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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. 

Research in Computational Topology

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).