Oriented matroids and combinatorial neural codes
A combinatorial neural code $\mathscr C\subseteq 2^{[n]} $ is convex if it arises as the
intersection pattern of convex open subsets of $\mathbb R^ d $. We relate the emerging …
intersection pattern of convex open subsets of $\mathbb R^ d $. We relate the emerging …
Nondegenerate neural codes and obstructions to closed-convexity
P Chan, K Johnston, J Lent, AR De Perez… - SIAM Journal on Discrete …, 2023 - SIAM
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 …
not closed-convex—or vice-versa. However, why a code is one but not the other, and how to …
Wheels: A new criterion for non-convexity of neural codes
L Matusevich, AR de Perez, A Shiu - arXiv preprint arXiv:2108.04995, 2021 - arxiv.org
We introduce new geometric and combinatorial criteria that preclude a neural code from
being convex, and use them to tackle the classification problem for codes on six neurons …
being convex, and use them to tackle the classification problem for codes on six neurons …
Wheels: A new criterion for non-convexity of neural codes
AR De Perez, LF Matusevich, A Shiu - Advances in Applied Mathematics, 2023 - Elsevier
We introduce new geometric and combinatorial criteria that preclude a neural code from
being convex, and use them to tackle the classification problem for codes on six neurons …
being convex, and use them to tackle the classification problem for codes on six neurons …
Combinatorial geometry of neural codes, neural data analysis, and neural networks
C Lienkaemper - arXiv preprint arXiv:2209.07583, 2022 - arxiv.org
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 …
We begin with convex neural codes, which model the activity of hippocampal place cells and …
New Tools for Classifying Convex Neural Codes: The Factor Complex and the Wheel
AMR De Perez - 2021 - search.proquest.com
The neural code has prompted many questions in pure mathematics concerning how much
topological data can be stored combinatorially. The question of whether one can determine …
topological data can be stored combinatorially. The question of whether one can determine …