Corpus ID: 235829909

# Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions

@article{Botnan2021SignedBF,
title={Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions},
author={Magnus Bakke Botnan and Steffen Oppermann and Steve Oudot},
journal={ArXiv},
year={2021},
volume={abs/2107.06800}
}
• Published 14 July 2021
• Mathematics, Computer Science
• ArXiv
In this paper we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of a poset representation. Like its unsigned counterpart in one-parameter persistence, the signed barcode encodes the rank invariant as a Z-linear combination of rank invariants of indicator modules supported on segments in the poset. It can also be enriched to encode the generalized rank invariant as a Z-linear… Expand
4 Citations
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The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that oneExpand
The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers
• Woojin Kim, Samantha Moore
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• 2021
We show that the generalized persistence diagram by Kim and Mémoli encodes the bigraded Betti numbers of finite 2-parameter persistence modules. More interestingly, the way to read off the bigradedExpand
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• Mathematics, Computer Science
• 2021
It is shown that on 1or 2-parameter persistence modules over prime fields, dp I is the universal metric satisfying a natural stability property; this result extends a stability result of Skraba and Turner for the p-Wasserstein distance on barcodes in the 1- parameter case, and is also a close analogue of a universality property for the interleaving distance given by the second author. Expand
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• Mathematics
• 2021
The persistent Betti numbers are used in topological data analysis to infer the scales at which topological features appear and disappear in the filtration of a topological space. Most commonly byExpand

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