CS 100 M Lecture 26

# CS 100 M Lecture 26 - 26 Models Data Simulation...

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26. Models, Data, Simulation Congressional Apportionment Google PageRank Sensitivity Analysis

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Quantifying Fairness How do you distribute 435 Congressional seats among the 50 states so that the ratio of population to delegation size is roughly the same from state to state? Quite possibly one of the greatest division problems of all time!
Quantifying Importance How do you rank web pages for importance given that you know the link structure of the Web, i.e., the in-links and out-links for each web page. Quite possibly one of the greatest ranking problems of all time!

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Related Questions How “close” is a state to losing a Congressional district because of population changes? How to do new or deleted links that involve a web page affect its PageRank?
Reasoning About Change Sensitivity analysis: How does the “answer” change if the input data changes or if the assumptions that underlie the computation change? VERY IMPORTANT IN SCIENCE & ENGINEERING

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An Earlier Example MyPi = 3.14; R = 3961.12345; EarthArea = 4*MyPi*R*R Math error in MyPi, measurement error in R, model error in spherical model, rounding error in arithmetic.
Subtext These examples provide distinct opportunities to review 100M programming techniques.

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The Apportionment Problem
Notation Number of states: n State populations: p(1),…,p(n) Total Population : P State delegation size: d(1),…,d(n) Number of seats: D

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Ideal: Equal Representation Number of states: n State populations: p(1),…,p(n) Total Population : P State delegation size: d(1),…,d(n) Number of seats: D ) ( ) ( ... ) 1 ( ) 1 ( n d n p d p D P = = =