Based on the first Workshop for Women in Computational Topology that took place in 2016, this volume assembles new research and applications in computational topology. Featured articles range over the breadth of the discipline, including topics such as surface reconstruction, topological data analysis, persistent homology, algorithms, and surface-embedded graphs. Applications in graphics, medical imaging, and GIS are discussed throughout the book. Four of the papers in this volume are the product of working groups that were established and developed during the workshop. Additional papers were also solicited from the broader Women in Computational Topology network. The volume is accessible to a broad range of researchers, both within the field of computational topology and in related disciplines such as statistics, computational biology, and machine learning.
Preface.- The Rank Invariant Stability via Interleavings (Claudia
Landi).- Persistent Homology Over Directed Acyclic Graphs (Erin Wolf Chambers
and David Letscher).- A Complete Characterization of the 1-Dimensional
Intrinsic Cech Persistence Diagrams for Metric Graphs (Ellen Gasparovic,
Maria Gommel, et al).- Comparing Directed and Weighted Road Maps (Alyson
Bittner, Brittany Terese Fasy, et al).- Sweeping Costs of Planar Domains
(Brooks Adams, Henry Adams, and Colin Roberts).- Scaffoldings and Spines:
Organizing High-Dimensional Data Using Cover Trees, Local Principal Component
Analysis, and Persistent Homology (Paul Bendich, Ellen Gasparovic, et al).-
Density of local maxima of the distance function to a set of points in the
plane (Nina Amenta, Erin Chambers, et al).- Mind the Gap: A Study in Global
Development through Persistent Homology (Andrew Banman and Lori
Ziegelmeier).- Cluster Identification via Persistent Homology and other
Clustering Techniques, with Application to Liver Transplant Data (Berhanu A.
Wubie, Axel Andres, et al).- Pseudo-multidimensional persistence and its
applications (Catalina Betancourt, Mathieu Chalifour, et al).
Erin Chambers is an Associate Professor at Saint Louis University.Brittany Terese Fasy is an Assistant Professor and Gianforte Faculty Fellow at Montana State University.Lori Ziegelmeier is an Assistant Professor at Macalester College.
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