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 invariants for 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.

Autorentext

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.

Inhalt

The Persistent Homology of Dual Digital Image Constructions (V. Robins).- Morse-based Fibering of the Persistence Rank Invariant (C. Landi).- Local Versus Global Distances for Zigzag and Multi Parameter Persistence Modules (E. Gasparovic).- Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons (V. Robins).- Graph Pseudometrics from a Topological Point of View (J. Tan).- Nerve theorems for fixed points of neural networks (C. Curto).- Combinatorial Conditions for Directed Collapsing (T. Fasy).- Lions and contamination, triangular grids, and Cheeger constants (L. Gibson).- A Topological Approach for Motion Track Discrimination (S. Tymochko).- Persistent topology of protein space (W. Hamilton).- Mappering Mecklenburg County: Exploring Census data for potential communities of interest (M. Thatcher).- Stitch Fix for Mapper and Topological Gains (B. Wang).