289 citations · 628 across the 35 of their papers we have counts for
5 papers · 1 filter
Lifespan Functors and Natural Dualities in Persistent Homology
Ulrich Bauer, Maximilian Schmahl
We introduce lifespan functors, which are endofunctors on the category of persistence modules that filter out intervals from barcodes according to their boundedness properties. The…
Homology of configuration spaces of hard squares in a rectangle
Hannah Alpert, Ulrich Bauer, Matthew Kahle +2
We study ordered configuration spaces of hard squares in a rectangle, a generalization of the well-known "15 Puzzle". Our main interest is in the topolo…
Universal Distances for Extended Persistence
Ulrich Bauer, Magnus Bakke Botnan, Benedikt Fluhr
The extended persistence diagram is an invariant of piecewise linear functions, which is known to be stable under perturbations of functions with respect to the bottleneck distance…
clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation
Suprosanna Shit, Johannes C. Paetzold, Anjany Sekuboyina +6
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their mo…
Combinatorial models of global dynamics: learning cycling motion from data
Ulrich Bauer, David Hien, Oliver Junge +2
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of…