451 47.413 46.053 47.691Q45.654 47.968 45.060 47.968Q44.510 47.968 44.158 47.632L43.861 47.945Q43.838 47.968 43.803 47.968L43.756 47.968Q43.732 47.968 43.701 47.937Q43.670 47.906 43.670 47.882M46.978 46.136Q46.978 45.656 47.211 45.240Q47.443 44.824 47.853 44.574Q48.264 44.324 48.740 44.324Q49.471 44.324 49.869 44.765Q50.267 45.206 50.267 45.937Q50.267 46.042 50.174 46.066L47.724 46.066L47.724 46.136Q47.724 46.546 47.846 46.902Q47.967 47.257 48.238 47.474Q48.510 47.691 48.939 47.691Q49.303 47.691 49.599 47.462Q49.896 47.234 49.998 46.882Q50.006 46.835 50.092 46.820L50.174 46.820Q50.267 46.847 50.267 46.929Q50.267 46.937 50.260 46.968Q50.197 47.195 50.058 47.378Q49.920 47.562 49.728 47.695Q49.537 47.828 49.318 47.898Q49.099 47.968 48.861 47.968Q48.490 47.968 48.152 47.831Q47.814 47.695 47.547 47.443Q47.279 47.191 47.129 46.851Q46.978 46.511 46.978 46.136M47.732 45.828L49.693 45.828Q49.693 45.523 49.592 45.232Q49.490 44.941 49.273 44.759Q49.056 44.578 48.740 44.578Q48.439 44.578 48.209 44.765Q47.978 44.953 47.855 45.244Q47.732 45.535 47.732 45.828M52.572 47.968Q52.092 47.968 51.683 47.724Q51.275 47.480 51.037 47.066Q50.799 46.652 50.799 46.163Q50.799 45.671 51.056 45.255Q51.314 44.839 51.746 44.601Q52.178 44.363 52.670 44.363Q53.291 44.363 53.740 44.800L53.740 43.171Q53.740 42.956 53.678 42.861Q53.615 42.765 53.498 42.744Q53.381 42.722 53.135 42.722L53.135 42.425L54.357 42.339L54.357 47.148Q54.357 47.359 54.420 47.454Q54.482 47.550 54.599 47.572Q54.717 47.593 54.967 47.593L54.967 47.890L53.717 47.968L53.717 47.484Q53.252 47.968 52.572 47.968M52.639 47.714Q52.978 47.714 53.271 47.523Q53.564 47.331 53.717 47.035L53.717 45.203Q53.568 44.929 53.306 44.773Q53.045 44.617 52.732 44.617Q52.107 44.617 51.824 45.064Q51.541 45.511 51.541 46.171Q51.541 46.816 51.793 47.265Q52.045 47.714 52.639 47.714\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M-5.605 56.558Q-5.605 56.074-5.203 55.779Q-4.800 55.484-4.250 55.365Q-3.699 55.245-3.207 55.245L-3.207 54.956Q-3.207 54.730-3.322 54.523Q-3.437 54.316-3.634 54.197Q-3.832 54.078-4.062 54.078Q-4.488 54.078-4.773 54.183Q-4.703 54.210-4.656 54.265Q-4.609 54.320-4.584 54.390Q-4.558 54.460-4.558 54.535Q-4.558 54.640-4.609 54.732Q-4.660 54.824-4.752 54.874Q-4.843 54.925-4.949 54.925Q-5.054 54.925-5.146 54.874Q-5.238 54.824-5.289 54.732Q-5.339 54.640-5.339 54.535Q-5.339 54.117-4.951 53.970Q-4.562 53.824-4.062 53.824Q-3.730 53.824-3.377 53.954Q-3.023 54.085-2.795 54.339Q-2.566 54.593-2.566 54.941L-2.566 56.742Q-2.566 56.874-2.494 56.984Q-2.421 57.093-2.293 57.093Q-2.168 57.093-2.099 56.988Q-2.031 56.882-2.031 56.742L-2.031 56.230L-1.750 56.230L-1.750 56.742Q-1.750 56.945-1.867 57.103Q-1.984 57.261-2.166 57.345Q-2.347 57.429-2.550 57.429Q-2.781 57.429-2.933 57.257Q-3.086 57.085-3.117 56.855Q-3.277 57.136-3.586 57.302Q-3.894 57.468-4.246 57.468Q-4.757 57.468-5.181 57.245Q-5.605 57.023-5.605 56.558M-4.918 56.558Q-4.918 56.843-4.691 57.029Q-4.464 57.214-4.171 57.214Q-3.925 57.214-3.701 57.097Q-3.476 56.980-3.341 56.777Q-3.207 56.574-3.207 56.320L-3.207 55.488Q-3.472 55.488-3.757 55.542Q-4.043 55.597-4.314 55.726Q-4.586 55.855-4.752 56.062Q-4.918 56.269-4.918 56.558M0.360 57.468Q-0.121 57.468-0.529 57.224Q-0.937 56.980-1.175 56.566Q-1.414 56.152-1.414 55.663Q-1.414 55.171-1.156 54.755Q-0.898 54.339-0.466 54.101Q-0.035 53.863 0.457 53.863Q1.079 53.863 1.528 54.300L1.528 52.671Q1.528 52.456 1.465 52.361Q1.403 52.265 1.286 52.244Q1.168 52.222 0.922 52.222L0.922 51.925L2.145 51.839L2.145 56.648Q2.145 56.859 2.207 56.954Q2.270 57.050 2.387 57.072Q2.504 57.093 2.754 57.093L2.754 57.390L1.504 57.468L1.504 56.984Q1.039 57.468 0.360 57.468M0.426 57.214Q0.766 57.214 1.059 57.023Q1.352 56.831 1.504 56.535L1.504 54.703Q1.356 54.429 1.094 54.273Q0.832 54.117 0.520 54.117Q-0.105 54.117-0.388 54.564Q-0.671 55.011-0.671 55.671Q-0.671 56.316-0.420 56.765Q-0.168 57.214 0.426 57.214M5.079 57.468Q4.598 57.468 4.190 57.224Q3.782 56.980 3.543 56.566Q3.305 56.152 3.305 55.663Q3.305 55.171 3.563 54.755Q3.821 54.339 4.252 54.101Q4.684 53.863 5.176 53.863Q5.797 53.863 6.247 54.300L6.247 52.671Q6.247 52.456 6.184 52.361Q6.122 52.265 6.004 52.244Q5.887 52.222 5.641 52.222L5.641 51.925L6.864 51.839L6.864 56.648Q6.864 56.859 6.926 56.954Q6.989 57.050 7.106 57.072Q7.223 57.093 7.473 57.093L7.473 57.390L6.223 57.468L6.223 56.984Q5.758 57.468 5.079 57.468M5.145 57.214Q5.485 57.214 5.778 57.023Q6.071 56.831 6.223 56.535L6.223 54.703Q6.075 54.429 5.813 54.273Q5.551 54.117 5.239 54.117Q4.614 54.117 4.330 54.564Q4.047 55.011 4.047 55.671Q4.047 56.316 4.299 56.765Q4.551 57.214 5.145 57.214\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M12.892 57.390L10.907 57.390L10.907 57.093Q11.181 57.093 11.349 57.046Q11.517 56.999 11.517 56.831L11.517 54.238L10.876 54.238L10.876 53.941L11.517 53.941L11.517 53.007Q11.517 52.742 11.634 52.505Q11.751 52.269 11.944 52.105Q12.138 51.941 12.386 51.849Q12.634 51.757 12.899 51.757Q13.185 51.757 13.409 51.915Q13.634 52.074 13.634 52.351Q13.634 52.507 13.528 52.617Q13.423 52.726 13.259 52.726Q13.103 52.726 12.993 52.617Q12.884 52.507 12.884 52.351Q12.884 52.144 13.044 52.038Q12.946 52.015 12.853 52.015Q12.622 52.015 12.450 52.171Q12.278 52.328 12.192 52.564Q12.107 52.800 12.107 53.023L12.107 53.941L13.075 53.941L13.075 54.238L12.130 54.238L12.130 56.831Q12.130 56.999 12.357 57.046Q12.583 57.093 12.892 57.093L12.892 57.390M13.419 55.695Q13.419 55.191 13.675 54.759Q13.931 54.328 14.366 54.076Q14.802 53.824 15.302 53.824Q15.689 53.824 16.030 53.968Q16.372 54.113 16.634 54.374Q16.896 54.636 17.038 54.972Q17.181 55.308 17.181 55.695Q17.181 56.187 16.917 56.597Q16.653 57.007 16.224 57.238Q15.794 57.468 15.302 57.468Q14.810 57.468 14.376 57.236Q13.942 57.003 13.681 56.595Q13.419 56.187 13.419 55.695M15.302 57.191Q15.759 57.191 16.011 56.968Q16.263 56.745 16.351 56.394Q16.439 56.042 16.439 55.597Q16.439 55.167 16.345 54.829Q16.251 54.492 15.997 54.285Q15.743 54.078 15.302 54.078Q14.653 54.078 14.409 54.494Q14.165 54.910 14.165 55.597Q14.165 56.042 14.253 56.394Q14.341 56.745 14.593 56.968Q14.845 57.191 15.302 57.191M19.673 57.390L17.692 57.390L17.692 57.093Q17.962 57.093 18.130 57.048Q18.298 57.003 18.298 56.831L18.298 54.695Q18.298 54.480 18.235 54.384Q18.173 54.288 18.056 54.267Q17.939 54.245 17.692 54.245L17.692 53.949L18.860 53.863L18.860 54.648Q18.939 54.437 19.091 54.251Q19.243 54.066 19.442 53.964Q19.642 53.863 19.868 53.863Q20.114 53.863 20.306 54.007Q20.497 54.152 20.497 54.382Q20.497 54.538 20.392 54.648Q20.286 54.757 20.130 54.757Q19.974 54.757 19.864 54.648Q19.755 54.538 19.755 54.382Q19.755 54.222 19.860 54.117Q19.536 54.117 19.321 54.345Q19.107 54.574 19.011 54.913Q18.915 55.253 18.915 55.558L18.915 56.831Q18.915 56.999 19.142 57.046Q19.368 57.093 19.673 57.093L19.673 57.390M20.978 55.636Q20.978 55.156 21.210 54.740Q21.442 54.324 21.853 54.074Q22.263 53.824 22.739 53.824Q23.470 53.824 23.868 54.265Q24.267 54.706 24.267 55.437Q24.267 55.542 24.173 55.566L21.724 55.566L21.724 55.636Q21.724 56.046 21.845 56.402Q21.966 56.757 22.237 56.974Q22.509 57.191 22.939 57.191Q23.302 57.191 23.599 56.962Q23.896 56.734 23.997 56.382Q24.005 56.335 24.091 56.320L24.173 56.320Q24.267 56.347 24.267 56.429Q24.267 56.437 24.259 56.468Q24.196 56.695 24.058 56.878Q23.919 57.062 23.728 57.195Q23.536 57.328 23.317 57.398Q23.099 57.468 22.860 57.468Q22.489 57.468 22.151 57.331Q21.814 57.195 21.546 56.943Q21.278 56.691 21.128 56.351Q20.978 56.011 20.978 55.636M21.732 55.328L23.692 55.328Q23.692 55.023 23.591 54.732Q23.489 54.441 23.273 54.259Q23.056 54.078 22.739 54.078Q22.439 54.078 22.208 54.265Q21.978 54.453 21.855 54.744Q21.732 55.035 21.732 55.328M24.798 57.382L24.798 56.160Q24.798 56.132 24.829 56.101Q24.860 56.070 24.884 56.070L24.989 56.070Q25.060 56.070 25.075 56.132Q25.138 56.453 25.276 56.693Q25.415 56.933 25.648 57.074Q25.880 57.214 26.189 57.214Q26.427 57.214 26.636 57.154Q26.845 57.093 26.982 56.945Q27.118 56.796 27.118 56.550Q27.118 56.296 26.907 56.130Q26.696 55.964 26.427 55.910L25.806 55.796Q25.399 55.718 25.099 55.462Q24.798 55.206 24.798 54.831Q24.798 54.464 24.999 54.242Q25.200 54.019 25.524 53.921Q25.849 53.824 26.189 53.824Q26.653 53.824 26.950 54.031L27.173 53.847Q27.196 53.824 27.228 53.824L27.278 53.824Q27.310 53.824 27.337 53.851Q27.364 53.878 27.364 53.910L27.364 54.894Q27.364 54.925 27.339 54.954Q27.314 54.984 27.278 54.984L27.173 54.984Q27.138 54.984 27.110 54.956Q27.083 54.929 27.083 54.894Q27.083 54.495 26.831 54.275Q26.579 54.054 26.181 54.054Q25.825 54.054 25.542 54.177Q25.259 54.300 25.259 54.605Q25.259 54.824 25.460 54.956Q25.661 55.089 25.907 55.132L26.532 55.245Q26.962 55.335 27.271 55.632Q27.579 55.929 27.579 56.343Q27.579 56.913 27.181 57.191Q26.782 57.468 26.189 57.468Q25.638 57.468 25.286 57.132L24.989 57.445Q24.966 57.468 24.931 57.468L24.884 57.468Q24.860 57.468 24.829 57.437Q24.798 57.406 24.798 57.382M29.966 57.390L28.189 57.390L28.189 57.093Q28.462 57.093 28.630 57.046Q28.798 56.999 28.798 56.831L28.798 54.695Q28.798 54.480 28.741 54.384Q28.685 54.288 28.571 54.267Q28.458 54.245 28.212 54.245L28.212 53.949L29.411 53.863L29.411 56.831Q29.411 56.999 29.558 57.046Q29.704 57.093 29.966 57.093L29.966 57.390M28.524 52.468Q28.524 52.277 28.659 52.146Q28.794 52.015 28.989 52.015Q29.110 52.015 29.214 52.078Q29.317 52.140 29.380 52.244Q29.442 52.347 29.442 52.468Q29.442 52.663 29.312 52.798Q29.181 52.933 28.989 52.933Q28.790 52.933 28.657 52.800Q28.524 52.667 28.524 52.468M30.466 57.999Q30.466 57.718 30.677 57.507Q30.888 57.296 31.173 57.206Q31.017 57.081 30.939 56.892Q30.860 56.703 30.860 56.503Q30.860 56.148 31.091 55.855Q30.724 55.515 30.724 55.046Q30.724 54.695 30.927 54.425Q31.130 54.156 31.450 54.009Q31.771 53.863 32.114 53.863Q32.634 53.863 33.005 54.144Q33.368 53.773 33.915 53.773Q34.095 53.773 34.222 53.900Q34.349 54.027 34.349 54.206Q34.349 54.312 34.271 54.390Q34.192 54.468 34.083 54.468Q33.974 54.468 33.898 54.392Q33.821 54.316 33.821 54.206Q33.821 54.105 33.860 54.054Q33.868 54.046 33.872 54.040Q33.876 54.035 33.876 54.031Q33.501 54.031 33.181 54.285Q33.501 54.624 33.501 55.046Q33.501 55.316 33.384 55.533Q33.267 55.749 33.062 55.908Q32.857 56.066 32.614 56.148Q32.372 56.230 32.114 56.230Q31.896 56.230 31.683 56.171Q31.470 56.113 31.274 55.992Q31.181 56.132 31.181 56.312Q31.181 56.519 31.317 56.671Q31.454 56.824 31.661 56.824L32.357 56.824Q32.845 56.824 33.257 56.908Q33.669 56.992 33.948 57.249Q34.228 57.507 34.228 57.999Q34.228 58.363 33.907 58.595Q33.587 58.828 33.146 58.929Q32.704 59.031 32.349 59.031Q31.993 59.031 31.550 58.929Q31.107 58.828 30.786 58.595Q30.466 58.363 30.466 57.999M30.970 57.999Q30.970 58.195 31.114 58.343Q31.259 58.492 31.472 58.581Q31.685 58.671 31.925 58.718Q32.165 58.765 32.349 58.765Q32.591 58.765 32.921 58.687Q33.251 58.609 33.487 58.435Q33.724 58.261 33.724 57.999Q33.724 57.593 33.314 57.484Q32.903 57.374 32.341 57.374L31.661 57.374Q31.392 57.374 31.181 57.552Q30.970 57.730 30.970 57.999M32.114 55.964Q32.837 55.964 32.837 55.046Q32.837 54.124 32.114 54.124Q31.388 54.124 31.388 55.046Q31.388 55.964 32.114 55.964M36.642 57.390L34.786 57.390L34.786 57.093Q35.060 57.093 35.228 57.046Q35.396 56.999 35.396 56.831L35.396 52.671Q35.396 52.456 35.333 52.361Q35.271 52.265 35.151 52.244Q35.032 52.222 34.786 52.222L34.786 51.925L36.009 51.839L36.009 54.542Q36.134 54.331 36.321 54.181Q36.509 54.031 36.735 53.947Q36.962 53.863 37.208 53.863Q38.376 53.863 38.376 54.941L38.376 56.831Q38.376 56.999 38.546 57.046Q38.716 57.093 38.985 57.093L38.985 57.390L37.130 57.390L37.130 57.093Q37.403 57.093 37.571 57.046Q37.739 56.999 37.739 56.831L37.739 54.956Q37.739 54.574 37.618 54.345Q37.497 54.117 37.146 54.117Q36.833 54.117 36.579 54.279Q36.325 54.441 36.179 54.710Q36.032 54.980 36.032 55.277L36.032 56.831Q36.032 56.999 36.202 57.046Q36.372 57.093 36.642 57.093\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M39.838 56.429L39.838 54.238L39.135 54.238L39.135 53.984Q39.491 53.984 39.733 53.751Q39.975 53.519 40.086 53.171Q40.198 52.824 40.198 52.468L40.479 52.468L40.479 53.941L41.655 53.941L41.655 54.238L40.479 54.238L40.479 56.413Q40.479 56.734 40.598 56.962Q40.717 57.191 40.998 57.191Q41.178 57.191 41.295 57.068Q41.413 56.945 41.465 56.765Q41.518 56.585 41.518 56.413L41.518 55.941L41.799 55.941L41.799 56.429Q41.799 56.683 41.694 56.923Q41.588 57.163 41.391 57.316Q41.194 57.468 40.936 57.468Q40.620 57.468 40.368 57.345Q40.116 57.222 39.977 56.988Q39.838 56.753 39.838 56.429\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M45.977 56.429L45.977 54.238L45.274 54.238L45.274 53.984Q45.630 53.984 45.872 53.751Q46.114 53.519 46.225 53.171Q46.337 52.824 46.337 52.468L46.618 52.468L46.618 53.941L47.794 53.941L47.794 54.238L46.618 54.238L46.618 56.413Q46.618 56.734 46.737 56.962Q46.856 57.191 47.137 57.191Q47.317 57.191 47.434 57.068Q47.551 56.945 47.604 56.765Q47.657 56.585 47.657 56.413L47.657 55.941L47.938 55.941L47.938 56.429Q47.938 56.683 47.833 56.923Q47.727 57.163 47.530 57.316Q47.333 57.468 47.075 57.468Q46.759 57.468 46.507 57.345Q46.255 57.222 46.116 56.988Q45.977 56.753 45.977 56.429M48.657 55.695Q48.657 55.191 48.913 54.759Q49.169 54.328 49.604 54.076Q50.040 53.824 50.540 53.824Q50.926 53.824 51.268 53.968Q51.610 54.113 51.872 54.374Q52.134 54.636 52.276 54.972Q52.419 55.308 52.419 55.695Q52.419 56.187 52.155 56.597Q51.891 57.007 51.462 57.238Q51.032 57.468 50.540 57.468Q50.048 57.468 49.614 57.236Q49.180 57.003 48.919 56.595Q48.657 56.187 48.657 55.695M50.540 57.191Q50.997 57.191 51.249 56.968Q51.501 56.745 51.589 56.394Q51.676 56.042 51.676 55.597Q51.676 55.167 51.583 54.829Q51.489 54.492 51.235 54.285Q50.981 54.078 50.540 54.078Q49.891 54.078 49.647 54.494Q49.403 54.910 49.403 55.597Q49.403 56.042 49.491 56.394Q49.579 56.745 49.831 56.968Q50.083 57.191 50.540 57.191\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M55.839 56.558Q55.839 56.074 56.241 55.779Q56.644 55.484 57.194 55.365Q57.745 55.245 58.237 55.245L58.237 54.956Q58.237 54.730 58.122 54.523Q58.007 54.316 57.810 54.197Q57.612 54.078 57.382 54.078Q56.956 54.078 56.671 54.183Q56.741 54.210 56.788 54.265Q56.835 54.320 56.860 54.390Q56.886 54.460 56.886 54.535Q56.886 54.640 56.835 54.732Q56.784 54.824 56.692 54.874Q56.601 54.925 56.495 54.925Q56.390 54.925 56.298 54.874Q56.206 54.824 56.155 54.732Q56.105 54.640 56.105 54.535Q56.105 54.117 56.493 53.970Q56.882 53.824 57.382 53.824Q57.714 53.824 58.067 53.954Q58.421 54.085 58.649 54.339Q58.878 54.593 58.878 54.941L58.878 56.742Q58.878 56.874 58.950 56.984Q59.023 57.093 59.151 57.093Q59.276 57.093 59.345 56.988Q59.413 56.882 59.413 56.742L59.413 56.230L59.694 56.230L59.694 56.742Q59.694 56.945 59.577 57.103Q59.460 57.261 59.278 57.345Q59.097 57.429 58.894 57.429Q58.663 57.429 58.511 57.257Q58.358 57.085 58.327 56.855Q58.167 57.136 57.858 57.302Q57.550 57.468 57.198 57.468Q56.687 57.468 56.263 57.245Q55.839 57.023 55.839 56.558M56.526 56.558Q56.526 56.843 56.753 57.029Q56.980 57.214 57.273 57.214Q57.519 57.214 57.743 57.097Q57.968 56.980 58.103 56.777Q58.237 56.574 58.237 56.320L58.237 55.488Q57.972 55.488 57.687 55.542Q57.401 55.597 57.130 55.726Q56.858 55.855 56.692 56.062Q56.526 56.269 56.526 56.558\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-41.82 -67.227)\">\u003Cpath d=\"M62.825 57.999Q62.825 57.718 63.036 57.507Q63.247 57.296 63.532 57.206Q63.376 57.081 63.298 56.892Q63.220 56.703 63.220 56.503Q63.220 56.148 63.450 55.855Q63.083 55.515 63.083 55.046Q63.083 54.695 63.286 54.425Q63.489 54.156 63.810 54.009Q64.130 53.863 64.474 53.863Q64.993 53.863 65.364 54.144Q65.728 53.773 66.275 53.773Q66.454 53.773 66.581 53.900Q66.708 54.027 66.708 54.206Q66.708 54.312 66.630 54.390Q66.552 54.468 66.442 54.468Q66.333 54.468 66.257 54.392Q66.181 54.316 66.181 54.206Q66.181 54.105 66.220 54.054Q66.228 54.046 66.232 54.040Q66.235 54.035 66.235 54.031Q65.860 54.031 65.540 54.285Q65.860 54.624 65.860 55.046Q65.860 55.316 65.743 55.533Q65.626 55.749 65.421 55.908Q65.216 56.066 64.974 56.148Q64.732 56.230 64.474 56.230Q64.255 56.230 64.042 56.171Q63.829 56.113 63.634 55.992Q63.540 56.132 63.540 56.312Q63.540 56.519 63.677 56.671Q63.814 56.824 64.021 56.824L64.716 56.824Q65.204 56.824 65.616 56.908Q66.028 56.992 66.308 57.249Q66.587 57.507 66.587 57.999Q66.587 58.363 66.267 58.595Q65.946 58.828 65.505 58.929Q65.064 59.031 64.708 59.031Q64.353 59.031 63.909 58.929Q63.466 58.828 63.146 58.595Q62.825 58.363 62.825 57.999M63.329 57.999Q63.329 58.195 63.474 58.343Q63.618 58.492 63.831 58.581Q64.044 58.671 64.284 58.718Q64.525 58.765 64.708 58.765Q64.950 58.765 65.280 58.687Q65.610 58.609 65.847 58.435Q66.083 58.261 66.083 57.999Q66.083 57.593 65.673 57.484Q65.263 57.374 64.700 57.374L64.021 57.374Q63.751 57.374 63.540 57.552Q63.329 57.730 63.329 57.999M64.474 55.964Q65.196 55.964 65.196 55.046Q65.196 54.124 64.474 54.124Q63.747 54.124 63.747 55.046Q63.747 55.964 64.474 55.964M67.071 55.695Q67.071 55.191 67.327 54.759Q67.583 54.328 68.019 54.076Q68.454 53.824 68.954 53.824Q69.341 53.824 69.683 53.968Q70.025 54.113 70.286 54.374Q70.548 54.636 70.691 54.972Q70.833 55.308 70.833 55.695Q70.833 56.187 70.569 56.597Q70.306 57.007 69.876 57.238Q69.446 57.468 68.954 57.468Q68.462 57.468 68.028 57.236Q67.595 57.003 67.333 56.595Q67.071 56.187 67.071 55.695M68.954 57.191Q69.411 57.191 69.663 56.968Q69.915 56.745 70.003 56.394Q70.091 56.042 70.091 55.597Q70.091 55.167 69.997 54.829Q69.903 54.492 69.650 54.285Q69.396 54.078 68.954 54.078Q68.306 54.078 68.062 54.494Q67.817 54.910 67.817 55.597Q67.817 56.042 67.905 56.394Q67.993 56.745 68.245 56.968Q68.497 57.191 68.954 57.191M71.415 56.558Q71.415 56.074 71.817 55.779Q72.220 55.484 72.771 55.365Q73.321 55.245 73.814 55.245L73.814 54.956Q73.814 54.730 73.698 54.523Q73.583 54.316 73.386 54.197Q73.189 54.078 72.958 54.078Q72.532 54.078 72.247 54.183Q72.317 54.210 72.364 54.265Q72.411 54.320 72.437 54.390Q72.462 54.460 72.462 54.535Q72.462 54.640 72.411 54.732Q72.360 54.824 72.269 54.874Q72.177 54.925 72.071 54.925Q71.966 54.925 71.874 54.874Q71.782 54.824 71.732 54.732Q71.681 54.640 71.681 54.535Q71.681 54.117 72.069 53.970Q72.458 53.824 72.958 53.824Q73.290 53.824 73.644 53.954Q73.997 54.085 74.226 54.339Q74.454 54.593 74.454 54.941L74.454 56.742Q74.454 56.874 74.526 56.984Q74.599 57.093 74.728 57.093Q74.853 57.093 74.921 56.988Q74.989 56.882 74.989 56.742L74.989 56.230L75.271 56.230L75.271 56.742Q75.271 56.945 75.153 57.103Q75.036 57.261 74.855 57.345Q74.673 57.429 74.470 57.429Q74.239 57.429 74.087 57.257Q73.935 57.085 73.903 56.855Q73.743 57.136 73.435 57.302Q73.126 57.468 72.775 57.468Q72.263 57.468 71.839 57.245Q71.415 57.023 71.415 56.558M72.103 56.558Q72.103 56.843 72.329 57.029Q72.556 57.214 72.849 57.214Q73.095 57.214 73.319 57.097Q73.544 56.980 73.679 56.777Q73.814 56.574 73.814 56.320L73.814 55.488Q73.548 55.488 73.263 55.542Q72.978 55.597 72.706 55.726Q72.435 55.855 72.269 56.062Q72.103 56.269 72.103 56.558M77.478 57.390L75.646 57.390L75.646 57.093Q75.919 57.093 76.087 57.046Q76.255 56.999 76.255 56.831L76.255 52.671Q76.255 52.456 76.192 52.361Q76.130 52.265 76.011 52.244Q75.892 52.222 75.646 52.222L75.646 51.925L76.868 51.839L76.868 56.831Q76.868 56.999 77.036 57.046Q77.204 57.093 77.478 57.093\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-68.537-39.35H56.655v-28.452H-68.537Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmr8\" font-size=\"8\">\u003Cg transform=\"translate(-40.76 -104.216)\">\u003Cpath d=\"M12.579 46.937L12.579 45.195Q12.579 44.980 12.516 44.884Q12.454 44.788 12.335 44.767Q12.216 44.745 11.970 44.745L11.970 44.449L13.216 44.363L13.216 46.913L13.216 46.937Q13.216 47.249 13.270 47.411Q13.325 47.574 13.475 47.644Q13.626 47.714 13.946 47.714Q14.376 47.714 14.649 47.376Q14.923 47.038 14.923 46.593L14.923 45.195Q14.923 44.980 14.860 44.884Q14.798 44.788 14.678 44.767Q14.559 44.745 14.313 44.745L14.313 44.449L15.559 44.363L15.559 47.148Q15.559 47.359 15.622 47.454Q15.684 47.550 15.803 47.572Q15.923 47.593 16.169 47.593L16.169 47.890L14.946 47.968L14.946 47.347Q14.778 47.636 14.497 47.802Q14.216 47.968 13.895 47.968Q12.579 47.968 12.579 46.937M17.239 46.929L17.239 44.738L16.536 44.738L16.536 44.484Q16.891 44.484 17.134 44.251Q17.376 44.019 17.487 43.671Q17.598 43.324 17.598 42.968L17.880 42.968L17.880 44.441L19.055 44.441L19.055 44.738L17.880 44.738L17.880 46.913Q17.880 47.234 17.999 47.462Q18.118 47.691 18.399 47.691Q18.579 47.691 18.696 47.568Q18.813 47.445 18.866 47.265Q18.919 47.085 18.919 46.913L18.919 46.441L19.200 46.441L19.200 46.929Q19.200 47.183 19.095 47.423Q18.989 47.663 18.792 47.816Q18.595 47.968 18.337 47.968Q18.020 47.968 17.768 47.845Q17.516 47.722 17.378 47.488Q17.239 47.253 17.239 46.929M21.778 47.890L20.001 47.890L20.001 47.593Q20.274 47.593 20.442 47.546Q20.610 47.499 20.610 47.331L20.610 45.195Q20.610 44.980 20.553 44.884Q20.497 44.788 20.384 44.767Q20.270 44.745 20.024 44.745L20.024 44.449L21.223 44.363L21.223 47.331Q21.223 47.499 21.370 47.546Q21.516 47.593 21.778 47.593L21.778 47.890M20.337 42.968Q20.337 42.777 20.471 42.646Q20.606 42.515 20.802 42.515Q20.923 42.515 21.026 42.578Q21.130 42.640 21.192 42.744Q21.255 42.847 21.255 42.968Q21.255 43.163 21.124 43.298Q20.993 43.433 20.802 43.433Q20.602 43.433 20.470 43.300Q20.337 43.167 20.337 42.968M24.192 47.890L22.360 47.890L22.360 47.593Q22.634 47.593 22.802 47.546Q22.970 47.499 22.970 47.331L22.970 43.171Q22.970 42.956 22.907 42.861Q22.845 42.765 22.725 42.744Q22.606 42.722 22.360 42.722L22.360 42.425L23.583 42.339L23.583 47.331Q23.583 47.499 23.751 47.546Q23.919 47.593 24.192 47.593L24.192 47.890M26.497 47.890L24.720 47.890L24.720 47.593Q24.993 47.593 25.161 47.546Q25.329 47.499 25.329 47.331L25.329 45.195Q25.329 44.980 25.272 44.884Q25.216 44.788 25.102 44.767Q24.989 44.745 24.743 44.745L24.743 44.449L25.942 44.363L25.942 47.331Q25.942 47.499 26.089 47.546Q26.235 47.593 26.497 47.593L26.497 47.890M25.055 42.968Q25.055 42.777 25.190 42.646Q25.325 42.515 25.520 42.515Q25.641 42.515 25.745 42.578Q25.848 42.640 25.911 42.744Q25.973 42.847 25.973 42.968Q25.973 43.163 25.843 43.298Q25.712 43.433 25.520 43.433Q25.321 43.433 25.188 43.300Q25.055 43.167 25.055 42.968M27.622 46.929L27.622 44.738L26.919 44.738L26.919 44.484Q27.274 44.484 27.516 44.251Q27.759 44.019 27.870 43.671Q27.981 43.324 27.981 42.968L28.262 42.968L28.262 44.441L29.438 44.441L29.438 44.738L28.262 44.738L28.262 46.913Q28.262 47.234 28.382 47.462Q28.501 47.691 28.782 47.691Q28.962 47.691 29.079 47.568Q29.196 47.445 29.249 47.265Q29.302 47.085 29.302 46.913L29.302 46.441L29.583 46.441L29.583 46.929Q29.583 47.183 29.477 47.423Q29.372 47.663 29.175 47.816Q28.977 47.968 28.720 47.968Q28.403 47.968 28.151 47.845Q27.899 47.722 27.761 47.488Q27.622 47.253 27.622 46.929\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.76 -104.216)\">\u003Cpath d=\"M30.494 49.187Q30.608 49.265 30.783 49.265Q31.072 49.265 31.293 49.052Q31.514 48.839 31.639 48.538L31.928 47.890L30.654 45.003Q30.572 44.828 30.428 44.783Q30.283 44.738 30.014 44.738L30.014 44.441L31.733 44.441L31.733 44.738Q31.311 44.738 31.311 44.921Q31.311 44.933 31.326 45.003L32.264 47.128L33.096 45.218Q33.135 45.128 33.135 45.050Q33.135 44.910 33.033 44.824Q32.932 44.738 32.791 44.738L32.791 44.441L34.143 44.441L34.143 44.738Q33.889 44.738 33.695 44.863Q33.502 44.988 33.397 45.218L31.951 48.538Q31.838 48.792 31.672 49.015Q31.506 49.238 31.277 49.380Q31.049 49.523 30.783 49.523Q30.486 49.523 30.246 49.331Q30.006 49.140 30.006 48.851Q30.006 48.695 30.111 48.593Q30.217 48.492 30.365 48.492Q30.471 48.492 30.551 48.538Q30.631 48.585 30.678 48.663Q30.725 48.742 30.725 48.851Q30.725 48.972 30.664 49.060Q30.604 49.148 30.494 49.187M36.670 46.441L34.416 46.441L34.416 45.890L36.670 45.890L36.670 46.441M38.303 47.890L38.022 47.890L38.022 43.171Q38.022 42.956 37.959 42.861Q37.897 42.765 37.779 42.744Q37.662 42.722 37.416 42.722L37.416 42.425L38.639 42.339L38.639 44.828Q39.115 44.363 39.815 44.363Q40.295 44.363 40.703 44.607Q41.111 44.851 41.348 45.265Q41.584 45.679 41.584 46.163Q41.584 46.538 41.436 46.867Q41.287 47.195 41.018 47.447Q40.748 47.699 40.404 47.833Q40.061 47.968 39.701 47.968Q39.381 47.968 39.082 47.820Q38.783 47.671 38.576 47.410L38.303 47.890M38.662 45.218L38.662 47.058Q38.815 47.355 39.074 47.535Q39.334 47.714 39.647 47.714Q40.072 47.714 40.340 47.495Q40.608 47.277 40.723 46.931Q40.838 46.585 40.838 46.163Q40.838 45.515 40.590 45.066Q40.342 44.617 39.744 44.617Q39.408 44.617 39.119 44.775Q38.830 44.933 38.662 45.218M42.205 47.058Q42.205 46.574 42.608 46.279Q43.010 45.984 43.561 45.865Q44.111 45.745 44.604 45.745L44.604 45.456Q44.604 45.230 44.488 45.023Q44.373 44.816 44.176 44.697Q43.979 44.578 43.748 44.578Q43.322 44.578 43.037 44.683Q43.108 44.710 43.154 44.765Q43.201 44.820 43.227 44.890Q43.252 44.960 43.252 45.035Q43.252 45.140 43.201 45.232Q43.151 45.324 43.059 45.374Q42.967 45.425 42.861 45.425Q42.756 45.425 42.664 45.374Q42.572 45.324 42.522 45.232Q42.471 45.140 42.471 45.035Q42.471 44.617 42.859 44.470Q43.248 44.324 43.748 44.324Q44.080 44.324 44.434 44.454Q44.787 44.585 45.016 44.839Q45.244 45.093 45.244 45.441L45.244 47.242Q45.244 47.374 45.317 47.484Q45.389 47.593 45.518 47.593Q45.643 47.593 45.711 47.488Q45.779 47.382 45.779 47.242L45.779 46.730L46.061 46.730L46.061 47.242Q46.061 47.445 45.943 47.603Q45.826 47.761 45.645 47.845Q45.463 47.929 45.260 47.929Q45.029 47.929 44.877 47.757Q44.725 47.585 44.693 47.355Q44.533 47.636 44.225 47.802Q43.916 47.968 43.565 47.968Q43.053 47.968 42.629 47.745Q42.205 47.523 42.205 47.058M42.893 47.058Q42.893 47.343 43.119 47.529Q43.346 47.714 43.639 47.714Q43.885 47.714 44.109 47.597Q44.334 47.480 44.469 47.277Q44.604 47.074 44.604 46.820L44.604 45.988Q44.338 45.988 44.053 46.042Q43.768 46.097 43.496 46.226Q43.225 46.355 43.059 46.562Q42.893 46.769 42.893 47.058M46.397 47.882L46.397 46.660Q46.397 46.632 46.428 46.601Q46.459 46.570 46.483 46.570L46.588 46.570Q46.658 46.570 46.674 46.632Q46.736 46.953 46.875 47.193Q47.014 47.433 47.246 47.574Q47.479 47.714 47.787 47.714Q48.026 47.714 48.234 47.654Q48.443 47.593 48.580 47.445Q48.717 47.296 48.717 47.050Q48.717 46.796 48.506 46.630Q48.295 46.464 48.026 46.410L47.404 46.296Q46.998 46.218 46.697 45.962Q46.397 45.706 46.397 45.331Q46.397 44.964 46.598 44.742Q46.799 44.519 47.123 44.421Q47.447 44.324 47.787 44.324Q48.252 44.324 48.549 44.531L48.772 44.347Q48.795 44.324 48.826 44.324L48.877 44.324Q48.908 44.324 48.936 44.351Q48.963 44.378 48.963 44.410L48.963 45.394Q48.963 45.425 48.938 45.454Q48.912 45.484 48.877 45.484L48.772 45.484Q48.736 45.484 48.709 45.456Q48.682 45.429 48.682 45.394Q48.682 44.995 48.430 44.775Q48.178 44.554 47.779 44.554Q47.424 44.554 47.141 44.677Q46.858 44.800 46.858 45.105Q46.858 45.324 47.059 45.456Q47.260 45.589 47.506 45.632L48.131 45.745Q48.561 45.835 48.869 46.132Q49.178 46.429 49.178 46.843Q49.178 47.413 48.779 47.691Q48.381 47.968 47.787 47.968Q47.236 47.968 46.885 47.632L46.588 47.945Q46.565 47.968 46.529 47.968L46.483 47.968Q46.459 47.968 46.428 47.937Q46.397 47.906 46.397 47.882M49.705 46.136Q49.705 45.656 49.938 45.240Q50.170 44.824 50.580 44.574Q50.990 44.324 51.467 44.324Q52.197 44.324 52.596 44.765Q52.994 45.206 52.994 45.937Q52.994 46.042 52.901 46.066L50.451 46.066L50.451 46.136Q50.451 46.546 50.572 46.902Q50.693 47.257 50.965 47.474Q51.236 47.691 51.666 47.691Q52.029 47.691 52.326 47.462Q52.623 47.234 52.725 46.882Q52.733 46.835 52.818 46.820L52.901 46.820Q52.994 46.847 52.994 46.929Q52.994 46.937 52.986 46.968Q52.924 47.195 52.785 47.378Q52.647 47.562 52.455 47.695Q52.264 47.828 52.045 47.898Q51.826 47.968 51.588 47.968Q51.217 47.968 50.879 47.831Q50.541 47.695 50.274 47.443Q50.006 47.191 49.856 46.851Q49.705 46.511 49.705 46.136M50.459 45.828L52.420 45.828Q52.420 45.523 52.318 45.232Q52.217 44.941 52 44.759Q51.783 44.578 51.467 44.578Q51.166 44.578 50.936 44.765Q50.705 44.953 50.582 45.244Q50.459 45.535 50.459 45.828M55.299 47.968Q54.818 47.968 54.410 47.724Q54.002 47.480 53.764 47.066Q53.526 46.652 53.526 46.163Q53.526 45.671 53.783 45.255Q54.041 44.839 54.473 44.601Q54.904 44.363 55.397 44.363Q56.018 44.363 56.467 44.800L56.467 43.171Q56.467 42.956 56.404 42.861Q56.342 42.765 56.225 42.744Q56.108 42.722 55.861 42.722L55.861 42.425L57.084 42.339L57.084 47.148Q57.084 47.359 57.147 47.454Q57.209 47.550 57.326 47.572Q57.443 47.593 57.693 47.593L57.693 47.890L56.443 47.968L56.443 47.484Q55.979 47.968 55.299 47.968M55.365 47.714Q55.705 47.714 55.998 47.523Q56.291 47.331 56.443 47.035L56.443 45.203Q56.295 44.929 56.033 44.773Q55.772 44.617 55.459 44.617Q54.834 44.617 54.551 45.064Q54.268 45.511 54.268 46.171Q54.268 46.816 54.520 47.265Q54.772 47.714 55.365 47.714\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.76 -104.216)\">\u003Cpath d=\"M-5.605 56.558Q-5.605 56.074-5.203 55.779Q-4.800 55.484-4.250 55.365Q-3.699 55.245-3.207 55.245L-3.207 54.956Q-3.207 54.730-3.322 54.523Q-3.437 54.316-3.634 54.197Q-3.832 54.078-4.062 54.078Q-4.488 54.078-4.773 54.183Q-4.703 54.210-4.656 54.265Q-4.609 54.320-4.584 54.390Q-4.558 54.460-4.558 54.535Q-4.558 54.640-4.609 54.732Q-4.660 54.824-4.752 54.874Q-4.843 54.925-4.949 54.925Q-5.054 54.925-5.146 54.874Q-5.238 54.824-5.289 54.732Q-5.339 54.640-5.339 54.535Q-5.339 54.117-4.951 53.970Q-4.562 53.824-4.062 53.824Q-3.730 53.824-3.377 53.954Q-3.023 54.085-2.795 54.339Q-2.566 54.593-2.566 54.941L-2.566 56.742Q-2.566 56.874-2.494 56.984Q-2.421 57.093-2.293 57.093Q-2.168 57.093-2.099 56.988Q-2.031 56.882-2.031 56.742L-2.031 56.230L-1.750 56.230L-1.750 56.742Q-1.750 56.945-1.867 57.103Q-1.984 57.261-2.166 57.345Q-2.347 57.429-2.550 57.429Q-2.781 57.429-2.933 57.257Q-3.086 57.085-3.117 56.855Q-3.277 57.136-3.586 57.302Q-3.894 57.468-4.246 57.468Q-4.757 57.468-5.181 57.245Q-5.605 57.023-5.605 56.558M-4.918 56.558Q-4.918 56.843-4.691 57.029Q-4.464 57.214-4.171 57.214Q-3.925 57.214-3.701 57.097Q-3.476 56.980-3.341 56.777Q-3.207 56.574-3.207 56.320L-3.207 55.488Q-3.472 55.488-3.757 55.542Q-4.043 55.597-4.314 55.726Q-4.586 55.855-4.752 56.062Q-4.918 56.269-4.918 56.558M0.360 57.468Q-0.121 57.468-0.529 57.224Q-0.937 56.980-1.175 56.566Q-1.414 56.152-1.414 55.663Q-1.414 55.171-1.156 54.755Q-0.898 54.339-0.466 54.101Q-0.035 53.863 0.457 53.863Q1.079 53.863 1.528 54.300L1.528 52.671Q1.528 52.456 1.465 52.361Q1.403 52.265 1.286 52.244Q1.168 52.222 0.922 52.222L0.922 51.925L2.145 51.839L2.145 56.648Q2.145 56.859 2.207 56.954Q2.270 57.050 2.387 57.072Q2.504 57.093 2.754 57.093L2.754 57.390L1.504 57.468L1.504 56.984Q1.039 57.468 0.360 57.468M0.426 57.214Q0.766 57.214 1.059 57.023Q1.352 56.831 1.504 56.535L1.504 54.703Q1.356 54.429 1.094 54.273Q0.832 54.117 0.520 54.117Q-0.105 54.117-0.388 54.564Q-0.671 55.011-0.671 55.671Q-0.671 56.316-0.420 56.765Q-0.168 57.214 0.426 57.214M5.079 57.468Q4.598 57.468 4.190 57.224Q3.782 56.980 3.543 56.566Q3.305 56.152 3.305 55.663Q3.305 55.171 3.563 54.755Q3.821 54.339 4.252 54.101Q4.684 53.863 5.176 53.863Q5.797 53.863 6.247 54.300L6.247 52.671Q6.247 52.456 6.184 52.361Q6.122 52.265 6.004 52.244Q5.887 52.222 5.641 52.222L5.641 51.925L6.864 51.839L6.864 56.648Q6.864 56.859 6.926 56.954Q6.989 57.050 7.106 57.072Q7.223 57.093 7.473 57.093L7.473 57.390L6.223 57.468L6.223 56.984Q5.758 57.468 5.079 57.468M5.145 57.214Q5.485 57.214 5.778 57.023Q6.071 56.831 6.223 56.535L6.223 54.703Q6.075 54.429 5.813 54.273Q5.551 54.117 5.239 54.117Q4.614 54.117 4.330 54.564Q4.047 55.011 4.047 55.671Q4.047 56.316 4.299 56.765Q4.551 57.214 5.145 57.214\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.76 -104.216)\">\u003Cpath d=\"M10.923 56.558Q10.923 56.074 11.325 55.779Q11.728 55.484 12.278 55.365Q12.829 55.245 13.321 55.245L13.321 54.956Q13.321 54.730 13.206 54.523Q13.091 54.316 12.894 54.197Q12.696 54.078 12.466 54.078Q12.040 54.078 11.755 54.183Q11.825 54.210 11.872 54.265Q11.919 54.320 11.944 54.390Q11.970 54.460 11.970 54.535Q11.970 54.640 11.919 54.732Q11.868 54.824 11.776 54.874Q11.685 54.925 11.579 54.925Q11.474 54.925 11.382 54.874Q11.290 54.824 11.239 54.732Q11.189 54.640 11.189 54.535Q11.189 54.117 11.577 53.970Q11.966 53.824 12.466 53.824Q12.798 53.824 13.151 53.954Q13.505 54.085 13.733 54.339Q13.962 54.593 13.962 54.941L13.962 56.742Q13.962 56.874 14.034 56.984Q14.107 57.093 14.235 57.093Q14.360 57.093 14.429 56.988Q14.497 56.882 14.497 56.742L14.497 56.230L14.778 56.230L14.778 56.742Q14.778 56.945 14.661 57.103Q14.544 57.261 14.362 57.345Q14.181 57.429 13.978 57.429Q13.747 57.429 13.595 57.257Q13.442 57.085 13.411 56.855Q13.251 57.136 12.942 57.302Q12.634 57.468 12.282 57.468Q11.771 57.468 11.347 57.245Q10.923 57.023 10.923 56.558M11.610 56.558Q11.610 56.843 11.837 57.029Q12.064 57.214 12.357 57.214Q12.603 57.214 12.827 57.097Q13.052 56.980 13.187 56.777Q13.321 56.574 13.321 56.320L13.321 55.488Q13.056 55.488 12.771 55.542Q12.485 55.597 12.214 55.726Q11.942 55.855 11.776 56.062Q11.610 56.269 11.610 56.558\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.76 -104.216)\">\u003Cpath d=\"M19.792 58.941L17.937 58.941L17.937 58.648Q18.206 58.648 18.374 58.603Q18.542 58.558 18.542 58.382L18.542 54.558Q18.542 54.351 18.386 54.298Q18.230 54.245 17.937 54.245L17.937 53.949L19.159 53.863L19.159 54.328Q19.390 54.105 19.704 53.984Q20.019 53.863 20.358 53.863Q20.831 53.863 21.235 54.109Q21.640 54.355 21.872 54.771Q22.105 55.187 22.105 55.663Q22.105 56.038 21.956 56.367Q21.808 56.695 21.538 56.947Q21.269 57.199 20.925 57.333Q20.581 57.468 20.222 57.468Q19.933 57.468 19.661 57.347Q19.390 57.226 19.183 57.015L19.183 58.382Q19.183 58.558 19.351 58.603Q19.519 58.648 19.792 58.648L19.792 58.941M19.183 54.726L19.183 56.566Q19.335 56.855 19.597 57.035Q19.858 57.214 20.167 57.214Q20.452 57.214 20.675 57.076Q20.898 56.937 21.050 56.706Q21.202 56.476 21.280 56.204Q21.358 55.933 21.358 55.663Q21.358 55.331 21.233 54.974Q21.108 54.617 20.860 54.380Q20.612 54.144 20.265 54.144Q19.941 54.144 19.646 54.300Q19.351 54.456 19.183 54.726M24.636 57.390L22.655 57.390L22.655 57.093Q22.925 57.093 23.093 57.048Q23.261 57.003 23.261 56.831L23.261 54.695Q23.261 54.480 23.198 54.384Q23.136 54.288 23.019 54.267Q22.901 54.245 22.655 54.245L22.655 53.949L23.823 53.863L23.823 54.648Q23.901 54.437 24.054 54.251Q24.206 54.066 24.405 53.964Q24.605 53.863 24.831 53.863Q25.077 53.863 25.269 54.007Q25.460 54.152 25.460 54.382Q25.460 54.538 25.355 54.648Q25.249 54.757 25.093 54.757Q24.937 54.757 24.827 54.648Q24.718 54.538 24.718 54.382Q24.718 54.222 24.823 54.117Q24.499 54.117 24.284 54.345Q24.069 54.574 23.974 54.913Q23.878 55.253 23.878 55.558L23.878 56.831Q23.878 56.999 24.105 57.046Q24.331 57.093 24.636 57.093L24.636 57.390M25.941 55.636Q25.941 55.156 26.173 54.740Q26.405 54.324 26.816 54.074Q27.226 53.824 27.702 53.824Q28.433 53.824 28.831 54.265Q29.230 54.706 29.230 55.437Q29.230 55.542 29.136 55.566L26.687 55.566L26.687 55.636Q26.687 56.046 26.808 56.402Q26.929 56.757 27.200 56.974Q27.472 57.191 27.901 57.191Q28.265 57.191 28.562 56.962Q28.858 56.734 28.960 56.382Q28.968 56.335 29.054 56.320L29.136 56.320Q29.230 56.347 29.230 56.429Q29.230 56.437 29.222 56.468Q29.159 56.695 29.021 56.878Q28.882 57.062 28.691 57.195Q28.499 57.328 28.280 57.398Q28.062 57.468 27.823 57.468Q27.452 57.468 27.114 57.331Q26.776 57.195 26.509 56.943Q26.241 56.691 26.091 56.351Q25.941 56.011 25.941 55.636M26.694 55.328L28.655 55.328Q28.655 55.023 28.554 54.732Q28.452 54.441 28.235 54.259Q28.019 54.078 27.702 54.078Q27.401 54.078 27.171 54.265Q26.941 54.453 26.817 54.744Q26.694 55.035 26.694 55.328M31.784 57.390L29.800 57.390L29.800 57.093Q30.073 57.093 30.241 57.046Q30.409 56.999 30.409 56.831L30.409 54.238L29.769 54.238L29.769 53.941L30.409 53.941L30.409 53.007Q30.409 52.742 30.526 52.505Q30.644 52.269 30.837 52.105Q31.030 51.941 31.278 51.849Q31.526 51.757 31.792 51.757Q32.077 51.757 32.302 51.915Q32.526 52.074 32.526 52.351Q32.526 52.507 32.421 52.617Q32.316 52.726 32.151 52.726Q31.995 52.726 31.886 52.617Q31.776 52.507 31.776 52.351Q31.776 52.144 31.937 52.038Q31.839 52.015 31.745 52.015Q31.515 52.015 31.343 52.171Q31.171 52.328 31.085 52.564Q30.999 52.800 30.999 53.023L30.999 53.941L31.968 53.941L31.968 54.238L31.023 54.238L31.023 56.831Q31.023 56.999 31.249 57.046Q31.476 57.093 31.784 57.093L31.784 57.390M32.312 55.636Q32.312 55.156 32.544 54.740Q32.776 54.324 33.187 54.074Q33.597 53.824 34.073 53.824Q34.804 53.824 35.202 54.265Q35.601 54.706 35.601 55.437Q35.601 55.542 35.507 55.566L33.058 55.566L33.058 55.636Q33.058 56.046 33.179 56.402Q33.300 56.757 33.571 56.974Q33.843 57.191 34.273 57.191Q34.636 57.191 34.933 56.962Q35.230 56.734 35.331 56.382Q35.339 56.335 35.425 56.320L35.507 56.320Q35.601 56.347 35.601 56.429Q35.601 56.437 35.593 56.468Q35.530 56.695 35.392 56.878Q35.253 57.062 35.062 57.195Q34.870 57.328 34.651 57.398Q34.433 57.468 34.194 57.468Q33.823 57.468 33.485 57.331Q33.148 57.195 32.880 56.943Q32.612 56.691 32.462 56.351Q32.312 56.011 32.312 55.636M33.066 55.328L35.026 55.328Q35.026 55.023 34.925 54.732Q34.823 54.441 34.607 54.259Q34.390 54.078 34.073 54.078Q33.773 54.078 33.542 54.265Q33.312 54.453 33.189 54.744Q33.066 55.035 33.066 55.328M38.097 57.390L36.116 57.390L36.116 57.093Q36.386 57.093 36.554 57.048Q36.722 57.003 36.722 56.831L36.722 54.695Q36.722 54.480 36.659 54.384Q36.597 54.288 36.480 54.267Q36.362 54.245 36.116 54.245L36.116 53.949L37.284 53.863L37.284 54.648Q37.362 54.437 37.515 54.251Q37.667 54.066 37.866 53.964Q38.066 53.863 38.292 53.863Q38.538 53.863 38.730 54.007Q38.921 54.152 38.921 54.382Q38.921 54.538 38.816 54.648Q38.710 54.757 38.554 54.757Q38.398 54.757 38.288 54.648Q38.179 54.538 38.179 54.382Q38.179 54.222 38.284 54.117Q37.960 54.117 37.745 54.345Q37.530 54.574 37.435 54.913Q37.339 55.253 37.339 55.558L37.339 56.831Q37.339 56.999 37.566 57.046Q37.792 57.093 38.097 57.093L38.097 57.390M39.401 55.636Q39.401 55.156 39.634 54.740Q39.866 54.324 40.276 54.074Q40.687 53.824 41.163 53.824Q41.894 53.824 42.292 54.265Q42.691 54.706 42.691 55.437Q42.691 55.542 42.597 55.566L40.148 55.566L40.148 55.636Q40.148 56.046 40.269 56.402Q40.390 56.757 40.661 56.974Q40.933 57.191 41.362 57.191Q41.726 57.191 42.023 56.962Q42.319 56.734 42.421 56.382Q42.429 56.335 42.515 56.320L42.597 56.320Q42.691 56.347 42.691 56.429Q42.691 56.437 42.683 56.468Q42.620 56.695 42.482 56.878Q42.343 57.062 42.151 57.195Q41.960 57.328 41.741 57.398Q41.523 57.468 41.284 57.468Q40.913 57.468 40.575 57.331Q40.237 57.195 39.970 56.943Q39.702 56.691 39.552 56.351Q39.401 56.011 39.401 55.636M40.155 55.328L42.116 55.328Q42.116 55.023 42.015 54.732Q41.913 54.441 41.696 54.259Q41.480 54.078 41.163 54.078Q40.862 54.078 40.632 54.265Q40.401 54.453 40.278 54.744Q40.155 55.035 40.155 55.328M45.108 57.390L43.253 57.390L43.253 57.093Q43.526 57.093 43.694 57.046Q43.862 56.999 43.862 56.831L43.862 54.695Q43.862 54.480 43.800 54.384Q43.737 54.288 43.618 54.267Q43.499 54.245 43.253 54.245L43.253 53.949L44.444 53.863L44.444 54.597Q44.558 54.382 44.751 54.214Q44.944 54.046 45.183 53.954Q45.421 53.863 45.675 53.863Q46.843 53.863 46.843 54.941L46.843 56.831Q46.843 56.999 47.013 57.046Q47.183 57.093 47.452 57.093L47.452 57.390L45.597 57.390L45.597 57.093Q45.870 57.093 46.038 57.046Q46.206 56.999 46.206 56.831L46.206 54.956Q46.206 54.574 46.085 54.345Q45.964 54.117 45.612 54.117Q45.300 54.117 45.046 54.279Q44.792 54.441 44.646 54.710Q44.499 54.980 44.499 55.277L44.499 56.831Q44.499 56.999 44.669 57.046Q44.839 57.093 45.108 57.093L45.108 57.390M47.941 55.663Q47.941 55.167 48.191 54.742Q48.441 54.316 48.860 54.070Q49.280 53.824 49.780 53.824Q50.319 53.824 50.710 53.949Q51.101 54.074 51.101 54.488Q51.101 54.593 51.050 54.685Q50.999 54.777 50.907 54.828Q50.816 54.878 50.706 54.878Q50.601 54.878 50.509 54.828Q50.417 54.777 50.366 54.685Q50.316 54.593 50.316 54.488Q50.316 54.265 50.483 54.160Q50.261 54.101 49.788 54.101Q49.491 54.101 49.276 54.240Q49.062 54.378 48.931 54.609Q48.800 54.839 48.741 55.109Q48.683 55.378 48.683 55.663Q48.683 56.058 48.816 56.408Q48.948 56.757 49.220 56.974Q49.491 57.191 49.890 57.191Q50.265 57.191 50.540 56.974Q50.816 56.757 50.917 56.398Q50.933 56.335 50.995 56.335L51.101 56.335Q51.136 56.335 51.161 56.363Q51.187 56.390 51.187 56.429L51.187 56.453Q51.054 56.933 50.669 57.201Q50.284 57.468 49.780 57.468Q49.417 57.468 49.083 57.331Q48.749 57.195 48.489 56.945Q48.230 56.695 48.085 56.359Q47.941 56.023 47.941 55.663M51.675 55.636Q51.675 55.156 51.907 54.740Q52.140 54.324 52.550 54.074Q52.960 53.824 53.437 53.824Q54.167 53.824 54.566 54.265Q54.964 54.706 54.964 55.437Q54.964 55.542 54.870 55.566L52.421 55.566L52.421 55.636Q52.421 56.046 52.542 56.402Q52.663 56.757 52.935 56.974Q53.206 57.191 53.636 57.191Q53.999 57.191 54.296 56.962Q54.593 56.734 54.694 56.382Q54.702 56.335 54.788 56.320L54.870 56.320Q54.964 56.347 54.964 56.429Q54.964 56.437 54.956 56.468Q54.894 56.695 54.755 56.878Q54.616 57.062 54.425 57.195Q54.233 57.328 54.015 57.398Q53.796 57.468 53.558 57.468Q53.187 57.468 52.849 57.331Q52.511 57.195 52.243 56.943Q51.976 56.691 51.825 56.351Q51.675 56.011 51.675 55.636M52.429 55.328L54.390 55.328Q54.390 55.023 54.288 54.732Q54.187 54.441 53.970 54.259Q53.753 54.078 53.437 54.078Q53.136 54.078 52.905 54.265Q52.675 54.453 52.552 54.744Q52.429 55.035 52.429 55.328\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.76 -104.216)\">\u003Cpath d=\"M58.341 57.382L58.341 56.160Q58.341 56.132 58.373 56.101Q58.404 56.070 58.427 56.070L58.533 56.070Q58.603 56.070 58.619 56.132Q58.681 56.453 58.820 56.693Q58.958 56.933 59.191 57.074Q59.423 57.214 59.732 57.214Q59.970 57.214 60.179 57.154Q60.388 57.093 60.525 56.945Q60.662 56.796 60.662 56.550Q60.662 56.296 60.451 56.130Q60.240 55.964 59.970 55.910L59.349 55.796Q58.943 55.718 58.642 55.462Q58.341 55.206 58.341 54.831Q58.341 54.464 58.542 54.242Q58.744 54.019 59.068 53.921Q59.392 53.824 59.732 53.824Q60.197 53.824 60.494 54.031L60.716 53.847Q60.740 53.824 60.771 53.824L60.822 53.824Q60.853 53.824 60.880 53.851Q60.908 53.878 60.908 53.910L60.908 54.894Q60.908 54.925 60.882 54.954Q60.857 54.984 60.822 54.984L60.716 54.984Q60.681 54.984 60.654 54.956Q60.626 54.929 60.626 54.894Q60.626 54.495 60.374 54.275Q60.123 54.054 59.724 54.054Q59.369 54.054 59.085 54.177Q58.802 54.300 58.802 54.605Q58.802 54.824 59.003 54.956Q59.205 55.089 59.451 55.132L60.076 55.245Q60.505 55.335 60.814 55.632Q61.123 55.929 61.123 56.343Q61.123 56.913 60.724 57.191Q60.326 57.468 59.732 57.468Q59.181 57.468 58.830 57.132L58.533 57.445Q58.509 57.468 58.474 57.468L58.427 57.468Q58.404 57.468 58.373 57.437Q58.341 57.406 58.341 57.382M61.693 55.663Q61.693 55.167 61.943 54.742Q62.193 54.316 62.613 54.070Q63.033 53.824 63.533 53.824Q64.072 53.824 64.462 53.949Q64.853 54.074 64.853 54.488Q64.853 54.593 64.802 54.685Q64.751 54.777 64.660 54.828Q64.568 54.878 64.458 54.878Q64.353 54.878 64.261 54.828Q64.169 54.777 64.119 54.685Q64.068 54.593 64.068 54.488Q64.068 54.265 64.236 54.160Q64.013 54.101 63.540 54.101Q63.244 54.101 63.029 54.240Q62.814 54.378 62.683 54.609Q62.552 54.839 62.494 55.109Q62.435 55.378 62.435 55.663Q62.435 56.058 62.568 56.408Q62.701 56.757 62.972 56.974Q63.244 57.191 63.642 57.191Q64.017 57.191 64.292 56.974Q64.568 56.757 64.669 56.398Q64.685 56.335 64.748 56.335L64.853 56.335Q64.888 56.335 64.914 56.363Q64.939 56.390 64.939 56.429L64.939 56.453Q64.806 56.933 64.421 57.201Q64.037 57.468 63.533 57.468Q63.169 57.468 62.835 57.331Q62.501 57.195 62.242 56.945Q61.982 56.695 61.837 56.359Q61.693 56.023 61.693 55.663M65.525 56.558Q65.525 56.074 65.927 55.779Q66.330 55.484 66.880 55.365Q67.431 55.245 67.923 55.245L67.923 54.956Q67.923 54.730 67.808 54.523Q67.693 54.316 67.496 54.197Q67.298 54.078 67.068 54.078Q66.642 54.078 66.357 54.183Q66.427 54.210 66.474 54.265Q66.521 54.320 66.546 54.390Q66.572 54.460 66.572 54.535Q66.572 54.640 66.521 54.732Q66.470 54.824 66.378 54.874Q66.287 54.925 66.181 54.925Q66.076 54.925 65.984 54.874Q65.892 54.824 65.841 54.732Q65.790 54.640 65.790 54.535Q65.790 54.117 66.179 53.970Q66.568 53.824 67.068 53.824Q67.400 53.824 67.753 53.954Q68.107 54.085 68.335 54.339Q68.564 54.593 68.564 54.941L68.564 56.742Q68.564 56.874 68.636 56.984Q68.708 57.093 68.837 57.093Q68.962 57.093 69.031 56.988Q69.099 56.882 69.099 56.742L69.099 56.230L69.380 56.230L69.380 56.742Q69.380 56.945 69.263 57.103Q69.146 57.261 68.964 57.345Q68.783 57.429 68.580 57.429Q68.349 57.429 68.197 57.257Q68.044 57.085 68.013 56.855Q67.853 57.136 67.544 57.302Q67.236 57.468 66.884 57.468Q66.373 57.468 65.949 57.245Q65.525 57.023 65.525 56.558M66.212 56.558Q66.212 56.843 66.439 57.029Q66.665 57.214 66.958 57.214Q67.205 57.214 67.429 57.097Q67.654 56.980 67.789 56.777Q67.923 56.574 67.923 56.320L67.923 55.488Q67.658 55.488 67.373 55.542Q67.087 55.597 66.816 55.726Q66.544 55.855 66.378 56.062Q66.212 56.269 66.212 56.558M71.587 57.390L69.755 57.390L69.755 57.093Q70.029 57.093 70.197 57.046Q70.365 56.999 70.365 56.831L70.365 52.671Q70.365 52.456 70.302 52.361Q70.240 52.265 70.121 52.244Q70.001 52.222 69.755 52.222L69.755 51.925L70.978 51.839L70.978 56.831Q70.978 56.999 71.146 57.046Q71.314 57.093 71.587 57.093L71.587 57.390M72.033 55.636Q72.033 55.156 72.265 54.740Q72.498 54.324 72.908 54.074Q73.318 53.824 73.794 53.824Q74.525 53.824 74.923 54.265Q75.322 54.706 75.322 55.437Q75.322 55.542 75.228 55.566L72.779 55.566L72.779 55.636Q72.779 56.046 72.900 56.402Q73.021 56.757 73.292 56.974Q73.564 57.191 73.994 57.191Q74.357 57.191 74.654 56.962Q74.951 56.734 75.052 56.382Q75.060 56.335 75.146 56.320L75.228 56.320Q75.322 56.347 75.322 56.429Q75.322 56.437 75.314 56.468Q75.251 56.695 75.113 56.878Q74.974 57.062 74.783 57.195Q74.591 57.328 74.373 57.398Q74.154 57.468 73.915 57.468Q73.544 57.468 73.206 57.331Q72.869 57.195 72.601 56.943Q72.333 56.691 72.183 56.351Q72.033 56.011 72.033 55.636M72.787 55.328L74.748 55.328Q74.748 55.023 74.646 54.732Q74.544 54.441 74.328 54.259Q74.111 54.078 73.794 54.078Q73.494 54.078 73.263 54.265Q73.033 54.453 72.910 54.744Q72.787 55.035 72.787 55.328\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-5.94 42.964v-6.136\"\u002F>\u003Cpath stroke=\"none\" d=\"m-5.94 34.828-1.6 3.2 1.6-1.2 1.6 1.2\"\u002F>\u003Cpath fill=\"none\" d=\"M-5.94 5.975V-.161\"\u002F>\u003Cpath stroke=\"none\" d=\"m-5.94-2.161-1.6 3.2 1.6-1.2 1.6 1.2\"\u002F>\u003Cpath fill=\"none\" d=\"M-5.94-31.014v-5.935\"\u002F>\u003Cpath stroke=\"none\" d=\"m-5.94-38.95-1.6 3.2 1.6-1.2 1.6 1.2\"\u002F>\u003Cpath fill=\"none\" d=\"M87.954 75.884h17.071V-72.07H87.954Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"rotate(-90 34.957 -5.892)\">\u003Cpath d=\"M-3.959 57.390L-5.562 57.390L-5.562 57.110Q-5.336 57.110-5.187 57.076Q-5.039 57.041-5.039 56.901L-5.039 53.282Q-5.039 53.012-5.146 52.950Q-5.254 52.889-5.562 52.889L-5.562 52.608L-4.485 52.533L-4.485 56.901Q-4.485 57.038-4.335 57.074Q-4.184 57.110-3.959 57.110L-3.959 57.390M-3.405 55.855Q-3.405 55.534-3.280 55.245Q-3.155 54.956-2.930 54.733Q-2.704 54.509-2.409 54.389Q-2.113 54.269-1.795 54.269Q-1.467 54.269-1.205 54.369Q-0.944 54.468-0.768 54.650Q-0.592 54.833-0.498 55.091Q-0.404 55.349-0.404 55.681Q-0.404 55.773-0.486 55.794L-2.742 55.794L-2.742 55.855Q-2.742 56.443-2.458 56.826Q-2.174 57.209-1.607 57.209Q-1.286 57.209-1.017 57.016Q-0.749 56.823-0.660 56.508Q-0.653 56.467-0.578 56.453L-0.486 56.453Q-0.404 56.477-0.404 56.549Q-0.404 56.556-0.411 56.583Q-0.524 56.980-0.894 57.219Q-1.265 57.458-1.689 57.458Q-2.127 57.458-2.526 57.250Q-2.926 57.041-3.166 56.674Q-3.405 56.307-3.405 55.855M-2.735 55.585L-0.920 55.585Q-0.920 55.308-1.017 55.056Q-1.115 54.803-1.313 54.647Q-1.511 54.492-1.795 54.492Q-2.072 54.492-2.285 54.650Q-2.499 54.809-2.617 55.064Q-2.735 55.319-2.735 55.585M0.242 56.662Q0.242 56.330 0.466 56.103Q0.690 55.876 1.033 55.748Q1.377 55.619 1.749 55.567Q2.122 55.514 2.426 55.514L2.426 55.261Q2.426 55.056 2.319 54.876Q2.211 54.697 2.030 54.594Q1.849 54.492 1.640 54.492Q1.233 54.492 0.997 54.584Q1.086 54.621 1.132 54.705Q1.179 54.789 1.179 54.891Q1.179 54.987 1.132 55.066Q1.086 55.144 1.006 55.189Q0.926 55.233 0.837 55.233Q0.686 55.233 0.586 55.136Q0.485 55.038 0.485 54.891Q0.485 54.269 1.640 54.269Q1.852 54.269 2.101 54.333Q2.351 54.396 2.553 54.515Q2.754 54.635 2.881 54.820Q3.007 55.004 3.007 55.247L3.007 56.823Q3.007 56.939 3.069 57.035Q3.130 57.130 3.243 57.130Q3.352 57.130 3.417 57.036Q3.482 56.942 3.482 56.823L3.482 56.375L3.749 56.375L3.749 56.823Q3.749 57.093 3.522 57.258Q3.294 57.424 3.014 57.424Q2.806 57.424 2.669 57.270Q2.532 57.117 2.508 56.901Q2.361 57.168 2.079 57.313Q1.797 57.458 1.473 57.458Q1.196 57.458 0.912 57.383Q0.628 57.308 0.435 57.129Q0.242 56.949 0.242 56.662M0.857 56.662Q0.857 56.836 0.958 56.966Q1.059 57.096 1.215 57.166Q1.370 57.236 1.534 57.236Q1.753 57.236 1.961 57.139Q2.170 57.041 2.298 56.860Q2.426 56.679 2.426 56.453L2.426 55.725Q2.101 55.725 1.736 55.816Q1.370 55.907 1.114 56.119Q0.857 56.330 0.857 56.662M5.916 57.390L4.180 57.390L4.180 57.110Q4.409 57.110 4.557 57.076Q4.706 57.041 4.706 56.901L4.706 55.052Q4.706 54.782 4.598 54.721Q4.491 54.659 4.180 54.659L4.180 54.379L5.208 54.304L5.208 55.011Q5.338 54.703 5.581 54.504Q5.824 54.304 6.142 54.304Q6.360 54.304 6.531 54.428Q6.702 54.553 6.702 54.765Q6.702 54.902 6.603 55.001Q6.504 55.100 6.371 55.100Q6.234 55.100 6.135 55.001Q6.036 54.902 6.036 54.765Q6.036 54.625 6.135 54.526Q5.844 54.526 5.644 54.722Q5.444 54.919 5.352 55.213Q5.260 55.507 5.260 55.787L5.260 56.901Q5.260 57.110 5.916 57.110L5.916 57.390M8.968 57.390L7.334 57.390L7.334 57.110Q7.563 57.110 7.712 57.076Q7.861 57.041 7.861 56.901L7.861 55.052Q7.861 54.782 7.753 54.721Q7.645 54.659 7.334 54.659L7.334 54.379L8.394 54.304L8.394 54.953Q8.565 54.645 8.869 54.474Q9.173 54.304 9.518 54.304Q10.024 54.304 10.308 54.527Q10.592 54.751 10.592 55.247L10.592 56.901Q10.592 57.038 10.740 57.074Q10.889 57.110 11.115 57.110L11.115 57.390L9.484 57.390L9.484 57.110Q9.713 57.110 9.862 57.076Q10.011 57.041 10.011 56.901L10.011 55.261Q10.011 54.926 9.891 54.726Q9.771 54.526 9.457 54.526Q9.187 54.526 8.953 54.662Q8.719 54.799 8.580 55.033Q8.442 55.267 8.442 55.541L8.442 56.901Q8.442 57.038 8.592 57.074Q8.743 57.110 8.968 57.110L8.968 57.390M13.319 57.390L11.767 57.390L11.767 57.110Q11.993 57.110 12.142 57.076Q12.290 57.041 12.290 56.901L12.290 55.052Q12.290 54.864 12.243 54.780Q12.195 54.697 12.097 54.678Q12 54.659 11.788 54.659L11.788 54.379L12.844 54.304L12.844 56.901Q12.844 57.041 12.976 57.076Q13.107 57.110 13.319 57.110L13.319 57.390M12.048 53.083Q12.048 52.912 12.171 52.793Q12.294 52.673 12.465 52.673Q12.632 52.673 12.755 52.793Q12.878 52.912 12.878 53.083Q12.878 53.258 12.755 53.381Q12.632 53.504 12.465 53.504Q12.294 53.504 12.171 53.381Q12.048 53.258 12.048 53.083M15.647 57.390L14.013 57.390L14.013 57.110Q14.242 57.110 14.391 57.076Q14.539 57.041 14.539 56.901L14.539 55.052Q14.539 54.782 14.432 54.721Q14.324 54.659 14.013 54.659L14.013 54.379L15.073 54.304L15.073 54.953Q15.244 54.645 15.548 54.474Q15.852 54.304 16.197 54.304Q16.703 54.304 16.987 54.527Q17.270 54.751 17.270 55.247L17.270 56.901Q17.270 57.038 17.419 57.074Q17.568 57.110 17.793 57.110L17.793 57.390L16.163 57.390L16.163 57.110Q16.392 57.110 16.541 57.076Q16.689 57.041 16.689 56.901L16.689 55.261Q16.689 54.926 16.570 54.726Q16.450 54.526 16.136 54.526Q15.866 54.526 15.632 54.662Q15.397 54.799 15.259 55.033Q15.121 55.267 15.121 55.541L15.121 56.901Q15.121 57.038 15.271 57.074Q15.421 57.110 15.647 57.110L15.647 57.390M18.340 57.923Q18.340 57.677 18.537 57.493Q18.733 57.308 18.990 57.229Q18.853 57.117 18.781 56.956Q18.709 56.795 18.709 56.614Q18.709 56.293 18.921 56.047Q18.586 55.749 18.586 55.339Q18.586 54.878 18.976 54.591Q19.366 54.304 19.844 54.304Q20.316 54.304 20.651 54.550Q20.825 54.396 21.035 54.314Q21.246 54.232 21.475 54.232Q21.639 54.232 21.760 54.339Q21.881 54.447 21.881 54.611Q21.881 54.707 21.809 54.779Q21.738 54.850 21.645 54.850Q21.546 54.850 21.476 54.777Q21.406 54.703 21.406 54.604Q21.406 54.550 21.420 54.519L21.427 54.505Q21.434 54.485 21.442 54.474Q21.451 54.464 21.454 54.457Q21.099 54.457 20.811 54.680Q21.099 54.973 21.099 55.339Q21.099 55.654 20.914 55.886Q20.729 56.119 20.441 56.247Q20.152 56.375 19.844 56.375Q19.642 56.375 19.451 56.325Q19.260 56.276 19.082 56.166Q18.990 56.293 18.990 56.436Q18.990 56.618 19.118 56.753Q19.246 56.888 19.431 56.888L20.063 56.888Q20.511 56.888 20.880 56.959Q21.249 57.031 21.509 57.260Q21.768 57.489 21.768 57.923Q21.768 58.244 21.473 58.446Q21.177 58.648 20.774 58.737Q20.371 58.826 20.056 58.826Q19.738 58.826 19.335 58.737Q18.932 58.648 18.636 58.446Q18.340 58.244 18.340 57.923M18.795 57.923Q18.795 58.152 19.014 58.301Q19.232 58.450 19.525 58.518Q19.817 58.586 20.056 58.586Q20.220 58.586 20.429 58.550Q20.637 58.515 20.844 58.434Q21.051 58.354 21.182 58.226Q21.314 58.098 21.314 57.923Q21.314 57.571 20.933 57.477Q20.552 57.383 20.049 57.383L19.431 57.383Q19.191 57.383 18.993 57.534Q18.795 57.684 18.795 57.923M19.844 56.136Q20.511 56.136 20.511 55.339Q20.511 54.539 19.844 54.539Q19.174 54.539 19.174 55.339Q19.174 56.136 19.844 56.136\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"rotate(-90 34.957 -5.892)\">\u003Cpath d=\"M26.470 57.363L25.489 54.864Q25.428 54.721 25.310 54.686Q25.192 54.652 24.976 54.652L24.976 54.372L26.456 54.372L26.456 54.652Q26.077 54.652 26.077 54.813Q26.077 54.823 26.091 54.864L26.805 56.696L27.478 54.991Q27.448 54.919 27.448 54.891Q27.448 54.864 27.420 54.864Q27.359 54.717 27.241 54.685Q27.123 54.652 26.911 54.652L26.911 54.372L28.309 54.372L28.309 54.652Q27.933 54.652 27.933 54.813Q27.933 54.844 27.940 54.864L28.695 56.802L29.382 55.052Q29.403 55.001 29.403 54.946Q29.403 54.806 29.290 54.729Q29.177 54.652 29.037 54.652L29.037 54.372L30.257 54.372L30.257 54.652Q30.052 54.652 29.897 54.758Q29.741 54.864 29.669 55.052L28.764 57.363Q28.729 57.458 28.617 57.458L28.548 57.458Q28.439 57.458 28.401 57.363L27.619 55.360L26.832 57.363Q26.798 57.458 26.685 57.458L26.617 57.458Q26.508 57.458 26.470 57.363M32.537 57.390L30.801 57.390L30.801 57.110Q31.030 57.110 31.178 57.076Q31.327 57.041 31.327 56.901L31.327 55.052Q31.327 54.782 31.219 54.721Q31.112 54.659 30.801 54.659L30.801 54.379L31.830 54.304L31.830 55.011Q31.959 54.703 32.202 54.504Q32.445 54.304 32.763 54.304Q32.981 54.304 33.152 54.428Q33.323 54.553 33.323 54.765Q33.323 54.902 33.224 55.001Q33.125 55.100 32.992 55.100Q32.855 55.100 32.756 55.001Q32.657 54.902 32.657 54.765Q32.657 54.625 32.756 54.526Q32.465 54.526 32.265 54.722Q32.065 54.919 31.973 55.213Q31.881 55.507 31.881 55.787L31.881 56.901Q31.881 57.110 32.537 57.110L32.537 57.390M33.966 56.662Q33.966 56.330 34.190 56.103Q34.414 55.876 34.757 55.748Q35.101 55.619 35.473 55.567Q35.846 55.514 36.150 55.514L36.150 55.261Q36.150 55.056 36.042 54.876Q35.935 54.697 35.753 54.594Q35.572 54.492 35.364 54.492Q34.957 54.492 34.721 54.584Q34.810 54.621 34.856 54.705Q34.902 54.789 34.902 54.891Q34.902 54.987 34.856 55.066Q34.810 55.144 34.730 55.189Q34.649 55.233 34.560 55.233Q34.410 55.233 34.309 55.136Q34.208 55.038 34.208 54.891Q34.208 54.269 35.364 54.269Q35.576 54.269 35.825 54.333Q36.075 54.396 36.276 54.515Q36.478 54.635 36.604 54.820Q36.731 55.004 36.731 55.247L36.731 56.823Q36.731 56.939 36.792 57.035Q36.854 57.130 36.967 57.130Q37.076 57.130 37.141 57.036Q37.206 56.942 37.206 56.823L37.206 56.375L37.473 56.375L37.473 56.823Q37.473 57.093 37.245 57.258Q37.018 57.424 36.738 57.424Q36.529 57.424 36.393 57.270Q36.256 57.117 36.232 56.901Q36.085 57.168 35.803 57.313Q35.521 57.458 35.196 57.458Q34.919 57.458 34.636 57.383Q34.352 57.308 34.159 57.129Q33.966 56.949 33.966 56.662M34.581 56.662Q34.581 56.836 34.682 56.966Q34.783 57.096 34.938 57.166Q35.094 57.236 35.258 57.236Q35.476 57.236 35.685 57.139Q35.893 57.041 36.022 56.860Q36.150 56.679 36.150 56.453L36.150 55.725Q35.825 55.725 35.459 55.816Q35.094 55.907 34.837 56.119Q34.581 56.330 34.581 56.662M39.534 58.747L37.903 58.747L37.903 58.467Q38.132 58.467 38.281 58.432Q38.430 58.398 38.430 58.258L38.430 54.912Q38.430 54.741 38.293 54.700Q38.156 54.659 37.903 54.659L37.903 54.379L38.983 54.304L38.983 54.710Q39.206 54.509 39.493 54.406Q39.780 54.304 40.087 54.304Q40.515 54.304 40.879 54.517Q41.243 54.731 41.456 55.095Q41.670 55.459 41.670 55.879Q41.670 56.324 41.431 56.688Q41.191 57.052 40.798 57.255Q40.405 57.458 39.961 57.458Q39.694 57.458 39.446 57.358Q39.199 57.257 39.011 57.076L39.011 58.258Q39.011 58.395 39.159 58.431Q39.308 58.467 39.534 58.467L39.534 58.747M39.011 55.059L39.011 56.669Q39.144 56.922 39.387 57.079Q39.629 57.236 39.906 57.236Q40.234 57.236 40.487 57.035Q40.740 56.833 40.873 56.515Q41.007 56.197 41.007 55.879Q41.007 55.650 40.942 55.421Q40.877 55.192 40.749 54.994Q40.621 54.796 40.426 54.676Q40.231 54.557 39.998 54.557Q39.705 54.557 39.436 54.686Q39.168 54.816 39.011 55.059M42.306 57.383L42.306 56.320Q42.306 56.296 42.333 56.269Q42.360 56.242 42.384 56.242L42.494 56.242Q42.559 56.242 42.572 56.300Q42.668 56.734 42.914 56.985Q43.160 57.236 43.574 57.236Q43.915 57.236 44.168 57.103Q44.421 56.970 44.421 56.662Q44.421 56.505 44.327 56.390Q44.233 56.276 44.095 56.207Q43.956 56.139 43.789 56.101L43.208 56.002Q42.852 55.934 42.579 55.713Q42.306 55.493 42.306 55.151Q42.306 54.902 42.417 54.727Q42.528 54.553 42.714 54.454Q42.900 54.355 43.116 54.312Q43.331 54.269 43.574 54.269Q43.987 54.269 44.268 54.451L44.483 54.276Q44.493 54.273 44.500 54.271Q44.507 54.269 44.517 54.269L44.568 54.269Q44.596 54.269 44.620 54.293Q44.643 54.317 44.643 54.345L44.643 55.192Q44.643 55.213 44.620 55.240Q44.596 55.267 44.568 55.267L44.456 55.267Q44.428 55.267 44.403 55.242Q44.377 55.216 44.377 55.192Q44.377 54.956 44.271 54.792Q44.165 54.628 43.982 54.546Q43.799 54.464 43.567 54.464Q43.239 54.464 42.982 54.567Q42.726 54.669 42.726 54.946Q42.726 55.141 42.909 55.250Q43.092 55.360 43.321 55.401L43.895 55.507Q44.141 55.555 44.355 55.683Q44.568 55.811 44.705 56.014Q44.842 56.218 44.842 56.467Q44.842 56.980 44.476 57.219Q44.110 57.458 43.574 57.458Q43.078 57.458 42.747 57.164L42.480 57.438Q42.459 57.458 42.432 57.458L42.384 57.458Q42.360 57.458 42.333 57.431Q42.306 57.404 42.306 57.383\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"rotate(-90 34.957 -5.892)\">\u003Cpath d=\"M48.240 56.662Q48.240 56.330 48.463 56.103Q48.687 55.876 49.031 55.748Q49.374 55.619 49.747 55.567Q50.119 55.514 50.424 55.514L50.424 55.261Q50.424 55.056 50.316 54.876Q50.208 54.697 50.027 54.594Q49.846 54.492 49.638 54.492Q49.231 54.492 48.995 54.584Q49.084 54.621 49.130 54.705Q49.176 54.789 49.176 54.891Q49.176 54.987 49.130 55.066Q49.084 55.144 49.003 55.189Q48.923 55.233 48.834 55.233Q48.684 55.233 48.583 55.136Q48.482 55.038 48.482 54.891Q48.482 54.269 49.638 54.269Q49.849 54.269 50.099 54.333Q50.348 54.396 50.550 54.515Q50.752 54.635 50.878 54.820Q51.005 55.004 51.005 55.247L51.005 56.823Q51.005 56.939 51.066 57.035Q51.128 57.130 51.241 57.130Q51.350 57.130 51.415 57.036Q51.480 56.942 51.480 56.823L51.480 56.375L51.746 56.375L51.746 56.823Q51.746 57.093 51.519 57.258Q51.292 57.424 51.012 57.424Q50.803 57.424 50.666 57.270Q50.530 57.117 50.506 56.901Q50.359 57.168 50.077 57.313Q49.795 57.458 49.470 57.458Q49.193 57.458 48.909 57.383Q48.626 57.308 48.433 57.129Q48.240 56.949 48.240 56.662M48.855 56.662Q48.855 56.836 48.956 56.966Q49.056 57.096 49.212 57.166Q49.367 57.236 49.532 57.236Q49.750 57.236 49.959 57.139Q50.167 57.041 50.295 56.860Q50.424 56.679 50.424 56.453L50.424 55.725Q50.099 55.725 49.733 55.816Q49.367 55.907 49.111 56.119Q48.855 56.330 48.855 56.662M53.845 57.390L52.211 57.390L52.211 57.110Q52.440 57.110 52.589 57.076Q52.738 57.041 52.738 56.901L52.738 55.052Q52.738 54.782 52.630 54.721Q52.522 54.659 52.211 54.659L52.211 54.379L53.271 54.304L53.271 54.953Q53.442 54.645 53.746 54.474Q54.050 54.304 54.395 54.304Q54.901 54.304 55.185 54.527Q55.469 54.751 55.469 55.247L55.469 56.901Q55.469 57.038 55.617 57.074Q55.766 57.110 55.992 57.110L55.992 57.390L54.361 57.390L54.361 57.110Q54.590 57.110 54.739 57.076Q54.888 57.041 54.888 56.901L54.888 55.261Q54.888 54.926 54.768 54.726Q54.648 54.526 54.334 54.526Q54.064 54.526 53.830 54.662Q53.596 54.799 53.457 55.033Q53.319 55.267 53.319 55.541L53.319 56.901Q53.319 57.038 53.469 57.074Q53.619 57.110 53.845 57.110\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"rotate(-90 34.957 -5.892)\">\u003Cpath d=\"M56.703 58.525Q56.833 58.593 56.970 58.593Q57.141 58.593 57.291 58.504Q57.442 58.415 57.553 58.270Q57.664 58.125 57.742 57.957L58.006 57.390L56.837 54.864Q56.762 54.717 56.632 54.685Q56.502 54.652 56.269 54.652L56.269 54.372L57.790 54.372L57.790 54.652Q57.442 54.652 57.442 54.799Q57.445 54.820 57.447 54.837Q57.449 54.854 57.449 54.864L58.306 56.723L59.079 55.052Q59.113 54.984 59.113 54.905Q59.113 54.792 59.029 54.722Q58.946 54.652 58.833 54.652L58.833 54.372L60.029 54.372L60.029 54.652Q59.810 54.652 59.638 54.756Q59.465 54.861 59.373 55.052L58.036 57.957Q57.866 58.327 57.596 58.573Q57.325 58.819 56.970 58.819Q56.700 58.819 56.481 58.653Q56.262 58.487 56.262 58.224Q56.262 58.087 56.355 57.998Q56.447 57.910 56.587 57.910Q56.724 57.910 56.813 57.998Q56.902 58.087 56.902 58.224Q56.902 58.327 56.849 58.405Q56.796 58.484 56.703 58.525\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">The four architectures as a ladder of added machinery, each keeping everything below it. Reflex maps percept to action; model-based adds memory of the unseen world; goal-based adds prediction toward a goal; utility-based adds a preference scale; and a learning agent can wrap any of them.\u003C\u002Ffigcaption>",1785117804356]