diff --git a/js/book.js b/js/book.js
index aa12e7e..dd8686c 100644
--- a/js/book.js
+++ b/js/book.js
@@ -1,697 +1 @@
-"use strict";
-
-// Fix back button cache problem
-window.onunload = function () { };
-
-// Global variable, shared between modules
-function playground_text(playground, hidden = true) {
- let code_block = playground.querySelector("code");
-
- if (window.ace && code_block.classList.contains("editable")) {
- let editor = window.ace.edit(code_block);
- return editor.getValue();
- } else if (hidden) {
- return code_block.textContent;
- } else {
- return code_block.innerText;
- }
-}
-
-(function codeSnippets() {
- function fetch_with_timeout(url, options, timeout = 6000) {
- return Promise.race([
- fetch(url, options),
- new Promise((_, reject) => setTimeout(() => reject(new Error('timeout')), timeout))
- ]);
- }
-
- var playgrounds = Array.from(document.querySelectorAll(".playground"));
- if (playgrounds.length > 0) {
- fetch_with_timeout("https://play.rust-lang.org/meta/crates", {
- headers: {
- 'Content-Type': "application/json",
- },
- method: 'POST',
- mode: 'cors',
- })
- .then(response => response.json())
- .then(response => {
- // get list of crates available in the rust playground
- let playground_crates = response.crates.map(item => item["id"]);
- playgrounds.forEach(block => handle_crate_list_update(block, playground_crates));
- });
- }
-
- function handle_crate_list_update(playground_block, playground_crates) {
- // update the play buttons after receiving the response
- update_play_button(playground_block, playground_crates);
-
- // and install on change listener to dynamically update ACE editors
- if (window.ace) {
- let code_block = playground_block.querySelector("code");
- if (code_block.classList.contains("editable")) {
- let editor = window.ace.edit(code_block);
- editor.addEventListener("change", function (e) {
- update_play_button(playground_block, playground_crates);
- });
- // add Ctrl-Enter command to execute rust code
- editor.commands.addCommand({
- name: "run",
- bindKey: {
- win: "Ctrl-Enter",
- mac: "Ctrl-Enter"
- },
- exec: _editor => run_rust_code(playground_block)
- });
- }
- }
- }
-
- // updates the visibility of play button based on `no_run` class and
- // used crates vs ones available on https://play.rust-lang.org
- function update_play_button(pre_block, playground_crates) {
- var play_button = pre_block.querySelector(".play-button");
-
- // skip if code is `no_run`
- if (pre_block.querySelector('code').classList.contains("no_run")) {
- play_button.classList.add("hidden");
- return;
- }
-
- // get list of `extern crate`'s from snippet
- var txt = playground_text(pre_block);
- var re = /extern\s+crate\s+([a-zA-Z_0-9]+)\s*;/g;
- var snippet_crates = [];
- var item;
- while (item = re.exec(txt)) {
- snippet_crates.push(item[1]);
- }
-
- // check if all used crates are available on play.rust-lang.org
- var all_available = snippet_crates.every(function (elem) {
- return playground_crates.indexOf(elem) > -1;
- });
-
- if (all_available) {
- play_button.classList.remove("hidden");
- } else {
- play_button.classList.add("hidden");
- }
- }
-
- function run_rust_code(code_block) {
- var result_block = code_block.querySelector(".result");
- if (!result_block) {
- result_block = document.createElement('code');
- result_block.className = 'result hljs language-bash';
-
- code_block.append(result_block);
- }
-
- let text = playground_text(code_block);
- let classes = code_block.querySelector('code').classList;
- let edition = "2015";
- if(classes.contains("edition2018")) {
- edition = "2018";
- } else if(classes.contains("edition2021")) {
- edition = "2021";
- }
- var params = {
- version: "stable",
- optimize: "0",
- code: text,
- edition: edition
- };
-
- if (text.indexOf("#![feature") !== -1) {
- params.version = "nightly";
- }
-
- result_block.innerText = "Running...";
-
- fetch_with_timeout("https://play.rust-lang.org/evaluate.json", {
- headers: {
- 'Content-Type': "application/json",
- },
- method: 'POST',
- mode: 'cors',
- body: JSON.stringify(params)
- })
- .then(response => response.json())
- .then(response => {
- if (response.result.trim() === '') {
- result_block.innerText = "No output";
- result_block.classList.add("result-no-output");
- } else {
- result_block.innerText = response.result;
- result_block.classList.remove("result-no-output");
- }
- })
- .catch(error => result_block.innerText = "Playground Communication: " + error.message);
- }
-
- // Syntax highlighting Configuration
- hljs.configure({
- tabReplace: ' ', // 4 spaces
- languages: [], // Languages used for auto-detection
- });
-
- let code_nodes = Array
- .from(document.querySelectorAll('code'))
- // Don't highlight `inline code` blocks in headers.
- .filter(function (node) {return !node.parentElement.classList.contains("header"); });
-
- if (window.ace) {
- // language-rust class needs to be removed for editable
- // blocks or highlightjs will capture events
- code_nodes
- .filter(function (node) {return node.classList.contains("editable"); })
- .forEach(function (block) { block.classList.remove('language-rust'); });
-
- code_nodes
- .filter(function (node) {return !node.classList.contains("editable"); })
- .forEach(function (block) { hljs.highlightBlock(block); });
- } else {
- code_nodes.forEach(function (block) { hljs.highlightBlock(block); });
- }
-
- // Adding the hljs class gives code blocks the color css
- // even if highlighting doesn't apply
- code_nodes.forEach(function (block) { block.classList.add('hljs'); });
-
- Array.from(document.querySelectorAll("code.hljs")).forEach(function (block) {
-
- var lines = Array.from(block.querySelectorAll('.boring'));
- // If no lines were hidden, return
- if (!lines.length) { return; }
- block.classList.add("hide-boring");
-
- var buttons = document.createElement('div');
- buttons.className = 'buttons';
- buttons.innerHTML = "
\ No newline at end of file
diff --git a/js/elasticlunr.min.js b/js/elasticlunr.min.js
index 94b20dd..897ef0d 100644
--- a/js/elasticlunr.min.js
+++ b/js/elasticlunr.min.js
@@ -1,10 +1 @@
-/**
- * elasticlunr - http://weixsong.github.io
- * Lightweight full-text search engine in Javascript for browser search and offline search. - 0.9.5
- *
- * Copyright (C) 2017 Oliver Nightingale
- * Copyright (C) 2017 Wei Song
- * MIT Licensed
- * @license
- */
-!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. This may cause problems when serialising the index.\n",e)},t.Pipeline.load=function(e){var n=new t.Pipeline;return e.forEach(function(e){var i=t.Pipeline.getRegisteredFunction(e);if(!i)throw new Error("Cannot load un-registered function: "+e);n.add(i)}),n},t.Pipeline.prototype.add=function(){var e=Array.prototype.slice.call(arguments);e.forEach(function(e){t.Pipeline.warnIfFunctionNotRegistered(e),this._queue.push(e)},this)},t.Pipeline.prototype.after=function(e,n){t.Pipeline.warnIfFunctionNotRegistered(n);var i=this._queue.indexOf(e);if(-1===i)throw new Error("Cannot find existingFn");this._queue.splice(i+1,0,n)},t.Pipeline.prototype.before=function(e,n){t.Pipeline.warnIfFunctionNotRegistered(n);var i=this._queue.indexOf(e);if(-1===i)throw new Error("Cannot find existingFn");this._queue.splice(i,0,n)},t.Pipeline.prototype.remove=function(e){var t=this._queue.indexOf(e);-1!==t&&this._queue.splice(t,1)},t.Pipeline.prototype.run=function(e){for(var t=[],n=e.length,i=this._queue.length,o=0;n>o;o++){for(var r=e[o],s=0;i>s&&(r=this._queue[s](r,o,e),void 0!==r&&null!==r);s++);void 0!==r&&null!==r&&t.push(r)}return t},t.Pipeline.prototype.reset=function(){this._queue=[]},t.Pipeline.prototype.get=function(){return this._queue},t.Pipeline.prototype.toJSON=function(){return this._queue.map(function(e){return t.Pipeline.warnIfFunctionNotRegistered(e),e.label})},t.Index=function(){this._fields=[],this._ref="id",this.pipeline=new t.Pipeline,this.documentStore=new t.DocumentStore,this.index={},this.eventEmitter=new t.EventEmitter,this._idfCache={},this.on("add","remove","update",function(){this._idfCache={}}.bind(this))},t.Index.prototype.on=function(){var e=Array.prototype.slice.call(arguments);return this.eventEmitter.addListener.apply(this.eventEmitter,e)},t.Index.prototype.off=function(e,t){return this.eventEmitter.removeListener(e,t)},t.Index.load=function(e){e.version!==t.version&&t.utils.warn("version mismatch: current "+t.version+" importing "+e.version);var n=new this;n._fields=e.fields,n._ref=e.ref,n.documentStore=t.DocumentStore.load(e.documentStore),n.pipeline=t.Pipeline.load(e.pipeline),n.index={};for(var i in e.index)n.index[i]=t.InvertedIndex.load(e.index[i]);return n},t.Index.prototype.addField=function(e){return this._fields.push(e),this.index[e]=new t.InvertedIndex,this},t.Index.prototype.setRef=function(e){return this._ref=e,this},t.Index.prototype.saveDocument=function(e){return this.documentStore=new t.DocumentStore(e),this},t.Index.prototype.addDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.addDoc(i,e),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));this.documentStore.addFieldLength(i,n,o.length);var r={};o.forEach(function(e){e in r?r[e]+=1:r[e]=1},this);for(var s in r){var u=r[s];u=Math.sqrt(u),this.index[n].addToken(s,{ref:i,tf:u})}},this),n&&this.eventEmitter.emit("add",e,this)}},t.Index.prototype.removeDocByRef=function(e){if(e&&this.documentStore.isDocStored()!==!1&&this.documentStore.hasDoc(e)){var t=this.documentStore.getDoc(e);this.removeDoc(t,!1)}},t.Index.prototype.removeDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.hasDoc(i)&&(this.documentStore.removeDoc(i),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));o.forEach(function(e){this.index[n].removeToken(e,i)},this)},this),n&&this.eventEmitter.emit("remove",e,this))}},t.Index.prototype.updateDoc=function(e,t){var t=void 0===t?!0:t;this.removeDocByRef(e[this._ref],!1),this.addDoc(e,!1),t&&this.eventEmitter.emit("update",e,this)},t.Index.prototype.idf=function(e,t){var n="@"+t+"/"+e;if(Object.prototype.hasOwnProperty.call(this._idfCache,n))return this._idfCache[n];var i=this.index[t].getDocFreq(e),o=1+Math.log(this.documentStore.length/(i+1));return this._idfCache[n]=o,o},t.Index.prototype.getFields=function(){return this._fields.slice()},t.Index.prototype.search=function(e,n){if(!e)return[];e="string"==typeof e?{any:e}:JSON.parse(JSON.stringify(e));var i=null;null!=n&&(i=JSON.stringify(n));for(var o=new t.Configuration(i,this.getFields()).get(),r={},s=Object.keys(e),u=0;u0&&t.push(e);for(var i in n)"docs"!==i&&"df"!==i&&this.expandToken(e+i,t,n[i]);return t},t.InvertedIndex.prototype.toJSON=function(){return{root:this.root}},t.Configuration=function(e,n){var e=e||"";if(void 0==n||null==n)throw new Error("fields should not be null");this.config={};var i;try{i=JSON.parse(e),this.buildUserConfig(i,n)}catch(o){t.utils.warn("user configuration parse failed, will use default configuration"),this.buildDefaultConfig(n)}},t.Configuration.prototype.buildDefaultConfig=function(e){this.reset(),e.forEach(function(e){this.config[e]={boost:1,bool:"OR",expand:!1}},this)},t.Configuration.prototype.buildUserConfig=function(e,n){var i="OR",o=!1;if(this.reset(),"bool"in e&&(i=e.bool||i),"expand"in e&&(o=e.expand||o),"fields"in e)for(var r in e.fields)if(n.indexOf(r)>-1){var s=e.fields[r],u=o;void 0!=s.expand&&(u=s.expand),this.config[r]={boost:s.boost||0===s.boost?s.boost:1,bool:s.bool||i,expand:u}}else t.utils.warn("field name in user configuration not found in index instance fields");else this.addAllFields2UserConfig(i,o,n)},t.Configuration.prototype.addAllFields2UserConfig=function(e,t,n){n.forEach(function(n){this.config[n]={boost:1,bool:e,expand:t}},this)},t.Configuration.prototype.get=function(){return this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oo;o++){for(var r=e[o],s=0;i>s&&(r=this._queue[s](r,o,e),void 0!==r&&null!==r);s++);void 0!==r&&null!==r&&t.push(r)}return t},t.Pipeline.prototype.reset=function(){this._queue=[]},t.Pipeline.prototype.get=function(){return this._queue},t.Pipeline.prototype.toJSON=function(){return this._queue.map(function(e){return t.Pipeline.warnIfFunctionNotRegistered(e),e.label})},t.Index=function(){this._fields=[],this._ref="id",this.pipeline=new t.Pipeline,this.documentStore=new t.DocumentStore,this.index={},this.eventEmitter=new t.EventEmitter,this._idfCache={},this.on("add","remove","update",function(){this._idfCache={}}.bind(this))},t.Index.prototype.on=function(){var e=Array.prototype.slice.call(arguments);return this.eventEmitter.addListener.apply(this.eventEmitter,e)},t.Index.prototype.off=function(e,t){return this.eventEmitter.removeListener(e,t)},t.Index.load=function(e){e.version!==t.version&&t.utils.warn("version mismatch: current "+t.version+" importing "+e.version);var n=new this;n._fields=e.fields,n._ref=e.ref,n.documentStore=t.DocumentStore.load(e.documentStore),n.pipeline=t.Pipeline.load(e.pipeline),n.index={};for(var i in e.index)n.index[i]=t.InvertedIndex.load(e.index[i]);return n},t.Index.prototype.addField=function(e){return this._fields.push(e),this.index[e]=new t.InvertedIndex,this},t.Index.prototype.setRef=function(e){return this._ref=e,this},t.Index.prototype.saveDocument=function(e){return this.documentStore=new t.DocumentStore(e),this},t.Index.prototype.addDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.addDoc(i,e),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));this.documentStore.addFieldLength(i,n,o.length);var r={};o.forEach(function(e){e in r?r[e]+=1:r[e]=1},this);for(var s in r){var u=r[s];u=Math.sqrt(u),this.index[n].addToken(s,{ref:i,tf:u})}},this),n&&this.eventEmitter.emit("add",e,this)}},t.Index.prototype.removeDocByRef=function(e){if(e&&this.documentStore.isDocStored()!==!1&&this.documentStore.hasDoc(e)){var t=this.documentStore.getDoc(e);this.removeDoc(t,!1)}},t.Index.prototype.removeDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.hasDoc(i)&&(this.documentStore.removeDoc(i),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));o.forEach(function(e){this.index[n].removeToken(e,i)},this)},this),n&&this.eventEmitter.emit("remove",e,this))}},t.Index.prototype.updateDoc=function(e,t){var t=void 0===t?!0:t;this.removeDocByRef(e[this._ref],!1),this.addDoc(e,!1),t&&this.eventEmitter.emit("update",e,this)},t.Index.prototype.idf=function(e,t){var n="@"+t+"/"+e;if(Object.prototype.hasOwnProperty.call(this._idfCache,n))return this._idfCache[n];var i=this.index[t].getDocFreq(e),o=1+Math.log(this.documentStore.length/(i+1));return this._idfCache[n]=o,o},t.Index.prototype.getFields=function(){return this._fields.slice()},t.Index.prototype.search=function(e,n){if(!e)return[];e="string"==typeof e?{any:e}:JSON.parse(JSON.stringify(e));var i=null;null!=n&&(i=JSON.stringify(n));for(var o=new t.Configuration(i,this.getFields()).get(),r={},s=Object.keys(e),u=0;u0&&t.push(e);for(var i in n)"docs"!==i&&"df"!==i&&this.expandToken(e+i,t,n[i]);return t},t.InvertedIndex.prototype.toJSON=function(){return{root:this.root}},t.Configuration=function(e,n){var e=e||"";if(void 0==n||null==n)throw new Error("fields should not be null");this.config={};var i;try{i=JSON.parse(e),this.buildUserConfig(i,n)}catch(o){t.utils.warn("user configuration parse failed, will use default configuration"),this.buildDefaultConfig(n)}},t.Configuration.prototype.buildDefaultConfig=function(e){this.reset(),e.forEach(function(e){this.config[e]={boost:1,bool:"OR",expand:!1}},this)},t.Configuration.prototype.buildUserConfig=function(e,n){var i="OR",o=!1;if(this.reset(),"bool"in e&&(i=e.bool||i),"expand"in e&&(o=e.expand||o),"fields"in e)for(var r in e.fields)if(n.indexOf(r)>-1){var s=e.fields[r],u=o;void 0!=s.expand&&(u=s.expand),this.config[r]={boost:s.boost||0===s.boost?s.boost:1,bool:s.bool||i,expand:u}}else t.utils.warn("field name in user configuration not found in index instance fields");else this.addAllFields2UserConfig(i,o,n)},t.Configuration.prototype.addAllFields2UserConfig=function(e,t,n){n.forEach(function(n){this.config[n]={boost:1,bool:e,expand:t}},this)},t.Configuration.prototype.get=function(){return this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();o
\ No newline at end of file
diff --git a/js/highlight.js b/js/highlight.js
index 18d2434..da14756 100644
--- a/js/highlight.js
+++ b/js/highlight.js
@@ -1,29 +1,5 @@
-/*
- Highlight.js 10.1.1 (93fd0d73)
- License: BSD-3-Clause
- Copyright (c) 2006-2020, Ivan Sagalaev
-*/
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path1.rglob(pattern1)","breadcrumbs":"Notes » Programming » Python » Path object","id":"1042","title":"Path object"},"1043":{"body":"remove subtree shuril.rmtree(path1)","breadcrumbs":"Notes » Programming » Python » shutil module","id":"1043","title":"shutil module"},"1044":{"body":"both pathlib and shutil are implemented using os","breadcrumbs":"Notes » Programming » Python » os module","id":"1044","title":"os module"},"1045":{"body":"","breadcrumbs":"Notes » Programming » Python » file","id":"1045","title":"file"},"1046":{"body":"","breadcrumbs":"Notes » Programming » Python » text file","id":"1046","title":"text file"},"1047":{"body":"","breadcrumbs":"Notes » Programming » Python » character encoding","id":"1047","title":"character encoding"},"1048":{"body":"carriage return \\r line feed \\n","breadcrumbs":"Notes » Programming » Python » line ending","id":"1048","title":"line ending"},"1049":{"body":"csv module write writer object csv.writer(file1) write one line writer1.writerow(list_of_str1) add ',' between all item and \\n at the end write multiple lines writer1.writerows(list_of_list_of_str1) dictionary writer object csv.DictWriter(file1,fieldname=list_of_str1) write header DictWriter1.writeheader() → int of character written write one line DictWriter1.writerow(dict1) write multiple lineDictWriter1.writerows(list_of_dict1) it in fact work with any object with write() method read reader object csv.reader(file1) → iterable of list of str dictionary reader object csv.DictReader(file1) → *iterable of dict of header:val","breadcrumbs":"Notes » Programming » Python » csv file","id":"1049","title":"csv file"},"105":{"body":"command/status line request: command GET / HTTP/1.1 response: status line HTTP/1.1 200 OK headers mandatory Content-Length: 69 empty line \\r\\n content","breadcrumbs":"Notes » Computer Science » Networking » HTTP message","id":"105","title":"HTTP message"},"1050":{"body":"can only interact with byte directly","breadcrumbs":"Notes » Programming » Python » binary file","id":"1050","title":"binary file"},"1051":{"body":"","breadcrumbs":"Notes » Programming » Python » file object","id":"1051","title":"file object"},"1052":{"body":"path1.open() from pathlib mode path1.open(mode=mode1) \"r\"—read \"w\"—write \"a\"—append \"~b\"—for binary file with ~ be one of the mentioned encoding path1.open(encoding=encoding1). \"ascii\" \"utf-8\" open(string1) built-in exactly like path1.open() except using a string with statement with … as file1:","breadcrumbs":"Notes » Programming » Python » create","id":"1052","title":"create"},"1053":{"body":"","breadcrumbs":"Notes » Programming » Python » close file1.close()","id":"1053","title":"close file1.close()"},"1054":{"body":"all at once file1.read() → str line by line file1.readlines() → iterable of str","breadcrumbs":"Notes » Programming » Python » read","id":"1054","title":"read"},"1055":{"body":"create file if not exist and parent exist write a string file1.write(string1) → int of character written overwrite when in write mode append when in append mode write a list of string file1.writelines(list1)","breadcrumbs":"Notes » Programming » Python » write","id":"1055","title":"write"},"1056":{"body":"","breadcrumbs":"Notes » Programming » Python » regular expression (regex)","id":"1056","title":"regular expression (regex)"},"1057":{"body":"","breadcrumbs":"Notes » Programming » Python » meta-character","id":"1057","title":"meta-character"},"1058":{"body":"* any number of the character left to it, greedy, excluding \\n . a character, excluding \\n *? any number of the character left to it, non-greedy, excluding \\n","breadcrumbs":"Notes » Programming » Python » wild card","id":"1058","title":"wild card"},"1059":{"body":"find all re.findall(pattern_string1,checked_string1) → list of str not case sensitive re.meth1(…,re.IGNORECASE) re.search(pattern_string1,checked_string1) → MatchObject match_object1.group() → the first greedy result find replace re.sub(pattern_string1,replace_string1,checked_string1)","breadcrumbs":"Notes » Programming » Python » string method","id":"1059","title":"string method"},"106":{"body":"client request & server respond (minimum 2 transmission) message oriented lower overhead than TCP stub allow function call protocol encode high-level data acknowledgement model send ACK response as ACK ping/working sync/async popular example: REST/gRPC","breadcrumbs":"Notes » Computer Science » Networking » remote procedure call (RPC)","id":"106","title":"remote procedure call (RPC)"},"1060":{"body":"","breadcrumbs":"Notes » Programming » Python » mistake","id":"1060","title":"mistake"},"1061":{"body":"syntax error run-time error","breadcrumbs":"Notes » Programming » Python » error","id":"1061","title":"error"},"1062":{"body":"try: execution1\nexcept ErrorClass as error_name: execution2\nfinally: execution3 multiple kinds of error except (error_name1,error_name2): catch error individually using multiple except bare exception clause except: catch any error","breadcrumbs":"Notes » Programming » Python » try","id":"1062","title":"try"},"1063":{"body":"block comment # block comment in-line comment code # in-line comment document code docstring \"\"\"description of this program\"\"\"","breadcrumbs":"Notes » Programming » Python » comment","id":"1063","title":"comment"},"1064":{"body":"kill the current tqdm progress bar: from tqdm import tqdm\ntqdm._instances.pop().close()","breadcrumbs":"Notes » Programming » Python » tqdm » tqdm","id":"1064","title":"tqdm"},"1065":{"body":"Mathematica approximation complex number variable assignment data structure list ` vector matrix hide output ; force simplify Simplify[] math function define f[var1_]:=… calculate f[…] integration equation polynomial non-polynomial plot space is seen as $\\times$","breadcrumbs":"Notes » Programming » Mathematica » Mathematica","id":"1065","title":"Mathematica"},"1066":{"body":"exact result by default, to get approximation add a dot at the end …. use N[]","breadcrumbs":"Notes » Programming » Mathematica » approximation","id":"1066","title":"approximation"},"1067":{"body":"imaginary unit I","breadcrumbs":"Notes » Programming » Mathematica » complex number","id":"1067","title":"complex number"},"1068":{"body":"unassigned variable treated as symbol assigned variable work like in other language clear variable Clear[]","breadcrumbs":"Notes » Programming » Mathematica » variable assignment","id":"1068","title":"variable assignment"},"1069":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » data structure","id":"1069","title":"data structure"},"107":{"body":"latency is vital monitor path property let application handle packet drop","breadcrumbs":"Notes » Computer Science » Networking » real-time protocol (RTP)","id":"107","title":"real-time protocol (RTP)"},"1070":{"body":"getter list1[[index1]] slicing list1[[start1;;end1]] show as list FullForm[]","breadcrumbs":"Notes » Programming » Mathematica » list `","id":"1070","title":"list `"},"1071":{"body":"vector are represented as list dot . or Dot[,] cross esc + cross + esc or Cross[,]","breadcrumbs":"Notes » Programming » Mathematica » vector","id":"1071","title":"vector"},"1072":{"body":"a list of list show as matrix MatrixForm[]","breadcrumbs":"Notes » Programming » Mathematica » matrix","id":"1072","title":"matrix"},"1073":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » hide output ;","id":"1073","title":"hide output ;"},"1074":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » force simplify Simplify[]","id":"1074","title":"force simplify Simplify[]"},"1075":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » math function","id":"1075","title":"math function"},"1076":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » define f[var1_]:=…","id":"1076","title":"define f[var1_]:=…"},"1077":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » calculate f[…]","id":"1077","title":"calculate f[…]"},"1078":{"body":"indefinite Integrate[fun1[var1],var1] definite Integrate[fun1[var1],{var1,start1,end1}] numerical NIntegrate","breadcrumbs":"Notes » Programming » Mathematica » integration","id":"1078","title":"integration"},"1079":{"body":"","breadcrumbs":"Notes » Programming » Mathematica » equation","id":"1079","title":"equation"},"108":{"body":"media delivery built-in media stream sync not depend on low-layer functionality common: IP + UDP example: WebRTC","breadcrumbs":"Notes » Computer Science » Networking » stream control transmission protocol (SCTP)","id":"108","title":"stream control transmission protocol (SCTP)"},"1080":{"body":"SolveValue[] gives precise solution NSolveValue[] gives approximate solution","breadcrumbs":"Notes » Programming » Mathematica » polynomial","id":"1080","title":"polynomial"},"1081":{"body":"FindRoot[] uses Newton's Method","breadcrumbs":"Notes » Programming » Mathematica » non-polynomial","id":"1081","title":"non-polynomial"},"1082":{"body":"search help","breadcrumbs":"Notes » Programming » Mathematica » plot","id":"1082","title":"plot"},"1083":{"body":"MATLAB syntax number special variable special constant numerical operator character syntax semicolon ; percentage sign % save and load variable assign vector matrix solve Ax=B variable management session management shell environment file system format format arg1 find help","breadcrumbs":"Notes » Programming » MATLAB » MATLAB","id":"1083","title":"MATLAB"},"1084":{"body":"","breadcrumbs":"Notes » Programming » MATLAB » syntax","id":"1084","title":"syntax"},"1085":{"body":"","breadcrumbs":"Notes » Programming » MATLAB » number","id":"1085","title":"number"},"1086":{"body":"most recent answer ans accuracy of floating-point precision eps","breadcrumbs":"Notes » Programming » MATLAB » special variable","id":"1086","title":"special variable"},"1087":{"body":"not a number Nan ∞ Inf −1 i or j π pi","breadcrumbs":"Notes » Programming » MATLAB » special constant","id":"1087","title":"special constant"},"1088":{"body":"plus + minus - matrix multiplication * array multiplication .* matrix exponential ^ array exponential .^ left-division \\ array left-division .\\ right-division / array right-division ./ square root sqrt()","breadcrumbs":"Notes » Programming » MATLAB » numerical operator","id":"1088","title":"numerical operator"},"1089":{"body":"regularly spaced elements or entire row or column : enclose function argument, array index; override precedence () enclosure array element [] decimal point . line-continuation ... separate statement and element in a row , quote sign and transpose _ non-conjugated transpose ._","breadcrumbs":"Notes » Programming » MATLAB » character syntax","id":"1089","title":"character syntax"},"109":{"body":"user send mail to domain server domain server send to other domain server other domain server push to other user other user retrieve message using IMAP or POP3 plain text: encode binary to string optional authentication: usually only between user/server","breadcrumbs":"Notes » Computer Science » Networking » simple mail transfer protocol (SMTP)","id":"109","title":"simple mail transfer protocol (SMTP)"},"1090":{"body":"end of statement hide output of statement","breadcrumbs":"Notes » Programming » MATLAB » semicolon ;","id":"1090","title":"semicolon ;"},"1091":{"body":"inline comment % comment multiline comment % { comment\n% }","breadcrumbs":"Notes » Programming » MATLAB » percentage sign %","id":"1091","title":"percentage sign %"},"1092":{"body":"save all variable in workspace as .mat file save file_name load the file load file_name","breadcrumbs":"Notes » Programming » MATLAB » save and load","id":"1092","title":"save and load"},"1093":{"body":"","breadcrumbs":"Notes » Programming » MATLAB » variable","id":"1093","title":"variable"},"1094":{"body":"all variable is either array or matrix no null type unassigned value are assigned to ans long assignment var1 = command1 ... command2 declare global variable global","breadcrumbs":"Notes » Programming » MATLAB » assign","id":"1094","title":"assign"},"1095":{"body":"1D array row vector [num1 …] column vector [row1;…]","breadcrumbs":"Notes » Programming » MATLAB » vector","id":"1095","title":"vector"},"1096":{"body":"2D array [r1c1 r1c2 …; r2c1 …] solve Ax=B x = A\\B","breadcrumbs":"Notes » Programming » MATLAB » matrix","id":"1096","title":"matrix"},"1097":{"body":"display all variable name who with information whos delete all variable clear delete variable var1 clear var1 check existence of variable exist var1","breadcrumbs":"Notes » Programming » MATLAB » variable management","id":"1097","title":"variable management"},"1098":{"body":"","breadcrumbs":"Notes » Programming » MATLAB » session management","id":"1098","title":"session management"},"1099":{"body":"open shell matlab -nodisplay -nodesktop close shell quit or exit","breadcrumbs":"Notes » Programming » MATLAB » shell environment","id":"1099","title":"shell environment"},"11":{"body":"Machine Learning general problem format machine learning is about building a function simplification using feature vector loss zero-one loss quadratic loss empirical risk three types of machine learning problems classification problem all possible training set signature of machine learning function λ classifier h define a partition of X regression problem clustering problem supervised/ unsupervised machine learning polynomial data fitting interpolation in polynomial data fitting k-nearest neighbors predictor Voronoi diagram gradient descent stochastic gradient descent (SGD) step size subgradient logistic-regression classifier score function for linear boundary signed distance to hyperplane logistic function softmax function cross entropy loss for binary classification cross entropy loss for K-class case support vector machine (SVM) binary support vector machine separating hyperplane for binary support vector machine hinge loss empirical risk of binary support vector machine soft linear support vector machine subgradient of hinge function support vector machine with kernel representer theorem support vector kernel for support vector machine","breadcrumbs":"Notes » Computer Science » Machine Learning » Machine Learning","id":"11","title":"Machine Learning"},"110":{"body":"router-based vs endhost-based priori resource reservation vs transmission-time feedback window-based vs rate-based throughput vs latency: power = throughput / latency","breadcrumbs":"Notes » Computer Science » Networking » congestion control","id":"110","title":"congestion control"},"1100":{"body":"shell script cd dir delete pwd","breadcrumbs":"Notes » Programming » MATLAB » file system","id":"1100","title":"file system"},"1101":{"body":"short format (default, 4 decimal place) format short display 16 decimal place format long display 2 decimal place format bank display in exponential form format arg1 e display as the closest rational form format rat","breadcrumbs":"Notes » Programming » MATLAB » format format arg1","id":"1101","title":"format format arg1"},"1102":{"body":"help topic help search help entry lookfor","breadcrumbs":"Notes » Programming » MATLAB » find help","id":"1102","title":"find help"},"1103":{"body":"MIPS Assembly register memory declaration line label inner label instruction format R-type I-type system call syscall syscall code","breadcrumbs":"Notes » Programming » MIPS Assembly » MIPS Assembly","id":"1103","title":"MIPS Assembly"},"1104":{"body":"$0: always 0 $v0, $v1: expression evaluation and function return value $a0 ~ $a3: argument $t0 ~ $t9: temporary variable saved by caller $s0 ~ $s7: temporary variable saved by callee $gp: global area pointer $sp: stack pointer $fp: frame pointer $ra: return address","breadcrumbs":"Notes » Programming » MIPS Assembly » register","id":"1104","title":"register"},"1105":{"body":".data\nvar0: .word number0, number1, …\nvar1: .space number_of_bytes\nvar2: .byte character0, character1, …\nvar3: .asciiz string\nvar4: .float floating_point_number .text\n.align 2 .global main\nmain: …\nfunction0: …","breadcrumbs":"Notes » Programming » MIPS Assembly » memory declaration","id":"1105","title":"memory declaration"},"1106":{"body":"label: instruction0 …","breadcrumbs":"Notes » Programming » MIPS Assembly » line label","id":"1106","title":"line label"},"1107":{"body":"start with underscore to distinguish from function","breadcrumbs":"Notes » Programming » MIPS Assembly » inner label","id":"1107","title":"inner label"},"1108":{"body":"opcode operands 6 bits 26 bits Op: opcode Rs: source register","breadcrumbs":"Notes » Programming » MIPS Assembly » instruction format","id":"1108","title":"instruction format"},"1109":{"body":"name Op Rs Rt Rd Sh Func bits 6 5 5 5 5 6 Rt: the other source register Rd: destination register Sh: shift register Func: function code","breadcrumbs":"Notes » Programming » MIPS Assembly » R-type","id":"1109","title":"R-type"},"111":{"body":"defined as (Source IP, Destination IP) or (Source IP, Source Port, Destination IP, Destination Port) aid router track soft state","breadcrumbs":"Notes » Computer Science » Networking » traffic flow","id":"111","title":"traffic flow"},"1110":{"body":"name Op Rs Rt Immed bits 6 5 5 16 Rt: target register Immed: immediate value name Op Target bits 6 26","breadcrumbs":"Notes » Programming » MIPS Assembly » I-type","id":"1110","title":"I-type"},"1111":{"body":"load syscall code into $v0 put argument into $a0, $a1, $f12 (float) syscall return value in $v0, $f0 (float)","breadcrumbs":"Notes » Programming » MIPS Assembly » system call syscall","id":"1111","title":"system call syscall"},"1112":{"body":"1: print integer 2: print float 3: print double 4: print string 5: read integer 6: read float 7: read double 8: read string arguments: buffer, length 9: sbrk (malloc) 10: exit","breadcrumbs":"Notes » Programming » MIPS Assembly » syscall code","id":"1112","title":"syscall code"},"1113":{"body":"Racket language type data type string boolean variable function (procedure) special form","breadcrumbs":"Notes » Programming » Racket » Racket","id":"1113","title":"Racket"},"1114":{"body":"specify the language used in the first line of a program #lang racket","breadcrumbs":"Notes » Programming » Racket » language type","id":"1114","title":"language type"},"1115":{"body":"","breadcrumbs":"Notes » Programming » Racket » data type","id":"1115","title":"data type"},"1116":{"body":"string literal can have new line","breadcrumbs":"Notes » Programming » Racket » string","id":"1116","title":"string"},"1117":{"body":"#t #f non-#f are considered #t","breadcrumbs":"Notes » Programming » Racket » boolean","id":"1117","title":"boolean"},"1118":{"body":"(define var_name expression)","breadcrumbs":"Notes » Programming » Racket » variable","id":"1118","title":"variable"},"1119":{"body":"(define (func_name args) (output)) call function (func_name args)","breadcrumbs":"Notes » Programming » Racket » function (procedure)","id":"1119","title":"function (procedure)"},"112":{"body":"Jain's fairness for n flow with throughput xi f(x1,⋯,xn)=n∑i=1nxi2(∑i=1nxi)2:Rn→[0,1] 1 is most fair","breadcrumbs":"Notes » Computer Science » Networking » resource allocation fairness","id":"112","title":"resource allocation fairness"},"1120":{"body":"(if test1 do_if_true do_if_false) (cond (test1 do_if_test1) (test2 do_if_test2) (else fallback_expr)) (begin first_thing_to_do second_to_do)","breadcrumbs":"Notes » Programming » Racket » special form","id":"1120","title":"special form"},"1121":{"body":"Ruby string string literal formatted string match string get all word from string array array method string array hash block call block control flow if case while statement modifier function define function main function class instance variable access instance variable method inherited method static method safe navigation syntax &. module exception","breadcrumbs":"Notes » Programming » Ruby » Ruby","id":"1121","title":"Ruby"},"1122":{"body":"","breadcrumbs":"Notes » Programming » Ruby » string","id":"1122","title":"string"},"1123":{"body":"simple string 'parsed as is' string considering \\ \"string where \\nis parsed\"","breadcrumbs":"Notes » Programming » Ruby » string literal","id":"1123","title":"string literal"},"1124":{"body":"str = \"yes\n\"say #{str}\"","breadcrumbs":"Notes » Programming » Ruby » formatted string","id":"1124","title":"formatted string"},"1125":{"body":"match a string with regex and return index of match str =~ regex match string with regex and name each part comp = /\\[(?.*)\\](?.*)/.match(str)\ncomp1 = comp[:comp1]\ncomp2 = comp[:comp2]","breadcrumbs":"Notes » Programming » Ruby » match string","id":"1125","title":"match string"},"1126":{"body":"str1.split(/[^[[:word:]]]+/)","breadcrumbs":"Notes » Programming » Ruby » get all word from string","id":"1126","title":"get all word from string"},"1127":{"body":"arr = [ \"a\", 1, true ]\narr[0] # => \"a\"\narr[1, 2] # => [ 1, true ]","breadcrumbs":"Notes » Programming » Ruby » array","id":"1127","title":"array"},"1128":{"body":".length .push(ele) .pop # loop through\narr.each do |ele| # …\nend\n# join with `str`\narr.join(str)\n# map\narr.map do |ele| # …\nend\n# map with index\narr.map.with_index do |ele, index| # …\nend","breadcrumbs":"Notes » Programming » Ruby » array method","id":"1128","title":"array method"},"1129":{"body":"%w(this will be split) # => [ \"this\", \"will\", \"be\", \"split\" ]","breadcrumbs":"Notes » Programming » Ruby » string array","id":"1129","title":"string array"},"113":{"body":"FIFO queue with tail-drop prevalent priority queing absolute priority: higher priority always first reserve a fraction of bandwidth diffserv: buy priority fair queuing number of flow variable and large flow send packet of different size random early drop (RED): drop packet before queue fill no drop below minTreshold increasing drop probability between minTreshold and maxThreshold","breadcrumbs":"Notes » Computer Science » Networking » TCP queue discipline","id":"113","title":"TCP queue discipline"},"1130":{"body":"# old way\nha = { 'a' => 1, 'b' => 2\n}\nha['a'] # => 1\nha['c'] # => nil\n# new way\nha = { 'a': 1, 'b': 2\n}\nha[:a] # => 1","breadcrumbs":"Notes » Programming » Ruby » hash","id":"1130","title":"hash"},"1131":{"body":"{ |args| # …\n}\n# or\ndo |args| # …\nend","breadcrumbs":"Notes » Programming » Ruby » block","id":"1131","title":"block"},"1132":{"body":"yield {|ele| puts ele}","breadcrumbs":"Notes » Programming » Ruby » call block","id":"1132","title":"call block"},"1133":{"body":"","breadcrumbs":"Notes » Programming » Ruby » control flow","id":"1133","title":"control flow"},"1134":{"body":"if a # …\nelsif b # …\nelse # …\nend","breadcrumbs":"Notes » Programming » Ruby » if","id":"1134","title":"if"},"1135":{"body":"case a\nwhen b # …\nwhen c # …\nend","breadcrumbs":"Notes » Programming » Ruby » case","id":"1135","title":"case"},"1136":{"body":"while a # …\nend","breadcrumbs":"Notes » Programming » Ruby » while","id":"1136","title":"while"},"1137":{"body":"do_something if a","breadcrumbs":"Notes » Programming » Ruby » statement modifier","id":"1137","title":"statement modifier"},"1138":{"body":"yield execute a block eval evaluate a string as code","breadcrumbs":"Notes » Programming » Ruby » function","id":"1138","title":"function"},"1139":{"body":"def func1(arg = default_value) # … # return last expression\nend","breadcrumbs":"Notes » Programming » Ruby » define function","id":"1139","title":"define function"},"114":{"body":"utilizing bandwidth & fairness introduced during \"congestion collapse\" implicit signal: drop packet","breadcrumbs":"Notes » Computer Science » Networking » classic TCP congestion control","id":"114","title":"classic TCP congestion control"},"1140":{"body":"if __FILE__ == $0 # main function\nend","breadcrumbs":"Notes » Programming » Ruby » main function","id":"1140","title":"main function"},"1141":{"body":"class ClassName # called with `new` def initialize(arg) # … end\nend","breadcrumbs":"Notes » Programming » Ruby » class","id":"1141","title":"class"},"1142":{"body":"@name","breadcrumbs":"Notes » Programming » Ruby » instance variable","id":"1142","title":"instance variable"},"1143":{"body":"attr_accessor :name","breadcrumbs":"Notes » Programming » Ruby » access instance variable","id":"1143","title":"access instance variable"},"1144":{"body":"# all instance method of class\nClassName.instance_methods\n# instance method excluding inherited\nClassName.instance_methods(false)","breadcrumbs":"Notes » Programming » Ruby » method","id":"1144","title":"method"},"1145":{"body":".respond_to?(str) check if object has method str .to_s convert to string .nil? check if nil","breadcrumbs":"Notes » Programming » Ruby » inherited method","id":"1145","title":"inherited method"},"1146":{"body":"def self.static_method_name(arg) # …\nend","breadcrumbs":"Notes » Programming » Ruby » static method","id":"1146","title":"static method"},"1147":{"body":"same as optional chaining","breadcrumbs":"Notes » Programming » Ruby » safe navigation syntax &.","id":"1147","title":"safe navigation syntax &."},"1148":{"body":"module ModuleName def self.static_method1 # … end\nend","breadcrumbs":"Notes » Programming » Ruby » module","id":"1148","title":"module"},"1149":{"body":"class CustomError < RuntimeError\nend","breadcrumbs":"Notes » Programming » Ruby » exception","id":"1149","title":"exception"},"115":{"body":"limit number of unacknowledged byte additive increase/ multiplicative decrease (AI/MD) packet dropped: cwnd = max(cwnd / 2, packet_size) not dropped: cwnd += packet_size mathematically proved to converge to same throughput","breadcrumbs":"Notes » Computer Science » Networking » congestion window cwnd","id":"115","title":"congestion window cwnd"},"1150":{"body":"Rails new rails project start rails server routing resourceful routing model generate model generate and save new model object update model object validation of model object when save or update query model object from database view html.erb file access instance variable in view link to other page in view partial template access partial template from another view controller generate controller instance variable in controller controller method for resourceful routing index method in controller show method in controller new method in controller create method in controller database migration console Hotwire Turbo","breadcrumbs":"Notes » Programming » Ruby » Rails » Rails","id":"1150","title":"Rails"},"1151":{"body":"rails new ","breadcrumbs":"Notes » Programming » Ruby » Rails » new rails project","id":"1151","title":"new rails project"},"1152":{"body":"rails s","breadcrumbs":"Notes » Programming » Ruby » Rails » start rails server","id":"1152","title":"start rails server"},"1153":{"body":"in config/routes.rb Rails.application.routes.draw do # root route is special root 'articles#index' # non-root route like this # trigger `index` action in `articles` when GET request on `articles` get 'articles', to: 'articles#index' # route with variable use `:` # the variable is passed to controller in the hash `params` # in this case `params[:id]` get 'articles/:id', to: 'articles#show' end more","breadcrumbs":"Notes » Programming » Ruby » Rails » routing","id":"1153","title":"routing"},"1154":{"body":"Rails.application.routes.draw do resources :articles\nend this map route URI pattern controller#action articles articles#index articles/new articles#new articles/:id articles#show (POST) articles articles#create articles/:id/edit articles#edit (PATCH) article/:id articles#update (DELETE) article/:id articles#destroy and set up URL and path helper method method return article_path \"articles/#{article.id}\"","breadcrumbs":"Notes » Programming » Ruby » Rails » resourceful routing","id":"1154","title":"resourceful routing"},"1155":{"body":"in app/models singular name","breadcrumbs":"Notes » Programming » Ruby » Rails » model","id":"1155","title":"model"},"1156":{"body":"generate model Article with two field rails g model Article title:string body:text also generate database migration","breadcrumbs":"Notes » Programming » Ruby » Rails » generate model","id":"1156","title":"generate model"},"1157":{"body":"# generate new article object\narticle = Article.new(title: 'Example', body: 'Example text.') # save to database\narticle.save # => true","breadcrumbs":"Notes » Programming » Ruby » Rails » generate and save new model object","id":"1157","title":"generate and save new model object"},"1158":{"body":"article.update # => true validation of model object when save or update # declare a `article_params` method to validate\ndef article_params params.require(:article).permit(:title, :author, :body, :status)\nend # use the method when try saving or updating\nif @article.update(article_params) redirect_to @article\nelse render :edit, status: :unprocessable_entity\nend","breadcrumbs":"Notes » Programming » Ruby » Rails » update model object","id":"1158","title":"update model object"},"1159":{"body":"# query article by id\nArticle.find(1) # => 1 Article object or Nil # query all articles\nArticle.all # => 1 ActiveRecord::Relation object","breadcrumbs":"Notes » Programming » Ruby » Rails » query model object from database","id":"1159","title":"query model object from database"},"116":{"body":"exponentially increase cwnd at start when dropped SSthresh = cwnd / 2 cwnd = packet_size slow start while cwnd < SSthresh, do AI/MD afterwards","breadcrumbs":"Notes » Computer Science » Networking » TCP slow start","id":"116","title":"TCP slow start"},"1160":{"body":"in app/views","breadcrumbs":"Notes » Programming » Ruby » Rails » view","id":"1160","title":"view"},"1161":{"body":"embedded Ruby in HTML run ruby code <% … %> run ruby code and render the return value <%= … %> write comment that does not render in result <%# comment %>","breadcrumbs":"Notes » Programming » Ruby » Rails » html.erb file","id":"1161","title":"html.erb file"},"1162":{"body":"<% @articles.each do |article| %> <%= article.title %> <% end %>\n ","breadcrumbs":"Notes » Programming » Ruby » Rails » access instance variable in view","id":"1162","title":"access instance variable in view"},"1163":{"body":"product a link with some_text to article_path <%= link_to some_text, article %> redirect to show a model object redirect_to @article the browser make a new request use redirect_to to mutate database render image <%= image_tag image_path %> link to the same page with different params <%= link_to some_text, url_for(params.permit!.merge(field_to_change: field_value)) %>","breadcrumbs":"Notes » Programming » Ruby » Rails » link to other page in view","id":"1163","title":"link to other page in view"},"1164":{"body":"partial has name starting with _ e.g. _form.html.erb access partial template from another view <%= render 'comments/form' %> relative path without _ add argument render 'form', article: @article # or the longer format\nrender partial: 'form', locals: { article: @article } # or even longer format\nrender partial: 'form', object: @article, as: 'article' render a collection render @products # or longer format\nrender partial: 'product', collection: @products or even longer format <% @products.each do |product| %> <%= render partial: \"product\", locals: { product: product } %>\n<% end %>","breadcrumbs":"Notes » Programming » Ruby » Rails » partial template","id":"1164","title":"partial template"},"1165":{"body":"in app/controllers controller for articles is articles_controller.rb plural name","breadcrumbs":"Notes » Programming » Ruby » Rails » controller","id":"1165","title":"controller"},"1166":{"body":"generate ArticlesController and its index action rails g controller Articles index by default, index action of Articles render app/views/articles/index.html.erb","breadcrumbs":"Notes » Programming » Ruby » Rails » generate controller","id":"1166","title":"generate controller"},"1167":{"body":"instance variable in controller can be accessed in view # this will be accessed in `articles/index.html.erb` def index @article = Article.all end","breadcrumbs":"Notes » Programming » Ruby » Rails » instance variable in controller","id":"1167","title":"instance variable in controller"},"1168":{"body":"index method in controller show method in controller need to query model object by params[:id]","breadcrumbs":"Notes » Programming » Ruby » Rails » controller method for resourceful routing","id":"1168","title":"controller method for resourceful routing"},"1169":{"body":"only initialize new model object create method in controller assign value to new model object and attempt to save it def create @article = Article.new(title: '…', body: '…') if @article.save redirect_to @article else render :new, status: :unprocessable_entity\nend strong parameter","breadcrumbs":"Notes » Programming » Ruby » Rails » new method in controller","id":"1169","title":"new method in controller"},"117":{"body":"receiver send duplicated ACK for each packet out of order sender retransmit on multiple duplicated ACK","breadcrumbs":"Notes » Computer Science » Networking » TCP fast retransmit","id":"117","title":"TCP fast retransmit"},"1170":{"body":"SQLite3 by default","breadcrumbs":"Notes » Programming » Ruby » Rails » database","id":"1170","title":"database"},"1171":{"body":"in db/migrate rails db:migrate","breadcrumbs":"Notes » Programming » Ruby » Rails » migration","id":"1171","title":"migration"},"1172":{"body":"open a rails irb console rails console","breadcrumbs":"Notes » Programming » Ruby » Rails » console","id":"1172","title":"console"},"1173":{"body":"","breadcrumbs":"Notes » Programming » Ruby » Rails » Hotwire","id":"1173","title":"Hotwire"},"1174":{"body":"Turbo events","breadcrumbs":"Notes » Programming » Ruby » Rails » Turbo","id":"1174","title":"Turbo"},"1175":{"body":"Rust function fn main function associated function method variable declare type String str enumeration variant result Result Ok variant Err variant .expect() method statement expression reference input/ output use std::io input macro print println!() debug print dbg!() todo todo!() unreachable unreachable!() comment package crate root convention import crate use import function import struct or enum alias re-exporting nesting path glob operator * trait define trait method implement trait on type implement trait method use trait as parameter multiple trait bound + where clause return type implement trait closure type annotation storing closure capture environment","breadcrumbs":"Notes » Programming » Rust » Rust","id":"1175","title":"Rust"},"1176":{"body":"","breadcrumbs":"Notes » Programming » Rust » function fn","id":"1176","title":"function fn"},"1177":{"body":"fn main(){}","breadcrumbs":"Notes » Programming » Rust » main function","id":"1177","title":"main function"},"1178":{"body":"a function that is implemented on a type `type1::fun1()`","breadcrumbs":"Notes » Programming » Rust » associated function","id":"1178","title":"associated function"},"1179":{"body":"call method on instance instance1 .method1();","breadcrumbs":"Notes » Programming » Rust » method","id":"1179","title":"method"},"118":{"body":"default in Linux since 2006 hybrid slow start identify ACK slowdown and do AI/MD stay at expected maximum cwnd, do AI after no drop for a while","breadcrumbs":"Notes » Computer Science » Networking » TCP cubic","id":"118","title":"TCP cubic"},"1180":{"body":"immutable by default","breadcrumbs":"Notes » Programming » Rust » variable","id":"1180","title":"variable"},"1181":{"body":"let declare mutable variable let mut","breadcrumbs":"Notes » Programming » Rust » declare","id":"1181","title":"declare"},"1182":{"body":"","breadcrumbs":"Notes » Programming » Rust » type","id":"1182","title":"type"},"1183":{"body":"new string String::new()","breadcrumbs":"Notes » Programming » Rust » String","id":"1183","title":"String"},"1184":{"body":"\"str literal\" // str literal\nr#\"str\nliteral\"# /* raw str\nliteral */","breadcrumbs":"Notes » Programming » Rust » str","id":"1184","title":"str"},"1185":{"body":"","breadcrumbs":"Notes » Programming » Rust » enumeration","id":"1185","title":"enumeration"},"1186":{"body":"","breadcrumbs":"Notes » Programming » Rust » variant","id":"1186","title":"variant"},"1187":{"body":"enumeration with variant Ok or Err handle error and convert to Option: result.map_err(|e|/*…*/).ok()` convert error to value: result.map_or_else(|e|/*…*/, identity) using anyhow, both Result and Option can be wrapped as Result using .context","breadcrumbs":"Notes » Programming » Rust » result Result","id":"1187","title":"result Result"},"1188":{"body":"indicate successful run, contain result","breadcrumbs":"Notes » Programming » Rust » Ok variant","id":"1188","title":"Ok variant"},"1189":{"body":"indicate failure, contain reason","breadcrumbs":"Notes » Programming » Rust » Err variant","id":"1189","title":"Err variant"},"119":{"body":"first try: \"hosts\" file /etc/hosts top-level domain by ICANN domain level hierarchy name resolution: ask name server from root up 13 root server each use different implementation distributed database","breadcrumbs":"Notes » Computer Science » Networking » domain name system (DNS)","id":"119","title":"domain name system (DNS)"},"1190":{"body":"crash on Err and display argument","breadcrumbs":"Notes » Programming » Rust » .expect() method","id":"1190","title":".expect() method"},"1191":{"body":"represent instruction for action end with ;","breadcrumbs":"Notes » Programming » Rust » statement","id":"1191","title":"statement"},"1192":{"body":"represent a value end without ; can be used as return statement","breadcrumbs":"Notes » Programming » Rust » expression","id":"1192","title":"expression"},"1193":{"body":"refer to variable &var1 mutable reference &mut var1","breadcrumbs":"Notes » Programming » Rust » reference","id":"1193","title":"reference"},"1194":{"body":"","breadcrumbs":"Notes » Programming » Rust » input/ output use std::io","id":"1194","title":"input/ output use std::io"},"1195":{"body":"io::stdin() → an instance of type std::io::Stdin standard input handle type std::io::Stdin","breadcrumbs":"Notes » Programming » Rust » input","id":"1195","title":"input"},"1196":{"body":"","breadcrumbs":"Notes » Programming » Rust » macro","id":"1196","title":"macro"},"1197":{"body":"","breadcrumbs":"Notes » Programming » Rust » print println!()","id":"1197","title":"print println!()"},"1198":{"body":"pass it a reference because it take ownership of argument","breadcrumbs":"Notes » Programming » Rust » debug print dbg!()","id":"1198","title":"debug print dbg!()"},"1199":{"body":"","breadcrumbs":"Notes » Programming » Rust » todo todo!()","id":"1199","title":"todo todo!()"},"12":{"body":"given input A, want output y∈Y f:A→Y,y=f(a)∈Yfor a∈A traditional approach hand-craft the function f machine learning build another function λ and use it to generate an approximation f","breadcrumbs":"Notes » Computer Science » Machine Learning » general problem format","id":"12","title":"general problem format"},"120":{"body":"canonical name nick name subdomain entry","breadcrumbs":"Notes » Computer Science » Networking » DNS entry","id":"120","title":"DNS entry"},"1200":{"body":"","breadcrumbs":"Notes » Programming » Rust » unreachable unreachable!()","id":"1200","title":"unreachable unreachable!()"},"1201":{"body":"inline comment //","breadcrumbs":"Notes » Programming » Rust » comment","id":"1201","title":"comment"},"1202":{"body":"","breadcrumbs":"Notes » Programming » Rust » package","id":"1202","title":"package"},"1203":{"body":"","breadcrumbs":"Notes » Programming » Rust » crate","id":"1203","title":"crate"},"1204":{"body":"binary crate root src/main.rs library crate root src/lib.rs both same name as package","breadcrumbs":"Notes » Programming » Rust » root convention","id":"1204","title":"root convention"},"1205":{"body":"absolute path crate::… relative path self::…","breadcrumbs":"Notes » Programming » Rust » import crate use","id":"1205","title":"import crate use"},"1206":{"body":"use the parent path","breadcrumbs":"Notes » Programming » Rust » import function","id":"1206","title":"import function"},"1207":{"body":"use the whole path","breadcrumbs":"Notes » Programming » Rust » import struct or enum","id":"1207","title":"import struct or enum"},"1208":{"body":"use … as …","breadcrumbs":"Notes » Programming » Rust » alias","id":"1208","title":"alias"},"1209":{"body":"pub use …","breadcrumbs":"Notes » Programming » Rust » re-exporting","id":"1209","title":"re-exporting"},"121":{"body":"","breadcrumbs":"Notes » Computer Science » Networking » attack","id":"121","title":"attack"},"1210":{"body":"both are children use common_path::{path1,path2…} parent and children use common_path::{self,path1…}","breadcrumbs":"Notes » Programming » Rust » nesting path","id":"1210","title":"nesting path"},"1211":{"body":"brings everything into scope","breadcrumbs":"Notes » Programming » Rust » glob operator *","id":"1211","title":"glob operator *"},"1212":{"body":"","breadcrumbs":"Notes » Programming » Rust » trait","id":"1212","title":"trait"},"1213":{"body":"pub trait Trait1 {…}","breadcrumbs":"Notes » Programming » Rust » define","id":"1213","title":"define"},"1214":{"body":"empty method `fn fun1(&self,…)->Type1;` default implementation `fn fun1(&self,…)->Type1 {…}`","breadcrumbs":"Notes » Programming » Rust » trait method","id":"1214","title":"trait method"},"1215":{"body":"`impl Trait1 for Type1 {…}` implement trait method use default implementation—do nothing override implementation `fn fun1(&self,…)->Type1 {…}`","breadcrumbs":"Notes » Programming » Rust » implement trait on type","id":"1215","title":"implement trait on type"},"1216":{"body":"shorthand `pub fn fun1(para1: &impl Trait1) {…}` trait bound syntax pub fn fun1(para1: &T) {…} multiple trait bound + shorthand pub fn fun1(para1: &(impl Trait1 + Trait2)) {…} trait bound syntax pub fn fun1(para1: &T) {…} where clause fn fun1(t: &T, u: &U)->Type1 where T: Trait1 + Trait2, U: Trait3 + Trait4\n{…}","breadcrumbs":"Notes » Programming » Rust » use trait as parameter","id":"1216","title":"use trait as parameter"},"1217":{"body":"`fn fun1(…)->impl Trait1 {…}`","breadcrumbs":"Notes » Programming » Rust » return type implement trait","id":"1217","title":"return type implement trait"},"1218":{"body":"anonymous function stored as variable that can capture its environment `let closure1 = |var1,…| {return_value};` implement FnOnce trait more overhead than function automatically detect and decide type and cannot have multiple set of them","breadcrumbs":"Notes » Programming » Rust » closure","id":"1218","title":"closure"},"1219":{"body":"|var1: type1,…| -> return_type {return_value};","breadcrumbs":"Notes » Programming » Rust » type annotation","id":"1219","title":"type annotation"},"122":{"body":"phishing: impersonation spoofing: hide source of attack countermeasure: HTTPS","breadcrumbs":"Notes » Computer Science » Networking » authenticity attack","id":"122","title":"authenticity attack"},"1220":{"body":"struct Store1\nwhere T: Fn(type_for_var1,…) -> return_type,\n{ attr1: T, …\n} use a Option<…> use a hashmap","breadcrumbs":"Notes » Programming » Rust » storing closure","id":"1220","title":"storing closure"},"1221":{"body":"borrow by default implement Fn trait , mutable as needed implement FnMut trait adopt ownership using move `move |var1,…| {return_value}`","breadcrumbs":"Notes » Programming » Rust » capture environment","id":"1221","title":"capture environment"},"1222":{"body":"R lang naming character allowed basic syntax command separation comment assignment function execute from .R file manipulate data storage show all object remove object store to disk data structure vector package managing install package","breadcrumbs":"Notes » Programming » R lang » R lang","id":"1222","title":"R lang"},"1223":{"body":"","breadcrumbs":"Notes » Programming » R lang » naming","id":"1223","title":"naming"},"1224":{"body":"letter, ., _ cannot start with _ cannot start with ..","breadcrumbs":"Notes » Programming » R lang » character allowed","id":"1224","title":"character allowed"},"1225":{"body":"","breadcrumbs":"Notes » Programming » R lang » basic syntax","id":"1225","title":"basic syntax"},"1226":{"body":"; or \\n","breadcrumbs":"Notes » Programming » R lang » command separation","id":"1226","title":"command separation"},"1227":{"body":"# last to the end of line","breadcrumbs":"Notes » Programming » R lang » comment","id":"1227","title":"comment"},"1228":{"body":"= assignee <- - assigner> assignee","breadcrumbs":"Notes » Programming » R lang » assignment","id":"1228","title":"assignment"},"1229":{"body":"","breadcrumbs":"Notes » Programming » R lang » function","id":"1229","title":"function"},"123":{"body":"censorship persecution blackmail countermeasure: VPN, TOR","breadcrumbs":"Notes » Computer Science » Networking » anonymity attack","id":"123","title":"anonymity attack"},"1230":{"body":"source(\"filename.R\")","breadcrumbs":"Notes » Programming » R lang » execute from .R file","id":"1230","title":"execute from .R file"},"1231":{"body":"","breadcrumbs":"Notes » Programming » R lang » manipulate data storage","id":"1231","title":"manipulate data storage"},"1232":{"body":"objects()","breadcrumbs":"Notes » Programming » R lang » show all object","id":"1232","title":"show all object"},"1233":{"body":"rm(obj1,obj2,…)","breadcrumbs":"Notes » Programming » R lang » remove object","id":"1233","title":"remove object"},"1234":{"body":"choose y when quit q() stored as .RData","breadcrumbs":"Notes » Programming » R lang » store to disk","id":"1234","title":"store to disk"},"1235":{"body":"","breadcrumbs":"Notes » Programming » R lang » data structure","id":"1235","title":"data structure"},"1236":{"body":"c(ele1,ele2,…) can also take vector as element, will expand","breadcrumbs":"Notes » Programming » R lang » vector","id":"1236","title":"vector"},"1237":{"body":"","breadcrumbs":"Notes » Programming » R lang » package managing","id":"1237","title":"package managing"},"1238":{"body":"install.packages(\"package_name\") install multiple packages use a vector install.packages(c(\"package1\",\"package2\",…))","breadcrumbs":"Notes » Programming » R lang » install package","id":"1238","title":"install package"},"1239":{"body":"Shell file & directory system information user manual history cursor navigation ANSI terminal escape sequence switch user to root and do sudo","breadcrumbs":"Notes » Programming » Shell » Shell","id":"1239","title":"Shell"},"124":{"body":"DDoS ransom","breadcrumbs":"Notes » Computer Science » Networking » availability attack","id":"124","title":"availability attack"},"1240":{"body":"print working directory pwd list file in path ls [path] change working directory to path, by default to ~ cd [path] go up one directory cd .. go back to the last directory cd - copy one file to a given directory [and name it as instructed (the new name cannot be a local folder’s name, or it will just copy it there)] cp [/] copy recursively one folder to a given directory if the new directory does not exist, the command will create it cp -r remove one file rm remove recursively one folder rm -r remove one empty folder rmdir make directory mkdir run the file ./","breadcrumbs":"Notes » Programming » Shell » file & directory","id":"1240","title":"file & directory"},"1241":{"body":"display [human-readable (i.e., in MB, GB, etc.)] file system disk space usage df [-h] disk usage for this directory du [path] free and used memory in the system [in megabytes] free [-m] table of processes top print all system information: name, kernel, etc. uname -a print version information for the linux release lsb_release -a","breadcrumbs":"Notes » Programming » Shell » system information","id":"1241","title":"system information"},"1242":{"body":"add a new user adduser assign password to the user passwd ","breadcrumbs":"Notes » Programming » Shell » user","id":"1242","title":"user"},"1243":{"body":"manual for the command man introduction to linux command-line man intro search in manual what is whatis -r ","breadcrumbs":"Notes » Programming » Shell » manual","id":"1243","title":"manual"},"1244":{"body":"show command you input with numbers before them history Ctrl + R search for command you input","breadcrumbs":"Notes » Programming » Shell » history","id":"1244","title":"history"},"1245":{"body":"Ctrl + A/ Home move cursor to start of line Ctrl + E/ End move cursor to end of line Ctrl + B move cursor to beginning of word Ctrl + K delete to the end of line Ctrl + U delete to start of line Ctrl + W delete word Alt + B go back one word Alt + F go forward one word Alt + C capitalize the letter and move cursor to end of word","breadcrumbs":"Notes » Programming » Shell » cursor navigation","id":"1245","title":"cursor navigation"},"1246":{"body":"control sequence introducer (CSI): \\033[ clear screen and return to home: \\033[2J\\033[H clear line and return to left: \\033[2K\\r","breadcrumbs":"Notes » Programming » Shell » ANSI terminal escape sequence","id":"1246","title":"ANSI terminal escape sequence"},"1247":{"body":"Silly ideas about how a language should have all its syntax trailing. Identifiers can be used as procedure arguments. Blocks are a comptime primitive type and can contain undefined identifiers. All code can be marked to be comptime. No generics. Instead, generate types or procedures needed using comptime procedure execution. No grouping executions using parentheses.","breadcrumbs":"Notes » Programming » Trail » The Trail Language","id":"1247","title":"The Trail Language"},"1248":{"body":"Keywords are capitalized letters. They will look fine with syntax highlighting. White spaces separate tokens. a+b is a single token, it can not involve procedure call. Expressions are evaluated left to right, with no operator precedence. Tuples are space-separated and expressions inside are lazy-evaluated. = and many other side-effects-only procedures return ( ). 1 = a -- Assign `1` to `a` by calling procedure `=` at comptime.\ntrue =M b -- Mutable variable.\na / 2.0 = a/2 -- Call procedure `/` with `a` and `2.0` and assign to `a/2`.\nfalse =R b -- Reassign `b`.\n0 .. 10 do { \"Hey\" print } -- Print \"Hey\" 10 times.\n( 1 2 ) nth 0 assert_eq 1","breadcrumbs":"Notes » Programming » Trail » Syntax","id":"1248","title":"Syntax"},"1249":{"body":"=> is a comptime procedure that takes a tuple of identifiers and a block as arguments and returns a procedure. The last expression of a block is its return value. No \"return\" keyword. Procedures that take arguments are automatically called with the expression before it and the appropriate number of expressions after it. If a procedure does not take any arguments, it cannot be called by itself and requires a comptime procedure call to call it. If an expression is not callable, the expression before it is discarded when the execution reaches it. Procedure +doc takes anything and a string as its two arguments, and apply the string as documentation to the first argument. Limited polymorphism: the first argument of the procedure decides what the rest of the procedure arguments could be. ( a b ) => { a + b } = add -- Procedure `add`. ( ) => { \"hell\" ++ \"o\" } +doc \"Return \\\"hello\\\".\" = greet -- Procedure `greet`.\ngreet doc starts_with \"Return\" assert -- Assert the documentation of `greet`. greet = also_greet\ngreet call = hello -- => \"hello\"","breadcrumbs":"Notes » Programming » Trail » Procedures","id":"1249","title":"Procedures"},"125":{"body":"block incoming, usually allow outgoing software/hardware cheap, flexible vs expensive, opaque low vs high performance stateful/stateless have vs no memory cheap, easy vs expressive","breadcrumbs":"Notes » Computer Science » Networking » firewall","id":"125","title":"firewall"},"1250":{"body":"Symbols can be names. ( a b ) => { a pow b } = ** -- Procedure `**`.","breadcrumbs":"Notes » Programming » Trail » Names","id":"1250","title":"Names"},"1251":{"body":"The program is interpreted into a program that gets compiled. During interpretation, expressions marked with C are calculated. Global variables are always calculated at compile time and immutable at run time. Comptime variables can also be declared \"mutable at comptime.\" 32 * 32 = TWO_TO_TEN -- Comptime. ( a b ) => { b * b = b_square -- Run-time. a * TWO_TO_TEN + b_square -- Run-time.\n} = hyperbole -- Comptime. ( x ) => { 2 hyperbole 7 C = LUCKY_NUMBER -- Comptime. LUCKY_NUMBER is_comptime assert -- Assert that `LUCKY_NUMBER` is comptime. x + LUCKY_NUMBER -- Run-time.\n} = add_luck -- Comptime. 2 =M TO_BE_CHANGED -- Comptime mutable.\n0 .. 10 do { TO_BE_CHANGED * TO_BE_CHANGED =R TO_BE_CHANGED } -- Comptime\n-- `TO_BE_CHANGED` = 4294967296 -- Assign a procedure type that take one argument of `Any` type and returns\n-- an instance of `( )` to `equal_type`.\n( Any ) proc_type ( ) = equal_type\n= s_type assert_eq equal_type -- Assert `=`'s type.","breadcrumbs":"Notes » Programming » Trail » Compile-time (comptime) computation","id":"1251","title":"Compile-time (comptime) computation"},"1252":{"body":"Server","breadcrumbs":"Notes » Server » Server","id":"1252","title":"Server"},"1253":{"body":"NFS enable nfs systemctl enable nfs-server add directory to export: edit etc/exports directory_to_export ip_to_allow(rw,insecure) export all specified directory sudo exportfs -arv mount on macOS sudo mount -t nfs -v source target automatically mount on macOS open /etc/fstab with sudo vifs add into the file: source /System/Volumes/Data/../Data/Volumes/target_name nfs rw,nolockd,resvport,hard,bg,intr,tcp,nfc,rsize=65536,wsize=65536 for pre-Catalina, it should be source /../Volumes/target_name nfs rw,nolockd,resvport,hard,bg,intr,tcp,nfc,rsize=65536,wsize=65536","breadcrumbs":"Notes » Server » NFS » NFS","id":"1253","title":"NFS"},"1254":{"body":"SSH rsync kitty ssh kitty +kitten ssh … port forwarding ssh -N -L 8080:127.0.0.1:8080 username@host","breadcrumbs":"Notes » Server » SSH » SSH","id":"1254","title":"SSH"},"1255":{"body":"general usage -P give a progress bar rsync -P source destination copy file from ssh server to client rsync -P username@host:dir local_dir copy file from client to ssh server rsync -P local_dir username@host:dir","breadcrumbs":"Notes » Server » SSH » rsync","id":"1255","title":"rsync"},"1256":{"body":"","breadcrumbs":"Notes » Soft Skill » Soft Skill","id":"1256","title":"Soft Skill"},"1257":{"body":"","breadcrumbs":"Notes » Soft Skill » Art and Business » Art and Business","id":"1257","title":"Art and Business"},"1258":{"body":"fund from UCCA Lab w/ corporate client give artist full control of space hint what's inside at the museum doorway reuse old art","breadcrumbs":"Notes » Soft Skill » Art and Business » UCCA talk","id":"1258","title":"UCCA talk"},"1259":{"body":"Housing USC housing JavaScript highlight keyword on page","breadcrumbs":"Notes » Soft Skill » Housing » Housing","id":"1259","title":"Housing"},"126":{"body":"accept, drop, reject default allow vs default deny IP, transport protocol, port, application data","breadcrumbs":"Notes » Computer Science » Networking » firewall access policy","id":"126","title":"firewall access policy"},"1260":{"body":"places DPS downtown farther: Santa Monica and Culver City (closer to the beach and Hollywood); Monterey Park and San Gabriel (tons of Chinese food and markets); Koreatown (many Korean food, markets and great hair saloons); Pasadena (a bit far but peaceful and beautiful) house vs apartment: house old, apartment expensive & small & have maintenance website: Zillow careful for: heat, floor noise","breadcrumbs":"Notes » Soft Skill » Housing » USC housing","id":"1260","title":"USC housing"},"1261":{"body":"function highlight(regex, classes) { let regExp = new RegExp(regex, \"gi\"); let openTag = ``; function processNode(node) { if (node.nodeType === Node.TEXT_NODE) { let parent = node.parentNode; if (parent && parent.nodeName !== \"SCRIPT\" && parent.nodeName !== \"STYLE\") { let html = node.nodeValue; if (regExp.test(html)) { let newHtml = html.replace(regExp, function(match) { return `${openTag}${match} `; }); let span = document.createElement(\"span\"); span.innerHTML = newHtml; parent.replaceChild(span, node); } } } else { let childNodes = Array.from(node.childNodes); childNodes.forEach(child => processNode(child)); } } processNode(document.body);\n} highlight(String.raw`\\b(?:\\$[\\d,]+|(?:\\d,?)?\\d{3})\\b`, [\"highlight\"]);\nhighlight(String.raw`\\b(?:female|girls?|wom[ea]n)`, [\"highlight-neg\"]); let style = document.createElement(\"style\");\nstyle.innerHTML = ` .highlight { background-color: yellow; } .highlight-neg { color: red; }\n`;\ndocument.head.appendChild(style);","breadcrumbs":"Notes » Soft Skill » Housing » JavaScript highlight keyword on page","id":"1261","title":"JavaScript highlight keyword on page"},"1262":{"body":"","breadcrumbs":"Notes » Soft Skill » Management » Management","id":"1262","title":"Management"},"1263":{"body":"aim → goal SMART goal: specific, measurable, achievable, relevant, timely","breadcrumbs":"Notes » Soft Skill » Management » basis & direction","id":"1263","title":"basis & direction"},"1264":{"body":"basics: goal, interest-related people","breadcrumbs":"Notes » Soft Skill » Management » meeting","id":"1264","title":"meeting"},"1265":{"body":"doubly sand glass declare goal synchronize information brainstorm limit time no interruption conclude the problem summarize ideas from brainstorm no further brainstorm grade ideas for importance based on goal pick out most important problem repeat previous two step on most important problems grade potential solutions on 2-4 standards","breadcrumbs":"Notes » Soft Skill » Management » meeting procedure","id":"1265","title":"meeting procedure"},"1266":{"body":"urge timely report","breadcrumbs":"Notes » Soft Skill » Management » meeting follow-up","id":"1266","title":"meeting follow-up"},"1267":{"body":"","breadcrumbs":"Notes » Storage » Storage","id":"1267","title":"Storage"},"1268":{"body":"GitHub linguist settings in .gitattributes ( reference ): /** linguist-vendored\n/** linguist-generated\n/** linguist-detectable Git large file system (Git LFS) settings in .gitattributes: filter=lfs diff=lfs merge=lfs -text GitHub repository size: https://api.github.com/repos/git/git","breadcrumbs":"Notes » Storage » GitHub » GitHub","id":"1268","title":"GitHub"},"1269":{"body":"Text Editor","breadcrumbs":"Notes » Text Editor » Text Editor","id":"1269","title":"Text Editor"},"127":{"body":"allow closely watched device to access more","breadcrumbs":"Notes » Computer Science » Networking » demilitarized zone","id":"127","title":"demilitarized zone"},"1270":{"body":"Vim movement arrow equivalent by word to start of word to end of word by WORD search search character move to result move to left of result backward search expression repeat expression end of line the end character the end non-whitespace character by chunk by paragraph by page half page whole page to some position in this page to past position change count go to line visual mode visual mode navigation undo and redo fold spelling buffer quit write as root regex replace","breadcrumbs":"Notes » Text Editor » Vim » Vim","id":"1270","title":"Vim"},"1271":{"body":"","breadcrumbs":"Notes » Text Editor » Vim » movement","id":"1271","title":"movement"},"1272":{"body":"↑ ← h j k l → ↓","breadcrumbs":"Notes » Text Editor » Vim » arrow equivalent","id":"1272","title":"arrow equivalent"},"1273":{"body":"","breadcrumbs":"Notes » Text Editor » Vim » by word","id":"1273","title":"by word"},"1274":{"body":"<–b– ○ –w–>\nword word word","breadcrumbs":"Notes » Text Editor » Vim » to start of word","id":"1274","title":"to start of word"},"1275":{"body":"ㅤㅤ<–ge–○ –e–>\nword word word","breadcrumbs":"Notes » Text Editor » Vim » to end of word","id":"1275","title":"to end of word"},"1276":{"body":"same as by word but capitalize the last letter a WORD contains any consecutive non-whitespace character","breadcrumbs":"Notes » Text Editor » Vim » by WORD","id":"1276","title":"by WORD"},"1277":{"body":"","breadcrumbs":"Notes » Text Editor » Vim » search","id":"1277","title":"search"},"1278":{"body":"type a character in replace of w below move to result ○–fw–>\nword word move to left of result ○–tw–>\nword sword backward capitalize the letter","breadcrumbs":"Notes » Text Editor » Vim » search character","id":"1278","title":"search character"},"1279":{"body":"/… + enter search forward ?… + enter search backward repeat n next match N last match expression exact regex","breadcrumbs":"Notes » Text Editor » Vim » search expression","id":"1279","title":"search expression"},"128":{"body":"monitor software/hardware to detect malicious activity network intrusion detection system (NIDS) host intrusion detection system (HIDS)","breadcrumbs":"Notes » Computer Science » Networking » intrusion detection system (IDS)","id":"128","title":"intrusion detection system (IDS)"},"1280":{"body":"","breadcrumbs":"Notes » Text Editor » Vim » end of line","id":"1280","title":"end of line"},"1281":{"body":"<–0– ○ –$–>\nㅤㅤlineㅤㅤ","breadcrumbs":"Notes » Text Editor » Vim » the end character","id":"1281","title":"the end character"},"1282":{"body":"ㅤㅤ<–^–– ○ ––g_–>\nㅤㅤnot whitespaceㅤㅤ","breadcrumbs":"Notes » Text Editor » Vim » the end non-whitespace character","id":"1282","title":"the end non-whitespace character"},"1283":{"body":"","breadcrumbs":"Notes » Text Editor » Vim » by chunk","id":"1283","title":"by chunk"},"1284":{"body":"paragraph 1\nstuff\n<–––– { ––––-+\nparagraph 2 ○\nmore stuff |\n<–––– } ––––-+\nparagraph 3","breadcrumbs":"Notes » Text Editor » Vim » by paragraph","id":"1284","title":"by paragraph"},"1285":{"body":"half page up ^u down ^d whole page up ^b down ^f to some position in this page Move to top of screen H Move to middle of screen M Move to bottom of screen L Top current line zt Center current line zz Bottom current line zb","breadcrumbs":"Notes » Text Editor » Vim » by page","id":"1285","title":"by page"},"1286":{"body":"go back to the previous jump position `` go back to the previous jump lien '' go to mark letter: ` + letter go to top of last visual selection `< go to bottom of last visual selection `> go to top of last yanked `[ go to bottom of last yanked `] go to last change g; go to previous change in change history g,","breadcrumbs":"Notes » Text Editor » Vim » to past position","id":"1286","title":"to past position"},"1287":{"body":"delete current character and switch to insert mode s delete current line and switch to insert mode S delete current word and switch to insert mode ciw increase (decrease) line indent > (<) automatically indent line = change to uppercase/ lowercase gU (gu) toggle case ~","breadcrumbs":"Notes » Text Editor » Vim » change","id":"1287","title":"change"},"1288":{"body":"number + keys is the same as pressing keys for number times","breadcrumbs":"Notes » Text Editor » Vim » count","id":"1288","title":"count"},"1289":{"body":"number + G or number + gg : + number","breadcrumbs":"Notes » Text Editor » Vim » go to line","id":"1289","title":"go to line"},"129":{"body":"tunneling protocol end-to-end encryption usage remote access site-to-site bypass firewall/proxy","breadcrumbs":"Notes » Computer Science » Networking » virtual private network (VPN)","id":"129","title":"virtual private network (VPN)"},"1290":{"body":"move the other border of selection instead o","breadcrumbs":"Notes » Text Editor » Vim » visual mode","id":"1290","title":"visual mode"},"1291":{"body":"select whole paragraph vip select all inside quotes vi\" (not only quotes, others are similar) select all inside tags vit select all and including quotes va\" (not only quotes, others are similar)","breadcrumbs":"Notes » Text Editor » Vim » visual mode navigation","id":"1291","title":"visual mode navigation"},"1292":{"body":"undo u redo ^r undo a line U","breadcrumbs":"Notes » Text Editor » Vim » undo and redo","id":"1292","title":"undo and redo"},"1293":{"body":"toggle all fold zi toggle current fold za","breadcrumbs":"Notes » Text Editor » Vim » fold","id":"1293","title":"fold"},"1294":{"body":"spelling suggestions for current word z= add spelling of current word to dictionary zg remove spelling of current word to dictionary zw","breadcrumbs":"Notes » Text Editor » Vim » spelling","id":"1294","title":"spelling"},"1295":{"body":"next buffer :bn, previous buffer :bp previous buffer ","breadcrumbs":"Notes » Text Editor » Vim » buffer","id":"1295","title":"buffer"},"1296":{"body":"save all and quit ZZ","breadcrumbs":"Notes » Text Editor » Vim » quit","id":"1296","title":"quit"},"1297":{"body":":w !sudo tee %","breadcrumbs":"Notes » Text Editor » Vim » write as root","id":"1297","title":"write as root"},"1298":{"body":"() [] are escaped by \\ if used as regex \\{-} is *? \\<…\\> is \\b…\\b capture groups are \\1, etc. capitalize first letter s/\\<./\\u&/g simple camelCase to snake_case s/\\l\\zs\\u/_\\l&/g \\( … \\) to $…$ s/\\\\( \\(.\\{-}\\) \\\\)/$\\1$/g","breadcrumbs":"Notes » Text Editor » Vim » regex replace","id":"1298","title":"regex replace"},"1299":{"body":"","breadcrumbs":"Notes » Text Editor » Xcode » Xcode","id":"1299","title":"Xcode"},"13":{"body":"training data L={(a1,y1),⋯,(an,yn)} class of allowed function F use a predefined algorithm to compute f∈F with the goal: y≈f(x)","breadcrumbs":"Notes » Computer Science » Machine Learning » machine learning is about building a function","id":"13","title":"machine learning is about building a function"},"130":{"body":"TLS, SSL IPsec authentication header (AH): after IP header encryption header (EH): after AH, before encrypted TCP header wrap all above as payload into another IP-AH-EH-encrypted payload","breadcrumbs":"Notes » Computer Science » Networking » secure tunnel","id":"130","title":"secure tunnel"},"1300":{"body":"⌘ + ⇧ + O - Open Quickly","breadcrumbs":"Notes » Text Editor » Xcode » Shortcuts","id":"1300","title":"Shortcuts"},"1301":{"body":"https://medium.com/@jozott/format-on-save-xcode-swift-8133d049b3ac brew install --cask swiftformat-for-xcode launch SwiftFormat for Xcode.app check Extensions -> Xcode Source Editor -> SwiftFormat restart Xcode","breadcrumbs":"Notes » Text Editor » Xcode » Format","id":"1301","title":"Format"},"1302":{"body":"Unstructured Class Notes some of these are generated from old docx file using Pandoc","breadcrumbs":"Notes » Unstructured Class Notes » Unstructured Class Notes","id":"1302","title":"Unstructured Class Notes"},"1303":{"body":"Algorithms and Databases sort insertion sort loop invariant heap sort max-heap build max-heap max-heapify priority queue max extract max increase key insert quicksort counting sort radix sort growth of function asymptotic notation Θ notation O notation Ω notation o notation ω notation median & order statistics ith order statistic (lower) median selection problem","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » Algorithms and Databases","id":"1303","title":"Algorithms and Databases"},"1304":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » sort","id":"1304","title":"sort"},"1305":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » insertion sort","id":"1305","title":"insertion sort"},"1306":{"body":"the first j keys but sorted","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » loop invariant","id":"1306","title":"loop invariant"},"1307":{"body":"make a max-heap throw the head out to the end of the array max-heapify the heap stop when the max-heap has 1 element","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » heap sort","id":"1307","title":"heap sort"},"1308":{"body":"an array A heap size size ≤ array size element in the array out of the heap are ignored heap head first array element A[0] no parent parent A[(n - 1)//2] ≥ A[n] left exist if 2n + 1 < size left child A[2n + 1] right exist if 2n + 2 < size right child A[2n + 2] build max-heap convert a heap to a max-heap from A[parent(size - 1)] to A[0], max-heapify the heap max-heapify convert a heap to a max-heap from A[i] provided that both left and right are max-heap find the maximum A[l] among A[i], left, right if A[i] is not the maximum, swap them and max-heapify from A[l]","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » max-heap","id":"1308","title":"max-heap"},"1309":{"body":"a max-heap that act as a queue max return largest (A[0]) extract max pop max swap A[0] and A[size] store A[size] kill A[size] and decrement size max-heapify from 0 increase key increase a key and keep the heap a max-heap swap A[i] with A[parent(i)] while i > 0 and A[parent(i)] < A[i] insert increment size A[size - 1] =−∞ increase key on A[size - 1]","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » priority queue","id":"1309","title":"priority queue"},"131":{"body":"","breadcrumbs":"Notes » Computer Science » Networking » the onion router (Tor)","id":"131","title":"the onion router (Tor)"},"1310":{"body":"partition the array so there is a point in the array, everything left to it is less than it and everything right to it is larger than it quicksort the left and the right","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » quicksort","id":"1310","title":"quicksort"},"1311":{"body":"sort integer know to be less than a constant initialize auxiliary array of 0 with length equal to the constant traverse the array and increment the index corresponding to the value in the auxiliary array traverse the auxiliary array and add the last element to this element, now the values represent the amount of elements less or equal to this element backwards traverse the array and fill in to index in the final array corresponding to the value in the auxiliary array, and decrement the value in the auxiliary array","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » counting sort","id":"1311","title":"counting sort"},"1312":{"body":"sort according to the last digit, then the previous, until the first","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » radix sort","id":"1312","title":"radix sort"},"1313":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » growth of function","id":"1313","title":"growth of function"},"1314":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » asymptotic notation","id":"1314","title":"asymptotic notation"},"1315":{"body":"bounded above and below","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » Θ notation","id":"1315","title":"Θ notation"},"1316":{"body":"bounded above","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » O notation","id":"1316","title":"O notation"},"1317":{"body":"bounded below","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » Ω notation","id":"1317","title":"Ω notation"},"1318":{"body":"bounded above, not asymptotically tight","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » o notation","id":"1318","title":"o notation"},"1319":{"body":"bounded below, not asymptotically tight","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » ω notation","id":"1319","title":"ω notation"},"132":{"body":"internet is overlay IP network over physical link VPN is overlay IP network over internet example overlay multicast","breadcrumbs":"Notes » Computer Science » Networking » overlay network","id":"132","title":"overlay network"},"1320":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » median & order statistics","id":"1320","title":"median & order statistics"},"1321":{"body":"the ith smallest element in the set","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » ith order statistic","id":"1321","title":"ith order statistic"},"1322":{"body":"halfway point of the set ⌊(n+1)/2⌋","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » (lower) median","id":"1322","title":"(lower) median"},"1323":{"body":"find an element in the set larger than exactly i−1 element","breadcrumbs":"Notes » Unstructured Class Notes » Algorithms and Databases » selection problem","id":"1323","title":"selection problem"},"1324":{"body":"Artificial Intelligence ethics codes of ethics engineering design process handling ethical issues definition of artificial intelligence Turing test total Turing test thinking humanly thinking rationally knowledge-based system intelligent agent rational agent task environment agent structure table-driven structure simple reflex agent search example application collaborative perception anomaly detection uninformed search breadth-first search uniform-cost search informed search (heuristic search) A* search (A-star search) reinforcement learning dynamic programming discrete Markov decision process (discrete MDP) find optimal policy continuous Markov decision process (continuous MDP) inverted pendulum discretization value function approximation Mealy machine MDP finite horizon MDP policy searching method partial observable MDP reinforce with baseline Monte Carlo method time-difference learning (TD-learning) on-policy TD (SARSA) off-policy TD: Q-learning most supervised learning when ppl talk about","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » Artificial Intelligence","id":"1324","title":"Artificial Intelligence"},"1325":{"body":"Mill's utilitarianism: maximize benefit for everyone, mostly equally bane: conflict of interest personal benefit Kant's formalism/ duty ethics: unconditional command for every individual bane: universal principle may harm specific people Locke's Right Ethics: individual has right simply by existence bane: what to do when two people's rights conflict Aristotle's virtue ethics: objective goodness from human qualities bane: how to find the \"golden mean\" the golden rule (all above agrees with) Do unto others as you would have others do unto you","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » ethics","id":"1325","title":"ethics"},"1326":{"body":"statements of general principles, followed by instructions for specific conduct defiens duties the professional owes to society/employers/clients/colleagues/subordinates/profession/self","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » codes of ethics","id":"1326","title":"codes of ethics"},"1327":{"body":"recognize problem/need, gather information define problem/goal generate/propose solution/method evaluate benefit&cost of alternatives","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » engineering design process","id":"1327","title":"engineering design process"},"1328":{"body":"correct the problem whistle blowing resign in protest","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » handling ethical issues","id":"1328","title":"handling ethical issues"},"1329":{"body":"humanly → acting ration → math/theory","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » definition of artificial intelligence","id":"1329","title":"definition of artificial intelligence"},"133":{"body":"unstructured peer-to-peer network: messy super node: big machines, store what file neighbor have coordination: maintain after super node leave tracker: broadcast what peer interested in same file peer exchange (PEX): list of known peer","breadcrumbs":"Notes » Computer Science » Networking » peer-to-peer network","id":"133","title":"peer-to-peer network"},"1330":{"body":"NLP knowledge representation automated reasoning ML total Turing test perceptional abilities computer vision robotics","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » Turing test","id":"1330","title":"Turing test"},"1331":{"body":"get inside the working of human mind general problem solver cognitive science","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » thinking humanly","id":"1331","title":"thinking humanly"},"1332":{"body":"correctness logic fact-check","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » thinking rationally","id":"1332","title":"thinking rationally"},"1333":{"body":"general-purpose search domain-specific knowledge knowledge bottleneck","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » knowledge-based system","id":"1333","title":"knowledge-based system"},"1334":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » intelligent agent","id":"1334","title":"intelligent agent"},"1335":{"body":"prior knowledge of environment performable action performance measurement perception","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » rational agent","id":"1335","title":"rational agent"},"1336":{"body":"PEAS: performance measurement, environment, actuators, sensors properties fully/partially observable single/multiple agent deterministic/stochastic episodic/sequential static/dynamic known/unknown","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » task environment","id":"1336","title":"task environment"},"1337":{"body":"function: perception → action architecture: sensory → actuator table-driven structure nentry=t=1∑T∣P∣T simplest e.g. industrial robot #cases explode simple reflex agent match input against rule, return action model-based: only work for fully observable goal-based utility-based: maximize gain expectation","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » agent structure","id":"1337","title":"agent structure"},"1338":{"body":"breadth/depth first","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » search","id":"1338","title":"search"},"1339":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » example application","id":"1339","title":"example application"},"134":{"body":"dedicated tracker track peer and torrent direct connection between peer for data transfer select peer by speed (tic-for-tat) seeder: peer with file leecher: peer looking for file distributed hash table (DHT) no need for tracker","breadcrumbs":"Notes » Computer Science » Networking » BitTorrent","id":"134","title":"BitTorrent"},"1340":{"body":"share raw data → huge overhead extract feature share object position","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » collaborative perception","id":"1340","title":"collaborative perception"},"1341":{"body":"bidirectional optimization","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » anomaly detection","id":"1341","title":"anomaly detection"},"1342":{"body":"backtracking search breadth-first search complete: will find shallowest goal if graph has finite depth optimal if path cost g(n) is non-decreasing of depth d O(bd) where b is branching factor uniform-cost search expand node with least path cost g(n) optimal O(b1+⌊C∗/ϵ⌋) where every action cost ≥ϵ informed search (heuristic search) A* search (A-star search) cost f(n)=g(n)+h(n) cost to reach node g(n) estimated cost to goal, heuristic, h(n) optimal if h(n) is admissible in tree search admissibility: never overestimate optimal if h(n) is consistent in graph search consistency: triangle inequality h(n)≤c(n,a,n′)+h(n′) optimally efficient if h(n) is consistent: expand fewest node among optimal algorithm","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » uninformed search","id":"1342","title":"uninformed search"},"1343":{"body":"control system model-based vs model-free","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » reinforcement learning","id":"1343","title":"reinforcement learning"},"1344":{"body":"key: sub-problem example Dijkstra's algorithm: per node Bellman-Ford algorithm: per hop","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » dynamic programming","id":"1344","title":"dynamic programming"},"1345":{"body":"finite tuple {S,A,{Psa},γ,R} space S action A state transition probabilities Psa discount factor γ∈[0,1) reward function R: evaluation metric total payoff. maximize this V=i∑γiR(si) policy π:s↦a. find this find optimal policy optimal policy π∗ π∗=aargmaxs′∑Psa(s′)V∗(s′) mapping state to expected total payoff Vπ:s↦R Vπ(s)=E[i∑γiR(si)s0=s]=E[[R(s)]+γVπ(s′)]⇒Vπ(s)=R(s)+γs′∑Psπ(s)(s′)Vπ(s′) Bellman equation value iteration V(s):=0 Bellman update: ∀ s, V(s):=R(s)+amaxγs′∑Psa(s′)V(s′) linear system Bellman back operator V′:=B(V) sync/async update γ force V to converge V∗ exponentially policy iteration random π repeat: V:=Vπby Bellman equationπ(s):=aargmaxs′∑Psa(s′)V(s′) when converge, guarantee optimal policy high complexity: linear system very step exploration and exploitation ε-greedy a={argmaxVrandom a∈Aprobability 1−εprobability ε ε is small and decrease softmax","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » discrete Markov decision process (discrete MDP)","id":"1345","title":"discrete Markov decision process (discrete MDP)"},"1346":{"body":"V(s)=R(s)+γamaxEs′∼Psa[V(s′)] inverted pendulum kinematic model discretization curse of dimensionality: ∣S∣=Rn bad for smooth function 4 ~ 8 dimension value function approximation approximate V∗ V∗(s)=θTϕ(s) trial model/simulator: s′↦Psa assume A discrete s′=s+Δts˙ learn from data n trial, each with T time step supervised learning (st,at)↦st+1 linear regression st+1=Ast+Bat,A∈Rm×n,B∈Rn×d deterministic/stochastic model noise term εt∈N(0,ε) model-based reinforcement learning fitted value iteration fitted value iteration approximate V∗(s) from s(i),i∈{1,…,n} trial: ramdomly sample s(i),i∈{1,…,n} initialization: θ:=0 repeat for i∈{1,…,n}: repeat for 1∈A: sample si′∼Psa(i),i∈{1,…,k} q(a):=k1j=1∑k[R(s(i))+γV(sj′)] is estimation of R(s)+γEs′∼Psa[V(s′)] y(i):=amaxq(a) any regression model, e.g. θ:=θargmini∑(θTϕ(s(i))−y(i))2 for deterministic model, can set k=1 Mealy machine MDP R:S×A→R Bellman equation: V∗(s)=amax[R(s,a)+γs′∑Psa(s′)V∗(s′)]⇒π∗=aargmax[R(s,a)+γs′∑Psa(s′)V∗(s′)] finite horizon MDP finite tuple {S,A,{Psa},T,R} time horizon T∈(0,+∞) maximize ∑t=0TR(st,at) action based on time πt∗ time-dependent dynamic Vt(s)=E[t′=t∑TR(st′,at′)]Vt∗(s)=⎩⎨⎧amax[R(t)(s,a)+Es′∼Psa(t)(Vt+1∗(s′))]amax[R(t)(s,a)]t∈{0,…,T−1}t=T solution by dynamic programming: work way back from VT∗(s) linear quadratic regulation S:Rn,A:Rd,n>d linear transition with noise Psa st+1=Ast+Bat+ωt negative quadratic reward to push system back ut:Ru×n,vt:Rn×n,ut,vt≥0 R(st,at)=−stTutst−atTvtat policy searching method stochastic policy πθ:S×A→R πθ(s,a): probability of taking action a at state s direct policy search: find reasonable θ θmaxE[t=0∑TR(st,at)πθ] fixed initial state greedy stochastic gradient ascent learning rate α∈(0,1] repeat: sample st,at reinforce θ:=θ+αt∑[πθ(st,at)∇θπθ(st,at)]t∑R(st,at) reason it converge: product rule","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » continuous Markov decision process (continuous MDP)","id":"1346","title":"continuous Markov decision process (continuous MDP)"},"1347":{"body":"reinforce with baseline arbitrary baseline b(s) independent of a θ:=θ+αt∑[∇θlnπθ(st,at)](f(τ)−b(s))","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » partial observable MDP","id":"1347","title":"partial observable MDP"},"1348":{"body":"trial: (st,at) wait until end of episode return Gt V(st):=V(st)+α(Gt−V(st)) drawback: slow if episode long","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » Monte Carlo method","id":"1348","title":"Monte Carlo method"},"1349":{"body":"at time t+1, update V(st) V(st):=V(st)+α(δt) TD error δt δt=R(st+1)+γV(st+1)−V(st) on-policy TD (SARSA) ε-greedy initialize arbitrary reward Q(s,a) repeat for episode initialize S behavior policy: select at based on Q repeat for each step select potential a′ for s′ based on Q update Q(s,a) Q(st,at):=Q(st,at)+α[R(st)+γQ(st+1,a′)−Q(st,at)] s:=s′ until s is terminal off-policy TD: Q-learning same as SARSA except Q(st,at):=Q(st,at)+α[R(st)+γamaxQ(st+1,a)−Q(st,at)] greedy","breadcrumbs":"Notes » Unstructured Class Notes » Artificial Intelligence » time-difference learning (TD-learning)","id":"1349","title":"time-difference learning (TD-learning)"},"135":{"body":"Data Science","breadcrumbs":"Notes » Data Science » Data Science","id":"135","title":"Data Science"},"1350":{"body":"Cloud Computing operational expense (OPEX), capital expense (CAPEX) → centralize server tenant isolation: challenge for cloud provider cloud provider classification: infrastructure/ platform/ software as a service data center hierarchy: rack, row & aisle, pod (building unit) top-of-rack (ToR) switch: 2 per rack, high capacity north-south traffic: outside to inside—load balancing east-west traffic: within inside—high bandwidth network topology fat tree. problem: require insane link capacity on top link aggregation: bond multiple link together leaf-spine topology (clos): layered multiple spine connected to multiple rack Internet redundancy: multiple ISP data storage classical approach: server with own HDD, data replication modern approach: separate compute/ storage unit, SSD, less data replication Hadoop automatic MapReduce management HDFS: Hadoop distributed file system assume each server has own storage append-only, 128MB block NameNode index, DataNode store try to compute with local data Spark multi-paradigm, high-performance building block: resilient distributed dataset (RDD) general, lazy, ephemeral, lineage, shareable aggressive caching with LRU paravirtualization: modify guest OS to not use kernel space high performance hard to modify OS full virtualization native performance need hardware support (e.g. ring -1 for hypervisor) container isolate: network namespace, file system, process information, user Linux containers (LXC): more full system than Docker automation level: deployment & configuration, → monitoring & measurement, → trends & prediction, → root cause analysis, → troubleshooting vendor-independent configuration: zero-touch provisioning & infrastructure as code orchestration building blocks: ephemeral, can be replicated, replaced, composed → update, autoscaling, restore load balancing early error detection during rollout Kubernetes pod: group of container, smallest unit to be managed init container: run before other microservice: smaller scope & team, modularity, less complexity, language flexibility, test coverage, rapid deployment, fault isolation; cascading error, functionality & data duplication, attack surface service mesh proxy: load balancing, convert conventional communication protocol hysteresis: delay in response to change cause instability, oscillation event-based controller stabilization window serverless/ FaaS: API redirection & runtime & DB by provider. event-driven, stateless, scale from zero to infinite classic software development → agile → DevOps → site reliability engineering (SRE): merge development, quality assurance, operation version management extensive testing in continuous integration sandbox & canary deployment SRE: half time development, max half time operation, overflow redirect to development team on-call shift post-mortem report, pager fatigue error budget: target < 100% availability, adjust development accordingly playbook: automate away human networking safety and isolation: harden north-south traffic, assume cooperation & prevent traffic among tenant on east-west traffic same tenant: overlay topology (virtual) & underlay (physical) different tenant: traffic like north-south implementation: VLAN, packet carry tag VXLAN (extended): encapsulate, solve 4096 VLAN limit remote storage interface: file/ block interface (NFS/ virtual disk) object storage: key-bytes pair","breadcrumbs":"Notes » Unstructured Class Notes » Cloud Computing » Cloud Computing","id":"1350","title":"Cloud Computing"},"1351":{"body":"Introduction to Databases information: data with meaning knowledge: actionable information exploratory data analysis (EDA) relation ≈ table data definition language (DDL): for schema data manipulation language (DML): for query and CRUD DML & DDL both in SQL data model (DM): entity, attribute, relationship, constraint entity relationship diagram (E-R diagram) (ER diagram) unified modeling language (UML): for OODM relation schema R=(A1,…) relation instance r(R) element t attribute usually atomic superkey K: subset of row tuple, bijection with row superset of K is also superkey candidate key = minimal superkey union compatibility/ type compatibility data control language (DCL) & transaction control language (TCL): management like: any substring %, any char _ for where clause filter: like, between, some, all for where clause standalone: exists, unique union, intersect, except (all) select x, fn(y) from _ group by x having … boolean type: true, false, unknown select _ from _ where x in y;\n-- lateral clause:\nselect _ from x, lateral (/* access outside variables */) …;\n-- with clause:\nwith alias_name as (…) select …;\ndelete from _ where _;\ninsert into table_name (attributes, …) values (…,), (…,), …\nupdate table_name set attributes = value where …;\n-- join using\nselect _ from relation1 join relation2 using (attr1, …);\n-- view/ materialized view\ncreate view view_name as select …;\ncreate materialized view view_name as select …; domain constraint on single relation: not null, unique, check (…) referential integrity: foreign key (attr1) references table_name on delete … named constraint: attr1 type, constraint constr_name check (…) drop named constraint: alter table table_name drop constraint constr_name; deferrable constraint: check at end of transaction assertion create assertion assert_name check (…); function call coalesce(attr1, default_value_in_place_of_null) cast(attr1 as type) data_format(value, 'format string') if(predicate, value_when_true, value_when_false) or decode in Oracle user-defined type (UDT): distinct type/ structured data type create type type_name as …;\ncreate domain domain_name as …; create table extension create table table2 like table1;\ncreate table table1 as (select …) with data; stored function/ stored procedure: delimiter $$\ncreate function fn_name(arg1 type1, …) returns type_out begin -- declare local variable, set to NULL by default declare local_var var_type default default_val; -- mutate local variable set local_var = …; select _ into local_var from …; return …;\nend $$\n-- `type_out` can be a `table (…)`—table function create procedure proc_name( in arg_input type1, out arg_output type2, inout arg_mutate type3, …\n) begin -- …\nend $$\n-- no returning for procedure delimiter ; -- call procedure\ncall proc_name(args…, @outside_var); stored function: deterministic/ non-deterministic (default) procedural SQL: -- expression with pattern matching\ncase -- optionally with value here when _ then _ … else _\nend; -- loop\nlabel1: loop iterate; -- continue leave; -- break\nend loop;\nwhile predicate1 do -- …\nend while;\nrepeat -- …\nuntil predicate1 end repeat;\nfor each_row as table_value1 do -- …\nend for; trigger: create trigger trigger_name after insert on table_name -- or `before`, `delete`\nreferencing new row as row_name for each row when ( -- or `old row`.\n-- or without renaming `new` or `old`. -- …\n)\nbegin -- compound statement rollback\nend; -- multiple trigger\ncreate trigger trigger_name before update on table_name\nfor each row follows another_trigger_name begin -- …\nend, $$ error handling: declare continue handle for sqlstate 'err_no' begin -- or for `not found` -- …\nend; -- or `set _ = …` cursor: declare cur_name for select _ from _;\nopen cur_name;\nfetch cur_name into var1, …;\nclose cur_name; entity-relationship model (E-R model): entity set, relationship set, attribute multi-valued attribute, composite attribute, derived attribute mapping cardinality, cardinality constraint (directed/undirected link) total participation (double line)/ partial participation weak entity set identifying entity set primary key → discriminator attribute descriptive attribute lossy decomposition: r⊂ΠR1(r)⋈ΠR2(r) (lossless: =) functional dependency (FD) X→Y: can uniquely identify Y by X trivial FD: Y⊆X R1∩R2→R1⇒ lossless decomposition (or swap 1&2) Boyce-Codd Normal Form (BCNF): α→β,α,β⊆R⇒β⊆α or α superkey mean time to failure MTTF RAID: data striping vs mirror fixed-length record: deletion: free list for deletion variable-length record: offset + length, null bitmap heap: free-space map (first/second-level) sequential file: linked list of sorted search key multi-table clustering file organization: faster some join & slower some other, cluster key table partitioning buffer manager: buffer replacement strategy (LRU/MRU), pin/unpin, shared/exclusive lock column-oriented storage: less IO, better caching & compression dense index: index for each search-key value dense clustering index: group by cluster key sparse index: index for some search-key value deadlock prevention: wait-die scheme, non-preemptive: older transaction wait for lock, younger transaction die wound-die scheme, preemptive: older transaction wound younger transaction when waiting for lock timeout-based scheme: hard to determine timeout, starvation wait-for graph: cycle → deadlock recovery system: log-based recovery: redo/undo, immediate/deferred DB modification","breadcrumbs":"Notes » Unstructured Class Notes » Introduction to Databases » Introduction to Databases","id":"1351","title":"Introduction to Databases"},"1352":{"body":"Introduction to Programming and Data Structures encryption one-time pad bitwise XOR: bitwise exclusive or ∧ caret (\\wedge) Boolean algebra ⎩⎨⎧a∧a=0a∧0=a(a∧b)∧c=a∧(b∧c) pseudo-random pseudo random bits: linear feedback shift register LFSR bit, cell, register, seed, initial state [N, k] LFSR: N-bit register with taps at N and k seed cannot be 0, at most 2 N − 1 fills in N -bit register k counts from 1… Java programming virtual terminal vs integrated development environment IDE Java program shell: public class program_name { public static void main(String[] args) { //begin body } //end } piping and redirecting—|, <, > | is two directional < and > take one’s output as the other one’s input, following the arrow for multiple piping, “parenthesis” are added as if convert to type: Type.parseType(String_needs_converting) cast: (type) what_needs_converting does not convert type when divide convert to the more precise type when operate between two types int Integer . MAX_VALUE + 1 = Integer . MIN_VALUE =-Integer . MIN_VALUE remainder % char—uses ASCII, can be operated as if int, cast to int if not assigned to a char a~z, A~Z, 0~9 are together in ASCII, this can give a range char array converts to String when called String .valueOf() StringBuilder—better way to concatenate strings concatenate strings: .append double special values: Infinity, NaN math library type operation(type variable, …) type: double, int, long, float operation: abs, max, sin, asin, exp, log, pow, round, random, sqrt variable: a, PI, E boolean operation and && or || not ! xor (!a && b) || (a && !b) (a && b) == (!(!a || !b)) naming camel case: moreThanOneWord constant: MORE_THAN_ONE_WORD loop if if (boolean) {execution1;} else {execution2;} while while (boolean) { execution1 } for for (initialization_statement1, …; boolean; increament_statement1, …) { execution } switch switch (variable) { case literal -> operation; … } do while do {execution1} while (boolean); at least does once array type[] name; //declare array name of type type new double[length]; //an array of length length, all 0.0s name[index] = literal //refer to array name by index index {literal1,…} //an array .length copy: copy the length and every single value assign: refer to the same array two dimentional array double [][] a a[0]. length decide all a[i]. length sorting: Arrays .sort() output: System.out.println(output) //print output \\n System.out.print(output) //print output System.out.printf(“string1%w1.p1c1… string2”,output1,…) //print string1 output1… string2 with field width w, precision .p, and conversion code c negative w counts from the right. for c , d : decimal, f : floating, e : scientific, s : string, b : boolean must have % and c this is the standard string format in Java https://docs.oracle.com/javase/tutorial/java/data/numberformat.html DecimalFormat df = new DecimalFormat( \"##.##\" ); StdDraw line( , , , ), point( , ), setCanvasSize(w,h), setXscale(x0,x1), setPenRadius(), shape, filledShape text(x,y,String) enableDoubleBuffering, show, clear, pause, System .exit(0); makes the program stop input: command-line argument: args[No.] //input in modyfy run configuration - program argument StdIn: isEmpty, readType, readAllTypes, hasNextChar, hasNextLine*//Type = Int, Double, Boolean, String, or Line* scanner:import java.util.Scanner; //import scanner Scanner sc= new Scanner(System. in ); //define a scanner Type variable = sc.nextType(); //let variable be input make an explanation / * * / function static void can change content of array as they are mutable, cannot change value of primitive type as they are immutable import static imports the method so that its prefix can be ommited don’t use applications programming interface API private static long [] makes the array global call: ClassName. method (object) final makes the variable immutatble recursion recurrence relation T(n)={2T(n−1)+1,n>11,n=1=2n−1(n>0) Gray codes: show all n -digit binary numbers by only changing 1 digit at a time start from i = 0, change the i th digit from 0 to 1 and do everything done to the first i − 1 digits backwards recursive graph fractal Brownian bridge: random path to bridge to points midpoint displacement method: take the midpoint and Gaussianly-randomly move it, and set it as one of the end point volatility: initial variance of the Gaussian dist Hurst exponent H : divide the variance of the Gaussian dist by 22 H H is ½ for Brownian bridge fractal dimension: 2 − H plasma clouds exponential waste: calculate the same thing again dynamic programming store calculated results in array top-down solution make global array and recursion bottom-up solution make local array and loop longest common subsequance LCS problem for x [ i … m ) and y [ j … n ), opt[i,j]=⎩⎨⎧0,i=mandj=n{opt[i+1,j+1]+1,x[i]=y[j]max([i+1,j],[i,j+1]),x[i]=y[j],otherwise percolation Monte Carlo simulation: apply randomness to estimate unknown qualities by simulation 2-dimentional n by n sites blocked site, open site; full site, empty site site vacancy probability p vertical percolation: go straight down object reference type vs primitive type create object: ClassName reference = new ClassName(argument1,argument2,…) Color import java.awt.Color; Color(r,g,b) col.getBlue() Luminance Y = 0.299 r + 0.587 g + 0.114 b reference type aliasing—pass by value orphaned object: don’t have a reference instance method: data-type operation for reference type reference.method(argument) create data-type public class ClassName { *// instance variable inside the reference type (not final if need to change value) * private final type instanceVariable1 ; … *// constructor, with the same name as the class * public ClassName( type parameterVariable1, …) { type localVariable = value; instanceVariable1 = parameterVariable1; … } / * explanation of the method */ * public double methodName( type argument1, …) { … return something; } use short name for instance variables for convenience use full name for parameter variables as the client can see them immutability: final makes the value of primitive type and the identity of the object of reference type immutable defensive copy: copy each of the values of the parameter variables to avoid aliasing interface type public interface interfaceName { public abstract type methodName( type parameterVariable); } abstract methods: includes nothing implements public class ClassName implements interfaceName{ public int methodName( type parameterVariable) { } } the class must have methods coresponding to all abstract methods in the interface interface enables a method name to call different methods according to the object functional interface: single method lambda expression (parameterVariable1,…) -> stuffToReturn; implementation inheritance subclass general equals method public boolean equals(Object x) { if (x == null ) return false ; if ( this .getClass() != x.getClass()) return false ; Class that = (Class) x; return ( this . instanceVariable1 == that. instanceVariable1 ) && …; } general hashcode method public int hashCode() { return Objects. hash ( instanceVariable1 ,…); } wrapper type: built-in reference type corresponding to primitive type autoboxing and unboxing performance running time: time when finish minus time when start (in millisecond) System. currentTimeMillis () System. nanoTime () algorithm tilde notation ∼ f ( n ) order of growth empirical analysis doubling hypothesis: double the input size, study the running time mathematical analysis memory usage: bool—1; char—2; int, float, padding—4; long, double, object reference—8; object overhead—16; array overhead—24 (b) big- O notation O ( g ( n )): running time | f ( n )| < c | g ( n )| ∀ n > n 0 binary search exception filter—determine whether a name is in a sorted array collection operations—create, insert, remove, test emptiness item (pushdown) stack last-in-first-out (LIFO) operations—push, pop, test emptiness queue first-in-first-out (FIFO) linked-list node—content + next node iterator resizing array—double the size if no enough space, halve it if less than ¼ used avoid loitering—set the variable to null generic type generic class—a class that can be fed with different data types public class GenericClass < typeParameter > type parameter—a name for the data type to be used in this class by the client constructor public GenericClass ( typeParameter parameter** ) { para = parameter; … } using the constructor GenericClass < String > variableName = new GenericClass < String >( \"blah\" ) **; symbol table key-value pairs—cannot be null get(key)/ put(key,val) contains(key) hashing binary search tree BST put get regular expression minimum RE concatenate union—| or {…,…} closure—x* grouping—() java REs String.matches(regex) Pattern pattern = Pattern.compile(RE) Matcher matcher = pattern.matcher(input) matcher.find() matcher.matches() shorthands wildcard—. beginning of line—^ end of line—$ range—[char1-char2] negation—^x closure operator extension one or more—x+ zero or one—x? length—{num} between—{low, high} deterministic finite-state automata DFA finite number of states transitions tape reader universal virtual DFA input format—number of states \\s alphabet \\s one line of each state nondeterministic finite-state automata DFA pushdown automaton PDA Turing machine universality computability David Hilbert’s questions: mathematics is consistent, complete, decidable? Kurt Gödel: axiomatic system cannot be both consistent and complete Alan Turing: mathematics is not complete halting problem—reductio ab absurdum totality problem, equivalence problem Henry Rice: determining whether a program has any given functional property is unsolvable intractability—no algorithm exists to efficently solve polynomial-time algorithm—bounded above by a**n b —efficient exponential-time algorithm—bounded below by 2 a**n b satisfiability problems search problems—the problems with solutions that polynomial-times algorithms can check NP —the set of all search problems NP -complete—every search problems polynomial-time reduces to it P —the set of all search problems that can be solved in poly-time representation binary—0 b convert to binary and print— System . out .print( String .format( \"%16s\" , Integer .toBinaryString(number)).replace( ' ' , '0' )); hexadecimal—0 x read hexadecimal—Integer.parseInt(input, 16) twos-complement—− x = ∼ x + 1 ∼ x —complement, flip all bits arithmetic shift right—add 1 to begin if negative logical shift right—always add 0 masking—get the bits wanted by bitwise or with a mask that only has 1s in the corresponding bits TOY machine 16 bit memory memory location M [00] ∼ M [ F**F ] memory dump M [ F**F ]—standard IO arithmetic and logic unit ALU computation engine register 16 words R [0] ∼ R [ F ] connect ALU & memory R [0] is always 0 program counter PC 8 bit memory address of next instruction instruction register IR current instruction fetch-inctemenat-execute cycle fetch from memory to IR increment PC execute as IR says and change memory or PC or calculate instruction format (16 bit) type RR—opcode + 3 registers (destination + 2 sources) arithmetic instruction—1, 2 for addition, subtraction logical instruction—3~6 type A—opcode + register (destination) + memory address (8 bits) memory address instruction—7, A, B memory instruction—8, 9 flow of control instruction—C~F branching halt—0 loop with branching self-modifying code TOY VM booting—using a small program, load input into M [00] ∼ M [ F**F ] to start the machine assembler—run assembly-language assembly-language—use symbolic name for operation and addresses interpreter—directly execute instruction written in a programming language compiler—transform source code into another computer language bootstrapping—use one virtual machine to create more powerful machine Boolean logic Boolean function and notation NOT(x) ¬x x’ AND(x,y) x∧y xy OR(x,y) x∨y x+y XOR(x,y) x⊕y x⊕y truth table Boolean arithmic absorption—x(x + y) = x + xy = x DeMorgan’s laws—(xy)’ = x’ + y’ (x + y)’ = x’y’ Boolean function of more variables majority—MAJ(…) = 1 iff more 1 than 0 odd-parity—ODD(…) = 1 iff number of 1 is odd sum-of-products representation—OR(AND(each of the cases that contribute to 1)…) circuit—interconnected network of wires, power connections, and control switchs that take value from input wire and output via output wire control switch relay—control line with electromagnet vacuum tube transistor gates recursive definition—a gate or a network of circuits that are connected with wires combinational circuit—no loop output depend only on input decoder—tell which output wire to activate n input, 2 n output demultiplexer (demux)—add another input to decoder add AND gate to decoder output act as 1-to-2 n logical switch multiplexer (mux)—AND all corresponding input and OR all of those n + 2 n input wires, 1 output wire act as 2 n -to-1 logical switch sum-of-product circuit ALU module—parts of the computer bus—group of wires to transmit data between modules sequential circuit buzzer flip-flop set reset register memory bit-slice design—same circuit for demux to write and mux to read clock tick-tock clock speed fetch and execute complementary run and halt input CPU control fetch fetch write execute execute write","breadcrumbs":"Notes » Unstructured Class Notes » Introduction to Programming and Data Structures » Introduction to Programming and Data Structures","id":"1352","title":"Introduction to Programming and Data Structures"},"1353":{"body":"Probability, Random Variables, and Stochastic Processes joint distribution: discrete uniform distribution independent uniform variables joint distribution: continuous conditional probability: discrete probability model rule of average conditional probability conditional expectation: discrete conditioning: continuous case probability over a region infinitesimal conditioning formula conditional density of Y given X=x joint density surface marginal density of X multiplication rule for density averaging conditional probability integral conditioning formula conditional expectation conditional variance ! another way to calculate variance ! for Xi i.i.d. with number N>0 independent to Xi Bayesian estimation general case conjugate prior indicator maximum a posteriori probability (MAP) rule point estimation least mean squares (LMS) estimation base case general case linear least mean squares estimation hypothesis testing MAP rule for hypothesis testing general case—two coins property discrete Markov chain one-step probability P(Xn+1=j∣Xn=i)=P(i,j)=pij transition probability matrix initial distribution π0 n-step transition matrix class structure closed class absorbing state transient & recurrent hitting time transient and recurrent state number of times pass y theorem stationary distribution find stationary distribution period of a state dx Stochastic process branching process generating function birth and death process gambler's ruin irreducible and stationary distribution random walk random walk on finite graph G random walk on positive integer random walk on integer Zd continuous Markov chain time-homogenous—s does nothing Chapman–Kolmogorov Equations holding time at state i proof embedded discrete Markov chain another representation of pij(t) recover pij(t) using Q long time behavior of continuous Markov chain stationary distribution relationship with stationary distribution of embedded chain Φ irreducible fundamental theorem continuous birth and death process pure birth recurrence Poisson process inter arrival time Ti arrival time Si alternative definition using exponential distribution combine independent Poisson process splitting Poisson process 1 occurrence time spot many occurrence time spot definition of o(h) alternative definition property of Stochastic process second order stationary process Gaussian process multivariate normal distribution Brownian motion standard Brownian motion covariance function connection between Brownian motion and discrete random walk relation between Gaussian process and Brownian motion transformation of Brownian motion hitting time some distributions Beta random variables Beta function exponential random variable memory-less property sum of n i.i.d. exponential distribution is gamma distribution comparison between X1∼Exp(λ1) and X2∼Exp(λ2) comparison between X1,X2⋯∼Exp with parameter λ1,λ2,⋯ minimum of n exponential distribution with λi's Gamma distribution Poisson distribution bivariate normal distribution joint density marginals conditionals","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » Probability, Random Variables, and Stochastic Processes","id":"1353","title":"Probability, Random Variables, and Stochastic Processes"},"1354":{"body":"P(B)=P((X,Y∈B))","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » joint distribution: discrete","id":"1354","title":"joint distribution: discrete"},"1355":{"body":"(X,Y)∈DP((X,Y)∈C)=area(D)area(C)for C⊂D independent uniform variables has uniform joint distribution use areas to find probability, always geometric method first","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » uniform distribution","id":"1355","title":"uniform distribution"},"1356":{"body":"f(x,y)≥0∀(x,y)∈R∬R2f(x,y)dxdy=1","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » joint distribution: continuous","id":"1356","title":"joint distribution: continuous"},"1357":{"body":"P(X=x∣Y=y)=P(Y=y)P(X=x,Y=y)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » conditional probability: discrete","id":"1357","title":"conditional probability: discrete"},"1358":{"body":"(S,A,P)S—sample spaceA—eventsP—probability rule of average conditional probability P(Y=y)=x∑P(Y=y∣X=x)P(X=x) conditional expectation: discrete E(Y∣A)=y∑yP(Y=y∣A) for random variable Y and event A properties linearity property E(X+Y∣A)=E(X∣A)+E(Y∣A) average conditional expectation E(Y)=i=1∑nE(Y∣Ai)P(Ai)if Ai is partition of outcome space⇒average conditional probability P(B)=i=1∑nP(B∣Ai)P(Ai) rule of average conditional expectation E(Y)=x∑E(Y∣X=x)P(X=x) aka the formula for E(Y) by conditioning on X conditional expectation of Y given X E(Y∣X) is a function g(x) of x E(Y)=x∑E(Y∣X=x)P(X=x)=x∑g(x)P(X=x)=E(g(x))⇒E(Y)=E[E(Y∣X)] to find a function, find its value first and replace the parameter with variable E.g.E(X=x)=f(x)⇒E(X)=f(X)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » probability model","id":"1358","title":"probability model"},"1359":{"body":"fX∣Y(X∣Y=y)=∫Rf(x,y)dxf(x,y)=fY(y)f(x,y) if fY(y)>0 ⇒f(x,y)=fX∣Y(x∣Y=y)fY(y) probability over a region P(x∈D∣Y=y)=∫DfX∣Y(x∣Y=y)dx","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » conditioning: continuous case","id":"1359","title":"conditioning: continuous case"},"136":{"body":"Visualization data type item attribute attribute type link position grid structured data unstructured data symbolic display graph mark channel characteristic of channel analysis framework user task graph theory centrality degree of vertex betweeness of vertex closeness of vertex geodesic distance between vertex eigenvector of vertex clustering coefficient time","breadcrumbs":"Notes » Data Science » Visualization » Visualization","id":"136","title":"Visualization"},"1360":{"body":"P(A∣X=x)=P(X∈dx)P(A,X∈dx) X∈dxX fall in small interval near x","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » infinitesimal conditioning formula","id":"1360","title":"infinitesimal conditioning formula"},"1361":{"body":"fY(y∣X=x)=fX(x)f(x,y) ⇒∫fY(y∣X=x)dy=1 joint density surface z=f(x,y) marginal density of X fX(x)=∫f(x,y)dy multiplication rule for density f(x,y)=fX(x)fY(y∣X=x)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » conditional density of Y given X=x","id":"1361","title":"conditional density of Y given X=x"},"1362":{"body":"integral conditioning formula P(A)=∫P(A∣X=x)fX(x)dx","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » averaging conditional probability","id":"1362","title":"averaging conditional probability"},"1363":{"body":"E[g(Y)∣X=x]=∫g(y)fY(y∣X=x) dyE[g(Y)]=∫E[g(Y)∣X=x] fX(x)dx","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » conditional expectation","id":"1363","title":"conditional expectation"},"1364":{"body":"var(X∣Y)≡E[(X−E[X∣Y])2 ∣Y]=E[X2∣Y]−(E[X∣Y])2","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » conditional variance","id":"1364","title":"conditional variance"},"1365":{"body":"Var(X)=E[Var(X∣Y)]+Var(E[X∣Y]) ! for Xi i.i.d. with number N>0 independent to Xi E[i=1∑NXi]=E[X] E[N]Var(i=1∑NXi)=E[N] Var(X)+(E[X])2 Var(N)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » ! another way to calculate variance","id":"1365","title":"! another way to calculate variance"},"1366":{"body":"take the wanted parameter θ as a random variable with distribution prior distribution take a sample and use it to update the posterior distribution","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » Bayesian estimation","id":"1366","title":"Bayesian estimation"},"1367":{"body":"want Θ in Xi∼distribution(Θ) let Θ∼priorDistribution⇒fΘ(θ) with observations (measurements) X=(X1,…,Xn) know conditional distribution fX∣Θ(x∣θ) ⇒ posterior distribution fΘ∣X(θ∣x)=fX(x)fX∣Θ(x∣θ)fΘ(θ)=∫fX∣Θ(x∣θ′)fΘ(θ′)dθ′fX∣Θ(x∣θ)fΘ(θ) i.e. posterior = likelihood ⋅ prior / evidence it does not matter if the observation points are used one by one or all at once","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » general case","id":"1367","title":"general case"},"1368":{"body":"the posterior distribution is of the same type as the prior distribution normal + normal = normal binomial + Beta = Beta","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » conjugate prior","id":"1368","title":"conjugate prior"},"1369":{"body":"1A(x)={10x∈Ax∈/A⇒E[X∣A]=P(A)E[X⋅1A(X)]","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » indicator","id":"1369","title":"indicator"},"137":{"body":"","breadcrumbs":"Notes » Data Science » Visualization » data type","id":"137","title":"data type"},"1370":{"body":"select θ^ so that posterior probability fΘ∣X(θ∣x) is maximized ⇔ maximize fX∣Θ(x∣θ)fΘ(θ) point estimation select point estimate θ^ to represent best guess of Θ estimator Θ^=g(X) maximum a posteriori probability (MAP) estimator conditional expectation estimator a.k.a. least mean squares (LMS) estimator ↓","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » maximum a posteriori probability (MAP) rule","id":"1370","title":"maximum a posteriori probability (MAP) rule"},"1371":{"body":"select an estimator/function with least squared error base case for θ, want θ^ such that E[(θ−θ^)2] is minimized ⇒ choose θ^=E[θ] general case with observations X=x, want θ^ to minimized E[(θ−θ^)2∣X=x] ⇒ choose θ^=E[θ∣X=x]","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » least mean squares (LMS) estimation","id":"1371","title":"least mean squares (LMS) estimation"},"1372":{"body":"the linear form of LMS","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » linear least mean squares estimation","id":"1372","title":"linear least mean squares estimation"},"1373":{"body":"denote Hi as event {Θ=θi}","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » hypothesis testing","id":"1373","title":"hypothesis testing"},"1374":{"body":"choose Hi iff it has a larger posterior P(Θ=θi∣X=x) or equivalently pΘ(θi)fX∣Θ(x∣θi)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » MAP rule for hypothesis testing","id":"1374","title":"MAP rule for hypothesis testing"},"1375":{"body":"coin 1 gets head by p1, coin 2 by p2>p1 toss an unknown coin, coin θ, n times and get k heads choose θ=1 iff P(θ=1∣X=k)≥P(θ=2∣X=k) critical k∗∈N choose θ=1 iff k≤k∗ probability of getting error Pe=P(θ=1,X>k∗)+P(θ=2,X≤k∗)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » general case—two coins","id":"1375","title":"general case—two coins"},"1376":{"body":"E[θ^]=E[E[θ∣X]]=E[X] θ~=θ−θ^ Cov(θ^,θ~)=0 Var(θ)=Var(θ^)+Var(θ~)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » property","id":"1376","title":"property"},"1377":{"body":"the Markov property the past does not matter for the future, only the present does P(Xn+1=j∣X0=a,⋯,Xn=i)=P(Xn+1=j∣Xn=i) discrete time state space S finite or countably infinite one-step probability P(Xn+1=j∣Xn=i)=P(i,j)=pij does not change","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » discrete Markov chain","id":"1377","title":"discrete Markov chain"},"1378":{"body":"p11⋮pm1⋯⋱⋯p1m⋮pmm initial distribution π0 n-step transition matrix pabn=P(Xm+n=b∣Xm=a) pijn+m=pijn⋅pijm⇒P(Xm+n=j∣X0=i)=k∈S∑P(Xm=k∣X0=i)P(Xm+n=j∣Xm=k) P(Xn=k)=x∑π0(x)pxkn","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » transition probability matrix","id":"1378","title":"transition probability matrix"},"1379":{"body":"site i leads to j, i.e. i⟶j ∃ n≥0,P(Xn=j∣X0=i)>0 i⟶j,j⟶i⇒i and j are in the same class closed class can not go to another class class C(C⊆S) is closed, i∈C,i⟶j⇒j∈C absorbing state","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » class structure","id":"1379","title":"class structure"},"138":{"body":"discrete entry","breadcrumbs":"Notes » Data Science » Visualization » item","id":"138","title":"item"},"1380":{"body":"hitting time let A⊆S, hitting time of A, TA: TA={min{n>0:Xn∈A}∞∃ n, Xn∈A∀ n, Xn∈/A⇒pxyn=m=1∑nPx(Ty=m)Pyyn−m transient and recurrent state ρxy=Px(Ty<∞)=P(Ty<∞∣X0=x) site y is recurrent if ρyy=1 always can get from y to y in finite steps transient if ρyy<1 & 1 a absorbed after all always and another around at be build chain class, closed distribution dx expected find finite from g(x,y)=1−ρyyρxy ∀ x∈S g(y,y)=∞ gcd get go if iff in independent infinite initial least let limn→∞pxyn=0 linear markov means moving n n(y)=n=1∑∞1y(Xn) n(y)≥1 notes null number n→∞limp(xn=y)=π(y)∀ y∈S n→∞limpxxn=0or=0 of on pass period positive probability probability, processes pxxn px(n(y)<∞)=ρxy px(n(y)≥1)=Px(Ty<∞)=ρxy px(n(y)≥m)=Px(Ty<∞)Pym−1(Ty<∞)=ρxyρyym−1 py(n(y)=∞)=1 random recurrent recurrent","id":"1380","title":"transient recurrent"},"1381":{"body":"let recurrent, result s said same space starting state state, states stationary stay steps steps: stochastic such system that the then theorem times to transient transient, ty<∞ unstructured variables, which will with x x, x∈ x∈s∑pxynπ(x)=π(y)∀ y∈S,n∈N∗ x∈s∑pxyπ(x)=π(y)∀ y∈S x∈{x1,⋯,xk}, y y,z∈ you y⟶z⇒z {x1,⋯,xk} {xn} » μx=y∑(1+μy) pxy=1+y∑μypxy","breadcrumbs":"Notes π π0 π0, ρyy=ρyz=ρzz=ρzy=1 ρ{x1,⋯,xk}(x)=∑iρ{x1,⋯,xk}(xi) pxxi ⇒ ⇒px(n(y)=m)=ρxyρyym−1(1−ρyy) ⇒∃ ∀ ⎩⎨⎧π(1)=∑x∈Spx1π(x)π(2)=∑x∈Spx2π(x)⋮π(n−1)=∑x∈Spx(n−1)π(x)∑x∈Sπ(x)=1⇒p11−1p12⋮p1(n−1)1p21p22−1p2(n−1)⋯⋯⋯⋯pn1pn2pn(n−1)1π1π2⋮πn=0⋮01>0 states in the same class have the same period x⟷y⇒dx=dy a chain is irreducible if S is a closed class if every state of a Markov chain has period 1 we say the chain is aperiodic suppose a Markov chain is irreducible and aperiodic and has a stationary distribution π n→∞limpxyn=π(y) suppose a Markov chain is irreducible and all states are recurrent average number of visits to y Nn(y)=m=1∑n1y(Xn)nNn(y)→Ey[Ty]1 mean return time to y my=Ey[Ty] suppose a Markov chain is irreducible and has a stationary distribution π π(y)=Ey[Ty]1 the stationary distribution is unique and n→∞limn∑m=1npxyn=π(y)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » stationary distribution","id":"1381","title":"stationary distribution"},"1382":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » Stochastic process","id":"1382","title":"Stochastic process"},"1383":{"body":"consider a population of individual: in every generation, n=0,1,2,⋯, each individual produce a random number of offspring in the next generation Z,Z∈{0,1,⋯}, i.i.d. with the other individual. Xn,n=0,1,⋯ denote the number of individual in the n-th generation P(Z=i)=pi question of interest n→∞limP(Xn=0)=? generating function ΦX(t)=E[tX]=x∑P(X=x) tx⇒ΦX′(t)=x∑xP(X=x) tx−1⇒⎩⎨⎧μ=E[X]=ΦX′(1)ΦX(0)=p0ΦX(1)=1 fixed point of ρ ρ=ρ1,0=k∑P(Z=k)ρk,0=k∑P(Z=k)ρk=Φ(ρ) analysis: study H(t)=ΦX(t)−t H′′(t)>0,H(0)=p0>0,H(1)=0 if μ=0, then p0=1⇒ρ=1 if 0<μ≤1,P(t=0)>0, then ρ=1 if μ>1, then ∃ 0<ρ<1 ","breadcrumbs":"notes and branching notes probability, process","id":"1383","title":"branching process"},"1384":{"body":"s={0,1,⋯,d}pxy=⎩⎨⎧qxrxpxy=x−1y=xy=x+1q0=0,qx processes random stochastic unstructured variables, »>0pd=0,px>0 (021 stationary distribution π(x)=(1−1−pp)x(1−pp)x iff recurrent random walk on integer Zd S consist of all points in Rd with integer coordinate Stirling's formula n!≈2πn nne−n when n is large random walk on Z1 pxx2n=(2nn)p2n(1−p)2n {=∞<∞p=21otherwise limit comparison test to check convergence","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » random walk","id":"1385","title":"random walk"},"1386":{"body":"continuous time finite or countably infinite P(X(s+t)=j∣X(s)=i,X(u)=xu)=P(X(s+t)=j∣X(s)=i)∀ u, 0≤u≤s","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » continuous Markov chain","id":"1386","title":"continuous Markov chain"},"1387":{"body":"P(X(s+t)=j∣X(s)=i)=P(X(t)=j∣X(0)=i)=pij(t)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » time-homogenous—s does nothing","id":"1387","title":"time-homogenous—s does nothing"},"1388":{"body":"pij(s+t)=k∈S∑pik(s)pkj(t)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » Chapman–Kolmogorov Equations","id":"1388","title":"Chapman–Kolmogorov Equations"},"1389":{"body":"the time τi staying at state i before changing τi∼Exp(qi) absorbing state qi=0, never move explosive qi=∞, never stay general proof prove P(τi>s+t∣ τi>s,X(0)=i)=P(τi>t∣X(0)=i) ⇒ the holding time is memory-less","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » holding time at state i","id":"1389","title":"holding time at state i"},"139":{"body":"measured property","breadcrumbs":"Notes » Data Science » Visualization » attribute","id":"139","title":"attribute"},"1390":{"body":"{Yi} consisting of the state the continuous Markov chain visit pij=P(Yn+1=j∣Yn=i)=P(Y1=j∣Y0=i)","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » embedded discrete Markov chain","id":"1390","title":"embedded discrete Markov chain"},"1391":{"body":"before jumping from i to j, holding time ∼Exp(qij) j∑qij=qipij=qiqij go to the earliest state transition matrix for the embedded Markov chain p~=0q2q21⋮q1q120⋮⋯⋯⋱ derivative at 0 pij′(0)={qij−qii=ji=j Kolmogorov backward equation pij′(t)=k=i∑qikpkj(t)−qipij(t)=k∑Qikpkj(t) Kolmogorov forward equation pij′(t)=k=j∑pik(t)qkj−qjpij(t)=k∑pik(t)Qkj infinitesimal generator Q—transition matrix for the Markov chain itself Q=−q1q21⋮q12−q2⋮q13q23⋮⋯⋯⋱Qij=pij′(0)={qij−qii=ji=j recover pij(t) using Q system of differential equation using the Kolmogorov equation (either forward or backward) matrix exponential square matrix A etA=n=0∑∞n!(tA)n∂t∂etA=AetA or differential equation of matrix p(t)=p11(t)⋮pn1(t)⋯⋱⋯p1n(t)⋮pnn(t)p′(t)=Qp(t)=p(t)Q⇒p(t)=etQ for Q=SDS−1,λi the eigenvalues p(t)=SetDS−1(etD)ij=⎩⎨⎧etλi0i=ji=j","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » another representation of pij(t)","id":"1391","title":"another representation of pij(t)"},"1392":{"body":"stationary distribution definition with π=[π(1),π(2),⋯] π=πp(t)⇔x∈S∑pxy(t)π(x)=π(y)∀ y∈S,t finding the stationary distribution πQ=0⇔i∑π(i)Qij=0∀ j is a limiting distribution if recurrent and finite closed class π(y)=t→∞limpxy(t)∀ x relationship with stationary distribution of embedded chain Φ let h(j)=π(j)qj Φ(j)=∑kh(k)h(j) irreducible ∃ t>0, ∀ i,j, pij(t)>0⇔ irreducible if ∃ t0>0, pij(t0)>0, then ∀ t>t0, pij(t)>0","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » long time behavior of continuous Markov chain","id":"1392","title":"long time behavior of continuous Markov chain"},"1393":{"body":"if the chain is finite or positive recurrent, if the chain is irreducible and S is positive recurrent, then ∃ unique stationary distribution and limiting distribution π","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » fundamental theorem","id":"1393","title":"fundamental theorem"},"1394":{"body":"{λx=qx,x+1μx=qx,x−1 pure birth μx=0pxy(t)=λy−1∫01e−λy(t−s)px,y−1dspx,x+1(t)=⎩⎨⎧λx+1−λxλx(e−λxt−e−λx+1t)λxte−λxtλx+1=λxλx+1=λx recurrence x=1∑∞λ1λ2⋯λxμ1μ2⋯μx={∞<∞recurrenttransient","breadcrumbs":"Notes » Unstructured Class Notes » Probability, Random Variables, and Stochastic Processes » continuous birth and death process","id":"1394","title":"continuous birth and death process"},"1395":{"body":"continuous time Stochastic process {N(t), t≥0} with parameter (rate) λ>0, and N(0)=0 N(t+s)−N(s)∼Poisson(tλ) N(t) has independent increment N(t1)−N(t0),⋯,N(tn)−N(tn−1) where t00 is discrete, but S (t)=⎩⎨⎧S(t)S(⌊t⌋)+X⌊t⌋+1(t−⌊t⌋)t∈N∗t∈/N∗ is continuous, can approximate Brownian motion after scaling and limiting using St(n)=nS (nt)→⋯W(t) relation between Gaussian process and Brownian motion standard Brownian motion ⇔ Gaussian process X(t) that P(X(0)=0)=1 μX(t)=0∀ t≥0 rX(t,s)=min{s,t}∀ s,t≥0 continuous path P(function t↦X(t) is continuous)=1 transformation of Brownian motion standard Brownian motion W(t)⇒ the following are standard Brownian motion (t≥0) reflection −W(t) new start W(t+s)−W(s) scaling aW(at) Gaussian X(t)=t⋅W(t1)(X(0)=0) hitting time first time reaching a Ta=min{t:W(t)=a} usage P(W(t)>a∣Taa)fTa(t)=2πt31exp{−2ta2}⇒t→∞limP(Ta0∫0∞λe−λxdx=1P(X≥t)=e−λtMX(t)=λ−tλE[X]=MX′(0)=λ1Var(X)=M′′(0)−(M′(0))2=λ21 memory-less property P(X>t+s ∣ X>t)=P(X>s) sum of n i.i.d. exponential distribution is gamma distribution fSn(x)=λe−λx(n−1)!(λx)n−1 proved by induction comparison between X1∼Exp(λ1) and X2∼Exp(λ2) P(X10,σy>0,−1<ρ<1f (un)bounded (x,y)=2πσxσy1−ρ21e−2(1−ρ2)1[(σxx−μx)2+(σyy−μy)2−2ρσxσy(x−μx)(y−μy)] (x∣y=y)∼N(μx+ρσyσx(y−μy),σ2=σx2(1−ρ2))(Y∣X=x)∼N(μy+ρσxσy(x−μx),σ2=σy2(1−ρ2))ρ=Corr(X,Y)=σxσyCov(X,Y)X,Y independent⇔Cov(X,Y)=0","breadcrumbs":"Notes above and arithmetic below bivariate bounded bounded, conditionals convergent distribution","id":"1404","title":"bivariate distribution"},"1405":{"body":"probability divergent explicit formulas geometric greatest harmonic index integer marginals monotone normal notes n→∞lim(1+br)a=erifn→∞limB′A′=1 p probability, processes random recurrence relation sequence sequences series series: smaller statistics stochastic sum than unstructured variable variables, vs x x∼n(μx,σx2)y∼n(μy,σy2) » ⇒ ∑n=1∞np1⎩⎨⎧convergent,p ⌊ ⌋=the>1divergent,p≤1 ∑n=1∞n21=6π2 ∑n=k∞an convergent ⇒ lim n → ∞ a n = 0 lim n → ∞ a n ≠ 0⇒ ∑n=k∞an divergent tests divergence test partial sum geometric: | q | < 1 integral: f , f ( n ) = a n , continuous, ultimately decreasing 🡪 same comparison: limn→∞bnan=c⇒⎩⎨⎧same,c=0anconvergent,c=0,bnconvergentandivergent,c=∞,bndivergent scaling with ∑n=1∞np1(p>1) or ∑n=1∞n1 alternating: | a n + 1| − | a n | < 0, ∀ n > n 0, lim n → ∞ a n = 0⇒ convergent absolute convergence: ∑∣an∣ convergent conditional convergence: ∑an convergent, but ∑∣an∣ divergent ∑∣an∣ convergent ⇒∑an convergent ratio: limn→∞anan+1⎩⎨⎧<1 ⇒∑anabsolutelyconvergent>1⇒∑andivergent root: limn→∞n∣an∣{>1⇒divergent<1 ( ) ): ) → , as converge convergence: f independent n to uniform x ε → ∞ ⇒convergent ∀ ∃> N , | f n ( x ) − f ( x )| < ε ⇔ uniform convergence: f n ⇉ f dominated convergence: f i ( x ) → f ( x ) as x → ∞, ∃ g , ∀ x , i , f i ( x ) < g ( x ) ⇒ lim i → ∞∫ a b f i ( x ) d**x = ∫ a b f ( x ) d**x power series: ∑n=0∞cn(x−a)n center a , coefficient c n ⇒ x = a ⇔ convergent or ∀ x ∈ ℝ, convergent or ∃ R > 0, | x − a | < R ⇒ convergent, | x − a | > R ⇒ divergent method: ρ=limn→∞cncn+1, radius of convergence R=ρ1 | x − a | < R ⇒ absolutely convergent, | x − a | > R ⇒ divergent from ratio test Bessel function of the first kind: J0=∑n=0∞22n(n!)2(−1)nx2n basic formula: 1−x1=∑n=0∞xnfor∣x∣<1 ( (1+x)k=∑n=0∞(kn)xn (kn)=n!(k−n)!k!=n!k(k−1)…(k−n+1) (nk)=k!(n−k)!n!,or0ifk<0ork (x+y)k=∑n=0∞(kn)xnyk−n=∑n=0k(kn)xnyk−n (⌀) = 0, ) ), ) =P ) ∈ [0, 1], ) − ) ∪ ( , , ( 1) + 1)… 1 − 1 ∩ 1 ∩ … ∩ 1 ∪ 1−x1=∑n=0∞xnfor∣x∣<1 2) + … 2 ∩ …) ≤ 2 ∪ … :=S [ ] ] ⊂ [ a and are as b binomial: boundary c cardinality: cauchy cn=∑k=0∞akbn−k collection combinatorics: complement: continuous convergence cosx=∑n=0∞(−1)n(2n)!x2n create de difference: differentiation disjoint disjoint, disjoint: distribution: do elements events events, events: ex=∑n=0∞n!xn f f(x)=∑n=0∞n!f(n)(a)(x−a)n f(x)g(x)=∑n=0∞anxn∑n=0∞bnxn=∑n=0∞cnxn, for f′(x)=∑n=1∞n!f(n)(a)((x−a)n)′=∑n=1∞n!f(n)(a)n(x−a)n−1, i if in inclusion-exclusion independent: integration: it, k laws: length ln(1+x)=∑n=0∞(−1)nn+1xn+1 lose maclaurin may measure more morgan mutually n necessarily nonempty not o of ordered out p p([x,y])=b−ay−x, p(a)=∣S∣∣A∣ p(⋃i=1nAi)=∑i=1nP(Ai) partition plug principle: probability probability: product: r range s=B sample sample: see series: set sinx=∑n=0∞(−1)n(2n+1)!x2n+1 something space subset symbols symmetric tan−1x=∑n=0∞(−1)n2n+1x2n+1 taylor terms, the two uniform x y | |, | | = | | < 1 | + | | − | Δ … ⇒ ⇒(n−k)!n!=nk ⇔ − −ln(1−x)=∑n=1∞nxn ∖ ∩ ∪ ∫f(x)dx=∑n=0∞n!f(n)(a)∫(x−a)ndx=∑n=0∞n!f(n)(a)n+1(x−a)n+1+C ⊆>n (nk)=(n−1k)+(n−1k−1) (2nn)=∑k=0n(nk)2 generating function: f(x)=∑n=0∞anxn exponential generating function: f(x)=∑n=0∞annxn Bayes’ theorem: P(B∣A)=P(A)P(B∩A)=P(A)P(B)P(A∣B) random variable X ( b l a ) = 2 discrete: ∑x∈RP(X=x)=1 PDF probability mass/ density function: p X ( x ) = P ( X = x ) P(X=x)=∑iP(Ai)P(X=x∣Ai) law of total probability: P(A)=∑x∈RP(X=x)P(A∣X=x) Bernoulli: p X (0) = q , p X (1) = p Binomial: pX(k)=(nk)pkqn−k r X ( t ) = ( t**p + q ) n geometric: p X ( k ) = p**q k E(X)=pq,var(X)=p2q negative-binomial: pX(k)=(r+k−1k)prqk=(−1)k(−rk)prqk Poisson: pX(k)=e−λk!λk E ( X ) = v a r ( X ) = λ hypergeometric: pX(k)=(nN)(Mk)(N−Mn−k) continuous distribution: p X ( k ) = 0 ∀ x ∈ ℝ,∫−∞∞ f ( x ) d**x = 1 uniform: f(x)={b−a1,a≤x≤b0 var(X)=12(b−a)2 exponential: f(x)={λe−λx,0≤x0,x<0 ( ) =e e(x)=λ1,var(X)=λ21 p rx(t)=λ−lntλifλ−lnt t x λ**t − ≥>0 normal: f(x)=n(x;μ,σ2):=2πσ1e−2σ2(x−μ)2 Φ(x)=2π1∫−∞xe−2t2dt gamma: f(x)={Γ(α)λαxα−1e−λx,x≥00,x<0 ( (0, 1) (or ) ) + 1) =x**Γ 12 + … + 2 2( cdf chi-squared: continuous, cumulative discrete, distribution distributions e f for fun fx(x)=P(X≤x)={∑yi≤xfX(yi),discrete∫−∞xfX(t)dt,continuous fz(z)=2πz1e−2z h i if joint monotone n of py(y)=∑x∈h−1yPX(x) student): t=nSnX−μ∼t(n−1) the then where with x y=h z=nX12+…+Xn2X z∼Γ(2n,21) Γ Γ(x)=∫0∞tx−1e−tdt={(x−1)!,x∈N∗π,x=21 Χ ∼ ≥ 0> 0, then fY(y)=∣h′(h−1(y))∣fX(h−1(y)) marginal distribution: F X ( x ) = lim y → ∞ F X , Y ( x , y ) joint probability fun marginal PDF: pX(x)=∑ypX,Y(x,y) table joint density fun: f ( x , y ), ∫−∞∞∫−∞∞ f ( x , y ) d x d**y = 1 marginal PDF f X ( x ) = ∫−∞∞ f X , Y ( x , y ) d**y independent P(A∣B)=P(B)P(A∩B) pY∣X(y∣x)=∑zpX,Y(x,z)pX,Y(x,y)=pX(x)pX,Y(x,y) or f continuous: P(a≤Y≤b,X=x)=∫abfX(x)fX,Y(x,y)dy law of total prob: P (( X , Y ) ∈ B ) = ∬ B f X ( x ) f Y | X ( y | x ) d x d**y independent random variables: ∀ B 1, B 2, P ( X ∈ B 1, Y ∈ B 2) = P ( X ∈ B 1) P ( Y ∈ B 2) expectation: E ( X**Y ) = E ( X ) E ( Y ) if X , Y independent variance: v a r ( X ) = E (( X − μ x )2) = E ( X 2) − E 2( X ), v a r ( X + Y ) = v a r ( X ) + v a r ( Y ) + 2 c o v ( X , Y ) covariance: c o v ( X , Y ) = E (( X − μ X )( Y − μ Y )) = E ( X**Y ) − E ( X ) E ( Y ) c o v ( a**X + b**Y , Z ) = a c o v ( X , Z ) + b c o v ( Y , Z ) correlation: corr(X,Y)=Sd(X)Sd(Y)cov(X,Y) i.i.d. mutually independent and identically distributed X 1, …, X n ∼ B e r n o u l l i ( p ) i . i . d . ⇒ X 1 + … + X n ∼ B ( n , p ) X 1 ∼ B ( n 1, p ), X 2 ∼ B ( n 2, p ) ⇒ X 1 + X 2 ∼ B ( n 1 + n 2, p ) X 1 ∼ P o i s s o n ( λ 1), X 2 ∼ P o i s s o n ( λ 2) ⇒ X 1 + X 2 ∼ P o i s s o n ( λ 1 + λ 2) generating fun: r X ( t ) = E ( t X ) r X + Y ( t ) = r X ( t ) r Y ( t ) k th moment: E ( X k ) k th central moment: E (( X − μ x ) k ) moment-generating fun: MX(s)=E(eXs)=rX(es)=∑n=0∞n!E(Xn)sn M X ( k )(0) = E ( X k ) M X + Y ( s ) = M X ( s ) M Y ( s ) X, Y independent, work for r X ( t ) uniqueness: if ∃ s 0 > 0, M X ( s ) < ∞ ∀ s ∈ (− s 0, s 0), M X ( s ) = M Y ( s ), then X , Y have the same distribution also work for r characteristic fun: c X ( s )= E ( e i X s ) inequalities Markov’s:P(X≥a)≤aE(X) X ≥ 0, a > 0 Chebychev’s: P(∣X−μX∣≥a)≤a2var(X) a > 0 Cauchy-Schwarz: ∣cov(X,Y)∣≤var(X)var(Y) =, iff X−μX=var(Y)cov(X,Y)(Y−μY) if v a r ( Y ) > 0 law of large number sample sum: S n = X 1 + … + X n for { X i } i. i. d. sample average: Mn=X=n1(X1+…+Xn)=nSn WLLN weak: lim n → ∞ P (| M n − μ | ≥ ε ) = 0 for { X i } same μ , v a r ≤ v , v < ∞, ε > 0 not necessarily i. i. d. Mn→Pμ SLLN strong: P {lim n → ∞ M n = μ } = 1 for { X i } i. i. d. Mn→a.s.μx central limit theorem: lim n → ∞ P ( Z n ≤ x ) = P ( Z ≤ x ) for { X i } i. i. d, Z ∼ N (0, 1), Zn=nσSn−nμ=n(σMn−μ) Φ(x)=limn→∞P(Zn≤x)=limn→∞P(Sn≤nμ+xnσ)=limn→∞P(Mn≤μ+nxσ) Zn→DZ∼N(0,1) convolution: for X , Y independent, Z = X + Y discrete: pZ(z)=∑wpX(z−w)pY(w) continuous: f Z ( z ) = ∫−∞∞ f X ( z − w ) f Y ( w ) d**w different convergence Xn→PY: { X n } converges in probability to Y , if lim n → ∞ P (| X n − Y | ≥ ε ) = 0 Xn→a.s.Y: { X n } converges with probability 1 (almost surely) to Y , if lim n → ∞ P ( X n = Y ) = 1 Xn→DY: { X n } converges in distribution to Y , if lim n → ∞ P ( X n ≤ x ) = P ( Y ≤ x ) ∀ x ∈ { x | P ( Y = x ) = 0} Xn→a.s.Y⇒Xn→DY⇒Xn→PY sample sample variance: Sn2=n−11∑j=1n(Xj−X)2 k th sample moment: xk point estimation the method of moments: μn=X,σ2=X2−X2 MLE maximum likelihood estimation: make L big as possible maximum likelihood fun: L ( θ ; x 1, …, x n ) = p ( X 1 = x 1, … X n = x n | θ ) or f x 1, …, x n independent: L(θ;x1,…,xn)=∏j=1np(Xj=xj∣θ) good point estimator unbiased: E ( θ̂ n ) = θ consistent: θn→Pθ mean squared error E (( θ̂ n − θ )2) is small confidence interval: P ( θ̂ n − ≤ θ ≤ θ̂ n +) ≥ 1 − α ⇐ P ( a ≤ g ( θ ) ≤ b ) ≥ 1 − α N , t : let − b = a , Χ 2: let a=X2α2(n),b=X1−2α2(n) deal with X i ∼ N ( μ , σ 2) S2=n−11∑i=1n(Xi−X)2 σ=σ0⇒σ0/nX−μ∼N(0,1)⇒μ Sn/nX−μ∼t(n−1)⇒μ μ = μ 0: σ21∑i=1n(Xi−μ0)2∼X2(n)⇒σ σ2(n−1)S2∼X2(n−1)⇒σ hypothesis testing null hypothesis H 0 type I / II error: H 0 true/ false level of significance α : probability for type I error power of the test 1 − β , β : probability for type II error p -value: probability that H 0 is true reject if p -value < α for { X i ∼ N ( μ , σ 02)} i.i.d., use σ0/nX−μ0∼N(0,1) for two samples, T=n1S12+n2S22(X1−μ1)−(X2−μ2)∼t(df),df=n1−11(n1S12)2+n2−11(n2S22)2(n1S12+n2S22)2 linear regression linear least squares {m=∑j=1n(xj−x)∑j=1n(xj−x)(yj−y)b=y−mx correlation coefficient: r=corr(X,Y)=[∑j=1nxj2−(∑j=1nxj)2][∑j=1nyj2−(∑j=1nyj)2]n∑j=1n(xjyj)−∑j=1nxj∑j=1nyj standard statistical model: Y j = β 0 + β 1 x j + e j , j = 1, 2, …, n E ( e j ) = 0, v a r ( e j ) = σ 2 intercept β 0, slope β 1, residual e j estimators ⎩⎨⎧β1=lXX1∑j=1n(xj−x)(yj−y)=lXX1(∑j=1nxjyj−nxy)β0=n∑j=1nxj2−(∑j=1nxj)2∑j=1nxj2∑j=1nyj−∑j=1nxj∑j=1nxjyj lXX=j=1∑n(xj−x)2=j=1∑nxj2−nx2 E ( β̂ 0) = β 0, E ( β̂ 1) = β 1 var(β0)=(n1+lXXx2)σ2,var(β1)=lXXσ2,cov(β0,β1)=−lXXxσ2 if e j ∼ N (0, σ 2) i.i.d., then β̂ 0, β̂ 1 normal dist sum of squared errors SSE: Se2=∑j=1n(Yj−β0−β1xj)2 σ2=n−2Se2 E(σ2)=σ2,σ2Se2∼X2(n−2),σ2 independent of β̂ 0, β̂ 1 σknownσ/lXXβ1−β1∼N(0,1)⇒β1 σ/lXXβ1−β1∼t(n−2)⇒β1 σknownσ/n1+lXXx2β0−β0∼N(0,1)⇒β0 σ/n1+lXXx2β0−β0∼t(n−2)⇒β0 1 − α confidence interval for β̂ 0, β̂ 1 1 − α confidence interval for σ 2 [X2α2(n−2)(n−2)σ2,X1−2α2(n−2)(n−2)σ2] y0∼N(β0+β1x0,(n1+lXX(x0−x)2)σ2) 1 − α confidence interval for y 0 = E ( ŷ 0): [y0−t1−2α(n−2)σn1+lXX(x0−x)2,y0+t1−2α(n−2)σn1+lXX(x0−x)2]","breadcrumbs":"Notes » Unstructured Class Notes » Probability and Statistics » Probability and Statistics","id":"1405","title":"Probability and Statistics"},"1406":{"body":"Linear Algebra linear system: {a1x1+…anxn=b… equivalent ∼—same solution set consistent—have solution; inconsistent—no solutions coefficient matrix: [a1………an…] augmented matrix: [a1………an…b…] row operation replacement interchange scaling row equivalent—same after proper row operation ⇒ equivalent matrix entry— a i**j o**r a i , j o**r A [ i , j ] o**r A i , j —the ( i , j ) entry of A leading entry—leftmost entry of a nonzero row (row) echelon form—step-like, leading entry going in to the right echelon matrix reduced echelon form—all leading entries are 1, entries below them are 0 an echelon form (REF) of… the reduced echelon form (RREF) of… only 1 for each matrix pivot position—position corresponding to the leading entry of its reduced echelon form pivot column—the column containing a pivot position pivot—nonzero number in a pivot position row reduction forward phase—make pivots the leading entries backward phase—eliminate non-pivots in pivot column partial pivoting—use greatest entry in a column as the pivot for programming solve linear system basic variable—corresponding to pivot column free variable—not so solution set element(s): 0— i n c o n s i s t e n**t o**r 1— c o n s i s t e n**t o**r ∞ parametric description—⎩⎨⎧basicvariable1=f(freevariable1,…)… back-substitution—solve for the basic variables one by one dealing with echelon form existence and uniqueness theorem—consistent⎩⎨⎧1uniquesolution,ifnofreevariable∞solutions,ifatleastonefreevariable ⇔ no rightmost column as pivot column vector equation— x 1 a 1 + … + x n a n = b column vector solution for vector equation x 1 a 1 + … + x n a n = b equivalent to solution of [a1…anb] S p a**n { v 1,⋯, v p }—subset of ℝ n spanned (/generated) by v 1,⋯, v p —the set of all linear combinations of v 1,⋯, v p b ∈ s p a**n { a 1, ⋯, a n } ⇔ A has a pivot in every row matrix equation A x = b : Ax=[a1…an]x1⋯xn=x1a1+…+xnan =a1⋮amx=a1⋅x⋮am⋅x bi=∑k=1n(ai,k⋅xk) A x = b solution equivalent to x 1 a 1 + … + x n a n = b existence of solutions—has solution iff b ∈ S p a**n { a 1, ⋯, a n } { v 1, ⋯, v p } spans (/ generates) ℝ m if S p a**n { v 1, ⋯, v p } = ℝ m identity matrix I n , {Ij,j=1,j=1,⋯,nIj,k=0,j=k I n x = x ∀ x ∈ ℝ n homogeneous linear system—can be writen as A x = 0 opposite: heterogeneous at least 1 solution x = 0 , a.k.a. trivial solution nontrivial solution iff ∃free variable parametric vector form— x **= s u** + t v ( s , t ∈ ℝ) parametric vector equation of the plane solution representation vector parameter vector form— x = p + t v ( t ∈ ℝ) the equation of the line through p parallele to v span solution set of A x = b — { w | w = p **+ v h } i**f ∃ s o l u t i o**n p ∀ s o l u t i o**n o**f A x** = 0 v h linear dependency of matrix columns a 1⋯ a n of A are linearly independent ⇐ A x = 0 has only the trivial solution dependent ⇐ ∃ c 1⋯ c n , c 1 a 1 + ⋯ + c n a n = 0 more vectors than entries in each vector ⇒ linearly dependent linearly dependent ⇔ at least one vector = linear combination of the others ⇒ ∃ v j ( j > i ), v j is a linear combination of v 1… v j − 1 if { v 1… v p } is linearly dependent AND v 1 ≠ 0 contains 0 ⇒ linearly dependent linear transformation transformation (/ function / mapping) T : ℝ n → ℝ m domain ℝ n codomain ℝ m image T ( x ) range: set of all images matrix transformation x ↦ A x ⇔ ∀ u **,** v , c , d , T ( c u + d v ) = c**T ( u ) + d**T ( v ) kernal N u l A range C o l A matrix operations diagonal entry— a i**i main diagonal diagonal matrix—square matrix with all non-diagonal entries 0 zero metrix 0 vector multiplication AB=A[b1⋯bp]=[Ab1⋯Abp] A ( B x ) = ( A**B ) x row-column rule—(AB)ij=ai1b1j+⋯ainbnj=∑k=1naikbkj *AB=a1⋮am[b1⋯bp]=a1b1⋮amb1⋯⋱⋯a1bp⋮ambp A is right-multiplied by B , B is left-multiplied by A A , B commute— A**B = B**A power of matrix Ak=∏i=1kA A 0 is the identity matrix transpose matrix A T ( A**B ) T = B T A T matrix inversion invertible—for n × n matrix A , ∃ n × n matrix C , C**A = I n = A**C C : an inverse of A (non)singular matrix—(not) invertible 2 × 2 matrix A=[acbd]⇒A−1=detA1[d−c−ba] iff det A = a**d − b**c ≠ 0 ∀ invertible n × n matrix A , b ∈ ℝ n , A x = b ⇒ x **=** A −1 b ( A**B )−1 = B −1 A −1 ( A T )−1 = ( A −1) T only product of invertible matrices is invertible for n × n matrix: A is invertible ⇔ row equivalent to I n ⇔ linear transformation x **↦ A x** is one-to-one ⇔ ∀ b **∈ ℝ n , A x** = b has solution ⇔ linear transformation x **↦ A x** maps ℝ n ***o***nto ℝ n ⇔ ∃ n × n matrix C , C**A = I ⇔ ∃ n × n m a t r i**x D , A**D = I ⇔ A T is invertible ⇔ det A ≠ 0 ⇔ columns of A forms a basis of ℝ n ⇔ C o l A = ℝ n ⇔ 0 is not an eigenvalue of A ⇔ det A ≠ 0 invertible linear transformation T : ℝ n **↦ ℝ n —∃ S : ℝ n ↦**ℝ n , ∀ x ∈ ℝ n , S ( T ( x )) = x , T ( S ( x )) = x S —the inverse T −1 elementary matrix—obtained by performing a single elementary row operation on identity matrix r o o**p A = E**A , where E = r o o**p I m , r o o**p is the single elementary row operation elementary matrix E is invertible, E −1 is another elementary matrix obtained by reversed row operation n × n matrix A is invertible iff row equivalent to I n A −1 = r o o**p I n if I n = r o o**p A find A −1—row reduce [AI] and get [IA−1] LU fractorization— A = L**U A : m × n matrix L : m × m unit lower triangular matrix lower triangular matrix—entries above the main diagonal are 0s U : m × n echelon matrix implementation—Ax=b⇔Ly=bUx=y calculation: p. 145 determinant detA=∑j=1n(−1)i+jaijdetAij A is quare matrix usually use i = 1 the first row origin—the last pivot in echelon form of the matrix obtained without division A i**j —obtained by deleting the i th row and j th column in A ( i , j )-cofactor C i**j = (−1) i + j det A i**j cofactor expansion across the i th row of A —detA=∑j=1naijCij triangular matrix A —detA=∏i=1naii the entries on the main diagonal row/ column operation replacement—same interchange—opposite scaling—scales the same way echelon form U by row replacements and r interchanges detA=⎩⎨⎧AisinvertibleAisnotinvertible(−1)r∏uii0whenwhen det A = det A T det A**B = (det A )(det B ) proved using elementary matrices detA−1=detA1 if A is invertible det k**A = k n det A if A has n rows linearity property—linear transformation T(x)=det[a1⋯aj−1xaj+1⋯an] where only x is a variable Cramer’s rule—the unique solution of A x = b has entries xi=detAdetAi(b) A is invertible n × n matrix, b ∈ ℝ Ai(b)=[a1⋯b⋯an] Laplace transfrom—converts system of linear differential equations to system of linear algebraic equations a way to find A −1— A ( A −1) j = ( I n ) j (A−1)ij=detAdetAi(In)j)=detACji adjugate/ classical adjoint of A —adjA=C11⋮C1n⋯⋱⋯Cn1⋮Cnn determinant as area or volume area of parallelogram of 2 × 2 matrix A is |det A | volume of parallelepiped of 3 × 3 matrix A is |det A | linear transformation T : ℝ2 → ℝ2 (ℝ3 → ℝ3) determined by 2 × 2 (3 × 3) matrix A ⇒ { a r e**a ( v o l u m**e ) o**f T ( S )} = |det A | ⋅ { a r e**a ( v o l u m**e ) o**f S } vector space—10 axioms subspace—3 axioms needed 0 ∈ H H is closed under vector addition— u + v ∈ H H is closed under multiplication by scalars— c u ∈ H S p a**n { v i } is a subset of vector space V if v i ∈ V null space of A , N u l A —solution set of A x = 0 —is a subspace of ℝ n explicit discription—with the vectors that span N u l A basis—solve and represent with free variables d i m N u l A = number of free variables column space of A , C o l A — S p a**n { a 1, ⋯, a n } —is a subspace of ℝ m C o l A = { b : b **= A x**, x ∈ ℝ n } C o l A = ℝ m iff ∀ b ∈ ℝ m , ∃ x , A x = b basis—pivot columns d i m C o l A = number of pivot columns row space of A , RowA—span{a1⋯an} —is a subspace of ℝ n = C o l A T basis—pivot rows kernal/ null space of linear transformation T — T ( u ) = 0 basis Β of subset H —linearly independent, span H standard basis for ℝ n { e 1, ⋯, e n } spanning set A small AP linearly dependent set A big AP coordinate system the unique representation theorem Β -coordinates of x —scalars that map them Β -coordinate vector of x —[x]B=c1⋮cn coordinate mapping x ↦ [ x ] Β it is a one-to-one linear transformation—isomorphism x = P Β [ x ] Β , where change of coordinate matrix P Β = [ b 1, ⋯, b n ] dimension finite-dimensional vector space—spanned by finite set 0 dimension—{ 0 } infinite-dimensional dim ℙ n = n + 1 rank— d i m C o l A rank thm— r a n**k A + d i m N u l A = n an eigenvector corresponding to λ — x ≠ 0 , A x = λ x , A i**s n × n an eigenvalue of A — λ main diagonal entries on triangular matrix 0 is an eigenvalue of A iff A is not invertible find eigenvector x given eigenvalue λ : A x = λ x ⇒ ( A − λ**I ) x = 0 （ A − λ**I ） T = A T − λ**I eigenspace of A — N u l ( A − λ**I ) characteristic equation of A —det ( A − λ**I ) = 0 ⇔ λ is an eigenvalue of A characteristic polynomial of A (with degree n ) multiplicity of eigenvalue λ —the multiplicity as root similarity—∃ P invertible, P −1 A**P = B P B P −1 = A A , B are similar similarity transformation— A → P −1 A**P same characteristic polynomial and same eigenvalues diagonalize— A = P D P −1 where D is diagonal diagonalizable—∃ P , D ⇔ A has n linearly independent eigenvectors ⇔ ∑dimensions of eigenspaces = n ⇔ characteristic polynomial factors completely into linear factors ⇔ dimension of eigenspace for each λ = multiplicity ⇔ basis of all eigenspaces form a basis of ℝ n ⇐ A has n distinct eigenvalues diagonizing—find eigenvalues ⇒ D ; find eigenspace basis ⇒ P ; check A**P = P**D vector operation inner product (dot product)— u ⋅ v **=** u T v length—∥v∥=v⋅v normalizing—get unit vector in the same direction as nonzero vector distance d i s**t ( u **,** v ) = ∥ u − v ∥ orthogonal relationship orthogonal— u ⋅ v **=**0 ⇔ ∥ u + v ∥ = ∥ u ∥ + ∥ v ∥ orthogonal complement W ⊥—the set of all vectors orthogonal to subspace W is a subset of ℝ n interactive— A ⊥ = B ⇔ B ⊥ = A ( R o w A )⊥ = N u l A ( C o l A )⊥ = N u l A T orthogonal set— u i **⋅** u j = 0 ∀ i ≠ j ⇒ linearly independent is a basis for the subspace orthogonal basis—basis that is orthogonal set weight—cj=uj⋅ujy⋅uj for y ∈ S p a**n { u j } y=∑cjuj orthogonal projection— projLy=y=u⋅uy⋅uu y=y+z where z **⊥** u subspace L spanned by u orthonormal set—unit vector orthogonal set orthonormal basis—basis that is orthonormal set Gram-Schmidt process—calculate orthonormal basis by subtracting projection QR factorization—orthonormal basis of linearly independent matrix Q , R = Q T A orthogonal matrix—square matrix with orthonormal columns ⇔ U −1 = U T ⇔ orthonormal rows ∥ U x ∥ = ∥ x ∥ ( U x ) ⋅ ( U y ) = x ⋅ y U x ⊥ U y ⇔ x **⊥** y product of orthogonal matrix is orthogonal matrix orthogonal projection—projWy=y=∑ui⋅uiy⋅uiui projWy=∑(y⋅ui)ui=UUTy for U of orthonormal basis u i best approximation theorem—y is the closest point in W to y general least-square problem—find x for smallest least-square error ∥ b − A x ∥ Ax=b=projColAb ⇔ normal equation— A T A x = A T b r a n**k A T A = r a n**k A A x = b has a unique least-square solution ∀ b ∈ ℝ m ⇔ A is linearly independent ⇔ A T A is invertible ⇔x=(ATA)−1ATb ⇔Rx=QTb⇔x=R−1QTb Χ β **=** y design matrix— Χ parameter vector— β observation vector— y least-square line (line of regression)— y = β 0 + β 1 x observed value— y i predicted value— β 0 + β 1 x i residual— β 0 + β 1 x i − y i Χ β = y where X=1x1⋮⋮1xn,β=[β0β1],y=y1⋮yn residual vector ϵ diagonalization of symmetric matrix symmetric matrix— A T = A eigenvectors from different eigenspaces are orthogonal orthogonally diagonalizable—could have orthogonal matrix P A = P D P −1 = P D P T ⇔ A is symmetric spectral decomposition—A=∑λiuiuiT where u i are the columns of P u i u i T is a projection matrix— p r o**j { u i } x **=**( u i u i T ) x single value decomposition SVD— A = U Σ V T left singular vectors form U is m × m orthogonal Σ=[D0(m−r)0(n−r)T0(m−r)×(n−r)] is m × n D=σ10⋱0σr, σ 1 ≥ ⋯ ≥ σ r > 0 right singular vectors form V is n × n orthogonal ∀ m × n matrix A , A T A is symmetic its eigenvalues λ 1 ≥ ⋯ ≥ λ i ≥ ⋯ ≥ 0 single values—σ1,⋯,σn=λ1,⋯,λn for { v 1 , ⋯****, v n } with eigenvectors of A T A correponding to λ 1 ≥ ⋯ ≥ λ i , and A has r nonzero singular values, { A v 1 , ⋯****, A v r } is an orthogonal basis for C o l A , r a n**k A = r find single value decomposition find orthogonal diagonalization of A T A — P , D ′ V = P to orthonomal = { v i } D and Σ U —ui=σiAvi","breadcrumbs":"Notes » Unstructured Class Notes » Linear Algebra » Linear Algebra","id":"1406","title":"Linear Algebra"},"1407":{"body":"Speech Recognition feature extraction broader speech processing wake-up word detection: binary classification small window → low latency multiple models, threshold & size echo cancellation: subtract (complex) echo of sound from speaker sound source localization: microphone array, delay online/streaming mode: continuous conversion omnidirectional/ cardioid/ hyper cardioid microphone sound sample rate need at lease 2x of highest frequency wanted, else aliasing (Nyquist theorem) 44.1kHz for CD 16kHz good enough for speech μ-curve audio format: use PCM .wav online endpointing format: push to talk, hit to talk, continuous listening","breadcrumbs":"Notes » Unstructured Class Notes » Speech Recognition » Speech Recognition","id":"1407","title":"Speech Recognition"},"1408":{"body":"spectrogram: energy distribution over frequency vs time preemphasize speech signal: boost high frequency spreemp(n)=s(n)−αs(n−1)α=0.95 spectrogram: from time series to frequency domain discrete Fourier transform (DFT) symmetric, only first half + midpoint meaningful (by Nyquist theorem) magnitude: 0∼2SRHz, frequency MiSR at point i SR: sample rate, M: number of sample power: magnitude squared flat noise from jump in sample windowing solution: multiple input by bell-shape windowing function and half-overlap windows to avoid losing information before using fast Fourier transform (FFT): zero padding cause fake interpolated detail auditory perception: from frequency to Bark mimic human ear, which distinguish low frequency better frequency warping with Mel curve filter bank: triangular filter on Mel curve to be multiplied evenly-spaced, half-overlap, 40 enough, 80 good translate back to equal-area triangles on frequency axis not directly on Mel curve for simplicity log Mel spectrum: log of integration of each filter bank Mel cepstrum discrete cosine transform (DCT) compression reduce redundancy from filter bank overlap subtract the mean to remove microphone/noise difference microphone response is speech with convolution convolution -DFT → multiplication -log → summation longest common subsequence: dynamic programming, dummy char padding, streaming, search trellis, sub-trellis, lexical tree pruning: hard threshold vs beam search DTW: dynamic time warping: disallow skipping (vertical on trellis), non-linear mapping (super diagonal) Pi,j: best path cost from origin to (i,j) Ci,j: local node cost (vector distance) global beam across templates for beam search combine multiple template template averaging: first align templates by DTW template segmentation: compress chunks of same phoneme actual method: iterate from uniform segments to stabilize variance Mahalanobis distance d(x,mj)=(x−mj)TCj−1(x−mj) can be estimated with negative Gaussian log likelihood d(x,mj)=21log((2π)D∣Cj∣)+(x−mj)TCj−1(x−mj) covariance Σ=σ11σ21⋮σd1σ12σ22⋮σd2⋯⋯⋱⋯σ1dσ2d⋮σdd estimated with diagonal covariance matrix when elements largely uncorrelated self-transition penalty: model phoneme duration MFCC (Mel frequency cepstrum coefficient) dynamic time warping (DTW) align multiple training sample segment all model sample uniformly by #phoneme, and average align each sample against model sample to get new segment and new average iterate until convergence transition probability: #segment switch over #frame in segment hidden Markov model for DTW use log probability so total score is log total probability simulation by transition probability matrix T (each row sum to 1) initial probability π expectation-maximization (EM) algorithm initialize with k-means clustering auxiliary function: conditional expectation of the complete data log likelihood Q(Θ,Θ(t))=y∑p(y∣X,Θt)log(p(X,y∣Θ)) evaluate Θt+1 Θt+1=ΘargmaxQ(Θ,Θt) iterate until convergence forward algorithm initialize α(s,1)=πsP(ot∣s) iterate α(s,t+1)=∑s′α(s′,1)P(s∣s′)P(ot+1∣s) Baum Welch: soft state alignment log-domain math log(xy)=log(x)2log(y)log(x+y)=log(x)+log(1+2log(y)−log(x)) continuous text recognition: small-scale problem, e.g. voice command wrap back from end of template to start dummy variable high wrap back cost → discourage space lextree non-emitting state/ null state: only for connecting, no self-transition no transition time prior probability for word: add to the start of its HMM word transition probability for edge cost between word HMM approximate sentence probability with best path grammar: only focus on syntax not semantics finite-state grammar (FSG) context-free grammar (CFG) backpointer: only word-level, additional script on word transition training with continuous speech: bootstrap & iterate silence: silence model, ε bypass arc, self-loop non-emitting state loop need to go through emitting state, else infinite N-gram N-gram assumption: P(wk∣w1,…,wk−1)=P(wk∣wk−(n−1),…,wk−1) start/end of sentence: , unigram, bigram. 5-gram good enough for commercial use N-gram with D words need ∑i=1N−1Di transition node good Turing Zipf's law backoff state-of-the-art system unit of sound by clustering large unlabelled dataset transfer learning with small labeled dataset phoneme: 39 English, Mandarin with tone few rare phoneme, much more common than rare word → beat Zipf's law defined by linguistic, or learned by clustering mono-phone/tri-phone: context-independent/dependent (for neighbor) absorbing/generating state → non-emitting locus: stable centers in spectrum multiple pronunciation: multiple internal model + probability mono-phone/ context-independent (CI) model di-phone: model previous and current phoneme. problem: cross-word effect tri-phone: model multiple current phoneme based on previous and next phoneme many cases not seen, back off to mono-phone share Gaussian with mono-phone, different weight decision tree inexact search: run n-gram on (n-1)-gram model by applying word-transition prob","breadcrumbs":"Notes » Unstructured Class Notes » Speech Recognition » feature extraction","id":"1408","title":"feature extraction"},"1409":{"body":"SGD > GD for online learning SGD problem: mini batch too big gated recurrent unit (GRU): a RNN principal component analysis (PCA): autoencoder, dimensionality reduction","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » Statistical Machine Learning","id":"1409","title":"Statistical Machine Learning"},"141":{"body":"relationship between item","breadcrumbs":"Notes » Data Science » Visualization » link","id":"141","title":"link"},"1410":{"body":"loss λik: take action αi when sample belong to Ck goal: minimize risk R(αi∣X)=k=1∑KλikP(Ck∣X) for 0-1 loss, R(αi∣X)=1−P(Ci∣X) reject class: a K+1th class w/ fixed loss λ∈(0,1) ⇒R(aK+1∣X)≡λ reject when mini=1…KR(αi∣X)>λ or, maximize discriminant function gi(x),i=1…K maximum likelihood estimator (MLE) parametric (distribution based on known parameters) vs non-parametric","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » Bayesian decision theory","id":"1410","title":"Bayesian decision theory"},"1411":{"body":"X∈RN×PY∈RN×1L(W)=∥WTX−Y∥2=WTXTXW−2WTXTY+YTYWargminL(W)⇒∂W∂L(W)=0⇒2XTXW−2XTY=0⇒W^=(XTX)−1XTY","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » linear regression","id":"1411","title":"linear regression"},"1412":{"body":"Wargmin[L(W)+λP(W)]⇒W^=(XTX+λI)−1XTY assuming P(W)=∥W∥2 XTX+λI invertible, proof by positive definite","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » regularization in lasso","id":"1412","title":"regularization in lasso"},"1413":{"body":"need to try different K","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » K-nearest neighbors (KNN)","id":"1413","title":"K-nearest neighbors (KNN)"},"1414":{"body":"","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » support vector machine (SVM)","id":"1414","title":"support vector machine (SVM)"},"1415":{"body":"y=−1,1 objective, maximize minimum margin: W,bargmaxi=1…Nmin∥W∥1∣WTXi+b∣ s.t. yi(WTXi+b)>0⇒W,bargmax∥W∥1⋅1 s.t. yi(WTXi+b)≥1⇒W,bargmin21∥W∥2 s.t. yi(WTXi+b)≥1 by ∣WTXi+b∣=yi(WTXi+b)i=1…Nmin∣WTXi+b∣:=1 apply Lagrange multiplier: L(W,b,λ)=21∥W∥2+i=1∑Nλi(1−yi(WTXi+b))⇒W,bminλi≥0maxL(W,b,λ)⇒λi≥0maxW,bminL(W,b,λ) ∂W∂L=∂b∂L=0⇒W^=i=1∑NλiyiXi,i=1∑Nλiyi=0⇒L^=−21∥W^∥2+i=1∑Nλi=−21i=1∑Nj=1∑NλiλjyiyjXiTXj+i=1∑Nλi final objective: λi≥0argmin(−L^)=21i=1∑Nj=1∑NλiλjyiyjXiTXj−i=1∑Nλi solution: sequential minimal optimization (SMO) fix all but 2 λi, and iterate 2 variable because ∑i=1Nλiyi=0","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » hard-margin binary SVM","id":"1415","title":"hard-margin binary SVM"},"1416":{"body":"hinge loss","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » soft-margin binary SVM","id":"1416","title":"soft-margin binary SVM"},"1417":{"body":"solve non-linear problem w/ linear classifier kernel , but w/o φ restriction objective: λi≥0argmin(−L^)=21i=1∑Nj=1∑NλiλjyiyjK(Xi,Xj)−i=1∑Nλi positive-definite kernel positive-definite kernel output positive-definite matrix positive-definite matrix: pivots > 0 or eigenvalues λi>0 or subdeterminant > 0 Hilbert space: symmetric, positive-definite, linear alternative definition of kernel: symmetric positive-definite: Gram matrix G semi-positive definite G:=K(X1,X1)⋮K(XN,X1)⋯⋱⋯K(X1,XN)⋮K(XN,XN)","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » kernel SVM","id":"1417","title":"kernel SVM"},"1418":{"body":"lossy transformation from p to q dimension mean: N1XT1 covariance: N1XTHX centering matrix: H:=I−N111T HT=H,H2=H proof: S=N1i=1∑N∥Xi−Xˉ∥2=N1∥[X1−Xˉ⋯XN−Xˉ]∥2 maximize variance uargmaxuTSu s.t. uTu=1⇒λargmaxL(u,λ)=uTSu+λ(1−uTu)⇒Su=λu minimize distance between full projection (p-dimensional) and principal component analysis (PCA, q-dimensional): centering: X~i=Xi−Xˉ lossless transformation with uk: Xi′=∑k=1p(X~iTuk)uk PCA transformation: X^i=∑k=1q(X~iTuk)uk objective: ukargminN1i=1∑N∥X^i−Xi′∥2=N1i=1∑Nk=q+1∑p(X iTuk)uk2=N1i=1∑Nk=q+1∑p(X iTuk)2⇒ukargmink=q+1∑pukTSuk s.t. ukTuk=1⇒Suk=λuk","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » dimensionality reduction by principal component analysis (PCA)","id":"1418","title":"dimensionality reduction by principal component analysis (PCA)"},"1419":{"body":"sampling purpose: determine parameter when doing sum/integral good: from area of high probability & independent Monte Carlo drawback does not work in high dimension assume sample independence","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » Monte Carlo sampling method","id":"1419","title":"Monte Carlo sampling method"},"142":{"body":"spatial location","breadcrumbs":"Notes » Data Science » Visualization » position","id":"142","title":"position"},"1420":{"body":"assume z∼p(z0) get sample x assume CDF h(z0=x) solve z1=h−1(x) get another sample and repeat","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » transformation method","id":"1420","title":"transformation method"},"1421":{"body":"define distribution q(z) s.t. ∃k,∀z,kq(z)≥p(z) get sample zi∼q(z) rate α:=kq(zi)p(zi)∈(0,1] select random variable x∼U(0,1)∈(0,1] if α≥x, accept sample zi; else reject reject most sample when k large k hard to determine waste iteration","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » rejection sampling","id":"1421","title":"rejection sampling"},"1422":{"body":"for value f following distribution with PDF p, do not know CDF, want expectation define distribution q(z) with known CDF weight (importance) ωi:=q(zi)p(zi) E(f):=∫f(z)p(z)dz=∫f(z)q(z)p(z)q(z)dz≈∫ωif(z)q(z)dz≈L1i=1∑Lωif(zi)","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » importance sampling","id":"1422","title":"importance sampling"},"1423":{"body":"get L sample zi from q(z) with known CDF ωi:=q(zi)p(zi) normalize ω~i:=∑iwiωi treat ω~i as probability for zi and resample","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » sampling-importance-resampling","id":"1423","title":"sampling-importance-resampling"},"1424":{"body":"to avoid trapped in local minimum still need to try multiple time when seeking minimum, accept increase in f with probability e−TΔf<1 (erm): (mcmc)","id":"1427","title":"markov (mcmc)"},"1428":{"body":"want (mh (model (training 1 : a acceptance algorithm algorithm)","id":"1428","title":"metropolis algorithm)"},"1429":{"body":"want all annealing","id":"1424","title":"simulated annealing"},"1425":{"body":"transition approximation at balance","id":"1426","title":"detailed balance"},"1427":{"body":"work based bayes-consistent be because between carlo case chain chain","id":"1425","title":"markov chain"},"1426":{"body":"markov classifier close complexity): consistent continuous converge, converge. convergence cross data data","breadcrumbs":"notes decision dependency dependent","breadcrumbs":"notes design detailed determine diagonal different dimension distribution do drawback: each easy eigenvalue empirical entries entropy entropy","id":"1430","title":"entropy"},"1431":{"body":"sup=lnp(x)1=−lnp(x)","breadcrumbs":"Notes entropy","id":"1432","title":"decision entropy"},"1433":{"body":"bayes equal error error): estimation expected f f: finite","breadcrumbs":"notes finite, fix following for f∗: gain get gibbs given grid","id":"143","title":"grid"},"1430":{"body":"randomness, grow h=E(sup)=x∑p(x)sup(x)=−x∑p(x)lnp(x) hasting high honor how i(y∣xi)=H(Y)−H(Y∣xi)whereH(Y∣xi)=x∑p(xi=x)H(Y∣xi=x) if impurity, in information know large learning loss loss","breadcrumbs":"notes m machine markov matrix matrix, maximize may method method: metropolis minimization minimize monte necessarily new not notes of on p p(f∈fsup∣rn(f)−r(f)∣ p(x−i∗)=p(x−i)⇒α(x,x∗)=p(x)p(xi∗∣x−i)p(x∗)p(xi∣x−i∗)=p(xi∣x−i)p(x−i)p(xi∗∣x−i)p(xi∗∣x−i∗)p(x−i∗)p(xi∣x−i∗)=p(xi∣x−i)p(x−i)p(xi∗∣x−i)p(xi∗∣x−i)p(x−i)p(xi∣x−i)=1","breadcrumbs":"Notes p(z), p(∣r(f)−rn(f)∣≥ε)→0 as n→∞ p(∣r(f∗)−rn(f)∣≥ε)→0 as n→∞ pdf previous probability q qx,x qx,x∗:=p(xi∗∣x−1) qx,x∗′:=α(x,x∗)Qx,x∗,x∗=x r(f) rate rest risk rn(f) row s.t. sample sample","breadcrumbs":"notes sampling sampling","id":"1429","title":"gibbs sampling"},"143":{"body":"sampling science set simulated special split","breadcrumbs":"notes state stationary statistical stochastic strategy sum surprise surprise","id":"1431","title":"surprise"},"1432":{"body":"information t take target temperature the theory","id":"1433","title":"statistical theory"},"1434":{"body":"empirical time to training tree true t∈(0,1),t←tγ,γ=0.99∈(0,1)","breadcrumbs":"Notes uniform universally unstructured use value variable visualization w when where with wrt x xi xi: x−i:={x1…xi−1,xi+1…} {qn} » Λn α(x,x∗):=min(1,p(x)Qx,x∗p(x∗)Qx∗,x) λin π=p π(x)pxy=π(y)pyx","breadcrumbs":"Notes π(z)=p(z)","breadcrumbs":"Notes πm+1=πm πt+1=πtQ πt ⇐ ⇒p(x)qx,x∗α(x,x∗)=p(x∗)Qx∗,xα(x∗,x) ⇔ ∀p ∑yqx,y=1 ∣f∣ ∣λ∣≤1>ε)→0 sufficiency P(∣R(f)−Rn(f)∣≥ε)≤P(f∈Fsup∣Rn(f)−R(f)∣≥2ε) P(∣R(f)−Rn(f)∣≥ε)≤2exp(−2nε2) generalization bound for finite class F={fi},i=1,…,m P(∣R(f)−Rn(f)∣≥ε)≤2mexp(−2nε2) proposition: choose δ∈(0,1)⇒ w/ at least 1−δ probability ∣R(f)−Rn(f)∣≤2nln(2m)−lnδ by δ:=2mexp(−2nε2) for infinite class F P(f∈Fsup∣R(f)−Rn(f)∣>ε)≤2N(F,2n)exp(4−nε2) proof: P(∣R(f)−Rn(f)∣≥ε)≤P(f∈Fsup∣R(f)−Rn(f)∣≥2ε)≤2P(f∈Fsup∣Rn(f)−Rn′(f)∣≥2ε)by Symmetrization Lemma where Rn′(f) is empirical risk of another n sample (ghost sample) ⇒∃c≤N(F,2n) class of f for sample & ghost sample problem: hard to compute shattering coefficient","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » consistence wrt F & P","id":"1434","title":"consistence wrt F & P"},"1435":{"body":"maximum number of FX1,…,Xn, function we can get by restricting F to X1,…,Xn","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » shattering coefficient N(F,n)","id":"1435","title":"shattering coefficient N(F,n)"},"1436":{"body":"maximum n s.t. ∃f∈F,∀X={X1…,Xn}, f classify X completely correctly for function class F w/ VC dimension d N(F,n)≤i=0∑d(dn) for n>d, N(F,n)≤(den)d ERM is consistence ⇔ VC dimension finite","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » (Vapnik-Chervonenkis dimension) VC dimension","id":"1436","title":"(Vapnik-Chervonenkis dimension) VC dimension"},"1437":{"body":"richness of function class F in sample set {Xi} sample label σi=±1,i=1,…,n Radn(F)=E[f∈Fsupn1i=1∑nσif(Xi)] solution: for each possible set of σi, find the function f to maximize the inner sum, then take weighted average generalization bound: with ≥ 1−δ probability, ∀f∈F, R(f)≤Rn(f)+2Radn(F)+2n−ln(δ)≤Rn(f)+2ndln(den)−lnδ","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » Rademacher complexity","id":"1437","title":"Rademacher complexity"},"1438":{"body":"to balance training error and model complexity e.g. regularization, linear SVM VC =d+1, RBF kernel ⇒∞","breadcrumbs":"Notes » Unstructured Class Notes » Statistical Machine Learning » structural risk minimization (SRM)","id":"1438","title":"structural risk minimization (SRM)"},"1439":{"body":"Unstructured Reading Notes How Smartphones Shrink Our Brains anticipation trump focus habit to rely on tool kill memory trying to split attention make though shallow paper is better for thinking (I think large screen help) ChatGPT from Scratch: How to Train an Enterprise AI Assistant • Phil Winder • GOTO 2023 post-GPT are decoder-only logistic regression is often superb for domain-specific task RLHF degrade performance parameter-efficient fine-tuning (PEFT): use adapter alongside frozen model quantization massively reduce RAM usage Falcon-7B LLM: used in demo, said to have cleaned training data, open-source fine tuning demo done on V100 in Colab","breadcrumbs":"Notes » Unstructured Reading Notes » Unstructured Reading Notes","id":"1439","title":"Unstructured Reading Notes"},"144":{"body":"table: item & attribute flat multi-dimensional network: item & attribute & link field: grid & attribute geometry: position","breadcrumbs":"Notes » Data Science » Visualization » structured data","id":"144","title":"structured data"},"1440":{"body":"Steven Hé (Sīchàng)'s Blog","breadcrumbs":"Blogs » Steven Hé (Sīchàng)'s Blog","id":"1440","title":"Steven Hé (Sīchàng)'s Blog"},"1441":{"body":"Creating Perfect Grayscale-Gradient Colormaps Result: hand-picked hues and perfect grayscale gradient Math: calculating linear RGB from hue and grayscale Linear RGB vs standard RGB Exercise for the reader When reviewing the submission instruction for a conference, I was reminded that the figures in my paper need to be \"accessible\" when printed in grayscale. Usually, this would be done by adding patterns like triangles and circles in the plot. However, we were plotting stacked areas like the left one below, which contains dense and tiny vertical bars, so a grayscale gradient seems to be our only option. I found nice grayscale-gradient \"sequential\" Matplotlib colormaps like the right one above, but they make it impossible to hand-pick a distinct and pretty color for each category. \"This is not a big deal,\" I thought, \"I'll just use HSL (hue-saturation-lightness), set s to 1, l to a gradient, and hand-pick the h.\" Except I was so wrong—lightness is not grayscale, and figuring everything out took me the whole morning.","breadcrumbs":"Blogs » Creating Perfect Grayscale-Gradient Colormaps » Creating Perfect Grayscale-Gradient Colormaps","id":"1441","title":"Creating Perfect Grayscale-Gradient Colormaps"},"1442":{"body":"After wasting an hour failing to find any implementation on the Internet, I rolled my own scripts to calculate RGB color values from hue and grayscale, which allowed hand-picking hues while still having perfect grayscale gradient: Below is the definition of these six colors. I hand-picked the hue values so each color looks natural, but the grayscale values are sampled linearly. COLORS6: Final = tuple( hue_grayscale_to_srgb(hue, grayscale) for hue, grayscale in zip( [60, 180, 120, 240, 0, 300], np.linspace(0.96, 0.2, 6), )\n) As a trade-off, I spent some time doing math on a whiteboard.","breadcrumbs":"Blogs » Creating Perfect Grayscale-Gradient Colormaps » Result: hand-picked hues and perfect grayscale gradient","id":"1442","title":"Result: hand-picked hues and perfect grayscale gradient"},"1443":{"body":"Math for hue-grayscale to RGB conversion on a whiteboard After some Wikipedia'ing, I extracted the formula for RGB-HSL and RGB-grayscale conversions, and did the math on the whiteboard above. For a color with linear red, green, blue values r,g,b∈[0,1], hue h∈[0,360), saturation s∈[0,1], lightness l∈[0,1], and grayscale p∈[0,1]: xyzchh′lsRp:=max{r,g,b}:=mid{r,g,b}:=min{r,g,b}:=x−z=:h′⋅60°=⎩⎨⎧cg−bmod6cb−r+2cr−g+4if x=rif x=gif x=b=2x+z=1−∣2l−1∣c:=0.2126,G:=0.7152,B:=0.0722b=Rr+Gg+Bbmaximum RGB valuemiddle RGB valueminimum RGB valuechroma601hueif l=0,1 Recall that we know h and p, and want to solve for r, g, and b. The easiest bit is exploiting saturation s=1 and the formula for it: 1=1−∣22x+z−1∣x−z⇒{x=1z=0if x+z≥1if x+z<1 a and conditions for formula fortunately, found hue h′ i if introduce k: k⇒k:=⎩⎨⎧6−h′,h′,2−h′,h′−2,4−h′,h′−4, if h′∈[5,6) if h′∈[0,1) if h′∈[1,2) if h′∈[2,3) if h′∈[3,4) if h′∈[4,5)(i.e. r many matters new nightmare observed of only order out rgb simplification. source the three values variable >b>g)(i.e. r>g>b)(i.e. g>r>b)(i.e. g>b>r)(i.e. b>g>r)(i.e. b>r>g)=x−zy−z Since we can get the order of r,g,b from h, we can also know the grayscale coefficient ki for i=x,y,z. For example, if r>g>b, then we have: x=r,y=g,z=bkx=R,ky=G,kz=B⇒p=kxx+kyy+kzz That is, we need to solve this linear system: ⇒{x=1z=0if x+z≥1if x+z<1 (srgb) , a above and answer are because boom! calculating case case, code colormaps colors compute computed conversion: creating csrgb={12.92Clinear1.055Clinear1/2.4−0.055if Clinear≤0.0031308if Clinear does don't.","breadcrumbs":"blogs fact, fall first found from gradient gradient. grayscale grayscale","id":"1443","title":"math: grayscale"},"1444":{"body":"rgb grayscale-gradient grayscale. have hue i if in instead, linear math: monitors not perfect potential produce program. resulting rgb second similar some standard the then then, this through to trivial use using values values, very we with x+z≥1, » k=x−zy−zp=kxx+kyy+kzz{x=kx+kykp,x=1,y=kx,y=(1−k)z+k,z=0z=ky(1−k)+kzp=kx−kykif x+z<1if x+z≥1 …except>0.0031308 Why apply a weakly concave curve to RGB values? It turns out that human eyes are less sensitive to changes in bright colors, and so the curved sRGB values better reflect the perceived brightness. Applying this knowledge to creating a grayscale gradient colormap, we need to first generate the gradient in sRGB, then convert each grayscale to linear RGB and apply the hue-grayscale to linear RGB conversion, and finally convert them back to sRGB. And, that is it! A perfect grayscale-gradient colormap with hand-picked hues.","breadcrumbs":"Blogs » Creating Perfect Grayscale-Gradient Colormaps » Linear RGB vs standard RGB","id":"1444","title":"Linear RGB vs standard RGB"},"1445":{"body":"We fixed s≡1 above, but what if we want to be able to change the saturation? Can you solve the system for r,g,b given h,s,p? 2024-05-25 Steven Hé (Sīchàng)'s Blog","breadcrumbs":"Blogs » Creating Perfect Grayscale-Gradient Colormaps » Exercise for the reader","id":"1445","title":"Exercise for the reader"},"1446":{"body":"What an mdBook Preprocessor Does—Code Walk-through of mdBook-KaTeX Topic: what an mdBook preprocessor does mdBook-KaTeX as a CLI App The supports command Reading and processing the book data from StdIn Processing book What next Configuration options Parallelism Conclusion and preview What does mdBook-KaTeX do? It is an mdBook preprocessor that pre-renders math expressions. For example, if you have this following snippet in your book: Define $f(x)$: $$\nf(x)=x^2\\\\\nx\\in\\R\n$$ mdBook-KaTeX would pre-rendered it as: Define f ( x ) f ( x ) = x 2 x ∈ R ; fn supports_renderer(&self, renderer: &str) -> bool;\n} name and supports_renderer are trivial, but run is where the fun lives. For KatexProcessor, it finds the math expressions in each chapter of book and render them.","breadcrumbs":"Blogs » What an mdBook Preprocessor Does » Reading and processing the book data from StdIn","id":"1450","title":"Reading and processing the book data from StdIn"},"1451":{"body":"Simply stated, we just loop over the all the chapters in the argument book above. For each chapter, we loop over its bytes, find the math expressions, and replace them with rendered HTML. Then, we stick these chapters back into book. fn run(&self, ctx: &PreprocessorContext, mut book: Book) -> Result { // … book.for_each_mut(|item| { if let BookItem::Chapter(chapter) = item { chapter.content = process_chapter(&chapter.content, /* … */) } }); Ok(book)\n} Above, we use the for_each_mut method on book to iterate over its items and mutate them. We filter out the item: &mut BookItems that are BookItem::Chapter. We then call process_chapter on their content: String and assign the results back. Below, we have a simplified version of process_chapter. scan: Scan is a custom scanner that scans through each byte in raw_content and produces Events that indicate the beginnings and ends of blocks. fn process_chapter(raw_content: String, /* other args */) -> String { let scan = Scan::new(&raw_content, /* … */); let mut rendered = Vec::new(); let mut checkpoint = 0; for event in scan { match event { Event::TextEnd(end) => rendered.push((&raw_content[checkpoint..end]).into()), Event::InlineEnd(end) => { rendered.push(render(&raw_content[checkpoint..end], /* … */)); checkpoint = end; } // … } } // … rendered.join(\"\")\n} Based on the types of the Event, we identify text blocks and math blocks, and apply the render function to the math blocks. The render function then uses the katex crate to render HTML. Finally, we join all the strings in rendered: Vec into the new content of the chapter.","breadcrumbs":"Blogs » What an mdBook Preprocessor Does » Processing book","id":"1451","title":"Processing book"},"1452":{"body":"If you have been following along, I hope you got a gist about how an mdBook preprocessor works and probably how to write one yourself! (If not, leave a question below). In reality, though, the code for mdBook-KaTeX is way more complicated due to:","breadcrumbs":"Blogs » What an mdBook Preprocessor Does » What next","id":"1452","title":"What next"},"1453":{"body":"mdBook-KaTeX offers a wide range of options . We read these options from the ctx: &PreprocessorContext argument passed into the run method. Then, we further parse the configurations and pass them around.","breadcrumbs":"Blogs » What an mdBook Preprocessor Does » Configuration options","id":"1453","title":"Configuration options"},"1454":{"body":"Parallelism is more interesting. Since the katex crate uses QuickJs to render KaTeX, which is ironically slow, KaTeX rendering has been the performance bottleneck. Initially, by manually scheduling rendering tasks using Tokio , I was able to get 5x speed on an M1 Mac, from 10sec to 2sec rendering my 30-thousand-word notes . In v0.5.0, we switched to Rayon for simplicity, but the basic ideas are the same. To spawn threads and get parallelism, each thread ideally needs to own its data. So, we need to scan for tasks first, save them in vectors, and then execute the tasks in the vector in parallel. For example, this is how we actually parallelize processing each chapter: let mut chapters = Vec::with_capacity(book.sections.len());\nbook.for_each_mut(|item| { if let BookItem::Chapter(chapter) = item { chapters.push(chapter.content.clone()); }\n});\nlet mut contents: Vec<_> = chapters .into_par_iter() .rev() .map(|raw_content| process_chapter(raw_content, /* … */)) .collect();\nbook.for_each_mut(|item| { if let BookItem::Chapter(chapter) = item { chapter.content = contents.pop().expect(\"Chapter number mismatch.\"); }\n}); We have to clone each chapter's content and save them into a vector chapters for each thread to own the chapter they process. We use the into_par_iter method for Vec and the map method, which Rayon provides, to process the chapters in parallel. We have to use for_each_mut even when gathering the chapters because iter unfortunately iterates them in a different order. We call rev to iterate the chapters in reverse order, so when we put the rendered chapters back into the book, we can simply call pop on the contents to get them in the correct order.","breadcrumbs":"Blogs » What an mdBook Preprocessor Does » Parallelism","id":"1454","title":"Parallelism"},"1455":{"body":"In summary, we have walked through mdBook-KaTeX as an mdBook preprocessor example to show what a preprocessor does: Handle supports command. Read the book from StdIn and parse it. Process the book by looping through its content and changing them. Print the book back to StdOut. Other enhancement such as option handling and parallelism. The reality, however, is that, like many other projects, mdBook preprocessors get messy easily. We will talk about the mess mdBook-KaTeX was in next time. 2023-05-27 , edited: 2023-06-11 , 2024-05-24 Steven Hé (Sīchàng)'s Blog","breadcrumbs":"Blogs » What an mdBook Preprocessor Does » Conclusion and preview","id":"1455","title":"Conclusion and preview"},"1456":{"body":"~300x Speed Up: Finding Inexact Matches in Nested Sets Simplified background Naive implementation Standard data structure changes Repetition reduction Custom data structure Tenable caching Appendix A: Flamegraphs I optimized my route analyzer and made it around 300 times faster, analyzing around 800 million routes within 3 hours [1] . The exact multiply of speedup does not matter; rather, I find it valuable to discuss the data structure changes, profiling, and algorithm experiments, the major gains, and the wasted effort. No, I did not rewrite a Python implementation to gain a trivial 50x speedup; I started with a multi-threaded Rust implementation. The main bottleneck of the route analyzer lay in finding inexact matches of IP address prefixes in nested sets. In our research, this matching was a core functionality because we used the analyzer to match routes on the Internet against public routing policies. The technicality of the research does not matter here, but some basic context is needed to understand the optimizations.","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » ~300x Speed Up: Finding Inexact Matches in Nested Sets","id":"1456","title":"~300x Speed Up: Finding Inexact Matches in Nested Sets"},"1457":{"body":"My task was to implement the match_nested_set method on the Matcher data structure, as the pseudo code below illustrates [2] . This method should output whether the (IP address) prefix self.prefix matches a nested set of prefixes called name. Additionally, it should accept a Range Operator op that can modify how the prefix matching is done. struct Matcher { prefix: IpNet, sets: BTreeMap>, nested_sets: BTreeMap,\n} impl Matcher { fn match_nested_set(self, name: String, op: RangeOperator) -> bool { unimplemented!() }\n} The example pseudo code below checks if the prefix 193.254.30.0/24 matches the nested set CUSTOMERS with the Range Operator Plus. The nested set CUSTOMERS has a member 69 that contains the prefix 193.254.0.0/16. Since 193.254.0.0/16 contains 193.254.30.0/24 and Plus specifies the \"contains\" relationship, then the method should return true. let matcher = Matcher { prefix: 193.254.30.0/24, sets: BTreeMap(69: 193.254.0.0/16), nested_sets: BTreeMap( \"CUSTOMERS\": NestedSet { sets: [69], nested_sets: [] } ),\n};\nmatcher.match_nested_set(\"CUSTOMERS\", RangeOperator::Plus)\n// => true To understand the problem, I started with a straightforward implementation.","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Simplified background","id":"1457","title":"Simplified background"},"1458":{"body":"impl Matcher { fn match_nested_set( self, name: String, op: RangeOperator, visited: Vec, ) -> bool { let Some(nested_set) = self.nested_sets.get(name) else { return false; }; for set in nested_set.sets { if self.match_set(set, op, visited) { return true; } } for nested_set in nested_set.nested_sets { if self.match_nested_set(nested_set, op, visited) { return true; } } false } fn match_set( self, name: String, op: RangeOperator, visited: Vec, ) -> bool { if visited.contains(name) { return false; } visited.push(name); let Some(set) = self.sets.get(name) else { return false; }; set.iter() .any(|prefix| prefix_and_op_matches(prefix, op, self.prefix)) }\n} The pseudo code above is mostly trivial for the average programmers, except for a few places. Using Rust's let else syntax, we look up name in the sets, and either bind the result to the variable, or return false early if name is not found. visited tracks the set names we have checked to prevent infinite recursions from nested sets that contain each other. prefix_and_op_matches is a helper function that checks if a prefix matches the Range Operator and another prefix.","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Naive implementation","id":"1458","title":"Naive implementation"},"1459":{"body":"Profiling and standard data structure changes were the lowest-handing fruit. Although I lost the exact performance record of early implementations, my benchmark code checking only 256 routes clearly took minutes to run. I understood that the naive implementation would not scale, so I immediately started profiling the benchmark code to find where most of the time was spent. Surprisingly, Cargo-FlameGraph showed that most of the time was spent on checking if set names have been visited (visited.contains). visited was a vector, and its linear search compounded with recursion to a cubic growth. I chose to use vectors because I thought most nested sets would have less than ten members, in which case linear search would be fine, but my assumption was clearly wrong. I changed visited to use HashSet and boosted the speed by perhaps 10 times. The other effective change was to replace the maps. Matcher contains two B-tree maps, which are amazing sorted binary trees with O(logn) lookup time complexity. However, hash maps have amortized O(1) lookup. Therefore, it was a no-brainer to try replacing BTreeMap with HashMap. I recall this find-replace change caused the get calls to occupy seemingly larger areas in the flame graph! However, I also saw a 30% faster benchmark, so the hash map was faster. The hash map being only slightly faster than the B-tree map was no surprise. The B-tree map is cache-efficient, and avoids the somewhat expensive operation of hashing the number or string, sometimes multiple times when the hash map would be probing. This means, for smaller maps, the B-tree may be faster. Though, it turned out that my maps are large enough and my string keys are small enough, such that the hash map won. These trivial changes turned out to be clear wins, and show some basics of performance optimization: Code profiling helps check our assumptions of run-time complexities. Data structure choices can greatly affect performance, and both complexity analysis and benchmarking help pick them.","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Standard data structure changes","id":"1459","title":"Standard data structure changes"},"146":{"body":"parallel coordinate treemap field choropleth map star plot","breadcrumbs":"Notes » Data Science » Visualization » symbolic display","id":"146","title":"symbolic display"},"1460":{"body":"","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Repetition reduction","id":"1460","title":"Repetition reduction"},"1461":{"body":"","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Custom data structure","id":"1461","title":"Custom data structure"},"1462":{"body":"Before flattening the nested sets After flattening the nested sets Flamegraph before Flattening the nested sets. Flamegraph after Flattening the nested sets. I ran the experiment on a server with dual EPYC 7763 64-Core processors with hyperthreading turned off. These are simplified pseudo Rust code based on my real code . I removed the numerous references (& or &mut) and parsing code, so readers unfamiliar with Rust can still understand it. I also changed the names to avoid explaining the research context.","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Tenable caching","id":"1462","title":"Tenable caching"},"1463":{"body":"After distinguishing special cases. After distinguishing special cases After flattening prefixes of nested sets' direct members. After flattening prefixes of nested sets' direct members After flattening each set to its prefixes. After flattening each set to its prefixes 2024-05-30 Steven Hé (Sīchàng)'s Blog","breadcrumbs":"Blogs » Drafts » ~300x Speed Up: Finding Inexact Matches in Nested Sets » Appendix A: Flamegraphs","id":"1463","title":"Appendix A: Flamegraphs"},"1464":{"body":"This summer, my parents and I have been giving advice to more than a dozen of relatives and friends in mainland China on their kids' education. I sense that Chinese parents are facing unprecedented challenges: Schools, and people generally, judge kids almost solely by their exam scores. The society spreads the common belief that each step of a kid's education the later steps and eventually their life success. The parent community is highly anxious and comparing. Schools work the asses out of kids in the hope of higher scores. Kids have more homework than they can finish without going to sleep late, even in elementary schools. After school, most kids are sent to tutoring organizations by their parents. High school kids study at school Monday through Saturday, 7 am to 9 pm. A kid is almost treated as a mere number. We all know a person is not measurable as a single number, but the important question is what to do under the environment's pressure. I believe it is time we revisit first principles and rethink the purpose of education. My conclusion is we should borrow many ideas from machine learning for human learning, both for kids and adults.","breadcrumbs":"Blogs » Drafts » Learn Like Machine Learning Models » Learn Like Machine Learning Models","id":"1464","title":"Learn Like Machine Learning Models"},"1465":{"body":"Last year, a conference talk on making Rust simpler for beginners recommended slapping async on every function and .await on every function call. It shows a void of understanding of programming async Rust. However, the phenomenon that most of us pause at some surface level understanding of async Rust has to do with the way we get introduced to it and the way we learn it. I believe we fool our async newcomers too much and patch their understanding as they hit confusing walls; instead, we should adequately explain the important bits of async Rust in the first place. I now understand that the key point in async is yielding the control back to the runtime (Future returning Poll::Pending when polled). This is an overhead, but it enables two very nice things: Cooperative scheduling. One task cannot block for too long, all tasks ideally get to be run. Cancellation. We the runtime gets back the control, it can then apply cancellation or check the other branches of select!. It also revealed why Rust would always suck compared to Erlang—cancellation is not free. In Erlang, when you kill a process, it dies immediately or runs the traps-exit code. In Rust, you cannot kill a thread (big sucker!), so you need to code the thread to constantly check whether it should stop. In Tokio, you can \"cancel\" a task, but it only may get stopped when it yields the control back to the runtime. If you have a sucker async function that runs for a whole millisecond before it yields, it surely will eat a whole millisecond as soon as it starts. This means any async function needs to be carefully written, with lots of yield points inserted (using yield_now()), and all heavy sync functions need to be wrapped in either spawn_blocking or block_in_place plus a yield_now() (I have tested, block_in_place does not yield).","breadcrumbs":"Blogs » Drafts » We are Learning Async Rust Wrong » We are Learning Async Rust Wrong","id":"1465","title":"We are Learning Async Rust Wrong"},"1466":{"body":"I finally got around to read the old legendary book, Design Patterns: Elements of Reusable Object-Oriented Software . I find it depicting an OOP landscape and philosophy much different that the OOP we see today. More importantly, it claims that OOP fundamentally sacrifices control and performance in favor of manageability, a sign to me that says OOP is unsuitable for systems programming, where control and performance is crucial.","breadcrumbs":"Blogs » Drafts » Design Patterns Reveal OOP is Inherently Unsuitable for Systems » Design Patterns Reveal OOP is Inherently Unsuitable for Systems","id":"1466","title":"Design Patterns Reveal OOP is Inherently Unsuitable for Systems"},"1467":{"body":"A type is a name used to denote a particular interface. We speak of an object as having the type \"Window\" if it accepts all requests for the operations defined in the interface named \"Window.\" An object may have many types, and widely different objects can share a type. Part of an object's interface may be characterized by one type, and other parts by other types. Two objects of the same type need only share parts of their interfaces. Interfaces can contain other interfaces as subsets. We say that a type is a subtype of another if its interface contains the interface of its supertype. Often we speak of a subtype inheriting the interface of its supertype. This is to say that OOP does not stress the importance of each object's implementation, but the messages it accepts (methods). Conceptually, the problem is, implementation details often decide the suitability. Calling a costly method in a long loop is almost bound to lead to performance issues. And, modern multi-threaded systems even have additional thread-safety concerns for each function. When one opts into programming on the abstraction level of interfaces, they become agnostic to these concerns. Concretely, interfaces-agnosticism forces inefficient implementations. Most OOP languages resolve to boxing every object and doing run-time lookups to determine if an object implements an interface. Languages like Objective C and Cpp create fat structures that bumble with them the method pointers, and languages like Python and JavaScript lies onto using dictionaries as objects for this dynamism. All of these options incur performance penalties from dynamic allocation, lookups, and pointer redirections. The popular alternative, generic programming with monomorphization, shifts this cost to compile-time and to the programmer. This is notorious in Cpp for its atrocious template function error messages, and in Rust for the complex where clause. To know that a data structure implements an interface, some work seems to be required. However, more powerful compilers may be able to handle this for the programmer. Roc seems to abstract automatic monomorphization away from the programmers. Cig works entirely around generic programming by evaluating part of the program at compile time. These efforts may be able to promote the idea of reuse from OOP without either run-time nor human overhead, but they still fundamentally depend on knowing the data structure implementations—the \"types\".","breadcrumbs":"Blogs » Drafts » Design Patterns Reveal OOP is Inherently Unsuitable for Systems » Lack of emphasis on object implementation","id":"1467","title":"Lack of emphasis on object implementation"},"1468":{"body":"An object-oriented program's run-time structure often bears little resemblance to its code structure. The code structure is frozen at compile-time; it consists of classes in fixed inheritance relationships. A program's run-time structure consists of rapidly changing networks of communicating objects. This comes to say that programmers do not see what the system actual does when they read the code. Translated to today's OOP, when you read a module, a class, or a method, you have little idea what domain-specific tasks it performs. This just makes it difficult to map real-world problems to the code, adding hurdles to reason about the system for any given tasks. For a concrete example, the authors details one aspect of why this indirection exists: the pervasive use of references (\"acquaintance\"). References connect objects into a graph, a costly task for a garbage collector, but more importantly, I believe, a constant though exercise for programmers to track.","breadcrumbs":"Blogs » Drafts » Design Patterns Reveal OOP is Inherently Unsuitable for Systems » Disconnection between code and reality","id":"1468","title":"Disconnection between code and reality"},"1469":{"body":"Deprecated These entries are stored only for the history.","breadcrumbs":"Blogs » Deprecated » Deprecated","id":"1469","title":"Deprecated"},"147":{"body":"framework scale content mark label title axis","breadcrumbs":"Notes » Data Science » Visualization » graph","id":"147","title":"graph"},"1470":{"body":"How did we get here? WordPress? WTF The reality What I get with WordPress Conclusion This was when I set up the blog in WordPress.","breadcrumbs":"Blogs » Deprecated » How did we get here? WordPress? » How did we get here? WordPress?","id":"1470","title":"How did we get here? WordPress?"},"1471":{"body":"Isn't WordPress for non-technical people? Why would I use WordPress? Also, why am I starting a blog? Didn't I say that I don't need a blog?","breadcrumbs":"Blogs » Deprecated » How did we get here? WordPress? » WTF","id":"1471","title":"WTF"},"1472":{"body":"Well, if I wrote something moderately decent and long, I need a more decent place for it other than GitHub issues and Reddit. Of course, I could use GitHub Pages to make a static site, but people wouldn't be able to comment on that. Of course, I could set up a whole server with a JavaScript front-end library (probably Svelte) and a back-end with Rust, deploy it on Amazon lambda, and connect it to a PostgreSQL database. That would be really cool. But, then, I would probably need to find a domain for it and pay $20 a year… I don't want to. Also, people don't care about you knowing how to mess with AWS, they only appreciate the silly CSS tricks they see that makes up the front-end. So, setting up a server manually and hosting a blog probably would not be worth it.","breadcrumbs":"Blogs » Deprecated » How did we get here? WordPress? » The reality","id":"1472","title":"The reality"},"1473":{"body":"A subdomain. Free content server. No setup, I just write and post.","breadcrumbs":"Blogs » Deprecated » How did we get here? WordPress? » What I get with WordPress","id":"1473","title":"What I get with WordPress"},"1474":{"body":"For now, that is it. I'll post random articles here. But, I will manually keep a Markdown copy on GitHub . 2023-05-26","breadcrumbs":"Blogs » Deprecated » How did we get here? WordPress? » Conclusion","id":"1474","title":"Conclusion"},"1475":{"body":"Diary Guests: don't read this. This is private.","breadcrumbs":"Private » Diary","id":"1475","title":"Diary"},"1476":{"body":"Diary Guests: don't read this. This is private.","breadcrumbs":"Private » Diary » Diary","id":"1476","title":"Diary"},"1477":{"body":"start choice for the diary my take on blogs generate HTML WordPress hand write Markdown Markdown flavor Hugo mdBook web server coda 2022-03-17 I have this feeling that I am about to be unable to write. Been having all sorts of math, stats, and CS courses, there is really not much writing to do. DKU provides little paper to write, specifically, little literature-ish things. All said, I decided to start writing diaries. Not for people to read, but more for me to stay sane on the writing side.","breadcrumbs":"Private » Diary » start » start","id":"1477","title":"start"},"1478":{"body":"","breadcrumbs":"Private » Diary » start » choice for the diary","id":"1478","title":"choice for the diary"},"1479":{"body":"Some people have blogs. It's a good idea to have your things on the web, so it lasts longer than your local file, or worse, a piece of paper made in the 2020s. But, I dislike the idea that you write something solely about yourself for others to read. That does not affect my adoption of the shell of blogs. I will put this diary on the web.","breadcrumbs":"Private » Diary » start » my take on blogs","id":"1479","title":"my take on blogs"},"148":{"body":"represent item, link point line area","breadcrumbs":"Notes » Data Science » Visualization » mark","id":"148","title":"mark"},"1480":{"body":"To post something on the web, you need HTML, and there are different ways to make HTML. WordPress The most popular way is WordPress . 43% of the web is built on WordPress. More bloggers, small businesses, and Fortune 500 companies use WordPress than all other options combined. Join the millions of people that call WordPress.com home. What a great ad from WordPress themselves! I would have fallen for it if I did not know how bloated WordPress is. The DKU website itself runs WordPress. And, the performance is \"insane\". You can open a small webpage in 5 seconds! Imagine? And also some webpage in 30 seconds! Amazing! The Intersection uses WordPress for its website (not published yet). I saw the source code it generates for a simple article: 7 layers of nested divs! And, it also has \"insane\" performance. If I look back from the future and see WordPress's dominance, what would I think? People were crazy? No, people are lazy and will not change if things work. hand write It is possible, but the HTML part probably would take much more time than the text part. Plus, the CSS part would be the most annoying. Markdown Markdown is a lightweight markup language that looks nice as source code. It is rendered by converting to HTML. I feel fast and delightful writing Markdown for my notes. Also, I used Markdown to write presentation slides and it is just minimum effort. Without more trash talk, it is sure that I would choose Markdown if possible. But, what flavor?","breadcrumbs":"Private » Diary » start » generate HTML","id":"1480","title":"generate HTML"},"1481":{"body":"Markdown has a shit ton of different flavors. Some does not eat your \\n, some support \\(\\TeX\\), and some support PHP. What I need is: Math support Code block support/ highlighting Nice look Simplicity Git friendliness (short lines) Live Preview I ended up considering Hugo and mdBook only for fast and simple Markdown-HTML conversion. Hugo I found Hugo by searching Markdown website (or something like that) for DKU iGEM Wiki (a future thing). It is marketed as an easy-to-use and fastest static site generator. It has many themes that the community made. Most of them look like PowerPoint templates (no offense). I spent way too much time looking around to find a nice looking theme, and found hugo-book and Doks . hugo-book just looks like a crappy version of GitBook, might as well use GitBook. But, GitBook is \"converted\" from open source to \"proprietary services\" (what a shame). Might as well use mdBook which is still open source. Doks look nice, but it shocked me by taking 500MB on my disk (how does some HTML and CSS text take so much space?). It is absolutely not anything lightweight, and it reminds me of WordPress… Without a good theme, I have no Nice look nor Simplicity and I need to implement Math support and Code highlighting myself (which, is just adding some