Collective behavior of biological

systems inferred from the

Maximum Entropy Principle

Rodrigo Cofre, Universidad de Valparaíso

Our sensations, thoughts, and memories emerge from interactions among many neurons. Physicists have long hoped that the emergent collective activity of populations of neurons could be described using the ideas and methods of statistical mechanics. Among the many ideas rooted in statistical physics that have been suggested to characterize the collective activity in the brain, perhaps the most intriguing is the idea of self-organized criticality [1]. While it is still unclear which biological mechanisms are behind the collective behavior, the idea that biological systems poise themselves at or near a critical point remains tantalizing. In the past few years, new experimental techniques have made it possible to build statistical mechanics models of biological systems directly from experimental recordings, allowing researchers to determine whether these ideas work in their models. In this talk, I will review the surprising successes of the maximum entropy approach in the field of spike train statistics [2,3,4] and some progress we have made to generalize and better characterize results obtained from this approach. In particular, I will focus on the mathematics and numerical approximations associated with this inference procedure. At the end of the talk, I will discuss the surprising fact that the statistical models that emerge from the experimental spike train statistics seem to be poised at a critical point in their parameter space [5], which suggests that there may be some deeper theoretical principle behind this collective behavior [1].