Publication Date

Summer 2016

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Advisor

Elizabeth Gross

Keywords

Algebra, Algebraic Geometry, Information Visualization, Neural Codes, Toric Ideals

Subject Areas

Mathematics

Abstract

A neural code is a collection of codewords (0-1 vectors) of a given length n; it captures the co-firing patterns of a set of neurons. A neural code is convexly realizable in dimension two if there exist n convex sets in the plane so that each codeword in the code corresponds to a unique intersection carved out by the convex sets. There are some methods to determine whether a neural code is convexly realizable; however, these methods do not describe how to draw a realization, that is, a place field diagram of the code. In this work, we construct toric ideals from neural codes, and we show how we can use these ideals, along with the theory of inductive piercings and Euler diagrams, to draw realizations for particular classes of codes.

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