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12/05/2022
Connecting Discrete Morse Theory and Persistence: Wrap Complexes and Lexicographic Optimal Cycles
We study the connection between discrete Morse theory and persistent hom...
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11/28/2022
Topologically faithful image segmentation via induced matching of persistence barcodes
Image segmentation is a largely researched field where neural networks f...
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11/16/2022
Keeping it sparse: Computing Persistent Homology revisited
In this work, we study several variants of matrix reduction via Gaussian...
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05/30/2022
Relative Interlevel Set Cohomology Categorifies Extended Persistence Diagrams
The extended persistence diagram introduced by Cohen-Steiner, Edelsbrunn...
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01/11/2022
Efficient Computation of Image Persistence
We present an algorithm for computing the barcode of the image of a morp...
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12/13/2021
Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations
Motivated by computational aspects of persistent homology for Vietoris-R...
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12/01/2021
Quasi-universality of Reeb graph distances
We establish bi-Lipschitz bounds certifying quasi-universality (universa...
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09/09/2021
Parameterized inapproximability of Morse matching
We study the problem of minimizing the number of critical simplices from...
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08/23/2021
The complexity of high-dimensional cuts
Cut problems form one of the most fundamental classes of problems in alg...
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08/20/2021
Structure and Interleavings of Relative Interlevel Set Cohomology
The relative interlevel set cohomology (RISC) is an invariant of real-va...
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06/14/2021
Topology identifies emerging adaptive mutations in SARS-CoV-2
The COVID-19 pandemic has lead to a worldwide effort to characterize its...
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12/23/2020
The Structure of Morphisms in Persistent Homology, I. Functorial Dualities
We prove duality results for absolute and relative versions of persisten...
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07/03/2020
Universality of the Bottleneck Distance for Extended Persistence Diagrams
The extended persistence diagram is an invariant of piecewise linear fun...
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10/21/2019
Parametrized Complexity of Expansion Height
Deciding whether two simplicial complexes are homotopy equivalent is a f...
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08/07/2019
Ripser: efficient computation of Vietoris-Rips persistence barcodes
We present an algorithm for the computation of Vietoris-Rips persistence...
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06/19/2018
On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces
Persistence diagrams are important descriptors in Topological Data Analy...
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06/19/2018
On the Metric Distortion of Embedding Persistence Diagrams into Reproducing Kernel Hilbert Spaces
Persistence diagrams are important feature descriptors in Topological Da...
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01/25/2018
Hardness of Approximation for Morse Matching
We consider the approximability of maximization and minimization variant...
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01/25/2018
Persistent Betti numbers of random Čech complexes
We study the persistent homology of random Čech complexes. Generalizing ...
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01/05/2018
The Reeb Graph Edit Distance is Universal
We consider the setting of Reeb graphs of piecewise linear functions and...
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09/12/2017
Persistence in sampled dynamical systems faster
We call a continuous self-map that reveals itself through a discrete set...
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12/21/2014