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4 December 2025
- 17:3017:30, 4 December 2025 数据科学基础 (Fall 2025)/Problem Set 6 (hist | edit) [8,502 bytes] Liumingmou (talk | contribs) (Created page with "*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。 *没有条件的同学可以用纸笔完成作业之后拍照。 == Assumption throughout Problem Set 6 == <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> == Problem 1...")
1 December 2025
- 15:0415:04, 1 December 2025 高级算法 (Fall 2025)/第二次作业提交名单 (hist | edit) [1,572 bytes] Zhangyiyao (talk | contribs) (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221502007 || 崔毓泽 |- | 221502008 || 梁今为 |- | 221502013 || 贺龄瑞 |- | 221502018 || 陈正道 |- | 221850037 || 王朝晖 |- | 221900156 || 韩加瑞 |- | 231098067 || 徐浩然 |- | 231220002 || 潘谟天 |- | 231220005 || 樊书岩 |- | 231220007 || 汪文韬 |- | 231220012 || 张启越 |- | 231220019 || 何云天 |- | 231220056 || 黄思远 |- | 231220...") Tag: Visual edit: Switched
30 November 2025
- 09:4309:43, 30 November 2025 Assignment 4, Fall 2025 (hist | edit) [2,459 bytes] Etone (talk | contribs) (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...")
10 November 2025
- 05:2705:27, 10 November 2025 高级算法 (Fall 2025)/Problem Set 2 (hist | edit) [6,050 bytes] Zhangyiyao (talk | contribs) (Created page with "*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。 == Problem 1 (Adjacency matrix) == Let <math>A</math> be the adjacency matrix of an undirected connected graph <math>G</math>, and <math>\alpha_1</math> be its largest eigenvalue. * ['''Lowerbounding <math>\alpha_1</math>'''] We proved <math>\alpha_1 \le d_{\mathrm{max}}</math> in class. Show that <math>\alpha_1 \ge d_{\mathrm{...")
30 October 2025
- 16:4116:41, 30 October 2025 数据科学基础 (Fall 2025)/Problem Set 5 (hist | edit) [7,759 bytes] Liumingmou (talk | contribs) (Created page with "*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。 *没有条件的同学可以用纸笔完成作业之后拍照。 == Assumption throughout Problem Set 5 == <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> == Problem 1...")
- 06:2206:22, 30 October 2025 高级算法 (Fall 2025)/第一次作业提交名单 (hist | edit) [1,665 bytes] Zhangyiyao (talk | contribs) (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221502007 || 崔毓泽 |- | 221502008 || 梁今为 |- | 221502013 || 贺龄瑞 |- | 221502018 || 陈正道 |- | 221850037 || 王朝晖 |- | 221900156 || 韩加瑞 |- | 231098067 || 徐浩然 |- | 231220002 || 潘谟天 |- | 231220005 || 樊书岩 |- | 231220007 || 汪文韬 |- | 231220012 || 张启越 |- | 231220019 || 何云天 |- | 231220056 || 黄思远 |- | 231220...")
26 October 2025
- 15:0015:00, 26 October 2025 Assignment 3, Fall 2025 (hist | edit) [1,087 bytes] Etone (talk | contribs) (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...")
20 October 2025
- 02:2202:22, 20 October 2025 Namelist Assignment 1 2025 (hist | edit) [1,190 bytes] Etone (talk | contribs) (Created page with "学号 姓名 221830009 丁潘宇 221840131 崔亚川 221830192 张梓轩 221830060 梁茗豪 221840001 檀纯芳 221840042 刘鑫磊 221840183 胡峻滔 221840252 徐玘 221830079 余秀蓝 221840217 于步涵 221840063 樊瑾奕 221840226 郑凯容 221840163 周若冰 221840204 张利荣 652025280008 李俊霖 502025280011 苟敏杰 502025280051 吴雨涵 502024280014 何昌霖 502025280038 齐若彤 502025280008 冯英飞 502025280022 蒋妍 50202...")
19 October 2025
- 12:3512:35, 19 October 2025 Theory@Suzhou 2025 (hist | edit) [17,102 bytes] Liumingmou (talk | contribs) (Created page with "==General Information == *'''<font size=4>Sunday, Nov 30, 2025: 9 am--5 pm.</font>''' * <font size=4>'''Location''': 南京大学苏州校区 * <font size=4>'''Venue''': TBA ==List of Speakers (in alphabetic order)== * [http://staff.ustc.edu.cn/~xuechen1989/ 陈雪]（中国科学技术大学） * [https://zengfenghuang.github.io/ 黄增峰]（复旦大学） * [https://www.shaofengjiang.cn/ 姜少峰]（北京大学） * [https://chaoxu.prof/ 许超]（电子科技大...")
16 October 2025
- 17:3817:38, 16 October 2025 数据科学基础 (Fall 2025)/Problem Set 4 (hist | edit) [6,052 bytes] Liumingmou (talk | contribs) (Created page with "*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。 *没有条件的同学可以用纸笔完成作业之后拍照。 == Assumption throughout Problem Set 4 == <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> == Problem 1...")
29 September 2025
- 03:4503:45, 29 September 2025 高级算法 (Fall 2025)/Dimension Reduction (hist | edit) [16,764 bytes] Etone (talk | contribs) (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...")
- 03:0703:07, 29 September 2025 Assignment 2, Fall 2025 (hist | edit) [2,522 bytes] Etone (talk | contribs) (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...")
27 September 2025
- 14:4814:48, 27 September 2025 高级算法 (Fall 2025)/Problem Set 1 (hist | edit) [8,542 bytes] Zhangyiyao (talk | contribs) (Created page with "*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。 == Problem 1 (s–t Min-Cut) == Consider adapting Karger's min-cut algorithm to the problem of finding an <math>s</math>–<math>t</math> min-cut in an undirected graph. In this problem, we are given an undirected graph <math>G</math> together with two distinguished vertices <math>s</math> and <math>t</math>. An <math>s</math>–...")
25 September 2025
- 09:3809:38, 25 September 2025 数据科学基础 (Fall 2025)/Problem Set 3 (hist | edit) [10,451 bytes] Liumingmou (talk | contribs) (Created page with "*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。 *没有条件的同学可以用纸笔完成作业之后拍照。 <h2 id="assumption"> Assumption throughout Problem Set 3</h2> <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.<...")
22 September 2025
- 14:3114:31, 22 September 2025 Assignment 1, Fall 2025 (hist | edit) [2,971 bytes] Etone (talk | contribs) (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...")
- 02:5002:50, 22 September 2025 高级算法 (Fall 2025)/Conditional expectations (hist | edit) [10,715 bytes] Etone (talk | contribs) (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...")
- 02:4902:49, 22 September 2025 高级算法 (Fall 2025)/Concentration of measure (hist | edit) [41,013 bytes] Etone (talk | contribs) (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...")
9 September 2025
- 05:0505:05, 9 September 2025 高级算法 (Fall 2025)/Basic deviation inequalities (hist | edit) [5,755 bytes] Etone (talk | contribs) (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...")
- 05:0405:04, 9 September 2025 高级算法 (Fall 2025)/Limited independence (hist | edit) [15,812 bytes] Etone (talk | contribs) (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...")
- 05:0405:04, 9 September 2025 高级算法 (Fall 2025)/Hashing and Sketching (hist | edit) [49,292 bytes] Etone (talk | contribs) (Created page with "=Balls into Bins= The following is the so-called balls into bins model. 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...")
7 September 2025
- 13:1913:19, 7 September 2025 高级算法 (Fall 2025)/Finite Field Basics (hist | edit) [6,210 bytes] Etone (talk | contribs) (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...")
- 13:1913:19, 7 September 2025 高级算法 (Fall 2025)/Fingerprinting (hist | edit) [38,283 bytes] Etone (talk | contribs) (Created page with "= Checking Matrix Multiplication= thumb|360px|right|The evolution of time complexity <math>O(n^{\omega})</math> for matrix multiplication. Let <math>\mathbb{F}</math> be a feild (you may think of it as the filed <math>\mathbb{Q}</math> of rational numbers, or the finite field <math>\mathbb{Z}_p</math> of integers modulo prime <math>p</math>). We suppose that each field operation (addition, subtraction, multiplication, division) has u...")
- 11:3611:36, 7 September 2025 General Circulation(Fall 2025) (hist | edit) [8,574 bytes] Etone (talk | contribs) (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...")
6 September 2025
- 15:2715:27, 6 September 2025 数据科学基础 (Fall 2025)/Problem Set 2 (hist | edit) [6,390 bytes] Liumingmou (talk | contribs) (Created page with "*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。 *没有条件的同学可以用纸笔完成作业之后拍照。 <h2 id="assumption"> Assumption throughout Problem Set 2</h2> <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p> <h2 id="problem-1">Problem 1 (Conditional probability)</h2> * ['''The prosecutor’s fallacy'''...")
- 15:2615:26, 6 September 2025 数据科学基础 (Fall 2025)/Problem Set 1 (hist | edit) [4,163 bytes] Liumingmou (talk | contribs) (Created page with "*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。 *没有条件的同学可以用纸笔完成作业之后拍照。 <h2 id="assumption"> Assumption throughout Problem Set 1</h2> <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p> * [<strong><math>\sigma</math>-algebra</strong>] Let <math>A</math> and <math>B</math> belong to...")