Persistence and stability of geometric complexes
Project Period: 2016-09-01 – 2020-08-31
Externally Funded
Principal Investigator
Herbert Edelsbrunner
Department(s)
Edelsbrunner Group
Grant Number
I02979-N35
Funder
FWF
30 Publications
2024 |Published| Thesis | IST-REx-ID: 15094 | 
Persistence and Morse theory for discrete geometric structures
S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.
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S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.
2024 |Published| Journal Article | IST-REx-ID: 15380 |
Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2024).
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2024).
2024 |Published| Conference Paper | IST-REx-ID: 17144 |
The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms
H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
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H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 |Epub ahead of print| Journal Article | IST-REx-ID: 17149 |
Average and expected distortion of Voronoi paths and scapes
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2024).
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H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2024).
2024 |Published| Conference Paper | IST-REx-ID: 17146 |
Maximum Betti numbers of Čech complexes
H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
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H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 |Published| Conference Paper | IST-REx-ID: 17170 |
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds
D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19.
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D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19.
2023 |Published| Journal Article | IST-REx-ID: 12086 |
A simple algorithm for higher-order Delaunay mosaics and alpha shapes
H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.
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H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.
2023 |Published| Journal Article | IST-REx-ID: 12544 |
Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives
P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.
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P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.
2023 |Published| Journal Article | IST-REx-ID: 13134
Discrete analytical objects in the body-centered cubic grid
L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).
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L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).
2023 |Epub ahead of print| Journal Article | IST-REx-ID: 14345 |
On angles in higher order Brillouin tessellations and related tilings in the plane
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).
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H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).
2022 |Submitted| Journal Article | IST-REx-ID: 11660 |
A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).
2022 |Submitted| Journal Article | IST-REx-ID: 11658 |
Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).
2021 |Published| Conference Paper | IST-REx-ID: 9824
Body centered cubic grid - coordinate system and discrete analytical plane definition
L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
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L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
2021 |Published| Journal Article | IST-REx-ID: 9317 |
The multi-cover persistence of Euclidean balls
H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.
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H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.
2021 |Published| Journal Article | IST-REx-ID: 10222 |
The beauty of random polytopes inscribed in the 2-sphere
A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.
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A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.
2020 |Published| Conference Paper | IST-REx-ID: 8135 |
Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.
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H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.
2020 |Published| Journal Article | IST-REx-ID: 9249 |
Digital objects in rhombic dodecahedron grid
R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.
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R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.
2020 |Published| Journal Article | IST-REx-ID: 7554 |
Weighted Poisson–Delaunay mosaics
H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.
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H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.
2020 |Published| Journal Article | IST-REx-ID: 7666 |
Tri-partitions and bases of an ordered complex
H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.
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H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.
2020 |Published| Journal Article | IST-REx-ID: 9157 |
The weighted mean curvature derivative of a space-filling diagram
A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.
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A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.