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06/06/2023
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
Persistent homology (PH) provides topological descriptors for geometric ...
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07/30/2022
On the bottleneck stability of rank decompositions of multi-parameter persistence modules
The notion of rank decomposition of a multi-parameter persistence module...
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12/22/2021
On the stability of multigraded Betti numbers and Hilbert functions
Multigraded Betti numbers are one of the simplest invariants of multipar...
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09/01/2021
A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis
We introduce a novel gradient descent algorithm extending the well-known...
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07/14/2021
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions
In this paper we introduce the signed barcode, a new visual representati...
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02/20/2020
On rectangle-decomposable 2-parameter persistence modules
This paper addresses two questions: (1) can we identify a sensible class...
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10/02/2019
A Framework for Differential Calculus on Persistence Barcodes
We define notions of differentiability for maps from and to the space of...
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07/31/2019
Intrinsic Interleaving Distance for Merge Trees
Merge trees are a type of graph-based topological summary that tracks th...
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07/23/2019
Level-sets persistence and sheaf theory
In this paper we provide an explicit connection between level-sets persi...
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12/21/2018
Exact computation of the matching distance on 2-parameter persistence modules
The matching distance is a pseudometric on multi-parameter persistence m...
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10/25/2018
Inverse Problems in Topological Persistence
In this survey, we review the literature on inverse problems in topologi...
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05/22/2018
Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport
Persistence diagrams (PDs) are now routinely used to summarize the under...
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06/11/2017
Sliced Wasserstein Kernel for Persistence Diagrams
Persistence diagrams (PDs) play a key role in topological data analysis ...
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06/01/2017
Statistical Analysis and Parameter Selection for Mapper
In this article, we study the question of the statistical convergence of...
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06/27/2014