1. Recitation 3
Steve Gu
Jan

2. 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

3. Part I

4. Review of LDSDDS

5. Review of LDSDDS
For example:

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

7. 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

8. PageRank
How to rank the importance of web pages?

9. PageRank

10. 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!

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

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

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

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

15. 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

16. From Deterministic to Stochastic
Part II
From Deterministic to Stochastic

17. Randomness

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

19. Some Common Histograms

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

21. The End
Thank you
Q&A