60 citations · 98 across the 27 of their papers we have counts for
6 papers · 1 filter
Grassmannian Persistence Diagrams
Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan
We introduce Orthogonal Möbius Inversion , a concept analogous to Möbius inversion on finite posets, which is applicable to order-preservings functions from a finite p…
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…
A generalization of the persistent Laplacian to simplicial maps
Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan +1
The graph Laplacian is a fundamental object in the analysis of and optimization on graphs. This operator can be extended to a simplicial complex and therefore offers a way to p…
The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs
Samantha Chen, Sunhyuk Lim, Facundo Mémoli +2
In this paper, we present a novel interpretation of the so-called Weisfeiler-Lehman (WL) distance, introduced by Chen et al. (2022), using concepts from stochastic processes. The W…
Extremal spherical polytopes and Borsuk's conjecture
Mikhail Katz, Facundo Mémoli, Qingsong Wang
We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and p…
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…