41 citations · 264 across the 40 of their papers we have counts for
50 papers
Discrimination of Dynamic Data via Curvature Sets
Nadezhda Belova, Maxwell Goldberg, Facundo Memoli +2
Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotempora…
The G-Gromov-Hausdorff Distance and Equivariant Topology
Sunhyuk Lim, Facundo Memoli
For each arbitrary finite group , we consider a suitable notion of Gromov Hausdorff distance between compact metric spaces and derive lower bounds based on equivariant topol…
Computation of degree-1 persistent homology on larger point-clouds using the Reduced Vietoris-Rips filtration
Musashi Ayrton Koyama, Facundo Mémoli, Vanessa Robins +1
Computing Persistent Homology for large point clouds remains a bottleneck for the wider adoption of persistent homology by the scientific community. We present an algorithm which c…
The Gromov-Wasserstein distance between spheres
Shreya Arya, Arnab Auddy, Ranthony Edmonds +3
In this paper we consider a two-parameter family {dGWp,q}p,q of Gromov- Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific v…
The Generalized Rank Invariant: Möbius invertibility, Discriminating Power, and Connection to Other Invariants
Nathaniel Clause, Woojin Kim, Facundo Mémoli
In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its app…
Classical Multidimensional Scaling on Metric Measure Spaces
Sunhyuk Lim, Facundo Memoli
We generalize the classical Multidimensional Scaling procedure to the setting of general metric measure spaces. We develop a related spectral theory for the generalized cMDS operat…