User contributions for Etone

05:5905:59, 6 November 2023 diff hist +55‎ General Circulation(Fall 2023) ‎ →‎Assignments

10:0110:01, 31 October 2023 diff hist 0‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes
10:0110:01, 31 October 2023 diff hist +10‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

14:2814:28, 29 October 2023 diff hist +55‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

12:3412:34, 24 October 2023 diff hist +1,130‎ N 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..." current
12:3012:30, 24 October 2023 diff hist +55‎ General Circulation(Fall 2023) ‎ →‎Assignments
03:2203:22, 24 October 2023 diff hist −57‎ 高级算法 (Fall 2023)/Problem Set 1 ‎No edit summary

07:5407:54, 21 October 2023 diff hist +5‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes
07:5207:52, 21 October 2023 diff hist +267‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes
07:5107:51, 21 October 2023 diff hist +16,764‎ N 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..." current
07:5107:51, 21 October 2023 diff hist +338‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

00:5700:57, 20 October 2023 diff hist +16‎ General Circulation(Fall 2023) ‎ →‎Assignments Tag: Visual edit

08:1508:15, 15 October 2023 diff hist +5‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Apply the mean trick to the \min-sketch current
08:1408:14, 15 October 2023 diff hist 0‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Apply the mean trick to the \min-sketch
08:1408:14, 15 October 2023 diff hist +9‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Apply the mean trick to the \min-sketch
08:1308:13, 15 October 2023 diff hist +32‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Apply the mean trick to the \min-sketch
08:1208:12, 15 October 2023 diff hist −28‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Apply the mean trick to the \min-sketch
08:1108:11, 15 October 2023 diff hist −103‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Distinct Elements
08:1008:10, 15 October 2023 diff hist −1,086‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Uniform Hash Assumption (UHA)
08:1008:10, 15 October 2023 diff hist +15‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Flajolet-Martin algorithm
08:0808:08, 15 October 2023 diff hist +14‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎The Min-Sketch
08:0708:07, 15 October 2023 diff hist −9‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎An estimator by hashing
08:0508:05, 15 October 2023 diff hist −113‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎No edit summary
08:0008:00, 15 October 2023 diff hist −43‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Set Membership
07:5807:58, 15 October 2023 diff hist +4,712‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Perfect Hashing
07:5107:51, 15 October 2023 diff hist −5,607‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Set Membership
07:5007:50, 15 October 2023 diff hist −393‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Collision number
07:4907:49, 15 October 2023 diff hist −7‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Birthday problem fro pairwise independent hashing
07:4807:48, 15 October 2023 diff hist +34‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Collision number
07:4707:47, 15 October 2023 diff hist +5‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Universal Hashing
07:4607:46, 15 October 2023 diff hist −20‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Birthday Problem and Hash Collision
07:4607:46, 15 October 2023 diff hist +41‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Birthday Problem
07:4407:44, 15 October 2023 diff hist −3,931‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Occupancy Problem
07:4407:44, 15 October 2023 diff hist −9,003‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎ →‎Coupon Collector
07:4407:44, 15 October 2023 diff hist +77‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎No edit summary
07:3907:39, 15 October 2023 diff hist +25,719‎ 高级算法 (Fall 2023)/Hashing and Sketching ‎No edit summary
07:3807:38, 15 October 2023 diff hist +38,918‎ N 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..."

05:5805:58, 11 October 2023 diff hist +2,522‎ N 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..." current
05:5405:54, 11 October 2023 diff hist +66‎ General Circulation(Fall 2023) ‎ →‎Assignments

10:5310:53, 10 October 2023 diff hist +41,013‎ N 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..." current
10:5310:53, 10 October 2023 diff hist +10,715‎ N 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..." current
10:5110:51, 10 October 2023 diff hist +229‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

13:1213:12, 7 October 2023 diff hist +176‎ General Circulation(Fall 2023) ‎ →‎Assignments

11:2511:25, 4 October 2023 diff hist −5‎ General Circulation(Fall 2023) ‎ →‎Course Slides
11:2411:24, 4 October 2023 diff hist +342‎ General Circulation(Fall 2023) ‎ →‎Course Slides
11:1911:19, 4 October 2023 diff hist +17‎ General Circulation(Fall 2023) ‎ →‎Assignments
11:0211:02, 4 October 2023 diff hist 0‎ Assignment 1, Fall 2023 ‎ →‎On the netcdf file current
11:0111:01, 4 October 2023 diff hist 0‎ Assignment 1, Fall 2019 ‎ →‎On the netcdf file current
11:0011:00, 4 October 2023 diff hist −1‎ Assignment 1, Fall 2023 ‎ →‎On the netcdf file
10:5210:52, 4 October 2023 diff hist +2,789‎ N 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..."
10:5110:51, 4 October 2023 diff hist +74‎ General Circulation(Fall 2023) ‎No edit summary

16:3916:39, 26 September 2023 diff hist +5,755‎ N 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..." current
16:3916:39, 26 September 2023 diff hist +10‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes
16:3816:38, 26 September 2023 diff hist +15,812‎ N 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..." current
16:3716:37, 26 September 2023 diff hist +294‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

12:2112:21, 19 September 2023 diff hist +56‎ 高级算法 (Fall 2023)/Fingerprinting ‎ →‎Schwartz-Zippel Theorem current
12:2012:20, 19 September 2023 diff hist −18‎ 高级算法 (Fall 2023)/Fingerprinting ‎ →‎Communication protocols for Equality by fingerprinting
12:1912:19, 19 September 2023 diff hist −11‎ 高级算法 (Fall 2023)/Fingerprinting ‎ →‎Randomized pattern matching
12:1912:19, 19 September 2023 diff hist −26‎ 高级算法 (Fall 2023)/Fingerprinting ‎ →‎Checking distinctness
12:1912:19, 19 September 2023 diff hist −3‎ 高级算法 (Fall 2023)/Fingerprinting ‎ →‎Checking distinctness
11:0511:05, 19 September 2023 diff hist +2,354‎ 高级算法 (Fall 2023)/Fingerprinting ‎ →‎Fingerprinting
11:0211:02, 19 September 2023 diff hist +5,391‎ 高级算法 (Fall 2023)/Fingerprinting ‎No edit summary
10:5810:58, 19 September 2023 diff hist +6,210‎ N 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..." current
10:5710:57, 19 September 2023 diff hist +30,540‎ N 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..."
10:5710:57, 19 September 2023 diff hist +203‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

08:5308:53, 14 September 2023 diff hist −2‎ 高级算法 (Fall 2023)/Min Cut, Max Cut, and Spectral Cut ‎ →‎Spectrum of Regular Graphs current
08:5208:52, 14 September 2023 diff hist +1‎ 高级算法 (Fall 2023)/Min Cut, Max Cut, and Spectral Cut ‎ →‎Spectrum of Regular Graphs
08:5208:52, 14 September 2023 diff hist +1‎ 高级算法 (Fall 2023)/Min Cut, Max Cut, and Spectral Cut ‎ →‎Spectrum of Regular Graphs
01:3001:30, 14 September 2023 diff hist −33‎ General Circulation(Fall 2023) ‎ →‎Course info
01:2901:29, 14 September 2023 diff hist 0‎ General Circulation(Fall 2023) ‎ →‎Course info
01:2901:29, 14 September 2023 diff hist +1‎ General Circulation(Fall 2023) ‎ →‎Course info
01:2901:29, 14 September 2023 diff hist −95‎ General Circulation(Fall 2023) ‎ →‎Announcement
01:2501:25, 14 September 2023 diff hist +8,324‎ N 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..."
01:1901:19, 14 September 2023 diff hist 0‎ Main Page ‎ →‎Home Pages for Courses and Seminars
01:1801:18, 14 September 2023 diff hist −34‎ General Circulation(Fall 2022) ‎ →‎Assignments current

10:3610:36, 12 September 2023 diff hist +44,308‎ N 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..."
10:3510:35, 12 September 2023 diff hist 0‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes
10:3410:34, 12 September 2023 diff hist +17,328‎ N 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..." current
10:3410:34, 12 September 2023 diff hist +23‎ 高级算法 (Fall 2023)/Min Cut, Min Cut, and Spectral Cut ‎No edit summary current
10:3310:33, 12 September 2023 diff hist +44,285‎ N 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..."
10:3310:33, 12 September 2023 diff hist +30‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes
10:3210:32, 12 September 2023 diff hist +193‎ 高级算法 (Fall 2023) ‎ →‎Lecture Notes

13:3913:39, 10 September 2023 diff hist 0‎ 高级算法 (Fall 2023) / Course materials ‎ →‎References and further readings
11:4411:44, 10 September 2023 diff hist +1,429‎ N 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..."
11:4311:43, 10 September 2023 diff hist 0‎ 高级算法 (Fall 2023) ‎ →‎Course materials

08:4208:42, 4 September 2023 diff hist +45‎ Main Page ‎ →‎Home Pages for Courses and Seminars
04:1604:16, 4 September 2023 diff hist +31‎ Main Page ‎ →‎Home Pages for Courses and Seminars
04:1504:15, 4 September 2023 diff hist −36‎ Main Page ‎ →‎Home Pages for Courses and Seminars

15:0515:05, 15 June 2023 diff hist +225‎ 组合数学 (Spring 2023) ‎ →‎Assignments

12:5012:50, 14 June 2023 diff hist +84‎ 概率论与数理统计 (Spring 2023) ‎ →‎Assignments

05:5005:50, 13 June 2023 diff hist 0‎ 组合数学 (Fall 2023)/Matching theory ‎ →‎König-Egerváry theorem current
05:4705:47, 13 June 2023 diff hist +253‎ 组合数学 (Spring 2023) ‎ →‎Concepts
05:4105:41, 13 June 2023 diff hist +109‎ 概率论与数理统计 (Spring 2023) ‎ →‎Announcement

08:0708:07, 5 June 2023 diff hist +185‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎一维随机游走 (1D random walk) current
08:0508:05, 5 June 2023 diff hist +31‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎一维随机游走 (1D random walk)
07:4807:48, 5 June 2023 diff hist −35‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎投票问题 (Ballot problem)
07:4707:47, 5 June 2023 diff hist +31‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎可选停时定理 (OST)
07:4407:44, 5 June 2023 diff hist −62‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎一维随机游走 (1D random walk)
07:4307:43, 5 June 2023 diff hist −35‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎可选停时定理 (OST)
07:4207:42, 5 June 2023 diff hist 0‎ 概率论与数理统计 (Spring 2023)/OST and applications ‎ →‎可选停时定理 (OST)

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