MIT6_042JS10_lec39

MIT6_042JS10_lec39 - 1 Lec 14W.1 Random Walks Mathematics for Computer Science MIT 6.042J/18.062J Albert R Meyer Lec 14W.2 Applications of Random

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Unformatted text preview: 1 Lec 14W.1 Random Walks Mathematics for Computer Science MIT 6.042J/18.062J Albert R Meyer, May 12, 2010 Lec 14W.2 Applications of Random Walk • Physics — Brownian motion • Finance — stocks, options • Algorithms — web search, clustering Albert R Meyer, May 12, 2010 Lec 14W.4 Graph With Probable Transitions Outgoing-edge probabilities sum to 1 1/4 1/4 2/3 1/3 1 1/2 B O G Albert R Meyer, May 12, 2010 Lec 14W.6 1/4 1 1/4 1/2 1/4 1/4 1/2 1/4 1/4 1/2 1/4 1/4 2/3 1/3 1 1/2 1 Distribution Over Nodes ( p B , p O , p G ) ( 1 , , ) Albert R Meyer, May 12, 2010 What are p’ B , p’ O , p’ G after 1 step? Suppose you start at B : Lec 14W.7 1/4 1 1/4 1/2 1/4 1/4 1/2 1/4 1/4 1/2 1/4 1/4 2/3 1/3 1 1/2 1 Distribution Over Nodes Albert R Meyer, May 12, 2010 only get places from B , so ( p’ B , p’ G , p’ O ) 1 2 , 1 4 , 1 4 Dist after 1 step: Distribution Over Nodes 1/4 1/4 2/3 1/3 1 1/2 1/2 1/4 1/4 Dist after 1 step: Albert R Meyer, May 12, 2010 1 2 , 1 4 , 1 4 Dist after 2 steps: ( p ’’ B , p ’’ O , p ’’ G ) 2 + Pr{ G to O |at G }• p’ G p’’ O = Pr{ B to O |at B }• p’ B Distribution Over Nodes 1/4 1/4 2/3 1/3 1 1/2 1/2 1/4 1/4 Dist after 1 step: Albert R Meyer, May 12, 2010 + Pr{ O to O |at O }• p’ o 1 2 , 1 4 , 1 4 p’’ O = p’’ O = Pr{B to O|at B} • p’ B + Pr{ G to O |at G }• p’ G Distribution Over Nodes 1/4 1/4 2/3 1/3 1 1/2 1/2 1/4 1/4 Dist after 1 step: Albert R Meyer, May 12, 2010 + Pr{ O to O |at O }• p’ o 1 2 , 1 4 , 1 4 1/2 1/4 1/4 1/4 1/3 = 5/24 1/4 1/3 Distribution Over Nodes 1/4 1/4 2/3 1/3 1 1/2 1/2 7/24 5/24...
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This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec39 - 1 Lec 14W.1 Random Walks Mathematics for Computer Science MIT 6.042J/18.062J Albert R Meyer Lec 14W.2 Applications of Random

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