[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8},"actionData","errors","root",{"_26":27,"_28":29,"_30":12,"_31":12,"_32":12,"_33":12,"_34":12,"_35":12,"_36":37},"routes/canvas.shared.$sharedTextdocId",{"_9":10,"_11":12},"sharedTextdoc",{"_13":14,"_15":-7,"_16":17,"_18":19,"_20":21,"_22":23,"_24":12,"_25":12},"isAuthenticated",false,"sharedTextdocId","68dabb29e9b881918131da8137f85696","versionInt","title","Ee274 AEP Visualization","type","code/react","content","import React, { useState, useEffect, useRef } from \"react\";\nimport { BarChart, Bar, XAxis, YAxis, CartesianGrid, Tooltip, ResponsiveContainer, Cell } from \"recharts\";\n\nfunction generateData(p, n, epsilon) {\n const data = [];\n const pp = Math.min(Math.max(p, 1e-12), 1 - 1e-12);\n const H = -(pp * Math.log2(pp) + (1 - pp) * Math.log2(1 - pp));\n\n let logFrac = n * Math.log(1 - pp);\n let frac = Math.exp(logFrac);\n let log2C = 0;\n\n for (let k = 0; k <= n; k++) {\n const logProb = -((k * Math.log2(pp)) + ((n - k) * Math.log2(1 - pp))) / n;\n const countFrac = Math.pow(2, log2C - n);\n\n data.push({\n k,\n logProb,\n frac,\n countFrac,\n typical: logProb >= H - epsilon && logProb <= H + epsilon,\n });\n\n if (k < n) {\n logFrac += Math.log((n - k) / (k + 1)) + Math.log(pp) - Math.log(1 - pp);\n frac = Math.exp(logFrac);\n if (!Number.isFinite(frac)) frac = 0;\n log2C += Math.log2((n - k) / (k + 1));\n }\n }\n\n const typicalProbMass = data.filter(d => d.typical).reduce((s, d) => s + d.frac, 0);\n const typicalCountFrac = data.filter(d => d.typical).reduce((s, d) => s + d.countFrac, 0);\n const totalCount = Math.pow(2, n);\n\n return { data, H, typicalProbMass, typicalCountFrac, totalCount };\n}\n\nexport default function AEPVisualizationBalancedAxis() {\n const [pInput, setPInput] = useState(0.5);\n const [epsilonInput, setEpsilonInput] = useState(0.1);\n const [nInput, setNInput] = useState(20);\n\n const [pView, setPView] = useState(0.5);\n const [epsilonView, setEpsilonView] = useState(0.1);\n const [nView, setNView] = useState(20);\n\n const [mode, setMode] = useState('prob');\n\n const [sliding, setSliding] = useState(false);\n const debounceRef = useRef(null);\n\n useEffect(() => {\n setSliding(true);\n if (debounceRef.current) clearTimeout(debounceRef.current);\n debounceRef.current = setTimeout(() => {\n setPView(pInput);\n setEpsilonView(epsilonInput);\n setNView(nInput);\n setSliding(false);\n }, 200);\n return () => { if (debounceRef.current) clearTimeout(debounceRef.current); };\n }, [pInput, epsilonInput, nInput]);\n\n const view = generateData(pView, nView, epsilonView);\n const input = generateData(pInput, nInput, epsilonInput);\n const { data: dataView, H, typicalProbMass, typicalCountFrac } = view;\n\n return (\n

EE274 – Asymptotic Equipartition Property (AEP) Visualization

\n\n

\n p (Bernoulli parameter): {pInput.toFixed(2)}\n setPInput(parseFloat(e.target.value))} className=\"w-full\" />\n

\n ε: {epsilonInput.toFixed(2)}\n setEpsilonInput(parseFloat(e.target.value))} className=\"w-full\" />\n

\n n: {nInput}\n setNInput(parseInt(e.target.value))} className=\"w-full\" />\n

\n\n

\n Chart mode:\n setMode('prob')}\n >Probability mass\n setMode('count')}\n >Count fraction\n

\n Probability: how much probability the typical set covers. Count: what fraction of all sequences are typical.\n

\n\n \n \n \n \n \n [Number(v).toPrecision(3), mode === 'prob' ? 'P[K=k]' : 'C(n,k)/2^n']} />\n\n \n {(sliding ? input.data : dataView).map((entry, index) => (\n \n ))}\n \n \n \n\n

\n Entropy H: {H.toFixed(3)} bits. Bars in green denote counts whose per-sequence probability falls within the typical band (H ± ε).\n

\n\n

\n {sliding && Calculating…}\n {mode === 'prob' ? (\n

Total probability of typical sequences: {(typicalProbMass * 100).toFixed(2)}%

\n ) : (\n

Total sequences ≈ 2^{nView}. Fraction of typical sequences ≈ {typicalCountFrac * 100 < 1 ? '< 1%' : (typicalCountFrac * 100).toFixed(2) + '%'}

\n )}\n

Tip: For skewed p and small ε, the probability mass approaches 1 quickly, but the fraction of sequences in the typical set remains exponentially small.

\n );\n}\n","access","public","isModerationBlocked","isAnonifyApiKeyDetected","dd",{"_38":39,"_40":41},"disablePrefetch",true,"shouldPrefetchAccount","shouldPrefetchUser","shouldPrefetchSystemHints","promoteCss","disableSSR","stripModulepreloadImports","statsigGateEvaluationsPromise",["P",37],"traceId","14747724769158397666","traceTime",1777318224502]