User contributions for Etone

For Etone talk block log uploads logs
A user with 1,032 edits. Account created on 30 August 2022.
Jump to navigation Jump to search
Search for contributionsExpandCollapse
⧼contribs-top⧽
⧼contribs-date⧽
(newest | oldest) View (newer 250 | ) (20 | 50 | 100 | 250 | 500)

24 April 2024

22 April 2024

  • 03:1403:14, 22 April 2024 diff hist +5,139‎ N 概率论与数理统计 (Spring 2024)/Weierstrass Approximation Theorem ‎ Created page with "[https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem '''魏尔施特拉斯逼近定理''']（'''Weierstrass approximation theorem'''）陈述了这样一个事实：闭区间上的连续函数总可以用多项式一致逼近。 {{Theorem|魏尔施特拉斯逼近定理| :设 <math>f:[a,b]\to\mathbb{R}</math> 为定义在实数区间 <math>[a,b]</math> 上的连续实值函数。对每个 <math>\epsilon>0</math>，存在一个多项式 <math>p</math> 使得对..." current
  • 03:1303:13, 22 April 2024 diff hist +7,005‎ N 概率论与数理统计 (Spring 2024)/Threshold of k-clique in random graph ‎ Created page with "在 Erdős-Rényi 随机图模型 <math>G(n,p)</math> 中，一个随机无向图 <math>G</math> 以如下的方式生成：图 <math>G</math> 包含 <math>n</math> 个顶点，每一对顶点之间都独立同地以概率 <math>p</math> 连一条无向边。如此生成的随机图记为 <math>G\sim G(n,p)</math>。 固定整数 <math>k\ge 3</math>，考虑随机图 <math>G\sim G(n,p)</math> 包含 <math>K_k</math>（<math>k</math>-团，<math>k</math>-clique）子图..." current
  • 03:1203:12, 22 April 2024 diff hist +8,968‎ N 概率论与数理统计 (Spring 2024)/Two-point sampling ‎ Created page with "= 利用线性同余方程构造两两独立的随机变量 = 令<math>p</math>为一质数。考虑模<math>p</math>余数构成的集合<math>[p]=\{0,1,\ldots,p-1\}=\mathbb{Z}_p</math>。众所周知，当<math>p</math>为质数时，<math>\mathbb{Z}_p</math>为对模<math>p</math>加法和乘法运算闭合的'''有限域'''。 我们现在构造一系列值域为<math>[p]</math>的'''两两独立'''（'''pairwise Independent'''）且'''均匀分布'''（'''uniforml..." current
  • 03:1203:12, 22 April 2024 diff hist +325‎ 概率论与数理统计 (Spring 2024) ‎ →‎Lectures current

15 April 2024

12 April 2024

9 April 2024

  • 13:2713:27, 9 April 2024 diff hist +14,440‎ N 组合数学 (Fall 2024)/Existence problems ‎ Created page with "== Existence by Counting == === Shannon's circuit lower bound=== This is a fundamental problem in in Computer Science. A '''boolean function''' is a function in the form <math>f:\{0,1\}^n\rightarrow \{0,1\}</math>. [http://en.wikipedia.org/wiki/Boolean_circuit Boolean circuit] is a mathematical model of computation. Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , x_n</math>. A circuit h..." current
  • 13:2613:26, 9 April 2024 diff hist +17,231‎ N 组合数学 (Fall 2024)/Cayley's formula ‎ Created page with "== Cayley's Formula == We now present a theorem of the number of labeled trees on a fixed number of vertices. It is due to [http://en.wikipedia.org/wiki/Arthur_Cayley Cayley] in 1889. The theorem is often referred by the name [http://en.wikipedia.org/wiki/Cayley's_formula Cayley's formula]. {{Theorem|Cayley's formula for trees| : There are <math>n^{n-2}</math> different trees on <math>n</math> distinct vertices. }} The theorem has several proofs, including the bijectio..." current
  • 13:2613:26, 9 April 2024 diff hist +87‎ 组合数学 (Spring 2024) ‎ →‎Lecture Notes
  • 13:2413:24, 9 April 2024 diff hist +80‎ 组合数学 (Spring 2024) ‎ →‎Lecture Notes

8 April 2024

27 March 2024

26 March 2024

25 March 2024

20 March 2024

19 March 2024

18 March 2024

  • 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..."

13 March 2024

12 March 2024

  • 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 == *'''<font size=4> 2019年10月19、20日: 9 am--5 pm.</font>''' * <font size=4> 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</font> [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

6 March 2024

4 March 2024

27 February 2024

26 February 2024

18 February 2024

3 December 2023

29 November 2023

  • 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

6 November 2023

31 October 2023

29 October 2023

24 October 2023

21 October 2023

20 October 2023

15 October 2023

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

26 September 2023

19 September 2023

14 September 2023

12 September 2023

10 September 2023

4 September 2023

15 June 2023

14 June 2023

13 June 2023

5 June 2023

4 June 2023

3 June 2023

(newest | oldest) View (newer 250 | ) (20 | 50 | 100 | 250 | 500)
Retrieved from "https://tcs.nju.edu.cn/wiki/index.php?title=Special:Contributions/Etone"