Course 11 Pattern formation in visual cortex

Abstract

The chapter reviews various theoretical approaches to studying spontaneous pattern formation in non-local neural models. The important role that symmetries play is emphasized throughout. The focus is on the discussion on activity-based patterns generated in primary visual cortex (V1), exploring the links between spontaneous cortical activity and the underlying functional architecture of V1. Such a link is recently indicated experimentally using single-unit recordings and real-time optical imaging, where it is found that very similar spatial patterns of ongoing population activity occur both when a neuron fires spontaneously and when it is driven by its optimal stimulus. The functional architecture of V1, emphasizing the correlations between the long-range recurrent circuitry and the various feature maps is reviewed. A number of large-scale continuum models of V1 that take into account such correlations are described and some of the basic methods for analyzing neural pattern formation including perturbation methods, the Fredholm alternative, amplitude equations, symmetric bifurcation theory, and mean field theory are introduced. These techniques are illustrated by considering the ring model of orientation tuning in a cortical hypercolumn. An example of pattern formation in a model of cortical development is discussed where the pattern is in the distribution of feedforward synaptic weights rather than in neural activity.