60 citations · 98 across the 27 of their papers we have counts for
33 papers
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…
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…
Embedding-Projection Correspondences for the estimation of the Gromov-Hausdorff distance
Facundo Mémoli, Zane T. Smith
This writeup describes ongoing work on designing and testing a certain family of correspondences between compact metric spaces that we call \emph{embedding-projection correspondenc…
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…