Recitation 3 Steve Gu Jan 31 2008.

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Presentation transcript:

Recitation 3 Steve Gu Jan 31 2008

Outline Part I: Review of LDSDDS Linear, Deterministic, Stationary, Discrete, Dynamic System Example: Google’s PageRank Part II: From Deterministic to Stochastic Randomness Some histograms

Part I

Review of LDSDDS

Review of LDSDDS For example:

Review of LDSDDS Interested? Confused? Doubted? Bored? Hey! Let’s take a real example

PageRank PageRank was developed at Stanford University by Larry Page (hence the name Page-Rank[1]) and later Sergey Brin as part of a research project about a new kind of search engine. The project started in 1995 and led to a functional prototype, named Google, in 1998

PageRank How to rank the importance of web pages?

PageRank http://en.wikipedia.org/wiki/Image:PageRanks-Example.svg

PageRank: Modelling Votes PR(v) is the PageRank of v L(v) is the number of pages linked to v PR(u) is a collection of votes by pages linked to it!

PageRank For example: A receives 3 votes B receives 1 votes C receives 1 votes D receives none B C A D

PageRank: Dynamic Systems? For N pages, say p1,…,pN Write the Equation to compute PageRank as: where l(i,j) is define to be:

PageRank: Dynamic Systems? Written in Matrix Form: F Look familiar?

PageRank: Dynamic Systems? Usually there is a damping factor d, which is used to guarantee convergence, that is:

PageRank: Dynamic Systems! PageRank is fully described by a LDSDDS There is no magic here! Ideas change the world (e.g. Google) LDSDDS is simple LDSDDS is powerful LDSDDS is useful LDSDDS is beautiful

From Deterministic to Stochastic Part II From Deterministic to Stochastic

Randomness

Randomness Stock Prices Games (Poker, Casino, etc) Biology: Evolution, Mutation Physics: Quantum Mechanics … Is the world deterministic or stochastic?

Some Common Histograms

Review LDSDDS Uncover the secret: Google’s PageRank DeterministicStochastic That’s more fascinating Welcome to the Stochastic World!

The End Thank you Q&A