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21 October 2023
- 07:5107:51, 21 October 2023 diff hist +338 高级算法 (Fall 2023) →Lecture Notes
20 October 2023
- 00:5700:57, 20 October 2023 diff hist +16 General Circulation(Fall 2023) →Assignments Tag: Visual edit
15 October 2023
- 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..."
11 October 2023
- 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 October 2023
- 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
7 October 2023
4 October 2023
- 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
26 September 2023
- 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
19 September 2023
- 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