Topological spaces of persistence modules and their properties

Author:

Bubenik PeterORCID,Vergili TaneORCID

Funder

Army Research Office

Directorate for Mathematical and Physical Sciences

Simons Foundation

Publisher

Springer Science and Business Media LLC

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference39 articles.

1. Bauer, U., Lesnick, M.: Induced matchings and the algebraic stability of persistence barcodes. J. Comput. Geom. 6(2), 162–191 (2015)

2. Bauer, U., Lesnick, M.: Persistence diagrams as diagrams: a categorification of the stability theorem (2016). arXiv preprint arXiv:1610.10085

3. Bjerkevik, H.B., Botnan, M.B.: Computational complexity of the interleaving distance. In: 34th International Symposium on Computational Geometry, vol. 12 (2017). arXiv preprint arXiv:1712.04281

4. Blumberg, A.J., Lesnick, M.: Universality of the homotopy interleaving distance (2017). arXiv preprint arXiv:1705.01690

5. Blumberg, A.J., Gal, I., Mandell, M.A., Pancia, M.: Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces. Found. Comput. Math. 14(4), 745–789 (2014)

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1. Basic metric geometry of the bottleneck distance;Proceedings of the American Mathematical Society;2024-06-12

2. Topological and metric properties of spaces of generalized persistence diagrams;Journal of Applied and Computational Topology;2024-01-23

3. Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams;Discrete & Computational Geometry;2023-05-05

4. Persistent extensions and analogous bars: data-induced relations between persistence barcodes;Journal of Applied and Computational Topology;2023-04-15

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