We study the open, closed, and non-degenerate embedding dimensions of neural codes,
which are the smallest respective dimensions in which one can find a realization of a code …

We prove algebraic and combinatorial characterizations of the class of inductively pierced
codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic …

Previous work on convexity of neural codes has produced codes that are open-convex but
not closed-convex—or vice-versa. However, why a code is one but not the other, and how to …

In this paper, we explore the concept of binary convex fuzzy vector spaces and binary
convex fuzzy linear subspaces over binary vector spaces F 2 n by formalizing their definition …

Every ordered collection of sets in Euclidean space can be associated to a combinatorial
code, which records the regions cut out by the sets in space. Given two ordered collections …

This dissertation explores applications of discrete geometry in mathematical neuroscience.
We begin with convex neural codes, which model the activity of hippocampal place cells and …