# User contributions for Etone

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#### 11 October 2024

- 12:3712:37, 11 October 2024 diff hist +82 数据科学基础 (Fall 2024) →Lectures

#### 9 October 2024

- 14:4614:46, 9 October 2024
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**+2,514** 数据科学基础 (Fall 2024) →Concepts

#### 30 September 2024

- 06:3106:31, 30 September 2024 diff hist −9 数据科学基础 (Fall 2024)/Average-case analysis of QuickSort No edit summary current
- 06:3106:31, 30 September 2024
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**+11,838** N 数据科学基础 (Fall 2024)/Average-case analysis of QuickSort Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''（'''Quicksort'''）]是由Tony Hoare发现的排序算法。该算法的伪代码描述如下（为方便起见，假设数组元素互不相同——更一般情况的分析易推广得到）： '''''QSort'''''(A): 输入A[1...n]是存有n个不同数字的数组 if n>1 then '''pivot''' = A[1]; 将A中<pivot的元素存于数组L，将A中>pivot的元素存于数组R; \\保持内部元素之..." - 06:3006:30, 30 September 2024 diff hist +118 数据科学基础 (Fall 2024) →Lectures

#### 29 September 2024

- 16:3216:32, 29 September 2024 diff hist +6 Assignment 1, Fall 2024 →Bonus Question current
- 16:2516:25, 29 September 2024 diff hist 0 Main Page No edit summary current
- 16:2516:25, 29 September 2024 diff hist −103 Main Page No edit summary
- 16:2416:24, 29 September 2024
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**−2,322** Assignment 1, Fall 2024 No edit summary - 16:2216:22, 29 September 2024
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**+2,498** Assignment 1, Fall 2024 →下载区 - 16:1916:19, 29 September 2024
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**+2,789** N Assignment 1, Fall 2024 Created page with "==Question #1== 请使用多年（>20年）的NCEP/NCAR月平均再分析资料，画出各季节（至少画出冬夏两季）纬向平均温度场、纬向平均纬向风场的高度－纬度剖面分布，并简述其分布特征和季节变化特征。 ==Question #2== 请使用多年（>20年）的NCEP/NCAR月平均再分析资料，画出各季节（至少画出冬夏两季）温度场、纬向风场在各高度（850、500、100 hPa， 对于温度场请再画..." - 16:1816:18, 29 September 2024 diff hist +1 General Circulation(Fall 2024) No edit summary current
- 16:1716:17, 29 September 2024 diff hist −42 General Circulation(Fall 2024) No edit summary
- 16:1616:16, 29 September 2024 diff hist +2 General Circulation(Fall 2024) →Course info
- 16:1416:14, 29 September 2024
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**−585** General Circulation(Fall 2024) →Announcement - 16:1316:13, 29 September 2024
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**+8,931** N General Circulation(Fall 2024) Created page with "{{Infobox |name = Infobox |bodystyle = |title = 大气环流 <br> General Circulation of the Atmosphere |titlestyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 张洋 |header3 = |label3 = Email |data3 = yangzhang@nju.edu.cn |header4 = |label4= office |data4= 仙林大气楼 B410 |header5 = Class |label5 = |data5 = |hea..." - 16:1016:10, 29 September 2024 diff hist +99 Main Page No edit summary

#### 27 September 2024

- 04:4004:40, 27 September 2024
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**+16,764** N 高级算法 (Fall 2024)/Dimension Reduction Created page with "= Metric Embedding= A '''metric space''' is a pair <math>(X,d)</math>, where <math>X</math> is a set and <math>d</math> is a '''metric''' (or '''distance''') on <math>X</math>, i.e., a function :<math>d:X^2\to\mathbb{R}_{\ge 0}</math> such that for any <math>x,y,z\in X</math>, the following axioms hold: # (identity of indiscernibles) <math>d(x,y)=0\Leftrightarrow x=y</math> # (symmetry) <math>d(x,y)=d(y,x)</math> # (triangle inequality) <math>d(x,z)\le d(x,y)+d(y,z)</ma..." current - 04:4004:40, 27 September 2024 diff hist +353 高级算法 (Fall 2024) →Lecture Notes

#### 22 September 2024

- 07:3907:39, 22 September 2024
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**−3,786** 数据科学基础 (Fall 2024)/Volume of Hamming balls No edit summary current - 07:3907:39, 22 September 2024
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**+6,589** N 数据科学基础 (Fall 2024)/Volume of Hamming balls Created page with "在求解抛掷公平硬币（fair coin）的尾概率时，我们经常会需要分析如下二项式系数求和： :<math>\sum_{k=0}^r{n\choose k}</math>，对于某个<math>1\le r\le n</math> 这其实等价与求一个 <math>n</math> 维汉明空间中半径为 <math>r</math> 的球的体积。 :{|border="2" width="100%" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" | :'..." - 07:3807:38, 22 September 2024 diff hist −24 数据科学基础 (Fall 2024) →Lectures
- 07:3807:38, 22 September 2024 diff hist +110 数据科学基础 (Fall 2024) →Lectures
- 07:1407:14, 22 September 2024 diff hist +131 数据科学基础 (Fall 2024) →Lectures

#### 19 September 2024

- 11:3211:32, 19 September 2024
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**+10,715** N 高级算法 (Fall 2024)/Conditional expectations Created page with "= Conditional Expectations = The '''conditional expectation''' of a random variable <math>Y</math> with respect to an event <math>\mathcal{E}</math> is defined by :<math> \mathbf{E}[Y\mid \mathcal{E}]=\sum_{y}y\Pr[Y=y\mid\mathcal{E}]. </math> In particular, if the event <math>\mathcal{E}</math> is <math>X=a</math>, the conditional expectation :<math> \mathbf{E}[Y\mid X=a] </math> defines a function :<math> f(a)=\mathbf{E}[Y\mid X=a]. </math> Thus, <math>\mathbf{E}[Y\mid..." current - 11:3111:31, 19 September 2024
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**+41,013** N 高级算法 (Fall 2024)/Concentration of measure Created page with "=Chernoff Bound= Suppose that we have a fair coin. If we toss it once, then the outcome is completely unpredictable. But if we toss it, say for 1000 times, then the number of HEADs is very likely to be around 500. This phenomenon, as illustrated in the following figure, is called the '''concentration''' of measure. The Chernoff bound is an inequality that characterizes the concentration phenomenon for the sum of independent trials. File:Coinflip.png|border|450px|cent..." current - 11:3011:30, 19 September 2024 diff hist +229 高级算法 (Fall 2024) →Lecture Notes

#### 18 September 2024

- 08:1008:10, 18 September 2024
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**+2,264** 数据科学基础 (Fall 2024) →Concepts

#### 16 September 2024

- 02:4502:45, 16 September 2024
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**+5,755** N 高级算法 (Fall 2024)/Basic deviation inequalities Created page with "=Markov's Inequality= One of the most natural information about a random variable is its expectation, which is the first moment of the random variable. Markov's inequality draws a tail bound for a random variable from its expectation. {{Theorem |Theorem (Markov's Inequality)| :Let <math>X</math> be a random variable assuming only nonnegative values. Then, for all <math>t>0</math>, ::<math>\begin{align} \Pr[X\ge t]\le \frac{\mathbf{E}[X]}{t}. \end{align}</math> }} {{Proo..." current - 02:4402:44, 16 September 2024
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**+15,812** N 高级算法 (Fall 2024)/Limited independence Created page with "= <math>k</math>-wise independence = Recall the definition of independence between events: {{Theorem |Definition (Independent events)| :Events <math>\mathcal{E}_1, \mathcal{E}_2, \ldots, \mathcal{E}_n</math> are '''mutually independent''' if, for any subset <math>I\subseteq\{1,2,\ldots,n\}</math>, ::<math>\begin{align} \Pr\left[\bigwedge_{i\in I}\mathcal{E}_i\right] &= \prod_{i\in I}\Pr[\mathcal{E}_i]. \end{align}</math> }} Similarly, we can define independence between..." current - 02:4402:44, 16 September 2024
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**+49,238** N 高级算法 (Fall 2024)/Hashing and Sketching Created page with "=Balls into Bins= The following is the so-called balls into bins model. Consider throwing <math>m</math> balls into <math>n</math> bins uniformly and independently at random. This is equivalent to a random mapping <math>f:[m]\to[n]</math>. Needless to say, random mapping is an important random model and may have many applications in Computer Science, e.g. hashing. We are concerned with the following three questions regarding the balls into bins model: * birthday problem..." - 02:4402:44, 16 September 2024 diff hist +304 高级算法 (Fall 2024) →Lecture Notes

#### 12 September 2024

- 11:2211:22, 12 September 2024
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**+6,210** N 高级算法 (Fall 2024)/Finite Field Basics Created page with "=Field= Let <math>S</math> be a set, '''closed''' under binary operations <math>+</math> (addition) and <math>\cdot</math> (multiplication). It gives us the following algebraic structures if the corresponding set of axioms are satisfied. {|class="wikitable" !colspan="7"|Structures !Axioms !Operations |- |rowspan="9" style="background-color:#ffffcc;text-align:center;"|'''''field''''' |rowspan="8" style="background-color:#ffffcc;text-align:center;"|'''''commutative<br>rin..." current - 11:2111:21, 12 September 2024
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**+38,283** N 高级算法 (Fall 2024)/Fingerprinting Created page with "= Checking Matrix Multiplication= thumb|360px|right|The evolution of time complexity <math>O(n^{\omega})</math> for matrix multiplication. Let <math>\mathbb{F}</math> be a feild (you may think of it as the filed <math>\mathbb{Q}</math> of rational numbers, or the finite field <math>\mathbb{Z}_p</math> of integers modulo prime <math>p</math>). We suppose that each field operation (addition, subtraction, multiplication, division) has u..." current - 11:2111:21, 12 September 2024 diff hist +203 高级算法 (Fall 2024) →Lecture Notes

#### 6 September 2024

- 09:4009:40, 6 September 2024 diff hist +159 数据科学基础 (Fall 2024) →Lectures

#### 5 September 2024

- 04:0804:08, 5 September 2024 diff hist 0 高级算法 (Fall 2024) →Lecture Notes
- 04:0704:07, 5 September 2024 diff hist +53 高级算法 (Fall 2024) →Lecture Notes

#### 29 August 2024

- 08:1508:15, 29 August 2024 diff hist −5 数据科学基础 (Fall 2024) No edit summary
- 08:1408:14, 29 August 2024 diff hist −4 数据科学基础 (Fall 2024) No edit summary

#### 28 August 2024

- 12:1812:18, 28 August 2024 diff hist +109 Main Page No edit summary
- 05:2405:24, 28 August 2024
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**+17,328** N 高级算法 (Fall 2024)/Probability Basics Created page with "=Probability Space= The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one of the greatest mathematician of the 20th century, who advanced various very different fields of mathematics. {{Theorem|Definition (Probability Space)| A '''probability space''' is a triple <math>(\Omega,\Sigma,\Pr)</math>. *<math>\Omega</math> is a set, called the '''sample space'''. *<math>\Sigma\subseteq 2^{\Omega}</math> is the..." current - 05:2405:24, 28 August 2024
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**+50,059** N 高级算法 (Fall 2024)/Min Cut, Max Cut, and Spectral Cut Created page with "= Graph Cut = Let <math>G(V, E)</math> be an undirected graph. A subset <math>C\subseteq E</math> of edges is a '''cut''' of graph <math>G</math> if <math>G</math> becomes ''disconnected'' after deleting all edges in <math>C</math>. Let <math>\{S,T\}</math> be a '''bipartition''' of <math>V</math> into nonempty subsets <math>S,T\subseteq V</math>, where <math>S\cap T=\emptyset</math> and <math>S\cup T=V</math>. A cut <math>C</math> is specified by this bipartition as..." - 05:2305:23, 28 August 2024
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**+2,043** N 高级算法 (Fall 2024) / Course materials Created page with "= Course textbooks = {|border="2" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" |border|100px |width="100%"| :Rajeev Motwani and Prabhakar Raghavan. :'''''Randomized Algorithms'''''. :Cambridge University Press, 1995. |- |border|100px|| : Vijay Vazirani. :'''''Approximation Algorithms'''''. :S..." current - 05:2205:22, 28 August 2024
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**+6,278** N 高级算法 (Fall 2024) Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>高级算法 <br>Advanced Algorithms</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = '''尹一通''' |header3 = |label3 = Email |data3 = yinyt@nju.edu.cn |header4 = |label4= office..." - 05:1405:14, 28 August 2024 diff hist +75 Main Page →Home Pages for Courses and Seminars

#### 10 July 2024

- 03:4603:46, 10 July 2024
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**+1,301** 概率论与数理统计 (Spring 2024) →Concepts current

#### 13 June 2024

- 07:5607:56, 13 June 2024 diff hist +66 组合数学 (Spring 2024) →Lecture Notes

#### 5 June 2024

- 03:0203:02, 5 June 2024
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**+34,076** N 组合数学 (Fall 2024)/Matching theory Created page with "== Systems of Distinct Representatives (SDR)== A '''system of distinct representatives (SDR)''' (also called a '''transversal''') for a sequence of (not necessarily distinct) sets <math>S_1,S_2,\ldots,S_m</math> is a sequence of <font color=red>''distinct''</font> elements <math>x_1,x_2,\ldots,x_m</math> such that <math>x_i\in S_i</math> for all <math>i=1,2,\ldots,m</math>. === Hall's marriage theorem === If the sets <math>S_1,S_2,\ldots,S_m</math> have a system of dist..." current - 03:0203:02, 5 June 2024 diff hist +75 组合数学 (Spring 2024) →Lecture Notes