Persistence and stability of geometric complexes

Project Period: 2016-09-01 – 2020-08-31
Funder: FWF
Principal Investigator
Department(s)
Edelsbrunner Group
Grant Number
I02979-N35
Funder
FWF

35 Publications

2024 | Published | Journal Article | IST-REx-ID: 14345 | OA
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 72 (2024) 29–48.
[Published Version] View | Files available | DOI | WoS | arXiv
 
2024 | Published | Conference Paper | IST-REx-ID: 17144 | OA
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.
[Published Version] View | Files available | DOI | arXiv
 
2024 | Published | Conference Paper | IST-REx-ID: 17146 | OA
Maximum Betti numbers of Čech complexes
H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version] View | Files available | DOI | arXiv
 
2024 | Epub ahead of print | Journal Article | IST-REx-ID: 17149 | OA
Average and expected distortion of Voronoi paths and scapes
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2024).
[Published Version] View | DOI | Download Published Version (ext.) | arXiv
 
2024 | Published | Conference Paper | IST-REx-ID: 17170 | OA
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.
[Published Version] View | Files available | DOI | arXiv
 
2024 | Published | Journal Article | IST-REx-ID: 17190 | OA
Brillouin zones of integer lattices and their perturbations
H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.
[Preprint] View | DOI | Download Preprint (ext.) | arXiv
 
2024 | Published | Thesis | IST-REx-ID: 15094 | OA
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.
[Published Version] View | Files available | DOI
 
2024 | Published | Journal Article | IST-REx-ID: 15380 | OA
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).
[Published Version] View | Files available | DOI | Download Published Version (ext.)
 
2024 | Published | Conference Paper | IST-REx-ID: 18097 | OA
The ultimate frontier: An optimality construction for homotopy inference (media exposition)
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.
[Published Version] View | Files available | DOI
 
2024 | Published | Conference Paper | IST-REx-ID: 18556 | OA
The Euclidean MST-ratio for bi-colored lattices
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version] View | Files available | DOI | arXiv
 
2024 | Epub ahead of print | Journal Article | IST-REx-ID: 18626 | OA
Order-2 Delaunay triangulations optimize angles
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2024).
[Preprint] View | DOI | Download Preprint (ext.) | arXiv
 
2024 | Submitted | Preprint | IST-REx-ID: 18673 | OA
Merge trees of periodic filtrations
H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
[Preprint] View | Files available | DOI | Download Preprint (ext.) | arXiv
 
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).
View | DOI | WoS
 
2023 | Published | Journal Article | IST-REx-ID: 12086 | OA
A simple algorithm for higher-order Delaunay mosaics and alpha shapes
H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.
[Published Version] View | Files available | DOI | WoS
 
2023 | Published | Journal Article | IST-REx-ID: 12544 | OA
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.
[Published Version] View | Files available | DOI | WoS | PubMed | Europe PMC
 
2022 | Submitted | Journal Article | IST-REx-ID: 11658 | OA
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.).
[Submitted Version] View | Files available
 
2022 | Submitted | Journal Article | IST-REx-ID: 11660 | OA
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.).
[Submitted Version] View | Files available
 
2021 | Published | Journal Article | IST-REx-ID: 10222 | OA
The beauty of random polytopes inscribed in the 2-sphere
A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.
[Published Version] View | Files available | DOI | WoS | arXiv
 
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.
View | DOI
 
2021 | Published | Journal Article | IST-REx-ID: 9317 | OA
The multi-cover persistence of Euclidean balls
H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.
[Published Version] View | Files available | DOI | WoS
 

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