Wheels: A New Criterion for Non-convexity of Neural Codes
Combinatorics
2023-02-16 v2 Metric Geometry
Neurons and Cognition
Abstract
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. Along the way, we give the first example of a code that is non-convex, has no local obstructions, and has simplicial complex of dimension two. We also characterize convexity for neural codes for which the simplicial complex is pure of low or high dimension.
Cite
@article{arxiv.2108.04995,
title = {Wheels: A New Criterion for Non-convexity of Neural Codes},
author = {Laura Matusevich and Alexander Ruys de Perez and Anne Shiu},
journal= {arXiv preprint arXiv:2108.04995},
year = {2023}
}
Comments
25 pages, 3 figures, 2 tables