4 papers · 1 filter
Ephemeral persistence features and the stability of filtered chain complexes
Facundo Mémoli, Ling Zhou
We strengthen the usual stability theorem for Vietoris-Rips (VR) persistent homology of finite metric spaces by building upon constructions due to Usher and Zhang in the context of…
Persistence and Topological Complexity
Facundo Mémoli, Ling Zhou
Topological complexity is a homotopy invariant that measures the minimal number of continuous rules required for motion planning in a space. In this work, we introduce persistent a…
Geometric Bounds for Persistence
Alexey Balitskiy, Baris Coskunuzer, Facundo Mémoli
In this paper, we offer a new perspective on persistent homology by integrating key concepts from metric geometry. For a given compact subset of a Banach space $\math…
-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…