This book assembles new research from the field of computational topology, a cutting-edge area emerging on the boundary between computer science and mathematics. Topics range over the breadth of the discipline, from surface reconstruction to persistent homology and its applications. Chapters are accessible to a broad range of researchers, both in the field of computational topology as well as in other related disciplines (e.g., statistics, computational biology, machine learning).This book highlights research that was initiated at WinCompTop 2023, a workshop held in July 2023 at the EPFL, where 25 women in the field of computational topology gathered to work on research problems. Additional contributions were also solicited from the broader Women in Computational Topology network.
Erin Wolf ChamberUniversity of Notre Dame,Department of Computer Science and Engineering,Notre Dame, Indiana, USA.Claudia LandiUniversità di Modena e Reggio EmiliaDipartimento di Scienze e Metodi dell'IngegneriaVia Amendola 2, 42100 Reggio EmiliaItaly
Preface.- Introduction.- Decompositions of the persistent homology transform.- Multilevel sparsification of higher-order data.- Studying self-similarity of complex networks with persistent magnitude.- Probabilistic Behavior of Prefalence-Augmented Barcodes.- Connections between dynamic programming and directed topology.- Bibliography.- Index.