Mathematics Department, Neurology Department, Committee on Computational Neuroscience, University of Chicago, USA
Friday 20 May 2005
B10 Seminar Room
Alexandra House, 17 Queen Square, LONDON, WC1N 3AR
Statistical Neural Field Theory
In 1972, 1973 Wilson and Cowan introduced a mathematical model for the population dynamics of nets of interacting neurons, 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 In 1978 Cowan (unpublished) showed that such a mean field can be derived from a master equation, and in 1991 that such a master equation can be conveniently represented in terms of the annihilation and creation operators of a quantum field theory. In effect, neural nets can be represented in terms of quantum spins. The resulting theory (Ohira & Cowan 1993) proved difficult to calculate. Recently Buice & Cowan (in preparation) have found a more tractable way to represent such quantum spins, and to calculate (perturbatively) the effects of fluctuations and correlations in such nets beyond the range of mean field theory. A short account of this will be given.