Journal of Vision - Topological analysis of population activity in visual cortex, by Singh, Memoli, Ishkhanov, Sapiro, Carlsson, & Ringach

Gurjeet Singh	Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
Facundo Memoli	Department of Mathematics, Stanford University, Stanford, CA, USA
Tigran Ishkhanov	Department of Mathematics, Stanford University, Stanford, CA, USA
Guillermo Sapiro	Department of Electrical and Computer Engineering, University of Minnesota, Minnesota, MN, USA
Gunnar Carlsson	Department of Mathematics, Stanford University, Stanford, CA, USA
Dario L. Ringach	Departments of Neurobiology and Psychology, Jules Stein Eye Institute, David Geffen School of Medicine, University of California, Los Angeles, CA, USA

Information in the cortex is thought to be represented by the joint activity of neurons. Here we describe how fundamental questions about neural representation can be cast in terms of the topological structure of population activity. A new method, based on the concept of persistent homology, is introduced and applied to the study of population activity in primary visual cortex (V1). We found that the topological structure of activity patterns when the cortex is spontaneously active is similar to those evoked by natural image stimulation and consistent with the topology of a two sphere. We discuss how this structure could emerge from the functional organization of orientation and spatial frequency maps and their mutual relationship. Our findings extend prior results on the relationship between spontaneous and evoked activity in V1 and illustrates how computational topology can help tackle elementary questions about the representation of information in the nervous system.