60 citations · 98 across the 27 of their papers we have counts for
5 papers · 1 filter
Grassmannian Persistence Diagrams: Special Properties in the 1-Parameter Setting
Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan
In this paper, we explore the discriminative power of Grassmannian persistence diagrams of 1-parameter filtrations, examine their relationships with other related constructions, an…
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…
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…
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…
Persistent Laplacians: properties, algorithms and implications
Facundo Mémoli, Zhengchao Wan, Yusu Wang
We present a thorough study of the theoretical properties and devise efficient algorithms for the \emph{persistent Laplacian}, an extension of the standard combinatorial Laplacian…