Persistence and stability of geometric complexes
Project Period: 2016-09-01 – 2020-08-31
Funder:
Austrian Science Fund
Acronym
DGD
Principal Investigator
Department(s)
Grant Number
I02979-N35
Grant DOI
Funder
Austrian Science Fund
Funder Schema
FWF-DFG-SFB
Funder Registry
41 Publications
2025 | Published | Journal Article | IST-REx-ID: 18626 |

Order-2 Delaunay triangulations optimize angles
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
[Preprint]
View
| DOI
| Download Preprint (ext.)
| WoS
| arXiv
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
2025 | Published | Journal Article | IST-REx-ID: 17149 |

Average and expected distortion of Voronoi paths and scapes
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 73 (2025) 490–499.
[Published Version]
View
| Files available
| DOI
| WoS
| PubMed | Europe PMC
| arXiv
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 73 (2025) 490–499.
2025 | Published | Thesis | IST-REx-ID: 18979 |

Structures and computations in topological data analysis
O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.
[Published Version]
View
| Files available
| DOI
O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.
2025 | Epub ahead of print | Journal Article | IST-REx-ID: 19937
Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality
M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).
View
| DOI
M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).
2025 | Published | Thesis | IST-REx-ID: 19630 |

Method for fluid simulation, surface tracking, and statistics of non-manifold structures
P. Synak, Method for Fluid Simulation, Surface Tracking, and Statistics of Non-Manifold Structures, Institute of Science and Technology Austria, 2025.
[Published Version]
View
| Files available
| DOI
P. Synak, Method for Fluid Simulation, Surface Tracking, and Statistics of Non-Manifold Structures, Institute of Science and Technology Austria, 2025.
2025 | Published | Conference Paper | IST-REx-ID: 20006 |

Banana trees for the persistence in time series experimentally
L. Ost, S. Cultrera di Montesano, H. Edelsbrunner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.
[Published Version]
View
| Files available
| DOI
| arXiv
L. Ost, S. Cultrera di Montesano, H. Edelsbrunner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.
2025 | Published | Conference Paper | IST-REx-ID: 20005 |

On spheres with k points inside
H. Edelsbrunner, A. Garber, M. Saghafian, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.
[Published Version]
View
| Files available
| DOI
| arXiv
H. Edelsbrunner, A. Garber, M. Saghafian, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.
2024 | Draft | Preprint | IST-REx-ID: 18673 |

Merge trees of periodic filtrations
H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
[Preprint]
View
| Files available
| DOI
| Download Preprint (ext.)
| arXiv
H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
2024 | Published | Conference Paper | IST-REx-ID: 18556 |

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
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.
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.
[Published Version]
View
| Files available
| DOI
| arXiv
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.
[Published Version]
View
| Files available
| DOI
| arXiv
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.
2024 | Published | Conference Paper | IST-REx-ID: 18097 |

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
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.
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.
[Published Version]
View
| Files available
| DOI
| arXiv
H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Journal Article | IST-REx-ID: 17190 |

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
H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.
2024 | Published | 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 72 (2024) 29–48.
[Published Version]
View
| Files available
| DOI
| WoS
| PubMed | Europe PMC
| arXiv
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.
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.
[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.
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 8 (2024) 557–578.
[Published Version]
View
| Files available
| DOI
| PubMed | Europe PMC
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.
2024 | Draft | Preprint | IST-REx-ID: 18981 |

Discrete microlocal Morse theory
A. Brown, O. Draganov, ArXiv (n.d.).
[Preprint]
View
| Files available
| DOI
| Download Preprint (ext.)
| arXiv
A. Brown, O. Draganov, ArXiv (n.d.).
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.
[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.
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
L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).