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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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