Universal Grobner bases of toric ideals of combinatorial neural codes

In the 1970s, O'Keefe and Dostrovsky discovered that certain neurons, called place cells, in an animal's brain are tied to its location within its arena. A combinatorial neural code is a collection of 0/1-vectors which encode the patterns of cofiring activity among the place cells. Gross, Obatake, and Youngs have recently used techniques from toric algebra to study when a neural code is 0-, 1-, or 2-inductively pierced: a property that allows one to reconstruct a Venn diagramlike planar figure that acts as a geometric schematic for the neural cofiring patterns. This article continues their work by closely focusing on an assortment of classes of combinatorial neural codes. In particular, we identify universal Grobner bases of the toric ideals for these codes.