Prof. Philip Holmes
Department of Mechanical and Aerospace Engineering, NIMH Silvio O. Conte Center for Neuroscience Research, Princeton University

Optimal Decisions in the Brain:
From Neural Oscillators to Stochastic Differential Equations

The sequential probability ratio test (SPRT) is optimal in that it allows one to accept or reject hypotheses, based on noisy incoming evidence, with the minimum number of observations for a given level of accuracy. There is increasing neural and behavioral evidence that primate and human brains employ a continuum analogue of SPRT: the drift-diffusion (DD) process. I will review this and describe how a biophysical model of a pool of spiking neurons can be simplified to a phase oscillator and analysed to yield spike rates in response to stimuli. These spike rates tune DD parameters. This study is a small step toward the construction of a series of models, at different time and space scales, linking neural spikes to human decisions.

This work is joint with Eric Brown, Jeff Moehlis, Rafał Bogacz and Jonathan Cohen at Princeton, and Garry Aston-Jones' group (Laboratory of Neuromodulation and Behavior, University of Pennsylvania). It provides a rich, if chaotic, example of applied mathematics in action, involving probability, stochastic differential equations, and nonlinear dynamical systems.

Philip Holmes was born in the UK in 1945 and studied Engineering at the universities of Oxford and Southampton. He taught at Cornell from 1977-1994 and is currently Professor of Mechanics and Applied Mathematics at Princeton. He works in nonlinear dynamics and `chaos theory,' studying spatio-temporal patterns in physical and biological contexts. He has also published four collections of poems.