User contributions for Etone

02:3102:31, 20 March 2024 diff hist 0‎ Assignment 1, Spring 2024 ‎ →‎Files to download
02:3002:30, 20 March 2024 diff hist +345‎ Assignment 1, Spring 2024 ‎No edit summary
02:2602:26, 20 March 2024 diff hist −1‎ Assignment 1, Spring 2024 ‎ →‎Question #1
02:2602:26, 20 March 2024 diff hist +2‎ Assignment 1, Spring 2024 ‎ →‎Question #1
02:2602:26, 20 March 2024 diff hist +322‎ Assignment 1, Spring 2024 ‎ →‎Question #1
02:2102:21, 20 March 2024 diff hist +2,619‎ N Assignment 1, Spring 2024 ‎ 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..."
01:3901:39, 20 March 2024 diff hist +2‎ General Circulation(Spring 2024) ‎ →‎Assignments current
01:3701:37, 20 March 2024 diff hist +2‎ General Circulation(Spring 2024) ‎No edit summary

15:5115:51, 18 March 2024 diff hist +15,498‎ N 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm ‎ Created page with "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 :<math>C=E(S,T..."

02:5602:56, 12 March 2024 diff hist +24,945‎ N Quantum ‎ Created page with "= 量子算法与物理实现研讨会= ==时间地点 == *''' 2019年10月19、20日: 9 am--5 pm.''' * 南京大学计算机科学与技术系（南京大学仙林校区常州楼）111报告厅 [http://map.baidu.com/?l=&s=s%26wd%3D南京仙林大道163号++南京大学（仙林校区）计算机系楼在线地图] ==联系人与联系方式 == * 姚鹏晖 pyao@nju.edu.cn * 张利剑 lijian.zhang@nju.edu.cn ==会议主旨..." current

11:4211:42, 6 March 2024 diff hist +1‎ 组合数学 (Spring 2024) ‎ →‎Lecture Notes
11:4111:41, 6 March 2024 diff hist +25,549‎ N 组合数学 (Fall 2024)/Generating functions ‎ Created page with "== Generating Functions == In Stanley's magnificent book ''Enumerative Combinatorics'', he comments the generating function as "the most useful but most difficult to understand method (for counting)". The solution to a counting problem is usually represented as some <math>a_n</math> depending a parameter <math>n</math>. Sometimes this <math>a_n</math> is called a ''counting function'' as it is a function of the parameter <math>n</math>. <math>a_n</math> can also be tre..." current
11:4111:41, 6 March 2024 diff hist +229‎ 组合数学 (Spring 2024) ‎ →‎Lecture Notes

10:5210:52, 27 February 2024 diff hist +44‎ Main Page ‎ →‎Home Pages for Courses and Seminars
10:3910:39, 27 February 2024 diff hist +39,712‎ N 组合数学 (Fall 2024)/Basic enumeration ‎ Created page with "== Basic Enumeration == The three basic rules for enumeration are: *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math>. *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|=|S|\cdot|T|</math>. *'''The bijection rule''': if there exists a bijection between finite sets <math>S</math> a..." current
10:3710:37, 27 February 2024 diff hist +76‎ 组合数学 (Spring 2024) ‎ →‎Lecture Notes
07:4407:44, 27 February 2024 diff hist −153‎ 概率论与数理统计 (Spring 2023) ‎ →‎Assignments current

07:4007:40, 18 February 2024 diff hist +1,438‎ N 组合数学 (Spring 2024)/Course materials ‎ Created page with "== 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%"| :J. H. van Lint and R. M. Wilson. ''A course in Combinatorics, 2nd Edition.'' Cambridge University Press, 2001. |- |border|100px|| :S. Jukna. ''Extremal Combinatorics: With Applications in Computer Science, 2nd Edition..." current
07:3907:39, 18 February 2024 diff hist −4‎ 组合数学 (Spring 2024) ‎ →‎Course info Tag: Manual revert
07:3907:39, 18 February 2024 diff hist +4‎ 组合数学 (Spring 2024) ‎ →‎Course info Tag: Reverted
07:3807:38, 18 February 2024 diff hist +4,631‎ N 组合数学 (Spring 2024) ‎ Created page with "{{Infobox |name = Infobox |bodystyle = |title = 组合数学 Combinatorics |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 尹一通 |header3 = |label3 = Email |data3 = yinyt@nju.edu.cn |header4 = |label4= office |data4=..."
07:3407:34, 18 February 2024 diff hist +4‎ 概率论与数理统计 (Spring 2024) ‎ →‎Course info
07:3307:33, 18 February 2024 diff hist +6,287‎ N 概率论与数理统计 (Spring 2024) ‎ Created page with "{{Infobox |name = Infobox |bodystyle = |title = '''概率论与数理统计''' '''Probability Theory''' & '''Mathematical Statistics''' |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = '''尹一通''' |header3 = |label3 = Em..."
07:2307:23, 18 February 2024 diff hist +123‎ Main Page ‎ →‎Home Pages for Courses and Seminars Tag: Visual edit: Switched

16:3316:33, 29 November 2023 diff hist +2,459‎ N Assignment 4, Fall 2023 ‎ Created page with "在第四章中，我们从准地转近似下的纬向平均风场、温度场的趋势方程出发，定义了E-P通量。但是该定义下的E-P通量并没有考虑到大气湿过程的影响。如果从第三章介绍的水汽方程出发，我们可以按照以下步骤定义出一个包含大气大尺度运动中湿过程作用的广义的E-P通量。 1）在准地转近似下，如果我们按照对热力学方程的简化方法，将比湿（specific humidity..." current
16:3316:33, 29 November 2023 diff hist +54‎ General Circulation(Fall 2023) ‎ →‎Assignments current

06:3006:30, 6 November 2023 diff hist −69‎ General Circulation(Fall 2023) ‎ →‎Course Slides
06:1906:19, 6 November 2023 diff hist +934‎ General Circulation(Fall 2023) ‎ →‎Course Slides
06:1406:14, 6 November 2023 diff hist +57‎ General Circulation(Fall 2023) ‎ →‎Course Slides
06:1206:12, 6 November 2023 diff hist +1,087‎ N 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..." current
06:1106:11, 6 November 2023 diff hist +59‎ General Circulation(Fall 2023) ‎ →‎Assignments
06:0506:05, 6 November 2023 diff hist +1,137‎ N 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..." current
06:0006:00, 6 November 2023 diff hist +1‎ General Circulation(Fall 2023) ‎ →‎Assignments
05:5905:59, 6 November 2023 diff hist +55‎ General Circulation(Fall 2023) ‎ →‎Assignments

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

05:5805:58, 11 October 2023 diff hist +2,522‎ N Assignment 2, Fall 2023 ‎ Created page with "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。 ==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

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 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

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

15:5615:56, 27 April 2023 diff hist +7‎ 组合数学 (Fall 2023)/The probabilistic method ‎ →‎Lovász Local Lemma current
15:5515:55, 27 April 2023 diff hist +7‎ 组合数学 (Fall 2023)/The probabilistic method ‎ →‎Lovász Local Lemma
15:5515:55, 27 April 2023 diff hist +10‎ 组合数学 (Fall 2023)/The probabilistic method ‎ →‎Lovász Local Lemma
15:5315:53, 27 April 2023 diff hist −2‎ 组合数学 (Fall 2023)/The probabilistic method ‎ →‎Coloring large-girth graphs
15:5315:53, 27 April 2023 diff hist +27,129‎ N 组合数学 (Fall 2023)/The probabilistic method ‎ Created page with "== The Probabilistic Method == The probabilistic method provides another way of proving the existence of objects: instead of explicitly constructing an object, we define a probability space of objects in which the probability is positive that a randomly selected object has the required property. The basic principle of the probabilistic method is very simple, and can be stated in intuitive ways: *If an object chosen randomly from a universe satisfies a property with posi..."
15:5215:52, 27 April 2023 diff hist +93‎ 组合数学 (Spring 2023) ‎ →‎Lecture Notes

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