Mathematical Biology Seminar

Michael A. Buice
University of Chicago
Wednesday March 23, 2005
3:05pm in LCB 121
" Stochastic Neural Field Theory"

Understanding the role of correlations has long been a problem in neural networks as well as other biological systems. Do they encode stimulus information? Do they have some other role? Standard methods of studying neural networks are mean field descriptions (i.e. the Wilson-Cowan equations) which neglect higher order statistics in the dynamics under study. We present a theoretical approach and formalism which aims to facilitate the computation of higher order statistics. This approach involves mapping the Master Equation description for a Markov process onto a Quantum Field Theory. This facilitates calculating corrections to the equations of motion for the correlation functions as well as calculating the solution to arbitrary order in a perturbation expansion. In addition, insights that Renormalization Group methods provide to Quantum Field Theories may yield similar results for neural networks. We will outline the concepts, advantages, and disadvantages of the method.