User contributions for Etone

Results for Etone talk block log uploads logs
A user with 1,243 edits. Account created on 30 August 2022.
Jump to navigation Jump to search
Search for contributionsExpandCollapse
⧼contribs-top⧽
⧼contribs-date⧽
(newest | oldest) View ( | ) (20 | 50 | 100 | 250 | 500)

22 September 2025

  • 14:3114:31, 22 September 2025 diff hist +2,971 N Assignment 1, Fall 2025 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..." current
  • 14:3114:31, 22 September 2025 diff hist +265 General Circulation(Fall 2025) →Assignments
  • 02:5002:50, 22 September 2025 diff hist +10,715 N 高级算法 (Fall 2025)/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
  • 02:4902:49, 22 September 2025 diff hist +41,013 N 高级算法 (Fall 2025)/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
  • 02:4902:49, 22 September 2025 diff hist +229 高级算法 (Fall 2025) →Lecture Notes

10 September 2025

9 September 2025

  • 05:0505:05, 9 September 2025 diff hist +5,755 N 高级算法 (Fall 2025)/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
  • 05:0405:04, 9 September 2025 diff hist +15,812 N 高级算法 (Fall 2025)/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
  • 05:0405:04, 9 September 2025 diff hist +49,292 N 高级算法 (Fall 2025)/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..." current
  • 05:0305:03, 9 September 2025 diff hist +304 高级算法 (Fall 2025) →Lecture Notes

7 September 2025

26 August 2025

  • 09:0809:08, 26 August 2025 diff hist +17,328 N 高级算法 (Fall 2025)/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
  • 09:0809:08, 26 August 2025 diff hist +49,923 N 高级算法 (Fall 2025)/Min Cut, Max Cut, and Spectral Cut Created page with "= Graph Cut = Let <math>G(V, E)</math> be an undirected graph. 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 defined by a bipartition <math>\{S,T\}</math> of <math>V</math> as :<math>C=E(S,T)\,</math>, where <math>E(S,T)</math> denotes the set of "crossing edges" with one endpoint in each of <math>S</math> and..." current
  • 09:0709:07, 26 August 2025 diff hist +227 高级算法 (Fall 2025) →Lecture Notes

25 August 2025

23 August 2025

6 June 2025

  • 02:3102:31, 6 June 2025 diff hist +34,076 N 组合数学 (Fall 2025)/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
  • 02:3002:30, 6 June 2025 diff hist +141 组合数学 (Spring 2025) →Lecture Notes

25 May 2025

21 April 2025

15 April 2025

13 April 2025

9 April 2025

1 April 2025

  • 10:3310:33, 1 April 2025 diff hist +5,139 N 概率论与数理统计 (Spring 2025)/Weierstrass Approximation Theorem Created page with "[https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem '''魏尔施特拉斯逼近定理''']（'''Weierstrass approximation theorem'''）陈述了这样一个事实：闭区间上的连续函数总可以用多项式一致逼近。 {{Theorem|魏尔施特拉斯逼近定理| :设 <math>f:[a,b]\to\mathbb{R}</math> 为定义在实数区间 <math>[a,b]</math> 上的连续实值函数。对每个 <math>\epsilon>0</math>，存在一个多项式 <math>p</math> 使得对..." current
  • 10:3310:33, 1 April 2025 diff hist +7,005 N 概率论与数理统计 (Spring 2025)/Threshold of k-clique in random graph Created page with "在 Erdős-Rényi 随机图模型 <math>G(n,p)</math> 中，一个随机无向图 <math>G</math> 以如下的方式生成：图 <math>G</math> 包含 <math>n</math> 个顶点，每一对顶点之间都独立同地以概率 <math>p</math> 连一条无向边。如此生成的随机图记为 <math>G\sim G(n,p)</math>。 固定整数 <math>k\ge 3</math>，考虑随机图 <math>G\sim G(n,p)</math> 包含 <math>K_k</math>（<math>k</math>-团，<math>k</math>-clique）子图..." current
  • 10:3210:32, 1 April 2025 diff hist +8,968 N 概率论与数理统计 (Spring 2025)/Two-point sampling Created page with "= 利用线性同余方程构造两两独立的随机变量 = 令<math>p</math>为一质数。考虑模<math>p</math>余数构成的集合<math>[p]=\{0,1,\ldots,p-1\}=\mathbb{Z}_p</math>。众所周知，当<math>p</math>为质数时，<math>\mathbb{Z}_p</math>为对模<math>p</math>加法和乘法运算闭合的'''有限域'''。 我们现在构造一系列值域为<math>[p]</math>的'''两两独立'''（'''pairwise Independent'''）且'''均匀分布'''（'''uniforml..." current
  • 10:3210:32, 1 April 2025 diff hist +325 概率论与数理统计 (Spring 2025) →Lectures

26 March 2025

(newest | oldest) View ( | ) (20 | 50 | 100 | 250 | 500)
Retrieved from "https://tcs.nju.edu.cn/wiki/index.php?title=Special:Contributions/Etone"