Conference abstracts

Session S01 - Computational Algebra and Applications of Algebra

July 29, 16:00 ~ 16:25

Algebraic signatures of convex and non-convex neural codes

Anne Shiu

Texas A&M University, USA   -

Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information via the collective behavior of populations of neurons. A code is called convex if its codewords correspond to regions defined by an arrangement of convex open sets in Euclidean space. Convex codes have been observed experimentally in many brain areas, including sensory cortices and the hippocampus, where neurons exhibit convex receptive fields. What makes a neural code convex? That is, how can we tell from the intrinsic structure of a code if there exists a corresponding arrangement of convex open sets? This talk describes how to use tools from combinatorics and commutative algebra to uncover a variety of signatures of convex and non-convex codes.

Joint work with Carina Curto (Pennsylvania State University), Elizabeth Gross (San Jose State University), Jack Jeffries (University of Michigan), Katherine Morrison (University of Northern Colorado), Mohamed Omar (Harvey Mudd College), Zvi Rosen (University of Pennsylvania) and Nora Youngs (Harvey Mudd College).

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