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 …

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 allow the brain to represent, process, and store information about the world.
Combinatorial codes, comprised of binary patterns of neural activity, encode information via …

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 …

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 …

Neural codes, represented as collections of binary strings, encode neural activity and show
relationships among stimuli. Certain neurons, called place cells, have been shown …

The brain processes information about the environment via neural codes. The neural ideal
was introduced recently as an algebraic object that can be used to better understand the …