13 citations · 63 across the 13 of their papers we have counts for
14 papers
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Realizing convex codes with axis-parallel boxes
Miguel Benitez, Siran Chen, Tianhui Han +3
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…
Recognizing and Realizing Inductively Pierced Codes
Ryan Curry, R. Amzi Jeffs, Nora Youngs +1
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 i…
Planar convex codes are decidable
Boris Bukh, R. Amzi Jeffs
We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be reali…
Colorful Words and d-Tverberg Complexes
Florian Frick, R. Amzi Jeffs
We give a complete combinatorial characterization of weakly -Tverberg complexes. These complexes record which intersection combinatorics of convex hulls necessarily arise in any…
Enumeration of interval graphs and -representable complexes
Boris Bukh, R. Amzi Jeffs
For each fixed , we obtain asymptotic estimates for the number of -representable simplicial complexes on vertices as a function of . The case corresponds to…
Open, Closed, and Non-Degenerate Embedding Dimensions of Neural Codes
R. Amzi Jeffs
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 consi…
Order-forcing in Neural Codes
R. Amzi Jeffs, Caitlin Lienkaemper, Nora Youngs
Convex neural codes are subsets of the Boolean lattice that record the intersection patterns of convex sets in Euclidean space. Much work in recent years has focused on finding com…
Embedding Dimension Phenomena in Intersection Complete Codes
R. Amzi Jeffs
Two tantalizing invariants of a combinatorial code are cdim and odim, the smallest dimension in which can be…
Sunflowers of Convex Open Sets
R. Amzi Jeffs
A sunflower is a collection of sets such that the pairwise intersection is the same for all choices of distinct and . We study sunflowers…
Convex Union Representability and Convex Codes
R. Amzi Jeffs, Isabella Novik
We introduce and investigate -convex union representable complexes: the complexes that arise as the nerve of a finite collection of convex open sets in whose union…
Morphisms of Neural Codes
R. Amzi Jeffs
We define a notion of morphism between combinatorial codes, making the class of all combinatorial codes into a category . We show that morphisms can be used to remov…
Neural Ideal Preserving Homomorphisms
R. Amzi Jeffs, Mohamed Omar, Nora Youngs
The neural ideal of a binary code is an ideal in closely related to the vanishing ideal of . The n…
Sparse Neural Codes and Convexity
R. Amzi Jeffs, Mohamed Omar, Natchanon Suaysom +2
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by…