2f:[{"id":"ec1530afab38eb74780948c090b3d7aa3fe999a1759560b4f07baa3978f7a2670f7b0b9f62556141de999547af7ddf64e4fcea7edd072d953963aa7a525db308","href":"https://static.observableusercontent.com/files/ec1530afab38eb74780948c090b3d7aa3fe999a1759560b4f07baa3978f7a2670f7b0b9f62556141de999547af7ddf64e4fcea7edd072d953963aa7a525db308","name":"image@2.png","type":"image/png","lastModified":1685893732588.18,"size":102959},{"id":"96e3c1e55f65ca62db4b2d55ded9b63b868709f821b0a1f766ed900c60249e2771849f473b66279ac375631856f010433a9ec7caa2ee702719f8b45eedb3db44","href":"https://static.observableusercontent.com/files/96e3c1e55f65ca62db4b2d55ded9b63b868709f821b0a1f766ed900c60249e2771849f473b66279ac375631856f010433a9ec7caa2ee702719f8b45eedb3db44","name":"InvisibleAI.gif","type":"image/gif","lastModified":1686138378437.194,"size":23368501},{"id":"0bc52c43801b018024e98e843e1cf8f7fecb163129528b2aef6adf9d0f470fb45c13064371971fff87609203d110c49445275a8cf5f13b51b5bc1b44aa51d024","href":"https://static.observableusercontent.com/files/0bc52c43801b018024e98e843e1cf8f7fecb163129528b2aef6adf9d0f470fb45c13064371971fff87609203d110c49445275a8cf5f13b51b5bc1b44aa51d024","name":"image@1.png","type":"image/png","lastModified":1685892944685.14,"size":216434},{"id":"060efdf587d738e724676770128eed47878c0c00bd019d55087eec7a85e1c7d44e2e38300dd3f971a3463f6135e055f030d0e0400ce8d30a4a78d03c70a1356e","href":"https://static.observableusercontent.com/files/060efdf587d738e724676770128eed47878c0c00bd019d55087eec7a85e1c7d44e2e38300dd3f971a3463f6135e055f030d0e0400ce8d30a4a78d03c70a1356e","name":"image.png","type":"image/png","lastModified":1684675722395.094,"size":988879}] 2d:{"title":"Basics of Machine Learning","cells":[{"id":0,"value":"# Basics of Machine Learning\n> Philosophy is written in this grand book the universe. But the book cannot be understood unless one first learns to comprehend the language and to read the alphabet in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it.\n> \n> - [Galileo Galilei](https://www.pbs.org/wgbh/nova/article/galileo-sobel/), [Il Saggatore](https://en.wikipedia.org/wiki/The_Assayer) (1623)","pinned":false,"hidden":false,"mode":"md"},{"id":735,"value":"toc(\"h2,h3,h4\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":1008,"value":"## [Rates of Change](https://en.wikipedia.org/wiki/Calculus) and Change of Rates\n${await FileAttachment(\"image.png\").image({height: 400, width: 700})}\n> -[***WealthTrack*** May 19, 2023 Episode #1947, Recession Evidence ](https://wealthtrack.com/recession-evidence-is-building-time-to-get-defensive-says-influential-economist-dave-rosenberg/)","pinned":false,"hidden":false,"mode":"md"},{"id":41,"value":"## A Human's Approach to Finding the [Minima/Maxima](https://www.mathsisfun.com/calculus/maxima-minima.html) of a [Dynamic](https://en.wikipedia.org/wiki/Dynamics_%28mechanics%29)","pinned":false,"hidden":false,"mode":"md"},{"id":279,"value":"viewof dynamic = Inputs.radio([\"Quadratic\", \"Trig\"], {\n label: tex`\\LARGE Dynamic:`,\n value: \"Quadratic\",\n format: (x) => tex`\\LARGE{y = f(x) = ${dynamics[x].tex}}` // https://katex.org/docs/supported.html\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":281,"value":"// https://github.com/observablehq/stdlib/blob/main/README.md#tex_options\ndynamics = ({\n Quadratic: {\n tex: `x^2`, // Tex string; used for KaTex display and JavaScript function via Nerdamer's buildFunction method\n xDomain: [-5, 5] // the value of x to be used in the anlaysis and plot domain\n },\n Trig: {\n tex: `sin(x)`,\n xDomain: [0, Math.PI * 2]\n }\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":951,"value":"plotDynamic([\n Plot.line(ends, { stroke: \"red\" }), // secant line\n Plot.dot(points, { fill: \"black\", r: 5 }) // secant intersect points to plotted function line y = f(x)\n])","pinned":false,"hidden":false,"mode":"ojs"},{"id":12,"value":"viewof x0 = Inputs.range([-5, 5], { step: 0.1, label: tex`\\LARGE x_0` })","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"viewof h = Inputs.range([0.001, 5], { step: 0.001, label: tex`\\LARGE h` })","pinned":false,"hidden":false,"mode":"ojs"},{"id":964,"value":"$${tex.options({\n trust: true,\n displayMode: true\n})`\\begin{aligned} \n \\text{slope of \\href{https://en.wikipedia.org/wiki/Secant_line}{secant line}} \n &= \\frac{f(x_0+h)-f(x_0)}{h} \\\\\n &= \\frac{${\"f(x)\".replace(\"x\",`${x0} + ${h}`)} - \n ${dynamics[dynamic].tex.replace(\"x\", \"f(x)\").replace(\"x\",`${x0}`)}}{${h}} \\\\\n &= \\frac{${dynamics[dynamic].tex\n .replace(\"x\", \"(x)\")\n .replace(\"x\", `${x0} + ${h}`)} - ${dynamics[dynamic].tex\n .replace(\"x\", \"(x)\")\n .replace(\"x\", `${x0}`)}}{${h}} \\\\\n &= \\frac{${dynamics[dynamic].tex\n .replace(\"x\", \"(x)\")\n .replace(\"x\", `${x0 + h}`)} - ${dynamics[dynamic].tex\n .replace(\"x\", \"(x)\")\n .replace(\"x\", `${x0}`)}}{${h}} \\\\\n &= \\frac{${d3.format(\".5f\")(f(x0 + h))} - ${f(x0)}}{${h}} \\\\\n &= \\frac{${d3.format(\".5f\")(f(x0 + h) - f(x0))}}{${h}} \\\\\n &= ${d3.format(\".2f\")((f(x0+h)-f(x0))/h)}\n \\end{aligned}`}","pinned":false,"hidden":false,"mode":"md"},{"id":96,"value":"## Determine the Minima or Maxima Computationally\nThe JavaScript [Nerdamer](https://github.com/jiggzson/nerdamer) math library is used to determine the [derivatives](https://www.mathsisfun.com/calculus/derivatives-introduction.html) of the function\n\n${tex.options({\n displayMode: true\n})`{y = f(x) = ${dynamics[dynamic].tex}}`}\nThis represents the slope of the secant at any given point along the curve:","pinned":false,"hidden":false,"mode":"md"},{"id":150,"value":"firstDerivative = nerdamer.diff(`${dynamics[dynamic].tex}`, `x`).text()","pinned":false,"hidden":false,"mode":"ojs"},{"id":211,"value":"The first derivative is a function representing the slope of the secant in the format of:\n\n${tex.options({\n displayMode: true\n})`{y' = f'(x) = ${firstDerivative}}`}\n\nThis new function is solved for:\n\n${tex.options({\n displayMode: true\n})`y'= f'(x) = ${firstDerivative} = 0`}","pinned":false,"hidden":false,"mode":"md"},{"id":425,"value":"minMax = {\n const solutions = nerdamer\n .solveEquations(`${firstDerivative}=0`, \"x\") // determine all solutions where first derivative is 0\n .map((solution) => Math.abs(Number(nerdamer(solution).evaluate().text()))); // Evaluate solutions and return number; abs used for trig fns\n\n return [...new Set(solutions)].sort((a, b) => a - b).slice(0, 2); // Only the first two uniques\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":478,"value":"\nTo computationally determine whether a given solution represents a minima or maxima the [second derivative](https://simple.wikipedia.org/wiki/Second_derivative) is first calculated: \n\n${tex.options({\n displayMode: true\n})`{y'' = f''(x) = ${nerdamer.diff(firstDerivative, \"x\").text()}}`}","pinned":false,"hidden":false,"mode":"md"},{"id":277,"value":"secondDerivative = nerdamer.diff(firstDerivative, \"x\").text()","pinned":false,"hidden":false,"mode":"ojs"},{"id":482,"value":"Then, for each of the possible minMax solutions, the [second derivative is evaluated](https://en.wikipedia.org/wiki/Second_derivative#Second_derivative_test) to determine if it is:\n* Less than 0 for a local maximum\n* Greater than 0 for a local minimum","pinned":false,"hidden":false,"mode":"md"},{"id":495,"value":"minMaxPoints = minMax.map((sol) => ({\n x: sol,\n y: f(sol),\n \"First Derivative\": Number(\n nerdamer(`${firstDerivative}`, { x: sol }).evaluate().text()\n ), // https://en.wikipedia.org/wiki/Signed_zero\n \"Second Derivative\": Number(\n nerdamer(`${secondDerivative}`, { x: sol }).evaluate().text()\n ),\n \"Minima/Maxima\":\n Number(nerdamer(`${secondDerivative}`, { x: sol }).evaluate().text()) < 0\n ? \"Maxima\"\n : \"Minima\"\n}))","pinned":false,"hidden":false,"mode":"ojs"},{"id":583,"value":"Inputs.table(minMaxPoints, { width: 700 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":213,"value":"Finally, we display the derived minima/maxima value(s):","pinned":false,"hidden":false,"mode":"md"},{"id":195,"value":"plotDynamic([\n Plot.dot(minMaxPoints, {\n x: \"x\",\n y: \"y\",\n fill: \"red\",\n r: 5,\n title: (d) => `x: ${d.x} y: ${d.y}`\n }),\n Plot.text(minMaxPoints, {\n x: \"x\",\n y: \"y\",\n text: (point) => `${point[\"Minima/Maxima\"]}`,\n dy: -10,\n dx: 20\n })\n])","pinned":false,"hidden":false,"mode":"ojs"},{"id":263,"value":"## [Video: Analyzing Concavity](https://www.khanacademy.org/math/ap-calculus-ab)\n\n","pinned":false,"hidden":false,"mode":"md"},{"id":995,"value":"## Machine Learning in Use\n","pinned":false,"hidden":false,"mode":"md"},{"id":998,"value":"","pinned":false,"hidden":false,"mode":"md"},{"id":1005,"value":"","pinned":false,"hidden":false,"mode":"md"},{"id":1039,"value":"[Invisible AI](https://www.invisible.ai/)![image@3.png](${await FileAttachment(\"InvisibleAI.gif\").url()})","pinned":false,"hidden":false,"mode":"md"},{"id":1025,"value":"* [Standardization and Control of Grignard Reactions in a Universal Chemical Synthesis Machine using online NMR](https://onlinelibrary.wiley.com/doi/10.1002/anie.202106323)\n* ![image@1.png](${await FileAttachment(\"image@1.png\").url()})\n* [Nuclear Magnetic Resonance spectroscopy (NMR)](https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance_spectroscopy)\n* [Chemical Integrated Development Environment](http://chemify.org)\n * ![image@2.png](${await FileAttachment(\"image@2.png\").url()}) \n* ","pinned":false,"hidden":false,"mode":"md"},{"id":1035,"value":"## Challenges and Opportunities for You and Your Loved Ones\n\"Learning to prompt ***good***.\"\n \n**AI in Healthcare** \n\n","pinned":false,"hidden":false,"mode":"md"},{"id":99,"value":"## Notebook Objects","pinned":false,"hidden":false,"mode":"md"},{"id":657,"value":"// https://nerdamer.com/functions/Expression.buildFunction.html\nf = nerdamer(dynamics[dynamic].tex).buildFunction()","pinned":false,"hidden":false,"mode":"ojs"},{"id":848,"value":"// https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Spread_syntax\n// https://github.com/d3/d3-array/blob/v3.2.3/README.md#range\n// https://github.com/d3/d3-array/issues/90\n// https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/map\ndata = d3\n .range(...dynamics[dynamic].xDomain, 0.1)\n .concat(dynamics[dynamic].xDomain[1])\n .map((d) => ({ x: d, y: f(d) }))","pinned":false,"hidden":false,"mode":"ojs"},{"id":38,"value":"points = [\n [x0, f(x0)],\n [x0 + h, f(x0 + h)]\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"line = function (x) {\n const slope = (f(x0 + h) - f(x0)) / h;\n const b = f(x0) - slope * x0;\n return slope * x + b;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"ends = [\n [-5, line(-5)],\n [5, line(5)]\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":945,"value":"function plotDynamic(additionalMarks) {\n // Adopted from https://observablehq.com/@credmond/the-derivative\n return Plot.plot({\n x: { domain: dynamics[dynamic].xDomain, label: \"x\", grid: true },\n y: {\n domain: d3.extent(data.map((d) => d.y)).map((d) => Math.round(d)),\n label: \"y\",\n grid: true\n },\n caption: tex`\\LARGE{y = f(x) = ${dynamics[dynamic].tex}}`,\n marks: [\n Plot.ruleX([0]), // y axis\n Plot.ruleY([0]), // x axis\n Plot.line(data, { x: \"x\", y: \"y\" }), // y = f(x) arrays plotted\n [...additionalMarks]\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"## Imports","pinned":false,"hidden":false,"mode":"md"},{"id":7,"value":"// https://nerdamer.com/\n// https://observablehq.com/@jbfil/nerdamer-import\nnerdamer = {\n var nerdamer = (window.nerdamer =\n await require(\"https://bundle.run/nerdamer-fork@1.0.4\"));\n await require(\"nerdamer-fork/Calculus.js\").catch(() => {});\n await require(\"nerdamer-fork/Algebra.js\").catch(() => {});\n await require(\"nerdamer-fork/Solve.js\").catch(() => {});\n await require(\"nerdamer-fork/Extra.js\").catch(() => {});\n return nerdamer;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":623,"value":"import { toc } from \"@sugi2000/toc\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W2f","stdlib":"1","titling":"auto"}