6 papers
Bifunction and Interlevel Delaunay Trifiltrations
Ángel Javier Alonso, Michael Kerber, Tung Lam +2
A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extend…
Dualities in Multiparameter Persistence
Ulrich Bauer, Fabian Lenzen, Michael Lesnick
In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated…
Limit Computation Over Posets via Minimal Initial Functors
Tamal K. Dey, Michael Lesnick
It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic impl…
Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics
Michael Lesnick, Kenneth McCabe
The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis, is notoriously sensitive to outliers. Sheehy's subdivision-Rips bifiltration $\ma…
Nerve Models of Subdivision Bifiltrations
Michael Lesnick, Kenneth McCabe
We study the size of Sheehy's subdivision bifiltrations, up to homotopy. We focus in particular on the subdivision-Rips bifiltration of a metric space , the on…
Delaunay Bifiltrations of Functions on Point Clouds
Ángel Javier Alonso, Michael Kerber, Tung Lam +1
The Delaunay filtration of a point cloud is a central tool of computational topology. Its use is justified by the topological equ…