45 citations · 163 across the 16 of their papers we have counts for
5 papers · 1 filter
Alpha magnitude
Miguel O'Malley, Sara Kalisnik, Nina Otter
Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encod…
The Higher-Dimensional Skeletonization Problem
Sara Kalisnik Verovsek, Vitaliy Kurlin, Davorin Lesnik
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for…
Parametrized Homology via Zigzag Persistence
Gunnar Carlsson, Vin de Silva, Sara Kalisnik +1
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding…
Tropical Coordinates on the Space of Persistence Barcodes
Sara Kalisnik Verovsek
The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation…
Alexander Duality for Parametrized Homology
Sara Kalisnik Verovsek
This paper extends Alexander duality to the setting of parametrized homology. Let X with be a compact subset of R^n x R (n \geq 2) satisfying certain conditions, let Y be its compl…