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- W4383860432 abstract "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 $Phi colon V to W$ 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." @default.
- W4383860432 created "2023-07-11" @default.
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- W4383860432 date "2023-07-07" @default.
- W4383860432 modified "2023-09-25" @default.
- W4383860432 title "Ladder Decomposition for Morphisms of Persistence Modules" @default.
- W4383860432 doi "https://doi.org/10.48550/arxiv.2307.03409" @default.
- W4383860432 hasPublicationYear "2023" @default.
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