Taylor's law for exponentially growing local populations linked by migration.

We consider the dynamics of a collection of n>1 populations in which each population has its own rate of growth or decay, fixed in continuous time, and migrants may flow from one population to another over a fixed network, at a rate, fixed over time, times the size of the sending population. This model is represented by an ordinary linear differential equation of dimension n with constant coefficients arrayed in an essentially nonnegative matrix. This paper identifies conditions on the parameters of the model (specifically, conditions on the eigenvalues and eigenvectors) under which the variance of the n population sizes at a given time is asymptotically (as time increases) proportional to a power of the mean of the population sizes at that given time. A power-law variance function is known in ecology as Taylor's Law and in physics as fluctuation scaling. Among other results, we show that Taylor's Law holds asymptotically, with variance asymptotically proportional to the mean squared, on an open dense subset of the class of models considered here.

Using social networks to improve team transition prediction in professional sports.

We examine whether social data can be used to predict how members of Major League Baseball (MLB) and members of the National Basketball Association (NBA) transition between teams during their career. We find that incorporating social data into various machine learning algorithms substantially improves the algorithms' ability to correctly determine these transitions in the NBA but only marginally in MLB. We also measure the extent to which player performance and team fitness data can be used to predict transitions between teams. This data, however, only slightly improves our predictions for players for both basketball and baseball players. We also consider whether social, performance, and team fitness data can be used to infer past transitions. Here we find that social data significantly improves our inference accuracy in both the NBA and MLB but player performance and team fitness data again does little to improve this score.