Research in Computational Topology

1. Front Matter

   Pages i-xiv

   PDF

2. The Rank Invariant Stability via Interleavings

   • Claudia Landi

   Pages 1-10

3. Persistent Homology over Directed Acyclic Graphs

   • Erin Wolf Chambers, David Letscher

   Pages 11-32

4. A Complete Characterization of the One-Dimensional Intrinsic Čech Persistence Diagrams for Metric Graphs

   • Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang et al.

   Pages 33-56

5. Comparing Directed and Weighted Road Maps

   • Alyson Bittner, Brittany Terese Fasy, Maia Grudzien, Sayonita Ghosh Hajra, Jici Huang, Kristine Pelatt et al.

   Pages 57-70

6. Sweeping Costs of Planar Domains

   • Brooks Adams, Henry Adams, Colin Roberts

   Pages 71-92

7. Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology

   • Paul Bendich, Ellen Gasparovic, John Harer, Christopher J. Tralie

   Pages 93-114

8. Density of Local Maxima of the Distance Function to a Set of Points in the Plane

   • Nina Amenta, Erin Wolf Chambers, Tegan Emerson, Rebecca Glover, Katharine Turner, Shirley Yap

   Pages 115-123

9. Mind the Gap: A Study in Global Development Through Persistent Homology

   • Andrew Banman, Lori Ziegelmeier

   Pages 125-144

10. Cluster Identification via Persistent Homology and Other Clustering Techniques, with Application to Liver Transplant Data

    • Berhanu A. Wubie, Axel Andres, Russell Greiner, Bret Hoehn, Aldo Montano-Loza, Norman Kneteman et al.

    Pages 145-177

11. Pseudo-Multidimensional Persistence and Its Applications

    • Catalina Betancourt, Mathieu Chalifour, Rachel Neville, Matthew Pietrosanu, Mimi Tsuruga, Isabel Darcy et al.

    Pages 179-202

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. 

• Computational Topology
• Data Analysis
• Metric Graphs
• Network Analysis
• Persistence Profiles
• Workshop
• Rank invariant stability
• scaffoldings and spines
• planar domains
• Pseudo-multidimensional persistence
• persistent homology
• WinCompTop

• Department of Computer Science, St Louis University, St Louis, USA

  Erin Wolf Chambers

• Gianforte School of Computing, and Department of Mathematical Sciences, Montana State University, Bozeman, USA

  Brittany Terese Fasy

• Department of Mathematics, Statistics, & Computer Science, Macalester College, Saint Paul, USA

  Lori Ziegelmeier

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.

Policies and ethics