Computational methods for multi-parameter persistence

Lenzen, Fabian

Fabian Lenzen

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Original title:: Computational methods for multi-parameter persistence
Translated title:: Methoden zur Berechnung von multi-Parameter Persistence
Author:: Lenzen, Fabian
Year:: 2023
Document type:: Dissertation
Faculty/School:: TUM School of Computation, Information and Technology
Advisor:: Bauer, Ulrich (Prof. Dr.)
Referee:: Bauer, Ulrich (Prof. Dr.); Kerber, Michael (Prof. Dr.); Botnan, Magnus (Prof., Ph.D..)
Language:: en
Subject group:: MAT Mathematik
TUM classification:: MAT 530
Abstract:: In the past, persistent cohomology was a major ingredient in improving the efficiency of persistent homology. However, persistent cohomology has not been successfully applied in multi-parameter persistence so far. In this thesis, we close this gap by providing a theoretical foundation for computing multi-parameter persistent cohomology, providing algorithms, and demonstrating the efficiency of this approach by experimental runtime data obtained with a software implementation of our algorithms.
Translated abstract:: Persistente Kohomologie hat einen erheblichen Beitrag an der Effizienz heutiger Implementierungen Persistenter Homologie. Allerdings ist Persistente Kohomologie bisher nicht erfolgreich für multi-Parameter Persistence angewandt worden. In dieser Arbeit schließen wir diese Lücke, indem wir ein theoretisches Fundament sowie entsprechende Algorithmen für multi-Parameter Persistente Kohomologie entwickeln, deren Effizienz wir in Software-Experimenten mit einer eigenen Implementierung demonstrieren.
WWW:: https://mediatum.ub.tum.de/?id=1713777
Date of submission:: 28.06.2023
Oral examination:: 01.12.2023
File size:: 11590846 bytes
Pages:: 156
Urn (citeable URL):: https://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91-diss-20231201-1713777-1-1
Last change:: 18.12.2023
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