Wheels: A New Criterion for Non-convexity of Neural Codes Institutional Repository Document uri icon

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.

altmetric score

  • 1.25

author list (cited authors)

  • Matusevich, L., de Perez, A. R., & Shiu, A.

citation count

  • 0

complete list of authors

  • Matusevich, Laura||de Perez, Alexander Ruys||Shiu, Anne

Book Title

  • arXiv

publication date

  • August 2021