4 papers
The Degree-Rips Complexes of an Annulus with Outliers
Alexander Rolle
The degree-Rips bifiltration is the most computable of the parameter-free, density-sensitive bifiltrations in topological data analysis. It is known that this construction is stabl…
Fast Minimal Presentations of Bi-graded Persistence Modules
Michael Kerber, Alexander Rolle
Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or mo…
Visualization tools for parameter selection in cluster analysis
Alexander Rolle, Luis Scoccola
We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of…
Central extensions and the classifying spaces of projective linear groups
Alexander Rolle
If is a presheaf of groupoids on a small site, and is a sheaf of abelian groups, we prove that the sheaf cohomology group is in bijection with a set of centra…