Algebra and Combinatorics Seminar

Date: September 13, 2019

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Alexander Ruys de Perez, Texas A&M University

Title: Max Intersection Complete Codes and the Factor Complex

Abstract: A place cell is a neuron corresponding to a subset of Euclidean space known as a place field, that will fire if and only if the individual to which the neuron belongs is within that place field. The firing patterns of a collection of n place fields can be represented by a neural code C on n neurons, which is a subset of 2n . Determining whether C is convex, meaning that there is an arrangement of convex place fields for which C is the code, remains an open problem. A sufficient condition for convexity is being max intersection complete: any intersection of maximal codewords is also a codeword. Currently, the only way to determine this property is to evaluate all such intersections. We present a new method to determine max intersection completeness by introducing a simplicial complex for a code C called the factor complex ∆O(C) of C. We show how to construct ∆O(C) using Stanley-Reisner theory, describe how ∆O(C) encodes information about C, and give an algorithm to check whether C is max intersection complete using the factor complex of a closely related code.