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2 November 2022
- 04:2404:24, 2 November 2022 diff hist +506 高级算法 (Fall 2022) →Lecture Notes
1 November 2022
- 10:2310:23, 1 November 2022 diff hist +198 General Circulation(Fall 2022) →Announcement
- 10:1010:10, 1 November 2022 diff hist +1,093 N Assignment 3, Fall 2022 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^3 \phi - \dfrac{1}{4})+\Delta_v..." current
- 10:0910:09, 1 November 2022 diff hist −11 General Circulation(Fall 2022) →Assignments
- 10:0810:08, 1 November 2022 diff hist +59 General Circulation(Fall 2022) →Assignments
- 10:0710:07, 1 November 2022 diff hist +59 General Circulation(Fall 2022) →Assignments
31 October 2022
- 07:4607:46, 31 October 2022 diff hist +183 高级算法 (Fall 2022) →Lecture Notes
27 October 2022
- 04:5504:55, 27 October 2022 diff hist +22 Namelist Assignment 1 2022 No edit summary current
- 02:4002:40, 27 October 2022 diff hist +33 Namelist Assignment 1 2022 No edit summary
- 02:3902:39, 27 October 2022 diff hist +789 N Namelist Assignment 1 2022 Created page with "姓名 学号 周榆杰 191870288 罗健峰 191830098 欧阳玥芸 191830111 孙森灿 191830136 代欣怡 652022280002 丁宇轩 502022280004 窦吉斌 502022280006 付凯杰 502022280009 何世诚 502022280011 胡书挥 502022280012 李晨曦 652022280005 李惠林 502022280016 李颜昀 502022280018 李颖 502022280019 林齐颢 502022280021 刘洪江 502022280024 刘芷含 502022280026 闵隽玉 502022280028 倪乘岚 502022280030 孙楚 5020..."
- 02:3102:31, 27 October 2022 diff hist +56 General Circulation(Fall 2022) →Assignments
24 October 2022
- 09:3209:32, 24 October 2022 diff hist +16,764 N 高级算法 (Fall 2022)/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
- 09:3209:32, 24 October 2022 diff hist 0 高级算法 (Fall 2022) →Lecture Notes
- 09:3209:32, 24 October 2022 diff hist +523 高级算法 (Fall 2022) →Lecture Notes
20 October 2022
13 October 2022
- 12:4012:40, 13 October 2022 diff hist +7 General Circulation(Fall 2022) →Course Slides
- 05:2505:25, 13 October 2022 diff hist +270 General Circulation(Fall 2022) →Course Slides
11 October 2022
- 12:5312:53, 11 October 2022 diff hist +10,715 N 高级算法 (Fall 2022)/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
- 12:5312:53, 11 October 2022 diff hist +41,013 N 高级算法 (Fall 2022)/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
- 12:5212:52, 11 October 2022 diff hist +415 高级算法 (Fall 2022) →Lecture Notes
- 05:5405:54, 11 October 2022 diff hist −216 高级算法 (Fall 2021) →Assignments current
- 05:5305:53, 11 October 2022 diff hist −66 高级算法 (Fall 2021) →Assignments
10 October 2022
- 07:4707:47, 10 October 2022 diff hist +2 高级算法 (Fall 2022) →Assignments
- 07:4707:47, 10 October 2022 diff hist +97 高级算法 (Fall 2022) →Assignments
- 07:4607:46, 10 October 2022 diff hist +2 高级算法 (Fall 2022)/Problem Set 1 →Problem 4 current
6 October 2022
5 October 2022
- 02:5502:55, 5 October 2022 diff hist +1 General Circulation(Fall 2022) →Assignments
- 02:5502:55, 5 October 2022 diff hist +16 General Circulation(Fall 2022) →Assignments
- 02:5202:52, 5 October 2022 diff hist +2 Assignment 2, Fall 2022 →Question 2 current
- 02:5102:51, 5 October 2022 diff hist 0 Assignment 2, Fall 2022 No edit summary
- 02:5102:51, 5 October 2022 diff hist +2,704 N Assignment 2, Fall 2022 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>\begin{align} Q&=Q_o \cdot s(x), \\ s(x)&=s_o \cdot P_o(x)+ s_2 \cdot P_2(x), \end{align}</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>, <..."
- 02:4902:49, 5 October 2022 diff hist +66 General Circulation(Fall 2022) →Assignments
- 02:4702:47, 5 October 2022 diff hist −99 Main Page No edit summary
4 October 2022
- 13:5913:59, 4 October 2022 diff hist +1 高级算法 (Fall 2022) →Lecture Notes
- 13:5813:58, 4 October 2022 diff hist +185 高级算法 (Fall 2022) →Lecture Notes
- 13:5813:58, 4 October 2022 diff hist +59 高级算法 (Fall 2022) →Lecture Notes
3 October 2022
- 15:5615:56, 3 October 2022 diff hist −1 高级算法 (Fall 2022) →Lecture Notes
- 15:5515:55, 3 October 2022 diff hist −5 高级算法 (Fall 2022) →Lecture Notes
- 15:5415:54, 3 October 2022 diff hist +217 高级算法 (Fall 2022) →Lecture Notes
- 15:5115:51, 3 October 2022 diff hist +97 高级算法 (Fall 2022) →Lecture Notes
- 15:4915:49, 3 October 2022 diff hist +5,755 N 高级算法 (Fall 2022)/Basic tail 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
- 15:4815:48, 3 October 2022 diff hist +25,717 N 高级算法 (Fall 2022)/Hashing and Sketching Created page with "=Distinct Elements= Consider the following problem of '''counting distinct elements''': Suppose that <math>\Omega</math> is a sufficiently large universe. *'''Input:''' a sequence of (not necessarily distinct) elements <math>x_1,x_2,\ldots,x_n\in\Omega</math>; *'''Output:''' an estimation of the total number of distinct elements <math>z=|\{x_1,x_2,\ldots,x_n\}|</math>. A straightforward way of solving this problem is to maintain a dictionary data structure, which costs..." current
- 15:4715:47, 3 October 2022 diff hist +1 高级算法 (Fall 2022)/Limited independence →2-universal hash families current
- 15:4515:45, 3 October 2022 diff hist +8,181 高级算法 (Fall 2022)/Balls into bins No edit summary current
- 15:4515:45, 3 October 2022 diff hist +1 高级算法 (Fall 2022)/Balls into bins →2-universal hash families
- 15:3915:39, 3 October 2022 diff hist +13,598 高级算法 (Fall 2022)/Balls into bins No edit summary
- 15:3815:38, 3 October 2022 diff hist +5,762 高级算法 (Fall 2022)/Balls into bins →Coupon Collector
- 15:3615:36, 3 October 2022 diff hist +157 高级算法 (Fall 2022) →Lecture Notes
30 September 2022
29 September 2022
- 04:1504:15, 29 September 2022 diff hist +9 Assignment 1, Fall 2022 →下载区 current
- 02:5602:56, 29 September 2022 diff hist +21 General Circulation(Fall 2022) No edit summary
28 September 2022
- 13:3913:39, 28 September 2022 diff hist +7 General Circulation(Fall 2022) →Course Slides
- 13:3813:38, 28 September 2022 diff hist +71 General Circulation(Fall 2022) →Course Slides
- 13:3713:37, 28 September 2022 diff hist +21 General Circulation(Fall 2022) →Course Slides
26 September 2022
- 08:5408:54, 26 September 2022 diff hist +175 General Circulation(Fall 2022) →Assignments
- 08:5308:53, 26 September 2022 diff hist 0 General Circulation(Fall 2022) →Assignments
- 08:3308:33, 26 September 2022 diff hist +407 General Circulation(Fall 2022) →Course Slides
- 08:2808:28, 26 September 2022 diff hist +3 Assignment 1, Fall 2022 →Bonus Question
- 08:2808:28, 26 September 2022 diff hist +228 Assignment 1, Fall 2022 No edit summary
- 08:1308:13, 26 September 2022 diff hist +6 Assignment 1, Fall 2022 →On the netcdf file
- 08:0908:09, 26 September 2022 diff hist −17 Assignment 1, Fall 2022 →下载区
- 08:0808:08, 26 September 2022 diff hist +2,560 N Assignment 1, Fall 2022 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..."
- 08:0708:07, 26 September 2022 diff hist −24 General Circulation(Fall 2021) No edit summary current
- 08:0508:05, 26 September 2022 diff hist +5,196 General Circulation(Fall 2022) No edit summary
- 08:0408:04, 26 September 2022 diff hist +1,062 General Circulation(Fall 2022) No edit summary
- 08:0308:03, 26 September 2022 diff hist +2,249 N General Circulation(Fall 2022) 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..."
- 08:0208:02, 26 September 2022 diff hist +99 Main Page No edit summary Tag: Visual edit: Switched
21 September 2022
- 11:4811:48, 21 September 2022 diff hist +15,811 N 高级算法 (Fall 2022)/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..."
- 11:4811:48, 21 September 2022 diff hist +75 高级算法 (Fall 2022) →Lecture Notes
- 11:4711:47, 21 September 2022 diff hist +11,376 N 高级算法 (Fall 2022)/Balls into bins 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..."
- 11:4711:47, 21 September 2022 diff hist +61 高级算法 (Fall 2022) →Lecture Notes
- 11:4611:46, 21 September 2022 diff hist 0 高级算法 (Fall 2022) →Lecture Notes
- 11:4611:46, 21 September 2022 diff hist −122 高级算法 (Fall 2022) →Lecture Notes
- 11:4611:46, 21 September 2022 diff hist +371 高级算法 (Fall 2022) →Lecture Notes
18 September 2022
- 12:2312:23, 18 September 2022 diff hist +14 高级算法 (Fall 2022) No edit summary
- 12:2212:22, 18 September 2022 diff hist 0 高级算法 (Fall 2022) →Course info
14 September 2022
- 05:2005:20, 14 September 2022 diff hist +2 高级算法 (Fall 2022) →Lecture Notes
- 05:2005:20, 14 September 2022 diff hist +123 高级算法 (Fall 2022) →Lecture Notes
- 05:1905:19, 14 September 2022 diff hist +66 高级算法 (Fall 2022) →Lecture Notes
- 05:1805:18, 14 September 2022 diff hist +61 高级算法 (Fall 2022) →Lecture Notes
13 September 2022
- 08:0708:07, 13 September 2022 diff hist −71 高级算法 (Fall 2022) →Lecture Notes
- 05:4305:43, 13 September 2022 diff hist +6,210 N 高级算法 (Fall 2022)/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
- 05:4305:43, 13 September 2022 diff hist +30,540 N 高级算法 (Fall 2022)/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..." current
- 05:4205:42, 13 September 2022 diff hist +73 高级算法 (Fall 2022) →Lecture Notes
- 05:4205:42, 13 September 2022 diff hist +134 高级算法 (Fall 2022) →Lecture Notes
6 September 2022
- 09:1109:11, 6 September 2022 diff hist 0 高级算法 (Fall 2022) →Lecture Notes
- 09:0909:09, 6 September 2022 diff hist +184 高级算法 (Fall 2022) →Lecture Notes
5 September 2022
- 07:3107:31, 5 September 2022 diff hist +17,328 N 高级算法 (Fall 2022)/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
- 07:3107:31, 5 September 2022 diff hist +71 高级算法 (Fall 2022) →Lecture Notes
- 07:3107:31, 5 September 2022 diff hist +44,285 N 高级算法 (Fall 2022)/Min-Cut and Max-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..." current
- 07:3007:30, 5 September 2022 diff hist +126 高级算法 (Fall 2022) →Lecture Notes
1 September 2022
- 05:0605:06, 1 September 2022 diff hist 0 Main Page No edit summary
30 August 2022
- 15:5815:58, 30 August 2022 diff hist −1 Main Page →Home Pages for Courses and Seminars
- 15:5815:58, 30 August 2022 diff hist +40 Main Page →Home Pages for Courses and Seminars
- 15:5815:58, 30 August 2022 diff hist −32 Main Page →Home Pages for Courses and Seminars
- 15:5715:57, 30 August 2022 diff hist +42 Main Page →Home Pages for Courses and Seminars
- 15:5615:56, 30 August 2022 diff hist −1 Main Page →Home Pages for Courses and Seminars
- 15:5615:56, 30 August 2022 diff hist −25 Main Page →Home Pages for Courses and Seminars
- 15:5615:56, 30 August 2022 diff hist 0 Main Page →Home Pages for Courses and Seminars
- 15:5515:55, 30 August 2022 diff hist −44 Main Page →Home Pages for Courses and Seminars