111 citations · 273 across the 31 of their papers we have counts for
8 papers · 1 filter
Wheels: A New Criterion for Non-convexity of Neural Codes
Laura Matusevich, Alexander Ruys de Perez, Anne Shiu
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. Alo…
Nondegenerate Neural Codes and Obstructions to Closed-Convexity
Patrick Chan, Katherine Johnston, Joseph Lent +2
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…
Neural Codes With Three Maximal Codewords: Convexity and Minimal Embedding Dimension
Katherine Johnston, Anne Shiu, Clare Spinner
Neural codes, represented as collections of binary strings called codewords, are used to encode neural activity. A code is called convex if its codewords are represented as an arra…
Non-monotonicity of closed convexity in neural codes
Brianna Gambacini, R. Amzi Jeffs, Sam Macdonald +1
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 reg…
Neural Codes and the Factor Complex
Alexander Ruys de Perez, Laura Felicia Matusevich, Anne Shiu
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain…
Neural codes, decidability, and a new local obstruction to convexity
Aaron Chen, Florian Frick, Anne Shiu
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 questi…
Convex Rank Tests and Semigraphoids
Jason Morton, Lior Pachter, Anne Shiu +2
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutation…
Three Counterexamples on Semigraphoids
Raymond Hemmecke, Jason Morton, Anne Shiu +2
Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection ar…