The IV AMMCS International Conference

Waterloo, Ontario, Canada | August 20-25, 2017

AMMSCS 2017 Plenary Talk

The Mathematical Limits of Sensory Integration and Control

André Longtin (University of Ottawa)

Theoretical studies of brain function have led to advances in a number of areas of applied mathematics. Recent advances are highlighted here in the context of sensory systems. These systems provide a particularly good window onto questions of neural dynamics, control and information processing, because they have a well-characterized physical input. This talk will first present recent work on information processing at the limits of sensory detection. The probabilistic encoding of sensory signals as modulations of intrinsically correlated neural point processes is shown to enhance their detectability and information content as sequences of firing or “spike” times. Downstream neurons further aim to derive optimal information about the position of objects in the environment. Their sensitivity is found to peak at a characteristic distance where the Fisher information is maximized. This result relies on a correction to the Fisher information for the positive correlations observed in the stochastic firing patterns. It provides a first mathematical description of a sensory “focus”, and this focal point corresponds to the transition from periodic to chaotic dynamics. Finally we discuss a stochastic optimal control problem to precisely target the spike times of a leaky integrate-and-fire (LIF) model of a neuron with noise. Such a model is in fact an Ornstein-Uhlenbeck process with an absorbing boundary, for which we are controlling the mean first passage time. The optimal control problem is solved using dynamic programming when the controller has access to the voltage (closed-loop control), and using a maximum principle for the transition density when the controller only has access to the spike times (open-loop control).
André Longtin is the University Research Chair in Neurophysics at the University of Ottawa, as well as Chairman of its Physics Department. He runs the Neurophysics and Nonlinear Dynamics Group, working at the interface of physics, applied mathematics, biology and medicine. His main interests lie in theoretical and computational neuroscience and the interaction of deterministic systems with noise. He received an honours B.Sc. Physics in 1983 and M.Sc. Physics in 1985 from the Université de Montréal, and his Ph.D. in Physics from McGill University in 1989. He joined Los Alamos National Laboratory as an NSERC Postdoctoral Fellow and a Los Alamos Director's Funded Fellow, where he held a joint position in the Theoretical Division T13 (Complex Systems) and the Center for Nonlinear Studies. He began as assistant professor of Physics in 1992 at the University of Ottawa. He is Professor since 2002, and cross-appointed to the Departments of Cellular and Molecular Medicine and of Mathematics and Statistics. He is founding co-director of the University of Ottawa Center for Neural Dynamics and a Fellow of the American Physical Society. He sits on the editorial board of Biological Cybernetics, Cognitive Neurodynamics, Bulletin of Mathematical Biology, Journal of Mathematical Neuroscience and Frontiers in Computational Neuroscience. He was awarded a Premiers Research Award in 1999, the inaugural award for Interdisciplinary research at U. Ottawa in 2004 (with Len Maler), a senior Humboldt Research Prize in 2010, and the NSERC Brockhouse Canada Prize in Interdisciplinary Research with Len Maler in 2017 for uncovering key features of the neural code.