PPT-Page Rank, Graph Eigenvalues, Kleinberg

Presentations  Nikhil Baradwaj and Seung Hwan Lee  1132017 Starting with  Page Rank  and the founders of Google it has become popular to model the web and social media as . 1 Introduction Spectral graph theory has a long history In the early days matrix theory and linear algebra were used to analyze adjacency matrices of graphs Algebraic meth ods have proven to be especially e64256ective in treating graphs which are reg The resilience of networks to various types of failures is an undercurrent in many parts of graph theory and network algorithms In this paper we study the resilience of networks in the presence of cascading failures failures that spread from one no Slides adapted from . Information Retrieval and Web Search, Stanford University, Christopher Manning and Prabhakar Raghavan. CS345A, Winter 2009: Data Mining. Stanford University, Anand Rajaraman, Jeffrey D. Ullman. Apache Spark. Patrick Wendell - Databricks. What is Spark?. Efficient. General execution graphs. In-memory storage. Usable. Rich APIs in Java, . Scala. , Python. Interactive shell. Fast. and . Expressive. . Negahban. . Sewoong. Oh Devavrat Shah. Yale + UIUC + MIT. Rank centrality: . Ranking from comparisons. Some scenarios. Given partial preferences. Compute . global. . ranking . with . scores to reflect . (Non-Commuting). . Random Symmetric Matrices? :. . A "Quantum Information" Inspired Answer. . Alan Edelman. Ramis. . Movassagh. July 14, 2011. FOCM. Random Matrices. Example Result. p=1 .  classical probability. families and . Ramanujan graphs. Tony Shaheen. CSU Los Angeles. Before we get started on expander . graphs I . want . to . give a definition that we will . use in this talk. .. A graph is . regular. if every . When . I had reached my fiftieth year, I had published a vast quantity of drawing. ;. . but . I am unsatisfied with all that I have . produced before my seventieth year”. . Hokusai. . Community . 4. The. . Gauß. . scheme. A . linear. system of . equations. Matrix. algebra . deals. . essentially. . with. . linear. . linear. systems.. Multiplicative. . elements. .. A . non-linear. system. and . eigenvectors. Births. Deaths. Population. . increase. Population. . increase. = . Births. – . deaths. t. Equilibrium. N: . population. . size. b: . birthrate. d: . deathrate. The. net . Prepared by Vince Zaccone. For Campus Learning Assistance Services at UCSB. Prepared by Vince Zaccone. For Campus Learning Assistance Services at UCSB. Consider the equation . , where A is an . nxn. Information Retrieval and Web Search, Stanford University, Christopher Manning and Prabhakar Raghavan. CS345A, Winter 2009: Data Mining. Stanford University, Anand Rajaraman, Jeffrey D. Ullman. 2. . (Non-Commuting). . Random Symmetric Matrices? :. . A "Quantum Information" inspired Answer. . Alan Edelman. Ramis. . Movassagh. Dec 10, 2010. MSRI. , Berkeley. Complicated Roadmap. Complicated Roadmap. Page Rank Overview Two dimensional arrays Monte Carlo algorithms Searching the world wide web Big data Page rank Goal: we will write a program to compute the relevancy of WWW documents based on the static structure of the WWW.