Sunday, June 23, 2013

Tragedy of Great Power Politics? Modeling International War

Recently I finished reading John Mearsheimer's excellent political science book The Tragedy of Great Power Politics. In this book, Mearscheimer lays out his ``offensive realism'' theory of how countries interact with each other in the world. The book is quite readable and well-thought-out -- I'd recommend it to anyone who has an inkling for political history and geopolitics. However, as I was reading this book, I decided that there was a point of Mearsheimer's argument which could be improved by a little mathematical analysis.

Sunday, January 20, 2013

Re-evaluating the values of the tiles in Scrabble™

Recently I have seen quite a few blog posts written about re-evaluating the points values assigned to the different letter tiles in the Scrabble™ brand Crossword Game.  The premise behind these posts is that the creator and designer of the game assigned point values to the different tiles according to their relative frequencies of occurrence in words in English text, supplemented by information gathered while playtesting the game.  The points assigned to different letters reflected how difficult it was to play those letters: common letters like E, A, and R were assigned 1 point, while rarer letters like J and Q were assigned 8 and 10 points, respectively.  These point values were based on the English lexicon of the late 1930’s.  Now, some 70 years later, that lexicon has changed considerably, having gained many new words (e.g.: EMAIL) and lost a few old ones.  So, if one were to repeat the analysis of the game designer in the present day, would one come to different conclusions regarding how points should be assigned to various letters?

Tuesday, January 1, 2013

The Skeleton Supporting Search Engine Ranking Systems

A lot of the research I’m interested in relates to networks – measuring the properties of networks and figuring out what those properties mean.  While doing some background reading, I stumbled upon some discussion of the algorithm that search engines use to rank search results.  The automatic ranking of the results that come up when you search for something online is a great example of how understanding networks (in this case, the World Wide Web) can be used to turn a very complicated problem into something simple. 

Ranking search results relies on the assumption that there is some underlying pattern to how information is organized on the WWW- there are a few core websites containing the bulk of the sought-after information surrounded by a group of peripheral websites that reference the core.  Recognizing that the WWW is a network representation of how information is organized and using the properties of the network to detect where that information is centered are the key components to figuring out what websites belong at the top of the search page.