Lai-Sang Young (CIMS, New York University) and Kevin K. Lin (University of Arizona)

Abstract: The overall theme of this talk is that the brain is a large and very complicated dynamical system about which we have only limited knowledge, and a challenge for dynamicists is to understand the neural basis, or dynamical mechanisms, for various brain functions. There are many types of brain functions: sensory, cognitive, motor-related… Sensory problems are especially amenable to bio-mathematical analysis, because one can directly measure the cortical responses to sensory inputs. In this talk I will focus on two of the most basic functions of the primate visual system: orientation selectivity (used for detecting edges) and direction selectivity (used for tracking moving objects). Biology-based explanations for the neural origins of these functions are proposed, along with mathematical justification in idealized models and simulation results from a large neuronal network built to replicate many major functions of the primate visual cortex.

Abstract: This talk focuses on coarse-grained (CG) modeling of cortical dynamics. CG models, by working with averaged quantities like firing rates, are easier to tune, run, and analyze, and greatly reduce the cost of modeling (measured in both human and computer time). But averaging inevitably means certain intrinsic features of neuronal networks – especially their structural and dynamic variability – are lost, and a priori it is unclear to what degree one can expect CG models to capture neuronal network dynamics. Here we propose a multiscale CG strategy inspired by ideas from nonequilibrium statistical mechanics. Our simulations show that this strategy can faithfully capture the response of the primary visual cortex to external stimuli.