Universal Gröbner 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 arena. A combinatorial neural code is a collection of $0/1$-vectors which encode patterns co-firing activity among cells. Gross, Obatake, Youngs have recently used techniques from toric algebra study when $0$- $1$-, or $2$-inductively pierced: property allows one reconstruct Venn diagram-like planar figure acts as geometric schematic for patterns. This article examines their work closely by focusing on variety classes codes. particular, we identify universal Gr\"obner bases ideal these