289 citations · 628 across the 35 of their papers we have counts for
39 papers
Dualities in Multiparameter Persistence
Ulrich Bauer, Fabian Lenzen, Michael Lesnick
In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated…
Efficient two-parameter persistence computation via cohomology
Ulrich Bauer, Fabian Lenzen, Michael Lesnick
Clearing is a simple but effective optimization for the standard algorithm of persistent homology (PH), which dramatically improves the speed and scalability of PH computations for…
Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theory
Ulrich Bauer, Fabian Roll
We study the connection between discrete Morse theory and persistent homology in the context of shape reconstruction methods. Specifically, we consider the construction of Wrap com…
Topologically faithful image segmentation via induced matching of persistence barcodes
Nico Stucki, Johannes C. Paetzold, Suprosanna Shit +2
Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentatio…
Multi-Parameter Persistence Modules are Generically Indecomposable
Ulrich Bauer, Luis Scoccola
Algebraic persistence studies persistence modules (typically, linear representations of the poset with ) and the algebraic relationships between persistenc…
Keeping it sparse: Computing Persistent Homology revisited
Ulrich Bauer, Talha Bin Masood, Barbara Giunti +3
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topo…
Relative Interlevel Set Cohomology Categorifies Extended Persistence Diagrams
Ulrich Bauer, Benedikt Fluhr
The extended persistence diagram introduced by Cohen-Steiner, Edelsbrunner, and Harer is an invariant of real-valued continuous functions, which are -tame in the sense…
A Unified View on the Functorial Nerve Theorem and its Variations
Ulrich Bauer, Michael Kerber, Fabian Roll +1
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often nee…
Efficient Computation of Image Persistence
Ulrich Bauer, Maximilian Schmahl
We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These a…
Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations
Ulrich Bauer, Fabian Roll
Motivated by computational aspects of persistent homology for Vietoris-Rips filtrations, we generalize a result of Eliyahu Rips on the contractibility of Vietoris-Rips complexes of…
Tight quasi-universality of Reeb graph distances
Ulrich Bauer, Håvard Bakke Bjerkevik, Benedikt Fluhr
We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, th…
Parameterized inapproximability of Morse matching
Ulrich Bauer, Abhishek Rathod
We study the problem of minimizing the number of critical simplices from the point of view of inapproximability and parameterized complexity. We first show inapproximability of Min…
The complexity of high-dimensional cuts
Ulrich Bauer, Abhishek Rathod, Meirav Zehavi
Cut problems form one of the most fundamental classes of problems in algorithmic graph theory. For instance, the minimum cut, the minimum - cut, the minimum multiway cut, and…
Structure and Interleavings of Relative Interlevel Set Cohomology
Ulrich Bauer, Magnus Bakke Botnan, Benedikt Fluhr
The relative interlevel set cohomology (RISC) is an invariant of real-valued continuous functions closely related to the Mayer--Vietoris pyramid introduced by Carlsson, de Silva, a…
Persistent homology for functionals
Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence d…
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…
Parametrized Complexity of Expansion Height
Ulrich Bauer, Abhishek Rathod, Jonathan Spreer
Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of th…
Ripser: efficient computation of Vietoris-Rips persistence barcodes
Ulrich Bauer
We present an algorithm for the computation of Vietoris-Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representati…
Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
Ulrich Bauer, Magnus B. Botnan, Steffen Oppermann +1
We give a full classification of representation types of the subcategories of representations of an rectangular grid with monomorphisms (dually, epimorphisms) in one o…
On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces
Mathieu Carriere, Ulrich Bauer
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances…