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Research in Computational Topology 2

  • Book
  • © 2022

Overview

Editors:
  1. Ellen Gasparovic

    1. Department of Mathematics, Union College, Schenectady, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Vanessa Robins

    1. Research School of Physics, Australian National University, Canberra, Australia

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    You can also search for this editor in PubMed   Google Scholar

  3. Katharine Turner

    1. Mathematical Sciences Institute, Australian National University, Canberra, Australia

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    You can also search for this editor in PubMed   Google Scholar

  • Includes contributions ranging from the purely theoretical to computations and applications
  • Contains papers accessible to a broad audience of researchers
  • Features a gender-diverse slate of contributing authors

Part of the book series: Association for Women in Mathematics Series (AWMS, volume 30)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
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  2. The Persistent Homology of Dual Digital Image Constructions

    • Bea Bleile, Adélie Garin, Teresa Heiss, Kelly Maggs, Vanessa Robins
    Pages 1-26

  3. Morse-Based Fibering of the Persistence Rank Invariant

    • Asilata Bapat, Robyn Brooks, Celia Hacker, Claudia Landi, Barbara I. Mahler
    Pages 27-62

  4. Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules

    • Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang et al.
    Pages 63-76

  5. Tile-Transitive Tilings of the Euclidean and Hyperbolic Planes by Ribbons

    • Benedikt Kolbe, Vanessa Robins
    Pages 77-98

  6. Graph Pseudometrics from a Topological Point of View

    • Ana Lucia Garcia-Pulido, Kathryn Hess, Jane Tan, Katharine Turner, Bei Wang, Naya Yerolemou
    Pages 99-128

  7. Nerve Theorems for Fixed Points of Neural Networks

    • Daniela Egas Santander, Stefania Ebli, Alice Patania, Nicole Sanderson, Felicia Burtscher, Katherine Morrison et al.
    Pages 129-165

  8. Combinatorial Conditions for Directed Collapsing

    • Robin Belton, Robyn Brooks, Stefania Ebli, Lisbeth Fajstrup, Brittany Terese Fasy, Nicole Sanderson et al.
    Pages 167-189

  9. Lions and Contamination, Triangular Grids, and Cheeger Constants

    • Henry Adams, Leah Gibson, Jack Pfaffinger
    Pages 191-210

  10. A Topological Approach for Motion Track Discrimination

    • Tegan H. Emerson, Sarah Tymochko, George Stantchev, Jason A. Edelberg, Michael Wilson, Colin C. Olson
    Pages 211-222

  11. Persistent Topology of Protein Space

    • W. Hamilton, J. E. Borgert, T. Hamelryck, J. S. Marron
    Pages 223-244

  12. Mappering Mecklenburg County: Exploring Census Data for Potential Communities of Interest

    • Alisha Husain, Kristine Jones, Anthony Kolshorn, David Retchless, Kelemua Tesfaye, Courtney M. Thatcher et al.
    Pages 245-264

  13. Stitch Fix for Mapper and Topological Gains

    • Youjia Zhou, Nathaniel Saul, Ilkin Safarli, Bala Krishnamoorthy, Bei Wang
    Pages 265-294
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Keywords

About this book

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. 


Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariantsfor directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.


Editors and Affiliations

  • Department of Mathematics, Union College, Schenectady, USA

    Ellen Gasparovic

  • Research School of Physics, Australian National University, Canberra, Australia

    Vanessa Robins

  • Mathematical Sciences Institute, Australian National University, Canberra, Australia

    Katharine Turner

About the editors

​Ellen Gasparovic is an Associate Professor in the department of mathematics at Union College in Schenectady, NY, USA. She has served as a co-organizer of multiple conferences and workshops around the world in both applied topology and data science, including the second Women in Computational Topology (WinCompTop) workshop in July 2019. Her research interests are in applied and computational topology and geometry, topological data analysis, image and shape analysis, and differential topology.

Vanessa Robins is an Associate Professor in the Research School of Physics at the Australian National University. Her research develops new ways of applying mathematical concepts to applications in the natural sciences. She has made foundational contributions to the mathematical theory and algorithms for computing persistent homology from data. Dr Robins has co-authored over 40 papers and studied applications in image analysis, porous and granular materials, crystallography, engineered framework materials, dynamical systems and plant sciences. 



Katharine Turner is a Senior Lecturer in the Mathematical Sciences Institute at The Australian National University. Her research focuses topological, geometric and statistical theory relating to topological data analysis, alongside motivating applications such as morphology, point pattern analysis and neuroscience.

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