2b:null 2c:["$","title",null,{"children":"Suddenly noisy down simulation | Chuncheng | Observable"}] 31:[{"id":"697943476580b15bae62dbca2b9450f2d2133c60a07ffad8645f399239880f9b6b71b3327f2725b371e90169502dfb712cacd641e32241a3d18bd3fb53a30b3e","href":"https://static.observableusercontent.com/files/697943476580b15bae62dbca2b9450f2d2133c60a07ffad8645f399239880f9b6b71b3327f2725b371e90169502dfb712cacd641e32241a3d18bd3fb53a30b3e","name":"Snipaste_2025-03-03_13-53-31.png","type":"image/png","lastModified":1740981228200.354,"size":67687}] 2f:{"id":"4c769f43181ff63c","slug":"suddenly-noisy-down-simulation","title":"Suddenly noisy down simulation","thumbnail":"a4d38d7fd674c25c74057a3a323bf6bb03ef5294f34035f42d969bcc0dabb45a","access_level":"public","create_time":"$D2025-03-02T12:41:24.290Z","update_time":"$D2025-03-10T14:08:50.406Z","view_time":null,"first_public_time":"$D2025-03-10T13:16:34.828Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024"},"version":375,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null}],"members":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null,"role":"editor"},{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Suddenly noisy down simulation","cells":[{"id":0,"value":"# Suddenly noisy down simulation\n\nSee the article for detail\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":256,"value":"snipaste_20250303_135331 = FileAttachment(\"Snipaste_2025-03-03_13-53-31.png\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"viewof numPopulation = Inputs.range([20, 40], {\n label: \"Num population\",\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"viewof paraN = Inputs.range([1, 5], {\n label: \"Para N (sensitive)\",\n step: 0.1,\n value: 1.5\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"viewof paraM = Inputs.range([5, 10], { label: \"Para M\", step: 1, value: 5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":204,"value":"viewof tStep = Inputs.range([0.01, 0.1], {\n label: \"T step\",\n step: 0.01,\n value: 0.05\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":333,"value":"viewof valueK = Inputs.range([2, 50], { label: \"Value k\", step: 1, value: 17 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"viewof button = Inputs.button(\"Restart\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"Plot.plot({\n y: { nice: true },\n marks: [\n Plot.line(\n data.filter((d) => d.n === 0),\n { x: \"t\", y: \"f\", opacity: 0.1 }\n ),\n Plot.line(staticData, { x: \"t\", y: \"mean\" }),\n Plot.line(staticData, { x: \"t\", y: \"std\", stroke: \"red\" })\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"staticData = {\n const array = [];\n let dd;\n\n [...new Set(data.map((d) => d.t))].map((t) => {\n dd = data.filter((d) => d.t === t);\n array.push({\n t,\n mean: d3.mean(dd, (d) => d.f),\n std: Math.sqrt(d3.variance(dd, (d) => d.f))\n });\n });\n\n return array;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":94,"value":"data = {\n const data = [];\n\n fnDataInitial.map((d) => data.push(d));\n\n let gnt, d1, d2, d33, a, b, fnt;\n\n for (let t = 5; t < 60; t += tStep) {\n d1 = data\n .filter((d) => (d.t < t) & (d.t > t - 0.3))\n .map((d) => d.f * tStep);\n d2 = data\n .filter((d) => (d.t < t) & (d.t > t - 0.25))\n .map((d) => d.f * tStep);\n d33 = data\n .filter((d) => (d.t < t - 0.5) & (d.t > t - 0.75))\n .map((d) => d.f * tStep);\n a = Math.log(1 + d3.sum(d1) / numPopulation / 0.3) / Math.log(2);\n b = d3.sum(d2) / numPopulation - d3.sum(d33) / numPopulation;\n for (let n = 0; n < numPopulation; ++n) {\n gnt = funcGn(n, t);\n fnt = gnt * a * 0.5 * (1 + tanh(paraM * (10 * b + paraN))) + 0.001 * gnt;\n data.push({ t, n, f: fnt });\n }\n }\n\n return data;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":110,"value":"data","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":90,"value":"fnDataInitial = {\n const fnt = [];\n for (let t = 0; t < 5; t += tStep) {\n for (let n = 0; n < numPopulation; ++n) {\n fnt.push({ n, t, f: funcGn(n, t) });\n }\n }\n return fnt;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"fnDataInitial","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":62,"value":"## Gn Example","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":72,"value":"viewof selectedN = Inputs.range([0, numPopulation], {\n label: \"Selected n\",\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"Plot.plot({\n x: { nice: true },\n y: { nice: true },\n color: { legend: true, scheme: \"Category10\" },\n marks: [\n Plot.line(exampleData, { x: \"t\", y: \"gn\", stroke: \"n\", opacity: 0.5 }),\n Plot.line(\n exampleData.filter((d) => d.n === selectedN),\n { x: \"t\", y: \"gn\", stroke: \"n\", strokeWidth: 5 }\n )\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":306,"value":"Plot.plot({\n height: 400,\n width: 400,\n color: { legend: true, scheme: \"RdBu\" },\n marks: [Plot.cell(corrMat, { x: \"i\", y: \"j\", fill: \"corr\" })]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":312,"value":"Plot.plot({\n height: 200,\n width: 400,\n color: { legend: true, scheme: \"RdBu\" },\n marks: [\n Plot.rectY(\n corrMat,\n Plot.binX({ y: \"count\", fill: \"x\" }, { x: \"corr\", tip: true })\n )\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":291,"value":"corrMat = {\n let slice1,\n slice2,\n corr,\n res = [];\n for (let i = 0; i < numPopulation; ++i) {\n for (let j = 0; j < numPopulation; ++j) {\n slice1 = [...exampleData.filter((d) => d.n === i).map((d) => d.gn)];\n slice2 = [...exampleData.filter((d) => d.n === j).map((d) => d.gn)];\n corr = computeCorrelation(slice1, slice2);\n res.push({ i, j, corr, n: slice1.length, m: slice2.length });\n }\n }\n return res;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":296,"value":"function computeCorrelation(a, b) {\n let num = 0,\n m1 = d3.mean(a),\n m2 = d3.mean(b),\n s1 = Math.sqrt(d3.variance(a)),\n s2 = Math.sqrt(d3.variance(b)),\n den = s1 * s2;\n for (let i = 0; i < a.length; ++i) {\n num += (a[i] - m1) * (b[i] - m2);\n }\n return num / den / (a.length - 1);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"exampleData = {\n const data = [],\n resolution = 1000,\n scale = d3.scaleLinear().domain([0, resolution]).range([0, 10]);\n\n let t;\n\n for (let n = 0; n < numPopulation; ++n) {\n for (let i = 0; i < resolution; ++i) {\n t = scale(i);\n data.push({ t, n, gn: funcGn(n, t) });\n }\n }\n\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":293,"value":"exampleData","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":84,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":11,"value":"funcGn = (i, t) => {\n // Select the i-th seed\n const s = seeds[i],\n shapeFactor = 7;\n\n let core = (t) => {\n return 1 + tanh(shapeFactor * d3.sum(s, (x) => x.b * Math.sin(x.a * t)));\n };\n\n let w1 = (t) => {\n let sum = 0;\n for (let i = 0; i < 10; ++i) {\n sum += core(t + i * 10);\n }\n return sum / 10;\n };\n\n let w2 = (t) => {\n let sum = 0;\n for (let i = 0; i < 4; ++i) {\n sum += w1(t + i * 100);\n }\n return sum / 4;\n };\n\n return core(t);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"seeds = generateSeeds()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"function generateSeeds() {\n button;\n const seeds = [],\n rnd = d3.randomUniform(valueK, valueK * 5);\n\n for (let i = 0; i < numPopulation; ++i) {\n seeds.push(\n [...new Array(7)].map((d) => {\n let r = rnd(),\n r2 = rnd();\n return {\n a: Math.sqrt(Math.sqrt(r * r - 1)),\n b: Math.sqrt(Math.sqrt(r2 * r2 - 1))\n };\n })\n );\n }\n return seeds;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"tanh = (t) => {\n return (Math.exp(t) - Math.exp(-t)) / (Math.exp(t) + Math.exp(-t));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"d3 = require(\"d3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"