60 citations · 98 across the 27 of their papers we have counts for
12 papers · 1 filter
Critical Diameters and Vietoris-Rips Filtrations
Facundo Mémoli, Qingsong Wang
We relate critical diameters of finite configurations to the topology of Vietoris-Rips complexes. For a compact metric space and , we prove that the canonical inclusion from…
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…
-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…
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…
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…
Persistent Cup Product Structures and Related Invariants
Facundo Mémoli, Anastasios Stefanou, Ling Zhou
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from da…