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
Funding Organisation
FWF
25 Publications
2018 | Conference Paper | IST-REx-ID: 188 |
Smallest enclosing spheres and Chernoff points in Bregman geometry
H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.
[Published Version]
View
| Files available
| DOI
H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.
2019 | Conference Paper | IST-REx-ID: 6648 |
Topological data analysis in information space
H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14.
[Published Version]
View
| Files available
| DOI
| arXiv
H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14.
2020 | 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.
[Submitted Version]
View
| Files available
| DOI
H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.
2020 | 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.
[Published Version]
View
| Files available
| DOI
R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.
2021 | 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
L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
2023 | 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.
[Published Version]
View
| Files available
| DOI
| WoS
H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.
2021 | 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.
[Published Version]
View
| Files available
| DOI
| WoS
H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.
2021 | 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.
[Published Version]
View
| Files available
| DOI
| WoS
| arXiv
A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.
2023 | 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.
[Published Version]
View
| Files available
| DOI
| WoS
| PubMed | Europe PMC
P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.
2020 | Journal Article | IST-REx-ID: 7554 |
Weighted Poisson–Delaunay mosaics
H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.
[Preprint]
View
| DOI
| Download Preprint (ext.)
| WoS
| arXiv
H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.
2020 | 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.
[Published Version]
View
| Files available
| DOI
| WoS
H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.
2019 | Journal Article | IST-REx-ID: 6756 |
Unexpected topology of the temperature fluctuations in the cosmic microwave background
P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).
[Published Version]
View
| Files available
| DOI
| WoS
| arXiv
P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).
2019 | Journal Article | IST-REx-ID: 5678 |
Poisson–Delaunay Mosaics of Order k
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.
[Published Version]
View
| Files available
| DOI
| WoS
| arXiv
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.
2017 | Journal Article | IST-REx-ID: 718 |
Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.
[Preprint]
View
| Files available
| DOI
| Download Preprint (ext.)
| arXiv
H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.
2019 | Journal Article | IST-REx-ID: 6608 |
Holes and dependences in an ordered complex
H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.
[Published Version]
View
| Files available
| DOI
| WoS
H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.
2018 | Conference Paper | IST-REx-ID: 187 |
The multi-cover persistence of Euclidean balls
H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.
[Published Version]
View
| Files available
| DOI
H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.
2018 | Journal Article | IST-REx-ID: 312 |
On the optimality of the FCC lattice for soft sphere packing
H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.
[Submitted Version]
View
| DOI
| Download Submitted Version (ext.)
| WoS
H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.
2018 | Journal Article | IST-REx-ID: 87 |
Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics
H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.
[Preprint]
View
| Files available
| DOI
| Download Preprint (ext.)
| WoS
| arXiv
H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.
2023 | 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
L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).
2020 | 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.
[Published Version]
View
| Files available
| DOI
A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.
2020 | Journal Article | IST-REx-ID: 9156 |
The weighted Gaussian curvature derivative of a space-filling diagram
A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.
[Published Version]
View
| Files available
| DOI
| arXiv
A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.
2023 | 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).
[Published Version]
View
| DOI
| Download Published Version (ext.)
| WoS
| arXiv
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).
2024 | 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.
[Published Version]
View
| Files available
| DOI
S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.
2022 | 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.).
[Submitted Version]
View
| Files available
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).
2022 | 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.).
[Submitted Version]
View
| Files available
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).