Wednesday October 30, 2002
Department of Mathematics, University of Utah
Abstract:One of the major simplifying assumptions in many large-scale models of cortical tissue is that the interactions between cell populations are invariant under the action of the Euclidean group of rigid body motions in the plane. Euclidean symmetry plays a key role in determining the types of activity patterns and waves that can be generated in these cortical networks. However, the assumptions of homogeneity and isotropy are no longer valid when the detailed microstructure of cortex is taken into account. In fact, cortex has a distinctly crystalline-like structure at the mm length-scale, as exemplified by the patchy nature of long-range horizontal (and feedback) connections in primary visual cortex. These patchy connections are correlated with a number of periodically repeating feature maps, in which local populations of neurons respond preferentially to stimuli with particular properties such as orientation, spatial frequency and left/right eye (ocular) dominance. In this talk we present some recent analytical results regarding the large-scale dynamics of cortex in the presence of periodically modulated long-range interactions.
For more information contact J. Keener, 1-6089