Open, closed, and non-degenerate embedding dimensions of neural codes
RA Jeffs - Discrete & Computational Geometry, 2024 - Springer
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 …
which are the smallest respective dimensions in which one can find a realization of a code …
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 …
Recognizing and realizing inductively pierced codes
R Curry, RA Jeffs, N Youngs, Z Zhao - arXiv preprint arXiv:2207.06266, 2022 - arxiv.org
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 …
codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic …
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 …
Non-monotonicity of closed convexity in neural codes
Neural codes are lists of subsets of neurons that fire together. Of particular interest are
neurons called place cells, which fire when an animal is in specific, usually convex regions …
neurons called place cells, which fire when an animal is in specific, usually convex regions …
Embedding dimension gaps in sparse codes
RA Jeffs, H Siegel, D Staudinger, Y Wang - arXiv preprint arXiv …, 2023 - arxiv.org
We study the open and closed embedding dimensions of a convex 3-sparse code $\mathcal
{FP} $, which records the intersection pattern of lines in the Fano plane. We show that the …
{FP} $, which records the intersection pattern of lines in the Fano plane. We show that the …
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 …
Realizing convex codes with axis-parallel boxes
M Benitez, S Chen, T Han, RA Jeffs, K Paguyo… - Involve, a Journal of …, 2024 - msp.org
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 …
code, which records the regions cut out by the sets in space. Given two ordered collections …