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math.AT2022
Parameterized Vietoris-Rips Filtrations via Covers
Bradley J. Nelson
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the developm…
math.AT2019
Persistent and Zigzag Homology: A Matrix Factorization Viewpoint
Gunnar Carlsson, Anjan Dwaraknath, Bradley J. Nelson
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundame…