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• 06:44, 14 November 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023)/第一次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 522023330115 || 杨闰凯 |- | 502023370027 || 梁天润 |- | 522023330065 || 马润泽 |- | 502023370019 || 江楠 |- | 201870048 || 张乃仁 |- | 652023330001 || 陈阳 |- | 201502007 || 高嘉成 |- | 652023330030 || 郑欣 |- | 201840058 || 蒋潇鹏 |- | 201250101 || 王锦朋 |- | 201220126 || 郑翰 |- | 201502002 || 洪睿琦 |- | 522023330100 || 吴浩杨 |-...")
• 05:51, 14 November 2023 Liuexp talk contribs created page File:L10 electrical networks.pdf
• 05:51, 14 November 2023 Liuexp talk contribs uploaded File:L10 electrical networks.pdf
• 05:58, 7 November 2023 Liuexp talk contribs uploaded a new version of File:L8 spectral-graph-theory.pdf
• 05:57, 7 November 2023 Liuexp talk contribs created page File:AA2023 L9 random walk.pdf
• 05:57, 7 November 2023 Liuexp talk contribs uploaded File:AA2023 L9 random walk.pdf
• 06:12, 6 November 2023 Etone talk contribs created page Assignment 3, Fall 2023 (Created page with "Held-Hou(1980) 讨论了当外部强迫的经向分布呈二次勒让德多项式，即<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\dfrac{2}{3}\Delta_H P_2(\sin \phi)+\Delta_v(\dfrac{z}{H}-\dfrac{1}{2})</math>的情况下，哈德莱环流内的风场、温度场、环流的空间范围等将怎样随纬度和外力强迫的强度而变化。如果将外力强迫的空间分布改为<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\Delta_H(\sin \phi -\frac{1}{2})+\Delta_v(\dfra...")
• 06:05, 6 November 2023 Etone talk contribs created page Namelist Assignment 2 2023 (Created page with "姓名 学号 魏斯诚 201830012 潘云逸 201830049 李宜卓 201830062 王若骥 201830143 吴佳根 201830196 王奕 201840022 张顺伟 201840065 范禹韬 201840173 谭金林 201840222 张宁萌 201840254 武越 201840285 谢卫宏 201850142 艾真珍 502023280001 曹珩 502023280003 岑琦胜 502023280004 陈石 502023280006 成柯蒙 502023280007 丁思聪 502023280010 樊浩然 502023280011 费照轩 502023...")
• 11:35, 31 October 2023 Liuexp talk contribs deleted page File:L8 spectral-graph-theory.pdf (Deleted old revision 20231031113444!L8_spectral-graph-theory.pdf: Duplicated file)
• 11:35, 31 October 2023 Liuexp talk contribs deleted page File:L8 spectral-graph-theory.pdf (Deleted old revision 20231031113146!L8_spectral-graph-theory.pdf: Duplicated file)
• 11:34, 31 October 2023 Liuexp talk contribs uploaded a new version of File:L8 spectral-graph-theory.pdf
• 11:31, 31 October 2023 Liuexp talk contribs uploaded a new version of File:L8 spectral-graph-theory.pdf
• 06:55, 31 October 2023 Liuexp talk contribs created page File:L8 spectral-graph-theory.pdf
• 06:55, 31 October 2023 Liuexp talk contribs uploaded File:L8 spectral-graph-theory.pdf
• 03:41, 27 October 2023 Liuexp talk contribs deleted page Talk:Main Page (Spam)
• 03:37, 27 October 2023 Liuexp talk contribs deleted page Talk:Combinatorics (Fall 2010)/Optimization (Spam: hacked content)
• 03:37, 27 October 2023 Liuexp talk contribs deleted page Talk:Combinatorics (Fall 2010)/Graph spectrum, expanders (Spam: hacked content)
• 03:35, 27 October 2023 Liuexp talk contribs deleted page Talk:Combinatorics (Fall 2010)/Duality, Matroid (Spam: hacked content)
• 03:18, 27 October 2023 Liuexp talk contribs deleted page Template talk:Infobox (Spam: hacked content)
• 03:10, 27 October 2023 Liuexp talk contribs deleted page Talk:Randomized Algorithms (Spring 2010)/Balls and bins (Spam: hacked content)
• 03:06, 27 October 2023 Liuexp talk contribs deleted page MediaWiki talk:Common.css (Spam: hacked content)
• 03:02, 27 October 2023 Liuexp talk contribs deleted page Talk:Combinatorics (Fall 2010)/Problem set 2 (Spam: hacked content)
• 03:00, 27 October 2023 Liuexp talk contribs deleted page Talk:Randomized Algorithms (Spring 2010)/Problem Set 1 (Spam: hacekd content)
• 12:34, 24 October 2023 Etone talk contribs created page Namelist Assignment 1 2023 (Created page with "姓名 学号 魏斯诚 201830012 潘云逸 201830049 李宜卓 201830062 王若骥 201830143 吴佳根 201830196 王奕 201840022 张顺伟 201840065 范禹韬 201840173 谭金林 201840222 张宁萌 201840254 武越 201840285 谢卫宏 201850142 樊浩然 501023280011 温康 501023280041 艾真珍 502023280001 曹珩 502023280003 岑琦胜 502023280004 陈石 502023280006 成柯蒙 502023280007 丁思聪 502023280010...")
• 05:21, 23 October 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023)/Problem Set 1 (Created page with "*作业目前正在更新中，不是最终版 *每道题目的解答都要有完整的解题过程，中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。")
• 07:51, 21 October 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 07:38, 15 October 2023 Etone talk contribs created page 高级算法 (Fall 2023)/Hashing and Sketching (Created page with "=Balls into Bins= 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: the probability that every bin contains at most one...")
• 05:58, 11 October 2023 Etone talk contribs created page Assignment 2, Fall 2023 (Created page with "<font color="red" size="2">请在题目一和题目二中任选一题作为本章的作业题目。另外的一题可作为选做题。</font> ==Question 1== 假设在大气层顶（TOA），在多年全年平均的情况下，入射的太阳辐射随纬度的分布满足 <math>Q=Q_o \cdot s(x)</math>, <math>s(x)=s_o \cdot P_o(x)+ s_2 \cdot P_2(x)</math>， 其中，<math>P_o(x)=1</math>, <math>P_2(x)=\frac{1}{2}(3x^2-1)</math>, <math>s_o=1</math>, <math>s_2=-0.473</ma...")
• 10:53, 10 October 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 10:53, 10 October 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 10:52, 4 October 2023 Etone talk contribs created page Assignment 1, Fall 2023 (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...")
• 16:39, 26 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 16:38, 26 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 10:58, 19 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 10:57, 19 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/Fingerprinting (Created page with "=Polynomial Identity Testing (PIT) = The '''Polynomial Identity Testing (PIT)''' is such a problem: given as input two polynomials, determine whether they are identical. It plays a fundamental role in ''Identity Testing'' problems. First, let's consider the univariate ("one variable") case: * '''Input:''' two polynomials <math>f, g\in\mathbb{F}[x]</math> of degree <math>d</math>. * Determine whether <math>f\equiv g</math> (<math>f</math> and <math>g</math> are identica...")
• 06:37, 14 September 2023 Hychen talk contribs created page File:Probability and Computing. 2nd Edition cover.jpg
• 06:37, 14 September 2023 Hychen talk contribs uploaded File:Probability and Computing. 2nd Edition cover.jpg
• 01:25, 14 September 2023 Etone talk contribs created page General Circulation(Fall 2023) (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...")
• 10:36, 12 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 10:34, 12 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/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...")
• 10:33, 12 September 2023 Etone talk contribs created page 高级算法 (Fall 2023)/Min Cut, Min 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...")
• 13:34, 10 September 2023 Zouzongrui talk contribs uploaded a new version of File:Eigenvalues and Polynomials.png
• 13:33, 10 September 2023 Zouzongrui talk contribs uploaded a new version of File:Eigenvalues and Polynomials.png
• 13:31, 10 September 2023 Zouzongrui talk contribs created page File:Eigenvalues and Polynomials.png
• 13:31, 10 September 2023 Zouzongrui talk contribs uploaded File:Eigenvalues and Polynomials.png
• 13:27, 10 September 2023 Zouzongrui talk contribs created page File:Lx=b.jpg
• 13:27, 10 September 2023 Zouzongrui talk contribs uploaded File:Lx=b.jpg
• 13:17, 10 September 2023 Zouzongrui talk contribs created page File:Combinatorial Optimization.webp
• 13:17, 10 September 2023 Zouzongrui talk contribs uploaded File:Combinatorial Optimization.webp
• 11:44, 10 September 2023 Etone talk contribs created page 高级算法 (Fall 2023) / 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...")