
Rank invariant for Zigzag Modules
The rank invariant is of great interest in studying both onedimensional...
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Steady and ranging sets in graph persistence
Generalised persistence functions (gpfunctions) are defined on (ℝ, ≤)i...
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Rankbased persistence
Persistence has proved to be a valuable tool to analyze real world data ...
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A Sparse Delaunay Filtration
We show how a filtration of Delaunay complexes can be used to approximat...
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Signed Barcodes for MultiParameter Persistence via Rank Decompositions and RankExact Resolutions
In this paper we introduce the signed barcode, a new visual representati...
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On rectangledecomposable 2parameter persistence modules
This paper addresses two questions: (1) can we identify a sensible class...
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Bisimilarity of diagrams
In this paper, we investigate diagrams, namely functors from any small c...
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Generalized Persistence Diagrams for Persistence Modules over Posets
When a category C satisfies certain conditions, we define the notion of rank invariant for arbitrary posetindexed functors F:P→C from a category theory perspective. This generalizes the standard notion of rank invariant as well as Patel's recent extension. Specifically, the barcode of any interval decomposable persistence modules F:P→vec of finite dimensional vector spaces can be extracted from the rank invariant by the principle of inclusionexclusion. Generalizing this idea allows freedom of choosing the indexing poset P of F: P→C in defining Patel's generalized persistence diagram of F. By specializing our idea to zigzag persistence modules, we also show that the barcode of a Reeb graph can be obtained in a purely settheoretic setting without passing to the category of vector spaces. This leads to a promotion of Patel's semicontinuity theorem about type A persistence diagram to Lipschitz continuity theorem for the category of sets.
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