Abstract: When visualizing an ambiguous scene (such as the Necker cube) one may perceive ongoing random alternations between the possible interpretations. Dynamical models implement competition as reciprocal inhibition between neuronal populations; dominance alternates - while slow negative feedback, adaptation, sets the basic time scale (seconds) for switching. When adaptation is strong enough it overcomes dominance and alternations occur intrinsically and periodically; noise perturbs the regularity.  In a different framework, attractor-based dynamics, adaptation is weak and switches are induced by noise operating on a bistable system. Concepts from dynamical systems are applied to understand the underlying mathematical structure.  We find that statistics of the observed alternations provide constraints that favor an operating range near the transition zone between the parameter regimes for the two mechanisms.

Prof. Rinzel works in New York University Center for Neural Sciences. He is interested in the biophysical mechanisms and theoretical foundations of dynamic neural computation. With a background in engineering (BS: Univ of Florida, 1967) and applied mathematics (PhD: Courant Institute, NYU, 1973) he uses mathematical models to understand how neurons and neural circuits generate and communicate with electrical and chemical signals for physiological function. He especially relishes developing reduced, but biophysically-based, models that capture a neural system's essence. Before joining the CNS faculty (and jointly that of NYU's Courant Institute of Mathematical Sciences) in 1997, he was in the Mathematical Research Branch at the NIH for nearly 25 years.