60 citations · 98 across the 27 of their papers we have counts for
9 papers · 1 filter
The Four Point Condition: An Elementary Tropicalization of Ptolemy's Inequality
Mario Gómez, Facundo Mémoli
Ptolemy's inequality is a classic relationship between the distances among four points in Euclidean space. Another relationship between six distances is the 4-point condition, an i…
The Gromov-Hausdorff distance between ultrametric spaces: its structure and computation
Facundo Mémoli, Zane Smith, Zhengchao Wan
The Gromov-Hausdorff distance () provides a natural way of quantifying the dissimilarity between two given metric spaces. It is known that computing …
The Persistent Topology of Optimal Transport Based Metric Thickenings
Henry Adams, Facundo Mémoli, Michael Moy +1
A metric thickening of a given metric space is any metric space admitting an isometric embedding of . Thickenings have found use in applications of topology to data analysis…
Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach
Gunnar Carlsson, Facundo Mémoli, Santiago Segarra
We provide a complete taxonomic characterization of robust hierarchical clustering methods for directed networks following an axiomatic approach. We begin by introducing three prac…
Persistent Cup-Length
Marco Contessoto, Facundo Mémoli, Anastasios Stefanou +1
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Rip…
Characterization of Gromov-type geodesics
Facundo Mémoli, Zhengchao Wan
The collection of all isometry classes of compact metric spaces endowed with the Gromov-Hausdorff distance is known to be a geodesic space. However,…