1 citations · 1 across the 4 of their papers we have counts for
5 papers
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…
-Stability of Weighted Persistence Diagrams
Aziz Burak Gülen, Facundo Mémoli, Amit Patel
We introduce the concept of weighted persistence diagrams and develop a functorial pipeline for constructing them from finite metric measure spaces. This builds upon an existing fu…
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…
Galois Connections in Persistent Homology
Aziz Burak Gulen, Alexander McCleary
We present a new language for persistent homology in terms of Galois connections. This language has two main advantages over traditional approaches. First, it simplifies and unifie…