## Departmental Colloquium

Jack Cowan

University of Chicago

Stochastic Wilson-Cowan equations for networks of excitatory and inhibitory neurons

**Abstract:**We have recently found a way to describe large-scale neural activity in terms of non-equilibrium statistical mechanics. This allows us to calculate the effects of fluctuations and correlations on neural activity. Major results of this formulation include a role for critical branching, and the demonstration that there exists a non-equilibrium phase transition in neocortical activity, which is in the same universality class as directed percolation. Here we show how the population dynamics of interacting excitatory and inhibitory neural populations can be described in similar terms, and how such a theory can be used to explain the origins and properties of random bursts of synchronous activity (avalanches), population oscillations (quasi-cycles), synchronous oscillations (limit-cycles) and fluctuation-driven spatial patterns (quasi-patterns). If time permits, we will also describe recent work on a way to incorporate spike-timing dependent plasticity into a model for self-organized criticality.

Friday March 8, 2013 at 3:00 PM in SEO 636