Representing two-parameter persistence modules via graphcodes

Authors: Kerber, Michael, Russold, Florian

Subject Terms: Mathematics - Algebraic Topology, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2503.07368

Graphcode: Learning from multiparameter persistent homology using graph neural networks

Authors: Kerber, Michael, Russold, Florian

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Machine Learning

Access URL: http://arxiv.org/abs/2405.14302

Experimental realisation of a universal inverse-design magnonic device

Authors: Zenbaa, Noura, Abert, Claas, Majcen, Fabian, Kerber, Michael, Serha, Rostyslav O., Knauer, Sebastian, Wang, Qi, Schrefl, Thomas, Suess, Dieter, Chumak, Andrii V.

Subject Terms: Physics - Applied Physics, Condensed Matter - Materials Science

Access URL: http://arxiv.org/abs/2403.17724

Probabilistic Analysis of Multiparameter Persistence Decompositions

Authors: Alonso, Ángel Javier, Kerber, Michael, Skraba, Primoz

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Computational Geometry

Access URL: http://arxiv.org/abs/2403.11939

Delaunay Bifiltrations of Functions on Point Clouds

Authors: Alonso, Ángel Javier, Kerber, Michael, Lam, Tung, Lesnick, Michael

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology

Access URL: http://arxiv.org/abs/2310.15902

Topological Data Analysis in smart manufacturing: State of the art and futuredirections

Authors: Uray, Martin, Giunti, Barbara, Kerber, Michael, Huber, Stefan

Subject Terms: Computer Science - Machine Learning, Mathematics - Algebraic Topology, Statistics - Applications

Access URL: http://arxiv.org/abs/2310.09319

The Localized Union-of-Balls Bifiltration

Authors: Kerber, Michael, Söls, Matthias

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology

Access URL: http://arxiv.org/abs/2303.07002

Sparse Higher Order \v{C}ech Filtrations

Authors: Buchet, Mickaël, Dornelas, Bianca B., Kerber, Michael

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology

Access URL: http://arxiv.org/abs/2303.06666

Decomposition of zero-dimensional persistence modules via rooted subsets

Authors: Alonso, Ángel Javier, Kerber, Michael

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Computational Geometry

Access URL: http://arxiv.org/abs/2303.06118

Keeping it sparse: Computing Persistent Homology revisited

Authors: Bauer, Ulrich, Masood, Talha Bin, Giunti, Barbara, Houry, Guillaume, Kerber, Michael, Rathod, Abhishek

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology

Access URL: http://arxiv.org/abs/2211.09075

Filtration-Domination in Bifiltered Graphs

Authors: Alonso, Ángel Javier, Kerber, Michael, Pritam, Siddharth

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology, F.2.2

Access URL: http://arxiv.org/abs/2211.05574

A Unified View on the Functorial Nerve Theorem and its Variations

Authors: Bauer, Ulrich, Kerber, Michael, Roll, Fabian, Rolle, Alexander

Source: Expo. Math. 41:4 (2023), 125503

Subject Terms: Mathematics - Algebraic Topology, 55N31 (Primary) 55-02, 55P10 (Secondary)

Access URL: http://arxiv.org/abs/2203.03571

Asymptotic Improvements on the Exact Matching Distance for 2-parameter Persistence

Authors: Bjerkevik, Håvard Bakke, Kerber, Michael

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Computational Geometry

Access URL: http://arxiv.org/abs/2111.10303

Expected Complexity of Barcode Computation via Matrix Reduction

Authors: Giunti, Barbara, Houry, Guillaume, Kerber, Michael, Söls, Matthias

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Computational Complexity

Access URL: http://arxiv.org/abs/2111.02125

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Compression for 2-Parameter Persistent Homology

Authors: Fugacci, Ulderico, Kerber, Michael, Rolle, Alexander

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Symbolic Computation, Mathematics - Commutative Algebra, 55N99, 13D02

Access URL: http://arxiv.org/abs/2107.10924

Improved Approximate Rips Filtrations with Shifted Integer Lattices and Cubical Complexes

Authors: Choudhary, Aruni, Kerber, Michael, Raghvendra, Sharath

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology

Access URL: http://arxiv.org/abs/2105.05151

Structure-dynamics relationships in cryogenically deformed bulk metallic glass

Authors: Spieckermann, Florian, Şopu, Daniel, Soprunyuk, Viktor, Kerber, Michael B., Bednarčík, Jozef, Schökel, Alexander, Rezvan, Amir, Ketov, Sergey, Sarac, Baran, Schafler, Erhard, Eckert, Jürgen

Source: Nat. Commun. 13, 127 (2022)

Subject Terms: Condensed Matter - Materials Science

Access URL: http://arxiv.org/abs/2104.09292

Computing the Multicover Bifiltration

Authors: Corbet, René, Kerber, Michael, Lesnick, Michael, Osang, Georg

Subject Terms: Computer Science - Computational Geometry, Mathematics - Algebraic Topology

Access URL: http://arxiv.org/abs/2103.07823

Fast Minimal Presentations of Bi-graded Persistence Modules

Authors: Kerber, Michael, Rolle, Alexander

Subject Terms: Mathematics - Algebraic Topology, Computer Science - Symbolic Computation, Mathematics - Commutative Algebra, 55N99, 13D02

Access URL: http://arxiv.org/abs/2010.15623