http://kisonecat.com research anecdotes. Mon, 21 Jul 2008 21:32:40 +0000 http://backend.userland.com/rss092 en I'll briefly introduce the Lights Out puzzle: the game is played on an n-by-n grid of buttons which, when pressed, toggle between a lit and unlit state. The twist is that toggling a light also toggles the state of its neighbors (above, below, right, left—although, on the boundary, lights ... http://kisonecat.com/2008/07/21/solutions-to-lights-out/ I made a movie recently for my advisor. The movie is so pretty, that I thought I'd share it here: may I present to you randomly drawn dots, where two dots are the same color when they touch! [flv:/wp-content/uploads/2008/07/percolation.flv /wp-content/uploads/2008/07/percolation-poster.png 250 250] I'll be a bit more explicit: a dot is ... http://kisonecat.com/2008/07/20/percolation/ In this fun paper, > MR1845679 it is pointed out that homology is a very basic invariant, and closed manifolds are very basic objects and so a very basic question is: what sequences of abelian groups are the homology groups of a closed simply connected manifold? It isn't very hard to realize any sequence of abelian ... http://kisonecat.com/2008/03/08/possible-homology-of-closed-manifolds/ I'm again applying Granger causality to time series data from Intrade. This time, however, I connect box A to box B with a green arrow if A becoming more likely causes B to become more likely, and with a red arrow if A becoming more likely causes B to become ... http://kisonecat.com/2008/03/08/political-relationships-hidden-in-markets/ Granger causality is a technique for determining whether one time series can be used to forecast another; since the Intrade market provides time series data for political questions, we can look at whether political outcomes can be used to forecast other political outcomes. There's a library for the statistical package R ... http://kisonecat.com/2008/03/06/granger-causality-and-intrade-data/ I made some movies of some of my favorite complexes: let $I^n$ be the $n$-dimensional cube, and let $e_1, \ldots, e_n$ be the $n$ edges around the origin, and let $e_i e_j$ be the square face containing the edges $e_i$ and $e_j$. Define a subcomplex $\Sigma^2_n \subset I^n$ consisting ... http://kisonecat.com/2008/02/24/movies-of-some-neat-cubical-complexes/ Drew Hevle raises a very interesting question: suppose you are stranded on a desert island; what books would be entirely useless in this situation? Here are a few books that I wouldn't want to be stranded on an island with: Federal Income Tax: Code and Regulations Selected Sections A Million Random Digits with ... http://kisonecat.com/2008/01/31/books-that-are-useless-on-a-desert-island/ The pineapple sauce pancake graph has English words as vertices, and a directed edge from $a$ to $b$ if the concatenation $ab$ is also an English word. For instance, there is a vertex labeled pine, and a vertex labeled apple, and an edge from pine to apple. Anyway, the graph ... http://kisonecat.com/2008/01/29/visualizing-pineapple-pancakes/ It was pointed out to me by Kenny Easwaran that I ought to try clustering texts that already have a natural grouping. So I ran the clustering program on 15 texts written by three authors, and here is the result: The largest eigenvalue is 25 times bigger than the next largest eigenvalue, ... http://kisonecat.com/2008/01/27/clustering-texts-with-an-obvious-grouping/ I ran my clustering program (which I just ran on the New Testament) on Shakespeare's plays—which were conveniently packaged into a text file by Open Source Shakespeare. The result was the following graph: I know little about Shakespeare, so I can't say too much about the above image. I'd love to ... http://kisonecat.com/2008/01/22/clustering-shakespeare/