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Keyword

persistence modules

Description: Algebraic structures that encode how features of a filtered space change across a parameter, central to persistent homology and topological data analysis.
Wikidata ID: wiki/Q117101306
OpenAlex ID: keywords/persistence-modules
Proximity of persistence modules and their diagrams
2009 · Frédéric Chazal, David Cohen-Steiner, et al. · Annual Symposium on Computational Geometry (SoCG) · 410
The Structure and Stability of Persistence Modules
2016 · Frédéric Chazal, Vin de Silva, et al. · SpringerBriefs in mathematics · 392
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Decomposition of pointwise finite-dimensional persistence modules
2014 · William Crawley-Boevey · Journal of Algebra and Its Applications · 211
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Dualities in persistent (co)homology
2011 · Vin de Silva, Dmitriy Morozov, et al. · Inverse Problems · 152
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Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules
2015 · Leonid Polterovich, Egor Shelukhin · Selecta Mathematica · 74
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Induced Matchings of Barcodes and the Algebraic Stability of Persistence
2014 · Ulrich Bauer, Michael Lesnick · 68
Induced Matchings and the Algebraic Stability of Persistence Barcodes
2013 · Bauer, Ulrich, Lesnick, Michael · Journal of computational geometry · 66
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Decomposition of persistence modules
2019 · Magnus Botnan, William Crawley-Boevey · Proceedings of the American Mathematical Society · 60
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Topological Persistence in Geometry and Analysis
2020 · Leonid Polterovich, Daniel Rosen, et al. · University lecture series · 53
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Generalized persistence diagrams for persistence modules over posets
2021 · Woojin Kim, Facundo Mémoli · Journal of Applied and Computational Topology · 49
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Persistence Modules on Commutative Ladders of Finite Type
2015 · Emerson G. Escolar, Yasuaki Hiraoka · Discrete & Computational Geometry · 48
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Bounds on spectral norms and barcodes
2021 · Asaf Kislev, Egor Shelukhin · Geometry & Topology · 42
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Persistent Homology of Geospatial Data: A Case Study with Voting
2021 · Michelle Feng, Mason A. Porter · SIAM Review · 39
Computing the Interleaving Distance is NP-Hard
2019 · Håvard Bakke Bjerkevik, Magnus Bakke Botnan, et al. · Foundations of Computational Mathematics · 38
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Topological spaces of persistence modules and their properties
2018 · Peter Bubenik, Tane Vergili · Journal of Applied and Computational Topology · 32
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The Rank Invariant Stability via Interleavings
2018 · Claudia Landi · Association for Women in Mathematics series · 32
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The observable structure of persistence modules
2014 · William Crawley-boevey, Vin, et al. · 31
Approximating persistent homology in Euclidean space through collapses
2015 · Magnus Bakke Botnan, Gard Spreemann · Applicable Algebra in Engineering Communication and Computing · 27
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The ℓ ∞-Cophenetic Metric for Phylogenetic Trees As an Interleaving Distance
2019 · Elizabeth Munch, Anastasios Stefanou · Association for Women in Mathematics series · 26
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Theory of interleavings on categories with a flow
2018 · V. de Silva, E. Munch, et al. · Theory and applications of categories · 26
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Stability of higher-dimensional interval decomposable persistence modules
2016 · Bjerkevik, Håvard Bakke · arXiv (Cornell University) · 26
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On the Stability of Interval Decomposable Persistence Modules
2021 · Håvard Bakke Bjerkevik · Discrete & Computational Geometry · 25
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Computational Complexity of the Interleaving Distance
2017 · Bjerkevik, Håvard Bakke, Botnan, Magnus Bakke · arXiv (Cornell University) · 24
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Ephemeral persistence modules and distance comparison
2021 · Nicolas Berkouk, François Petit · Algebraic & Geometric Topology · 23
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Homological Algebra for Persistence Modules
2021 · Peter Bubenik, Nikola Milićević · Foundations of Computational Mathematics · 23
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Works count: 399
Citation count: 2,678
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