Professor Jeffrey Giansiracusa jeffrey.giansiracusa@durham.ac.uk
Professor
Professor Jeffrey Giansiracusa jeffrey.giansiracusa@durham.ac.uk
Professor
Ziva Urbancic ziva.urbancic@durham.ac.uk
PGR Student Doctor of Philosophy
The output of persistent homology is an algebraic object called a persistence module. This object admits a decomposition into a direct sum of interval persistence modules described entirely by the barcode invariant. In this paper we investigate when a morphism Φ:V→W of persistence modules admits an analogous direct sum decomposition. Jacquard et al. showed that a ladder decomposition can be obtained whenever the barcodes of V and W do not have any strictly nested bars. We refine this result and show that even in the presence of nested bars, a ladder decomposition exists when the morphism is sufficiently close to being invertible relative to the scale of the nested bars.
Giansiracusa, J., & Urbančič, Ž. (2024). Ladder Decomposition for Morphisms of Persistence Modules. Journal of Applied and Computational Topology, https://doi.org/10.1007/s41468-024-00174-9
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 8, 2024 |
Online Publication Date | May 10, 2024 |
Publication Date | May 10, 2024 |
Deposit Date | Apr 26, 2024 |
Publicly Available Date | May 10, 2024 |
Journal | Journal of Applied and Computational Topology |
Print ISSN | 2367-1726 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
DOI | https://doi.org/10.1007/s41468-024-00174-9 |
Public URL | https://durham-repository.worktribe.com/output/2397266 |
Accepted Journal Article
(667 Kb)
PDF
Algebraic Dynamical Systems in Machine Learning
(2024)
Journal Article
A general framework for tropical differential equations
(2023)
Journal Article
The universal tropicalization and the Berkovich analytification
(2022)
Journal Article
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
Apache License Version 2.0 (http://www.apache.org/licenses/)
Apache License Version 2.0 (http://www.apache.org/licenses/)
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search