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- 08:22, 27 March 2024 Liuexp talk contribs created page File:计算方法5-高斯消元.pdf
- 08:22, 27 March 2024 Liuexp talk contribs uploaded File:计算方法5-高斯消元.pdf
- 05:48, 27 March 2024 Liuexp talk contribs deleted page File:计算方法4-最小二乘法.pdf (Deleted old revision 20240327054842!计算方法4-最小二乘法.pdf: Duplicated file: content was: "最小二乘法、FFT", and the only contributor was "Liuexp" (talk))
- 05:48, 27 March 2024 Liuexp talk contribs uploaded a new version of File:计算方法4-最小二乘法.pdf
- 05:05, 27 March 2024 Kvrmnks talk contribs created page 计算方法 Numerical method (Spring 2024)/Homework2 提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221840201 || 钟锦立 |- | 221240027 || 唐诗博 |- | 221220067 || 刘思远 |- | 221502009 || 李嘉洲 |- | 221220118 || 但佳霖 |- | 221502005 || 王昕浩 |- | 221870052 || 吴隽雨 |- | 221220146 || 王浩然 |- | 221502001 || 赵子轩 |- | 221220029 || 陈俊翰 |- | 221240093 || 陈力峥 |- | 221502006 || 张文权 |- | 221502016 || 张晓言 |- | 221220...")
- 04:27, 27 March 2024 Etone talk contribs created page 组合数学 (Fall 2024)/Pólya's theory of counting (Created page with "== Groups == A group <math>(G,\cdot)</math> is set <math>G</math> along with a binary operator <math>\cdot</math> which satisfies the following axioms: * ''closure'': <math>\forall g,h\in G, g\cdot h \in G</math>; * ''associativity'': <math>\forall f,g,h\in G, f\cdot(g\cdot h)=(f\cdot g)\cdot h</math>; * ''identity'': there exists a special element <math>e\in G</math>, called the '''identity''', such that <math>e\cdot g=g</math> for any <math>g\in G</math>; * ''inverse''...")
- 07:48, 21 March 2024 User account Houzhe talk contribs was created by Liuexp talk contribs
- 05:23, 20 March 2024 Liuexp talk contribs deleted page File:计算方法3-Chebyshev-Spring2024.pdf (Deleted old revision 20240320052235!计算方法3-Chebyshev-Spring2024.pdf: Duplicated file: updated)
- 05:22, 20 March 2024 Liuexp talk contribs uploaded a new version of File:计算方法3-Chebyshev-Spring2024.pdf
- 05:19, 20 March 2024 Liuexp talk contribs created page File:计算方法4-最小二乘法.pdf
- 05:19, 20 March 2024 Liuexp talk contribs uploaded File:计算方法4-最小二乘法.pdf
- 02:21, 20 March 2024 Etone talk contribs created page 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...")
- 15:55, 19 March 2024 Etone talk contribs created page General Circulation(Spring 2024) (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...")
- 12:42, 19 March 2024 Gispzjz talk contribs created page 组合数学 (Fall 2024)/Problem Set 1 (Created page with "== Problem 1 == How many <math>n\times m</math> matrices of <math>0</math>'s and <math>1</math>'s are there, such that every row and column contains an even number of <math>1</math>'s? An odd number of <math>1</math>'s? == Problem 2 == * There is a set of <math>2n</math> people: <math>n</math> male and <math>n</math> female. A good party is a set with the same number of male and female. How many possibilities are there to build such a good party? * Try to express the a...")
- 09:51, 19 March 2024 Etone talk contribs created page 组合数学 (Fall 2024)/Sieve methods (Created page with "== Principle of Inclusion-Exclusion == Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is :<math>|A\cup B|=|A|+|B|-{\color{Blue}|A\cap B|}</math>. For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is computed as :<math>|A\cup B\cup C|=|A|+|B|+|C|-{\color{Blue}|A\cap B|}-{\color{Blue}|A\cap C|}-{\color{Blue}|B\cap C|}+{\color{Red}|A\cap B\cap C|}</math>. This is illu...")
- 05:30, 19 March 2024 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2024)/Problem Set 1 (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。 == Assumption throughout Problem Set 1== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <h2 id="problem-2-principle-of-inclusion-and-exclusion">Problem 1 (Principle of Inclusion and Exclusion)</h2> <p>Let <math>n\ge 1</math> be a positive integer and <math>A_1,A_2...")
- 15:51, 18 March 2024 Etone talk contribs created page 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...")
- 06:52, 13 March 2024 Kvrmnks talk contribs created page 计算方法 Numerical method (Spring 2024)/Homework1 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240035 || 王祉天 |- | 221220158 || 颜伟坤 |- | 221870199 || 黄一凡 |- | 221502010 || 梁志浩 |- | 221220118 || 但佳霖 |- | 221502009 || 李嘉洲 |- | 221870222 || 刘烨 |- | 221240092 || 杨煜申 |- | 221220019 || 洪观澜 |- | 221220034 || 王旭 |- | 221502016 || 张晓言 |- | 221502001 || 赵子轩 |- | 221502005 || 王昕浩 |- | 221220067 |...")
- 02:58, 12 March 2024 Etone talk contribs deleted page 量子计算的算法与物理实现研讨会 (content was: "==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] == 日程安...", and the only contributor was "[[Special:Contributions/imported>Qinminglong|imported>Qinminglong]]" ([[User talk:imported>Qinminglong|talk]]))
- 02:56, 12 March 2024 Etone talk contribs created page 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...")
- 02:56, 12 March 2024 Etone talk contribs deleted page Quantum (content was: "= 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...", and the only contributor was "[[Special:Contributions/imported>Qinminglong|imported>Qinminglong]]" ([[User talk:imported>Qinminglong|talk]]))
- 11:43, 11 March 2024 Kvrmnks talk contribs created page File:Computational Method 2024 Assignments 2.pdf (Computational_Method_2024_Assignments_2)
- 11:43, 11 March 2024 Kvrmnks talk contribs uploaded File:Computational Method 2024 Assignments 2.pdf (Computational_Method_2024_Assignments_2)
- 14:05, 8 March 2024 Kvrmnks talk contribs created page File:Computational Method 2024 Assignments1 new.pdf
- 14:05, 8 March 2024 Kvrmnks talk contribs uploaded File:Computational Method 2024 Assignments1 new.pdf
- 11:41, 6 March 2024 Etone talk contribs created page 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...")
- 10:01, 6 March 2024 Liuexp talk contribs created page File:计算方法3-Chebyshev-Spring2024.pdf
- 10:01, 6 March 2024 Liuexp talk contribs uploaded File:计算方法3-Chebyshev-Spring2024.pdf
- 09:18, 6 March 2024 Liuexp talk contribs deleted page File:计算方法2-插值-Spring2024.pdf (Deleted old revision 20240306091751!计算方法2-插值-Spring2024.pdf: Duplicated file: content was: "计算方法2-插值-Spring2024", and the only contributor was "Liuexp" (talk))
- 09:17, 6 March 2024 Liuexp talk contribs uploaded a new version of File:计算方法2-插值-Spring2024.pdf
- 05:37, 6 March 2024 Liuexp talk contribs deleted page File:计算方法2-插值-Spring2024.pdf (Deleted old revision 20240306053643!计算方法2-插值-Spring2024.pdf: Duplicated file: content was: "计算方法2-插值-Spring2024", and the only contributor was "Liuexp" (talk))
- 05:36, 6 March 2024 Liuexp talk contribs uploaded a new version of File:计算方法2-插值-Spring2024.pdf
- 15:53, 5 March 2024 Liuexp talk contribs created page File:计算方法2-插值-Spring2024.pdf
- 15:53, 5 March 2024 Liuexp talk contribs uploaded File:计算方法2-插值-Spring2024.pdf
- 15:49, 5 March 2024 Liuexp talk contribs deleted page File:计算方法2-插值-Spring2024.pdf.pdf (Duplicated file: content was: "计算方法2-插值-Spring2024.pdf", and the only contributor was "Liuexp" (talk))
- 15:48, 5 March 2024 Liuexp talk contribs created page File:计算方法2-插值-Spring2024.pdf.pdf
- 15:48, 5 March 2024 Liuexp talk contribs uploaded File:计算方法2-插值-Spring2024.pdf.pdf
- 03:44, 28 February 2024 Liuexp talk contribs deleted page File:计算方法1-课程简介-Spring2024.pdf (Deleted old revision 20240228034400!计算方法1-课程简介-Spring2024.pdf: Duplicated file: content before blanking was: "")
- 03:44, 28 February 2024 Liuexp talk contribs uploaded a new version of File:计算方法1-课程简介-Spring2024.pdf
- 03:37, 28 February 2024 Liuexp talk contribs deleted page File:计算方法1-课程简介-Spring2024.pdf (Deleted old revision 20240228033729!计算方法1-课程简介-Spring2024.pdf: Duplicated file: content before blanking was: "")
- 03:37, 28 February 2024 Liuexp talk contribs uploaded a new version of File:计算方法1-课程简介-Spring2024.pdf
- 02:13, 28 February 2024 Kvrmnks talk contribs created page File:Computational Method 2024 Assignments.pdf
- 02:13, 28 February 2024 Kvrmnks talk contribs uploaded File:Computational Method 2024 Assignments.pdf
- 01:50, 28 February 2024 Liuexp talk contribs created page File:计算方法1-课程简介-Spring2024.pdf
- 01:50, 28 February 2024 Liuexp talk contribs uploaded File:计算方法1-课程简介-Spring2024.pdf
- 10:39, 27 February 2024 Etone talk contribs created page 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...")
- 10:17, 27 February 2024 Roundgod talk contribs created page 计算复杂性 (Spring 2024) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>计算复杂性 <br>Computational Complexity</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 姚鹏晖 |header3 = |label3 = Email |data3 = pyao@nju.edu.cn |header4 = |label4= Offi...")
- 12:13, 23 February 2024 Liuexp talk contribs created page 计算方法 Numerical method (Spring 2024) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>计算方法 <br>Numerical method</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 刘景铖 |header3 = |label3 = Email |data3 = liu [at] nju [dot] edu [dot] cn |header4 = |label4=...") Tag: Visual edit: Switched
- 07:40, 18 February 2024 Etone talk contribs created page 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...")
- 07:38, 18 February 2024 Etone talk contribs created page 组合数学 (Spring 2024) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>组合数学 <br> Combinatorics</font> |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=...")
- 07:33, 18 February 2024 Etone talk contribs created page 概率论与数理统计 (Spring 2024) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>'''概率论与数理统计'''<br> '''Probability Theory''' <br> & '''Mathematical Statistics'''</font> |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...")
- 13:54, 16 February 2024 Liuexp talk contribs changed group membership for Hlx from (none) to administrator
- 13:48, 16 February 2024 User account Kvrmnks talk contribs was created by Liuexp talk contribs
- 04:25, 2 January 2024 Zouzongrui talk contribs uploaded a new version of File:Advanced algorithm 2023 Fall take home final.pdf
- 04:11, 2 January 2024 Zouzongrui talk contribs created page File:Advanced algorithm 2023 Fall take home final.pdf (final_2023)
- 04:11, 2 January 2024 Zouzongrui talk contribs uploaded File:Advanced algorithm 2023 Fall take home final.pdf (final_2023)
- 06:24, 19 December 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023)/第二次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 502023370027 || 梁天润 |- | 522023330115 || 杨闰凯 |- | 201220073 || 曹云帆 |- | 201870048 || 张乃仁 |- | 522023330065 || 马润泽 |- | 201502007 || 高嘉成 |- | 652023330030 || 郑欣 |- | 652023330001 || 陈阳 |- | 652023330023 || 于逸潇 |- | 502023330010 || 陈一涵 |- | 201840184 || 刘可 |- | 502023330057 || 王光展 |- | 201220092 || 吴杰...")
- 13:39, 1 December 2023 Liuexp talk contribs changed group membership for Shili from (none) to administrator
- 13:36, 1 December 2023 Shili talk contribs created page File:Greedy-handout.pdf (Handout for Greedy Algorithms)
- 13:36, 1 December 2023 Shili talk contribs uploaded File:Greedy-handout.pdf (Handout for Greedy Algorithms)
- 12:37, 1 December 2023 Shili talk contribs created page File:Greedy.pdf
- 12:37, 1 December 2023 Shili talk contribs uploaded File:Greedy.pdf
- 16:33, 29 November 2023 Etone talk contribs created page 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...")
- 15:23, 28 November 2023 Liuexp talk contribs created page File:Advanced algorithm 2023 peiwu expander.pdf
- 15:23, 28 November 2023 Liuexp talk contribs uploaded File:Advanced algorithm 2023 peiwu expander.pdf
- 13:05, 24 November 2023 Liuexp talk contribs deleted page File:L11 MCMC.pdf (Deleted old revision 20231124130459!L11_MCMC.pdf: Duplicated file)
- 13:04, 24 November 2023 Liuexp talk contribs uploaded a new version of File:L11 MCMC.pdf
- 07:24, 24 November 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023)/Problem Set 2 (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 (Min-cut/Max-cut) == * ['''Counting <math>\alpha</math>-approximate min-cut'''] For any '''<math>\alpha \ge 1</math>''', a cut is called an '''<math>\alpha</math>'''-approximate min-cut in a multigraph '''<math>G</math>''' if the number of edges in it is at most '''<math>\alpha</math>''' times that of the min-cut....")
- 12:51, 21 November 2023 Liuexp talk contribs deleted page File:L11 MCMC.pdf (Deleted old revision 20231121125124!L11_MCMC.pdf: Duplicated file)
- 12:51, 21 November 2023 Liuexp talk contribs uploaded a new version of File:L11 MCMC.pdf
- 12:50, 21 November 2023 Liuexp talk contribs deleted page File:L10 electrical networks.pdf (Deleted old revision 20231121125048!L10_electrical_networks.pdf: Duplicated file)
- 12:50, 21 November 2023 Liuexp talk contribs uploaded a new version of File:L10 electrical networks.pdf
- 06:53, 21 November 2023 Liuexp talk contribs created page File:L11 MCMC.pdf
- 06:53, 21 November 2023 Liuexp talk contribs uploaded File:L11 MCMC.pdf
- 11:06, 14 November 2023 Liuexp talk contribs deleted page File:L10 electrical networks.pdf (Deleted old revision 20231114110557!L10_electrical_networks.pdf: Duplicated file)
- 11:05, 14 November 2023 Liuexp talk contribs uploaded a new version of File:L10 electrical networks.pdf
- 11:05, 14 November 2023 Liuexp talk contribs deleted page File:AA2023 L9 random walk.pdf (Deleted old revision 20231114110452!AA2023_L9_random_walk.pdf: Duplicated file)
- 11:04, 14 November 2023 Liuexp talk contribs uploaded a new version of File:AA2023 L9 random walk.pdf
- 10:21, 14 November 2023 Liuexp talk contribs deleted page File:AA2023 L9 random walk.pdf (Deleted old revision 20231114102049!AA2023_L9_random_walk.pdf: Duplicated file)
- 10:20, 14 November 2023 Liuexp talk contribs uploaded a new version of File:AA2023 L9 random walk.pdf
- 06:44, 14 November 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023)/第一次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 522023330115 || 杨闰凯 |- | 502023370027 || 梁天润 |- | 522023330065 || 马润泽 |- | 502023370019 || 江楠 |- | 201870048 || 张乃仁 |- | 652023330001 || 陈阳 |- | 201502007 || 高嘉成 |- | 652023330030 || 郑欣 |- | 201840058 || 蒋潇鹏 |- | 201250101 || 王锦朋 |- | 201220126 || 郑翰 |- | 201502002 || 洪睿琦 |- | 522023330100 || 吴浩杨 |-...")
- 05:51, 14 November 2023 Liuexp talk contribs created page File:L10 electrical networks.pdf
- 05:51, 14 November 2023 Liuexp talk contribs uploaded File:L10 electrical networks.pdf
- 05:58, 7 November 2023 Liuexp talk contribs uploaded a new version of File:L8 spectral-graph-theory.pdf
- 05:57, 7 November 2023 Liuexp talk contribs created page File:AA2023 L9 random walk.pdf
- 05:57, 7 November 2023 Liuexp talk contribs uploaded File:AA2023 L9 random walk.pdf
- 06:12, 6 November 2023 Etone talk contribs created page 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...")
- 06:05, 6 November 2023 Etone talk contribs created page 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...")
- 11:35, 31 October 2023 Liuexp talk contribs deleted page File:L8 spectral-graph-theory.pdf (Deleted old revision 20231031113444!L8_spectral-graph-theory.pdf: Duplicated file)
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- 06:55, 31 October 2023 Liuexp talk contribs created page File:L8 spectral-graph-theory.pdf
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- 03:41, 27 October 2023 Liuexp talk contribs deleted page Talk:Main Page (Spam)
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- 12:34, 24 October 2023 Etone talk contribs created page 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...")
- 05:21, 23 October 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023)/Problem Set 1 (Created page with "*作业目前正在更新中,不是最终版 *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。")
- 07:51, 21 October 2023 Etone talk contribs created page 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...")
- 07:38, 15 October 2023 Etone talk contribs created page 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...")
- 05:58, 11 October 2023 Etone talk contribs created page 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...")
- 10:53, 10 October 2023 Etone talk contribs created page 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...")
- 10:53, 10 October 2023 Etone talk contribs created page 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...")
- 10:52, 4 October 2023 Etone talk contribs created page 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...")
- 16:39, 26 September 2023 Etone talk contribs created page 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...")
- 16:38, 26 September 2023 Etone talk contribs created page 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...")
- 10:58, 19 September 2023 Etone talk contribs created page 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<br>rin...")
- 10:57, 19 September 2023 Etone talk contribs created page 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...")
- 06:37, 14 September 2023 Hychen talk contribs created page File:Probability and Computing. 2nd Edition cover.jpg
- 06:37, 14 September 2023 Hychen talk contribs uploaded File:Probability and Computing. 2nd Edition cover.jpg
- 01:25, 14 September 2023 Etone talk contribs created page General Circulation(Fall 2023) (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...")
- 10:36, 12 September 2023 Etone talk contribs created page 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...")
- 10:34, 12 September 2023 Etone talk contribs created page 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...")
- 10:33, 12 September 2023 Etone talk contribs created page 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...")
- 13:34, 10 September 2023 Zouzongrui talk contribs uploaded a new version of File:Eigenvalues and Polynomials.png
- 13:33, 10 September 2023 Zouzongrui talk contribs uploaded a new version of File:Eigenvalues and Polynomials.png
- 13:31, 10 September 2023 Zouzongrui talk contribs created page File:Eigenvalues and Polynomials.png
- 13:31, 10 September 2023 Zouzongrui talk contribs uploaded File:Eigenvalues and Polynomials.png
- 13:27, 10 September 2023 Zouzongrui talk contribs created page File:Lx=b.jpg
- 13:27, 10 September 2023 Zouzongrui talk contribs uploaded File:Lx=b.jpg
- 13:17, 10 September 2023 Zouzongrui talk contribs created page File:Combinatorial Optimization.webp
- 13:17, 10 September 2023 Zouzongrui talk contribs uploaded File:Combinatorial Optimization.webp
- 11:44, 10 September 2023 Etone talk contribs created page 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...")
- 10:41, 5 September 2023 User account Shili talk contribs was created by Liuexp talk contribs
- 08:00, 4 September 2023 User account Hychen talk contribs was created by Liuexp talk contribs
- 07:32, 4 September 2023 Zouzongrui talk contribs created page 高级算法 (Fall 2023) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>高级算法 <br>Advanced Algorithms</font> |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 |data...")
- 03:55, 22 June 2023 Roundgod talk contribs created page 组合数学 (Spring 2023)/第四次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220060 || 林荣恩 |- | 191250004 || 曹雨森 |- | 191250127 || 孙伟杰 |- | 191250145 || 王子鉴 |- | 191820255 || 臧正贻 |- | 191840186 || 彭欣昂 |- | 201220011 || 章振辉 |- | 201220035 || 丁天行 |- | 201220043 || 吕培锋 |- | 201220073 || 曹云帆 |- | 201220092 || 吴杰伦 |- | 201220098 || 杨林 |- | 201220107 || 贺柄毓 |- | 20122012...")
- 11:19, 19 June 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework8 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211502020 || 周相羽 |- | 211098322 || 陈思翔 |- | 211502014 || 刘奕 |- | 211502007 || 黄宸宇 |- | 211502005 || 黄逸飞 |- | 211850020 || 王雷宇 |- | 211240009 || 陆一阳 |- | 211240002 || 张毅 |- | 211220018 || 陈润涛 |- | 211220121 || 唐周旋 |- | 211502004 || 陈雨婷 |- | 211098324 || 肖卓凡 |- | 211502003 || 郭引商 |- | 211502013 || 张逸飞 |...")
- 08:49, 16 June 2023 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2023)/第四次作业提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240005 || 张明轩 |- | 211240069 || 陈子元 |- | 201840176 || 曾安达 |- | 211250182 || 胡皓明 |- | 211250235 || 陈荣锴 |- | 211850020 || 王雷宇 |- | 211240073 || 李鸿毅 |- | 211240036 || 邵钰乾 |- | 211240094 || 陈卓 |- | 211240047 || 徐研 |- | 211240066 || 肖雨辰 |- | 211240065 || 赵欣玥 |- | 211240035 || 王祉天 |- | 211240040...")
- 14:15, 8 June 2023 Gispzjz talk contribs created page 组合数学 (Fall 2023)/Problem Set 4 (Created page with "== Problem 1 == Prove that * <math>R(4,3)\leq 9</math>. (Hint: Proof by contradiction. Color the edges of <math>K_9</math> in red and blue, and assume that there are no red triangles and no blue <math>4</math>-cliques. Try to determine the number of red and blue edges adjacent to each vertex) * <math>R(4,4)\leq 18</math>. ==Problem 2== We color each non-empty subset of <math>[n]=\{1,2,\ldots,n\}</math> with one of the <math>r</math> colors in <math>[r]</math>. Show tha...")
- 06:27, 8 June 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法16.pdf
- 06:27, 8 June 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法16.pdf
- 09:57, 7 June 2023 Liuexp talk contribs created page File:Stat02-2023.pdf
- 09:57, 7 June 2023 Liuexp talk contribs uploaded File:Stat02-2023.pdf
- 09:07, 5 June 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法15.pdf
- 09:07, 5 June 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法15.pdf
- 15:11, 3 June 2023 Liuexp talk contribs deleted page File:Stat01-2023.pdf (filename)
- 15:10, 3 June 2023 Liuexp talk contribs created page File:Stat01.pdf
- 15:10, 3 June 2023 Liuexp talk contribs uploaded File:Stat01.pdf
- 15:08, 3 June 2023 Liuexp talk contribs undeleted page File:Stat01-2023.pdf (1 revision and 1 file)
- 15:06, 3 June 2023 Liuexp talk contribs deleted page File:Stat01-2023.pdf (filename)
- 14:59, 3 June 2023 Liuexp talk contribs created page File:Stat01-2023.pdf
- 14:59, 3 June 2023 Liuexp talk contribs uploaded File:Stat01-2023.pdf
- 14:01, 3 June 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/OST and applications (Created page with "=可选停时定理= '''可选停时定理''' ('''Optional Stopping Theorem''', '''OST'''),有事也被称为'''鞅停时定理''' ('''Martingale Stopping Theorem''')、'''可选抽样定理''' ('''Optional Sampling Theorem''') 等,是约瑟夫·杜布 ([https://en.wikipedia.org/wiki/Joseph_L._Doob Joseph Doob]) 发现的关于鞅的停时的刻画定理。 首先定义鞅 (martingale)。这是一类由公平赌博定义的随机过程。 {{Theorem|定义| :令 <ma...")
- 11:44, 3 June 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Matching theory (Created page with "== Systems of Distinct Representatives (SDR)== A '''system of distinct representatives (SDR)''' (also called a '''transversal''') for a sequence of (not necessarily distinct) sets <math>S_1,S_2,\ldots,S_m</math> is a sequence of <font color=red>''distinct''</font> elements <math>x_1,x_2,\ldots,x_m</math> such that <math>x_i\in S_i</math> for all <math>i=1,2,\ldots,m</math>. === Hall's marriage theorem === If the sets <math>S_1,S_2,\ldots,S_m</math> have a system of dist...")
- 09:59, 1 June 2023 Roundgod talk contribs created page 组合数学 (Spring 2023)/第三次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220060 || 林荣恩 |- | 191250004 || 曹雨森 |- | 191250127 || 孙伟杰 |- | 191250145 || 王子鉴 |- | 191820255 || 臧正贻 |- | 201220011 || 章振辉 |- | 201220035 || 丁天行 |- | 201220043 || 吕培锋 |- | 201220073 || 曹云帆 |- | 201220092 || 吴杰伦 |- | 201220098 || 杨林 |- | 201220107 || 贺柄毓 |- | 201220112 || 徐雪梅 |- | 20122012...")
- 07:04, 1 June 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework7 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211502013 || 张逸飞 |- | 211240066 || 肖雨辰 |- | 211850020 || 王雷宇 |- | 211220009 || 韦玮 |- | 211220093 || 曹博晗 |- | 211220018 || 陈润涛 |- | 211240074 || 余今 |- | 201240012 || 尹安周 |- | 211240002 || 张毅 |- | 211502003 || 郭引商 |- | 211240019 || 姜宇翔 |- | 211240032 || 黄文橼 |- | 211502004 || 陈雨婷 |- | 211240077 || 刘鹏飞 |- |...")
- 06:55, 1 June 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments8.pdf
- 06:55, 1 June 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments8.pdf
- 06:01, 30 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法14.pdf
- 06:01, 30 May 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法14.pdf
- 06:39, 26 May 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Ramsey theory (Created page with "== Ramsey's Theorem == === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem| :Let <math>k,\ell</math> be positive integers. Then there exists an integer <math>R(k,\ell)</math> satisfying: :If <math>n\ge R(k,\ell)</math>, for any coloring of edges of <math>K_n</math> with two colors red and blue, there exists a red <math>K_k</math> or a blue <math>K_\ell</math>. }} {{Proof| We show that <math>R(k,\ell)</math> is finite by induction on <math>k+\ell</math>. For the...")
- 05:40, 25 May 2023 Chenxiaoyu talk contribs uploaded a new version of File:计算方法 Numerical method (Spring 2023)-Assignments7.pdf
- 20:08, 24 May 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Hoeffding's lemma (Created page with "霍夫丁引理(Hoeffding's lemma)在霍夫丁不等式([https://en.wikipedia.org/wiki/Hoeffding%27s_inequality Hoeffding's inequality])的证明中,扮演着关键角色。该引理陈述如下: {{Theorem|霍夫丁引理| :若随机变量 <math>Y</math> 满足 <math>\mathbb{E}[Y]=0</math> 且存在实数 <math>a,b\in\mathbb{R}</math> 使得几乎必然地 (a.s.) <math>a\le Y\le b</math>,则对于任意 <math>\lambda\in\mathbb{R}</math>,都有 ::<math>\ma...")
- 12:27, 24 May 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Entropy and volume of Hamming balls (Created page with "在求解抛掷公平硬币(fair coin)的尾概率时,我们经常会需要分析如下二项式系数求和: :<math>\sum_{1\le k\le r}{n\choose k}</math>,对于某个<math>1\le r\le n</math> 这其实等价与求一个 <math>n</math> 维汉明空间中半径为 <math>r</math> 的球的体积。 :{|border="2" width="100%" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;...")
- 08:01, 22 May 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 4 (Created page with "*目前作业非最终版本! *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。 == Assumption throughout Problem Set 3== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> <p>The term <math>\log</math> used in thi...")
- 05:47, 22 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法13.pdf
- 05:47, 22 May 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法13.pdf
- 12:14, 21 May 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Extremal set theory (Created page with "== Sunflowers == An set system is a '''sunflower''' if all its member sets intersect at the same set of elements. {{Theorem|Definition (sunflower)| : A set family <math>\mathcal{F}\subseteq 2^X</math> is a '''sunflower''' of size <math>r</math> with a '''core''' <math>C\subseteq X</math> if ::<math>\forall S,T\in\mathcal{F}</math> that <math>S\neq T</math>, <math>S\cap T=C</math>. }} Note that we do not require the core to be nonempty, thus a family of disjoint sets is...")
- 16:44, 18 May 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework6 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211220009 || 韦玮 |- | 211850020 || 王雷宇 |- | 211502008 || 李诚希 |- | 211502014 || 刘奕 |- | 211220093 || 曹博晗 |- | 211220038 || 胡文菁 |- | 201180187 || 曾俊凯 |- | 211502002 || 王文萱 |- | 211502003 || 郭引商 |- | 211240077 || 刘鹏飞 |- | 211220118 || 刘艺葳 |- | 211240090 || 林锟珉 |- | 211502004 || 陈雨婷 |- | 211240066 || 肖雨辰 |...")
- 13:47, 17 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments7.pdf
- 13:47, 17 May 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments7.pdf
- 12:39, 14 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法12.pdf
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- 05:50, 14 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法11.pdf
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- 12:28, 10 May 2023 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2023)/第三次作业提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240076 || 刘嘉欣 |- | 211240066 || 肖雨辰 |- | 211850020 || 王雷宇 |- | 201840176 || 曾安达 |- | 211240013 || 李昀芃 |- | 211250001 || 鞠哲 |- | 211240005 || 张明轩 |- | 211240065 || 赵欣玥 |- | 211240009 || 陆一阳 |- | 211240045 || 杨镇源 |- | 211240073 || 李鸿毅 |- | 211240004 || 马尧 |- | 211250235 || 陈荣锴 |- | 211098200 |...")
- 15:58, 8 May 2023 Roundgod talk contribs created page 组合数学 (Fall 2023)/Problem Set 3 (Created page with "== Problem 1 == Solve the following two existence problems: * You are given <math>n</math> integers <math>a_1,a_2,\dots,a_n</math>, such that for each <math> 1\leq i\leq n</math> it holds that <math>i-n\leq a_i\leq i-1</math>. Show that there exists a nonempty subset of these integers, whose sum is equal to <math> 0 </math>.")
- 08:55, 4 May 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Extremal graph theory (Created page with "== Forbidden Cliques == Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" === Mantel's theorem === We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</math>. {{Theorem|Theorem (Mantel 1907)| :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <m...")
- 06:14, 4 May 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework5 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 201180187 || 曾俊凯 |- | 211502020 || 周相羽 |- | 211220009 || 韦玮 |- | 211502013 || 张逸飞 |- | 211502016 || 谢模阳 |- | 211240066 || 肖雨辰 |- | 211098322 || 陈思翔 |- | 211850020 || 王雷宇 |- | 211502003 || 郭引商 |- | 211220038 || 胡文菁 |- | 211502019 || 朱星宇 |- | 211240077 || 刘鹏飞 |- | 211502023 || 祝晨曦 |- | 2115020...")
- 06:05, 4 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments6.pdf
- 06:05, 4 May 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments6.pdf
- 14:47, 2 May 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法10.pdf
- 14:47, 2 May 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法10.pdf
- 14:35, 30 April 2023 Roundgod talk contribs created page 组合数学 (Spring 2023)/第二次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220020 || 戴一帆 |- | 191220060 || 林荣恩 |- | 191250004 || 曹雨森 |- | 191250127 || 孙伟杰 |- | 191250145 || 王子鉴 |- | 191820255 || 臧正贻 |- | 191840186 || 彭昕昂 |- | 201220011 || 章正辉 |- | 201220035 || 丁天行 |- | 201220043 || 吕培锋 |- | 201220073 || 曹云帆 |- | 201220092 || 吴杰伦 |- | 201220098 || 杨林 |- | 20122010...")
- 15:53, 27 April 2023 Etone talk contribs created page 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...")
- 09:56, 24 April 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 3 (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。 == Assumption throughout Problem Set 3== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> <p>The term <math>\log</math> used in this context refers to the natural l...")
- 16:05, 20 April 2023 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2023)/第二次作业提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211830008 || 缪天顺 |- | 211240066 || 肖雨辰 |- | 211250182 || 胡皓明 |- | 211240076 || 刘嘉欣 |- | 211250235 || 陈荣锴 |- | 211850008 || 林朗 |- | 211240059 || 孙骞 |- | 211250044 || 朱家辰 |- | 211240046 || 吴奕胜 |- | 211240045 || 杨镇源 |- | 211870257 || 黄泽方 |- | 211850020 || 王雷宇 |- | 211098336 || 王远博 |- | 211240040 |...")
- 06:51, 20 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法9.pdf
- 06:51, 20 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法9.pdf
- 06:50, 20 April 2023 Chenxiaoyu talk contribs uploaded a new version of File:计算方法 Numerical method (Spring 2023)-Assignments5.pdf
- 06:48, 20 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments5.pdf
- 06:48, 20 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments5.pdf
- 06:47, 20 April 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework4 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211502020 || 周相羽 |- | 211502005 || 黄逸飞 |- | 211502013 || 张逸飞 |- | 211502016 || 谢模阳 |- | 211502003 || 郭引商 |- | 211502002 || 王文萱 |- | 211240009 || 陆一阳 |- | 211220038 || 胡文菁 |- | 201240012 || 尹安周 |- | 211220093 || 曹博晗 |- | 211240032 || 黄文橼 |- | 211502004 || 陈雨婷 |- | 211240066 || 肖雨辰 |- | 211502008 || 李...")
- 12:56, 18 April 2023 Etone talk contribs created page 组合数学 (Fall 2023)/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...")
- 11:44, 18 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/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)子图概...")
- 02:29, 18 April 2023 User account Hlx talk contribs was created by Liuexp talk contribs
- 18:17, 17 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/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: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> 使得对于 <math>[a,b]</math>...")
- 14:58, 17 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/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...")
- 02:27, 17 April 2023 Xyfu talk contribs moved page File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf.pdf to File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf
- 02:03, 17 April 2023 Xyfu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf.pdf
- 02:03, 17 April 2023 Xyfu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf.pdf
- 12:46, 13 April 2023 Gispzjz talk contribs created page 组合数学 (Fall 2023)/Problem Set 2 (Created page with "Let <math>S=\{P_1,...,P_n\}</math> be a set of properties, and let <math>f_k</math> (respectively, <math>f_{\geq k}</math>) denote the number of objects in a finite set <math>U</math> that have '''exactly''' <math>k</math> (respectively, '''at least''' <math>k</math>) of the properties. Let <math>A_i</math> denote the set of objects satisfies <math>P_i</math> in <math>U</math>, for any <math>I\subseteq\{1,...,n\}</math>, we denote <math>A_I=\bigcap_{i\in I}A_i</math> wi...")
- 11:36, 13 April 2023 Etone talk contribs created page 组合数学 (Fall 2023)/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...")
- 13:06, 12 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Average-case analysis of QuickSort (Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''('''Quicksort''')]是由Tony Hoare发现的基于比较的(comparison-based)排序算法。该算法的伪代码描述如下(为方便起见,假设数组元素互不相同——更一般情况的分析易推广得到): '''''QSort'''''(A): 输入A[1...n]是存有n个不同数字的数组 if n>1 then '''pivot''' = A[1]; 将A中<pivot的元素存于数组L,将>pivot的元素存于...")
- 05:48, 11 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法7.pdf
- 05:48, 11 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法7.pdf
- 02:22, 6 April 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework3 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240009 || 陆一阳 |- | 211502020 || 周相羽 |- | 211502005 || 黄逸飞 |- | 211240066 || 肖雨辰 |- | 211502025 || 吴文翔 |- | 211502016 || 谢模阳 |- | 211098322 || 陈思翔 |- | 211220009 || 韦玮 |- | 211850020 || 王雷宇 |- | 211240032 || 黄文橼 |- | 211098324 || 肖卓凡 |- | 211220038 || 胡文菁 |- | 211240090 || 林锟珉 |- | 211502014 || 刘奕...")
- 02:16, 6 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments4.pdf
- 02:16, 6 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments4.pdf
- 15:05, 1 April 2023 Liuexp talk contribs created page File:计算方法6.pdf
- 15:05, 1 April 2023 Liuexp talk contribs uploaded File:计算方法6.pdf
- 14:25, 29 March 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Pólya's theory of counting (Created page with "== Groups == A group <math>(G,\cdot)</math> is set <math>G</math> along with a binary operator <math>\cdot</math> which satisfies the following axioms: * ''closure'': <math>\forall g,h\in G, g\cdot h \in G</math>; * ''associativity'': <math>\forall f,g,h\in G, f\cdot(g\cdot h)=(f\cdot g)\cdot h</math>; * ''identity'': there exists a special element <math>e\in G</math>, called the '''identity''', such that <math>e\cdot g=g</math> for any <math>g\in G</math>; * ''inverse''...")
- 10:29, 27 March 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 2 (Created page with "== Problem 1 (Warm-up problems) == <ul> <li>[<strong>Function of random variable (I)</strong>] Let [math]X[/math] be a random variable and [math]g:\mathbb{R} \to \mathbb{R}[/math] be continuous and strictly increasing. Show that [math]Y = g(X)[/math] is a random variable.</li> <li>[<strong>Function of random variable (II)</strong>] Let [math]X[/math] be a random variable with distribution function [math]\max(0,\min(1,x))[/math]. Let [math]F[/math] be a distribution func...") Tag: Visual edit: Switched
- 09:08, 27 March 2023 Roundgod talk contribs created page 组合数学 (Spring 2023)/第一次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220020 || 戴一帆 |- | 191220060 || 林荣恩 |- | 191250004 || 曹雨森 |- | 191250127 || 孙伟杰 |- | 191250145 || 王子鉴 |- | 191820255 || 臧正贻 |- | 201180088 || 陈浩楠 |- | 201220011 || 章正辉 |- | 201220035 || 丁天行 |- | 201220043 || 吕培锋 |- | 201220073 || 曹云帆 |- | 201220092 || 吴杰伦 |- | 201220098 || 杨林 |- | 20122010...")
- 04:03, 26 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法5.pdf
- 04:03, 26 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法5.pdf
- 07:30, 24 March 2023 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2023)/第一次作业提交名单 (submission_list) Tag: Visual edit
- 06:56, 17 March 2023 Xyfu talk contribs moved page File:计算方法4.pdf to File:计算方法 Numerical method (Spring 2023)-计算方法4.pdf
- 06:46, 17 March 2023 Xyfu talk contribs created page File:计算方法4.pdf
- 06:46, 17 March 2023 Xyfu talk contribs uploaded File:计算方法4.pdf
- 12:45, 16 March 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Sieve methods (Created page with "== Principle of Inclusion-Exclusion == Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is :<math>|A\cup B|=|A|+|B|-{\color{Blue}|A\cap B|}</math>. For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is computed as :<math>|A\cup B\cup C|=|A|+|B|+|C|-{\color{Blue}|A\cap B|}-{\color{Blue}|A\cap C|}-{\color{Blue}|B\cap C|}+{\color{Red}|A\cap B\cap C|}</math>. This is illu...")
- 07:00, 16 March 2023 Roundgod talk contribs created page 组合数学 (Fall 2023)/Problem Set 1 (Created page with "== Problem 1 == Fix positive integers <math>n</math> and <math>k</math>. Let <math>S</math> be a set with <math>|S|=n</math>. Find the number of <math>k</math>-tuples <math>(T_1,T_2,\dots,T_k)</math> of subsets <math>T_i</math> of <math>S</math> subject to each of the following conditions separately. Briefly explain your solution. * <math>T_1\subseteq T_2\subseteq \cdots \subseteq T_k.</math> * The <math> T_i</math>s are pairwise disjoint. * <math> T_1\cup T_2\cup \cdot...")
- 16:10, 15 March 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework2 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240009 || 陆一阳 |- | 211240066 || 肖雨辰 |- | 211502005 || 黄逸飞 |- | 211220118 || 刘艺葳 |- | 211502013 || 张逸飞 |- | 211220009 || 韦玮 |- | 201180132 || 徐宸宇 |- | 211502014 || 刘奕 |- | 211502020 || 周相羽 |- | 211502008 || 李诚希 |- | 211220093 || 曹博晗 |- | 211220121 || 唐周旋 |- | 211220018 || 陈润涛 |- | 211240019 || 姜宇翔 |...")
- 11:18, 15 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments3.pdf
- 11:18, 15 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments3.pdf
- 17:35, 11 March 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Karger's min-cut algorithm (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...")
- 16:43, 11 March 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Polynomial identity testing (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...")
- 06:12, 10 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法3.pdf
- 06:12, 10 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法3.pdf
- 15:25, 3 March 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 1 (Created page with "*目前作业非最终版本。 *每道题目的解答都要有<font color="red" size=5>完整的解题过程</font>。中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。 Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})<\math>. == Problem 1 ==")
- 08:31, 3 March 2023 Etone talk contribs created page 组合数学 (Fall 2023)/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...")
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- 07:27, 2 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法2.pdf
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- 07:25, 2 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments2.pdf
- 07:25, 2 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments2.pdf
- 16:41, 1 March 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework1 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240009 || 陆一阳 |- | 211840271 || 许宏洋 |- | 211220148 || 唐子汉 |- | 211240066 || 肖雨辰 |- | 211870268 || 唐炫 |- | 211220076 || 杨景越 |- | 211098322 || 陈思翔 |- | 211220118 || 刘艺葳 |- | 211220018 || 陈润涛 |- | 211502003 || 郭引商 |- | 211220166 || 王诚昊 |- | 211850020 || 王雷宇 |- | 211240090 || 林锟珉 |- | 211840165 || 孙源...")
- 05:40, 25 February 2023 User account Xyfu talk contribs was created by Liuexp talk contribs
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- 13:28, 17 February 2023 Roundgod talk contribs created page 计算复杂性 (Spring 2023) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>计算复杂性 <br>Computational Complexity</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 姚鹏晖 |header3 = |label3 = Email |data3 = pyao@nju.edu.cn |header4 = |label4= Offi...") Tag: Visual edit: Switched
- 13:22, 16 February 2023 Etone talk contribs created page 组合数学 (Fall 2023)/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...")
- 10:26, 16 February 2023 Etone talk contribs created page File:Stanley-2e.jpg
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- 13:57, 15 February 2023 Liuexp talk contribs created page 计算方法 Numerical method (Spring 2023) (Created page with "test")
- 07:28, 13 February 2023 Etone talk contribs created page File:Probability and Computing 2ed.jpg
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- 07:18, 13 February 2023 Etone talk contribs uploaded a new version of File:Grimmett probability.jpg
- 07:16, 13 February 2023 Etone talk contribs created page File:Grimmett probability.jpg
- 07:16, 13 February 2023 Etone talk contribs uploaded File:Grimmett probability.jpg
- 07:14, 13 February 2023 Etone talk contribs created page File:概率导论.jpeg
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- 07:04, 13 February 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>概率论与数理统计<br> Probability Theory and <br> Mathematical Statistics</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructors |label1 = |data1 = |header2 = |label2 = |data2 = 尹一通 |header3 = |label3 = Email |data3 = yinyt@...")
- 05:23, 13 February 2023 Etone talk contribs created page File:TheBook-6ed.jpeg
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- 05:19, 13 February 2023 Etone talk contribs created page File:Alon-Spencer-4ed.jpg
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- 05:17, 13 February 2023 Etone talk contribs created page File:Lovasz-matching-theory.jpg
- 05:17, 13 February 2023 Etone talk contribs uploaded File:Lovasz-matching-theory.jpg
- 05:17, 13 February 2023 Etone talk contribs created page 组合数学 (Spring 2023)/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...")
- 05:07, 13 February 2023 Etone talk contribs created page 组合数学 (Spring 2023) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>组合数学 <br> Combinatorics</font> |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 = yitong.yin@gmail.com yinyt@nju.edu.cn |header4 = |la...")
- 18:52, 5 January 2023 Roundgod talk contribs created page 高级算法 (Fall 2022)/第四次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220153 || 张丁楚 |- | 191240080 || 周晓 |- | 201220035 || 丁天行 |- | 201250217 || 章豪 |- | 201830122 || 邹忠奇 |- | 201840106 || 张弈垚 |- | 502022330003 || 陈浩宇 |- | 502022330007 || 陈瑄 |- | 502022330010 || 董世晨 |- | 502022330013 || 方子伊 |- | 502022330013 || 韩翔宇 |- | 502022330020 || 黄嘉铧 |- | 502022330044 || 王常新...")
- 06:48, 13 December 2022 Roundgod talk contribs created page 高级算法 (Fall 2022)/第三次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220153 || 张丁楚 |- | 191240080 || 周晓 |- | 201220035 || 丁天行 |- | 201250217 || 章豪 |- | 201830122 || 邹忠奇 |- | 201840106 || 张弈垚 |- | 502022330003 || 陈浩宇 |- | 502022330007 || 陈瑄 |- | 502022330010 || 董世晨 |- | 502022330013 || 方子伊 |- | 502022330013 || 韩翔宇 |- | 502022330020 || 黄嘉铧 |- | 502022330044 || 王常新...")
- 07:29, 12 December 2022 Gispzjz talk contribs created page 高级算法 (Fall 2022)/Problem Set 4 (Created page with "== Problem 1 == Suppose there is a coin <math> C </math>. During each query, it outputs HEAD with probability <math>p</math> and TAIL with probability <math>1-p</math>, where <math> p \in (0, 1) </math> is a real number. * Let <math> q \in (0, 1) </math> be another real number. Design an algorithm that outputs HEAD with probability <math>q</math> and TAIL with probability <math>1-q</math>. There is no other random sources for your algorithm except the coin <math>C</math...")
- 15:23, 29 November 2022 Etone talk contribs created page Assignment 4, Fall 2022 (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...")
- 06:53, 28 November 2022 Roundgod talk contribs created page 高级算法 (Fall 2022)/Problem Set 3 (Created page with "== Problem 1 == Let <math>N</math> be a set (the "universe") and <math>F</math> a function mapping subsets of <math>N</math> to real numbers. There are two different standard definitions of what it means for <math>F</math> to be '''submodular''': (i) For all <math>A</math>, <math>B</math>, :<math>F(A\cap B)+F(A\cup B)\leq F(A)+F(B)</math>. (ii) For all <math>A\subseteq B</math>, <math>j\notin B</math>, :<math>F(A\cup\{j\})-F(A)\geq F(B\cup\{j\})-F(B)</math>. Your ta...")
- 13:01, 24 November 2022 Roundgod talk contribs created page 高级算法 (Fall 2022)/第二次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220153 || 张丁楚 |- | 191240080 || 周晓 |- | 191250084 || 林均劼 |- | 201220035 || 丁天行 |- | 201250217 || 章豪 |- | 201840106 || 张弈垚 |- | 201830122 || 邹忠奇 |- | 502022330003 || 陈浩宇 |- | 502022330007 || 陈瑄 |- | 502022330010 || 董世晨 |- | 502022330013 || 方子伊 |- | 502022330013 || 韩翔宇 |- | 502022330020 || 黄嘉铧 |-...")
- 05:51, 23 November 2022 Etone talk contribs created page Namelist Assignment 3 2022 (Created page with "姓名 学号 周榆杰 191870288 罗健峰 191830098 欧阳玥芸 191830111 代欣怡 652022280002 丁宇轩 502022280004 窦吉斌 502022280006 方旭 502022280008 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 5020222...")
- 15:45, 19 November 2022 Etone talk contribs created page 高级算法 (Fall 2022)/Greedy and Local Search (Created page with "= Scheduling = We consider the following scheduling problem: * There are <math>n</math> '''jobs''' to be processed. * There are <math>m</math> identical parallel '''machines'''. Each machine can start processing jobs at time 0 and can process at most one job at a time. * Each job <math>j=1,2,\ldots, n</math> must be processed on one of these machines for <math>p_j</math> time units without interruption. <math>p_j</math> is called the '''processing time''' of job <math>j...")
- 11:17, 9 November 2022 Etone talk contribs created page Namelist Assignment 2 2022 (Created page with "姓名 学号 周榆杰 191870288 罗健峰 191830098 欧阳玥芸 191830111 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 502022...")
- 10:10, 1 November 2022 Etone talk contribs created page 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...")
- 02:59, 31 October 2022 Roundgod talk contribs created page 高级算法 (Fall 2022)/Problem Set 2 (added hw2 page)
- 02:39, 27 October 2022 Etone talk contribs created page 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...")
- 08:52, 25 October 2022 Roundgod talk contribs created page 高级算法 (Fall 2022)/第一次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220076 || 吕玉龙 |- | 191220153 || 张丁楚 |- | 191240080 || 周晓 |- | 191250084 || 林均劼 |- | 201220035 || 丁天行 |- | 201250217 || 章豪 |- | 201840106 || 张弈垚 |- | 201830122 || 邹忠奇 |- | 502022330003 || 陈浩宇 |- | 502022330007 || 陈瑄 |- | 502022330010 || 董世晨 |- | 502022330013 || 方子伊 |- | 502022330013 || 韩翔宇 |- |...")
- 09:32, 24 October 2022 Etone talk contribs created page 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...")
- 12:53, 11 October 2022 Etone talk contribs created page 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...")
- 12:53, 11 October 2022 Etone talk contribs created page 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...")
- 08:39, 9 October 2022 Gispzjz talk contribs created page 高级算法 (Fall 2022)/Problem Set 1 (Created page with "== Problem 1 == Modify the Karger's Contraction algorithm so that it works for the ''weighted min-cut problem''. Prove that the modified algorithm returns a weighted minimum cut with probability at least <math>\frac{2}{n(n-1)}</math>. The weighted min-cut problem is defined as follows. *'''Input''': an undirected weighted graph <math>G(V, E)</math>, where every edge <math>e \in E</math> is associated with a positive real weight <math>w_e</math>; *'''Output''': a cut <ma...")
- 02:51, 5 October 2022 Etone talk contribs created page 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>, <...")
- 15:49, 3 October 2022 Etone talk contribs created page 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...")
- 15:48, 3 October 2022 Etone talk contribs created page 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...")
- 08:08, 26 September 2022 Etone talk contribs created page 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...")
- 08:03, 26 September 2022 Etone talk contribs created page 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...")
- 11:48, 21 September 2022 Etone talk contribs created page 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...")
- 11:47, 21 September 2022 Etone talk contribs created page 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...")
- 05:43, 13 September 2022 Etone talk contribs created page 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...")
- 05:43, 13 September 2022 Etone talk contribs created page 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...")
- 13:57, 5 September 2022 Gispzjz talk contribs created page File:DPV.jpg
- 13:57, 5 September 2022 Gispzjz talk contribs uploaded File:DPV.jpg
- 13:53, 5 September 2022 Roundgod talk contribs created page 高级算法 (Fall 2022) / 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...")
- 13:48, 5 September 2022 Roundgod talk contribs created page File:Algo.jpg
- 13:48, 5 September 2022 Roundgod talk contribs uploaded File:Algo.jpg
- 07:31, 5 September 2022 Etone talk contribs created page 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...")
- 07:31, 5 September 2022 Etone talk contribs created page 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...")
- 07:29, 1 September 2022 User account Gispzjz talk contribs was created by Etone talk contribs
- 06:54, 1 September 2022 Roundgod talk contribs created page 高级算法 (Fall 2022) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>高级算法 <br>Advanced Algorithms</font> |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 |data...")
- 06:49, 1 September 2022 User account Roundgod talk contribs was created by Etone talk contribs
- 13:30, 30 August 2022 Liuexp talk contribs changed group membership for Etone from (none) to administrator
- 13:24, 30 August 2022 User account Etone talk contribs was created by Liuexp talk contribs (etone)
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