The neural ring: using algebraic geometry to analyze neural codes

Start: 11/03/2014 - 12:00pm
End  : 11/03/2014 - 12:50pm

Applied Math Seminar

Nora Youngs (Mathematics, Harvey Mudd College)


Navigation is one of the most important functions of the brain. This year, the Nobel Prize in Medicine and Physiology was awarded for the discovery of place cells and grid cells, the neurons responsible for this ability. Though the external observed correspondence of these neurons to 2D receptive fields has been carefully recorded and proven, the animal itself navigates the world without access to these mapsAn important problem confronted by the brain is to infer what properties of a stimulus space can - in principle - be extracted from the stimulus space. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode the combinatorial data of a neural code. We find that these objects can be expressed in a "canonical form'' that directly translates to a minimal description of the receptive field structure intrinsic to the neural code, and present an algorithm to compute this canonical form.

CMC, Kravis Center, KRV 164