41 citations · 264 across the 40 of their papers we have counts for
18 papers · 1 filter
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…
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 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…
Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications
Tamal K. Dey, Woojin Kim, Facundo Mémoli
The notion of generalized rank invariant in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as gen…
Elder-Rule-Staircodes for Augmented Metric Spaces
Chen Cai, Woojin Kim, Facundo Memoli +1
An augmented metric space is a metric space equipped with a function . This type of data arises commonly in practice, e.g, a point cloud in $\…
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Sunhyuk Lim, Facundo Memoli, Osman Berat Okutan
In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information f…