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math.AT2022
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…
math.AT2020
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…