Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

Complex systems, composed at the most basic level of units and their interactions, describe
phenomena in a wide variety of domains, from neuroscience to computer science and …

Neuroscience is undergoing a period of rapid experimental progress and expansion. New
mathematical tools, previously unknown in the neuroscience community, are now being …

Neural codes serve as a language for neurons in the brain. Open (or closed) convex codes,
which arise from the pattern of intersections of collections of open (or closed) convex sets in …

Rapid search and localization for nuclear sources can be an important aspect in preventing
human harm from illicit material in dirty bombs or from contamination. In the case of a single …

Given an intersection pattern of arbitrary sets in Euclidean space, is there an arrangement of
convex open sets in Euclidean space that exhibits the same intersections? This question is …

We introduce and investigate-convex union representable complexes: the simplicial
complexes that arise as the nerve of a finite collection of convex open sets in whose union is …

Much work has been done to identify which binary codes can be represented by collections
of open convex or closed convex sets. While not all binary codes can be realized by such …

A convex code is a binary code generated by the pattern of intersections of a collection of
open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as …

In this paper we develop a novel mathematical formalism for the modeling of neural
information networks endowed with additional structure in the form of assignments of …