3 papers
math.AT2023
Meta-Diagrams for 2-Parameter Persistence
Nate Clause, Tamal K. Dey, Facundo Mémoli +1
We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the modu…
math.MG2023
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…
math.AT2017
New families of simplicial filtration functors
Samir Chowdhury, Nathaniel Clause, Facundo Memoli +2
The so called Čech and Vietoris-Rips simplicial filtrations are designed to capture information about the topological structure of metric datasets. These filtrations are two of the…