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Applied Mathematics Colloquium

Friday, November 2, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Collective Neuronal Dynamics and Drift-Diffusion Models for Decision Making

Philip Holmes

Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering

Princeton University

Princeton, NJ

Abstract

Behavioral and neural data from humans and animals identifying randomly-presented stimuli can be described by a simple stochastic differential equation: the drift-diffusion (DD) process. In the two-alternative, forced-choice task the DD process describes how the logarithm of a likelihood ratio evolves as noisy incoming evidence accumulates. DD and related Ornstein-Uhlenbeck processes emerge as reductions of multi-component neural networks on stochastic center manifolds, and also as continuum limits of an optimal decision maker: the sequential probability ratio test. I will outline some background from cognitive psychology and neuroscience, and explain how DD models with variable drift rates can represent `bottom-up' information on stimulus identity and reward magnitudes for correct choices, and can capture `top-down' phenomena such as attention and cognitive control. I will also discuss attempts to link these `high-level' descriptions with biophysical models of neural substrates

I will draw on joint work with Eric Brown, Jeff Moehlis, Juan Gao, Philip Eckhoff, Sophie Liu, Angela Yu, Rafal Bogacz, Pat Simen, Kong-Fatt Wong, Joshua Gold and Jonathan Cohen.

More info and (p)reprints at: http://www.princeton.edu/mae/people/faculty/holmes/