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.
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Mathematical Biology Program
Department of Mathematics
University of Utah
155 South 1400 East Room 233
Salt Lake City, UT 84112
rasmusse@math.utah.edu
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