seminar: Statistical Mechanics of the Neocortex
speaker: Jack Cowan (University of Chicago)abstract: In 1972 Wilson and Cowan introduced a mathematical model for the population dynamics of the neocortex, based on a mean field description of the activity. In 1978 Cowan (unpublished) showed that such a mean field can be derived from a master equation, and in 1991 that such a master equation can be conveniently represented in terms of annihilation and creation operators. The resulting theory (Ohira & Cowan 1993) proved difficult to calculate. Recently Buice & Cowan (2006, submitted for publication) have found a more tractable way to represent such operators, and to calculate (perturbatively) the effects of fluctuations and correlations on neocortical activity. Major results of this formulation include a role for critical branching, and the demonstration that there exist non-equilibrium phase transitions in neocortical activity which are in the same universality class as directed percolation. This result leads to explanations for the origin of many of the scaling laws found in local field potentials and EEG, and interspike interval distributions. It also leads to ways of calculating how correlations can affect neocortical activity, and is therefore relevant for analyzing the binding problem.
timetable:
Wed 6 Sep, 14:30 - 15:30, Aula Dini
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