---
OA_place: repository
OA_type: green
_id: '20585'
abstract:
- lang: eng
text: Motivated by applications in medical sciences, we study finite chromatic sets
in Euclidean space from a topological perspective. Based on the persistent homology
for images, kernels and cokernels, we design provably stable homological quantifiers
that describe the geometric micro- and macro-structure of how the color classes
mingle. These can be efficiently computed using chromatic variants of Delaunay
and alpha complexes, and code that does these computations is provided.
acknowledgement: "This project has received funding from the European Research\r\nCouncil
(ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund\r\n(FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR\r\n109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
alpha complexes. Foundations of Data Science. 2025;8:30-62. doi:10.3934/fods.2025003
apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (2025). Chromatic alpha complexes. Foundations of Data Science. American
Institute of Mathematical Sciences. https://doi.org/10.3934/fods.2025003
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “Chromatic Alpha Complexes.” Foundations of Data Science.
American Institute of Mathematical Sciences, 2025. https://doi.org/10.3934/fods.2025003.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“Chromatic alpha complexes,” Foundations of Data Science, vol. 8. American
Institute of Mathematical Sciences, pp. 30–62, 2025.
ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2025. Chromatic
alpha complexes. Foundations of Data Science. 8, 30–62.
mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” Foundations
of Data Science, vol. 8, American Institute of Mathematical Sciences, 2025,
pp. 30–62, doi:10.3934/fods.2025003.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations
of Data Science 8 (2025) 30–62.
corr_author: '1'
date_created: 2025-11-02T23:01:33Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2025-11-04T12:25:47Z
day: '01'
department:
- _id: HeEd
doi: 10.3934/fods.2025003
ec_funded: 1
external_id:
arxiv:
- '2212.03128'
intvolume: ' 8'
language:
- iso: eng
month: '03'
oa_version: Preprint
page: 30-62
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Foundations of Data Science
publication_identifier:
eissn:
- 2639-8001
publication_status: epub_ahead
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
related_material:
record:
- id: '15091'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Chromatic alpha complexes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20657'
abstract:
- lang: eng
text: 'The Upper Bound Theorem for convex polytopes implies that the p-th Betti
number of the Čech complex of any set of N points in ℝ^d and any radius satisfies
β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions,
which prove that this upper bound is asymptotically tight. For example, we describe
a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number
of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of
the Čech complex at the other radius is n². '
acknowledgement: The first author is supported by the European Research Council (ERC),
grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant no. I 02979-N35. The second author is supported by the
European Research Council (ERC), grant “GeoScape” and by the Hungarian Science Foundation
(NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian
Science Fund (FWF), grant no. Z 342-N31.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
citation:
ama: Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. Discrete
& Computational Geometry. 2025. doi:10.1007/s00454-025-00796-5
apa: Edelsbrunner, H., & Pach, J. (2025). Maximum Betti numbers of Čech complexes.
Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-025-00796-5
chicago: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
Discrete & Computational Geometry. Springer Nature, 2025. https://doi.org/10.1007/s00454-025-00796-5.
ieee: H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” Discrete
& Computational Geometry. Springer Nature, 2025.
ista: Edelsbrunner H, Pach J. 2025. Maximum Betti numbers of Čech complexes. Discrete
& Computational Geometry.
mla: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
Discrete & Computational Geometry, Springer Nature, 2025, doi:10.1007/s00454-025-00796-5.
short: H. Edelsbrunner, J. Pach, Discrete & Computational Geometry (2025).
corr_author: '1'
date_created: 2025-11-19T09:44:58Z
date_published: 2025-11-10T00:00:00Z
date_updated: 2025-12-01T15:19:21Z
day: '10'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-025-00796-5
ec_funded: 1
external_id:
arxiv:
- '2310.14801'
isi:
- '001610592600001'
has_accepted_license: '1'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-025-00796-5
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '17146'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Maximum Betti numbers of Čech complexes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20658'
abstract:
- lang: eng
text: The medial axis of a smoothly embedded surface in R^3 consists of all points
for which the Euclidean distance function on the surface has at least two global
minima. We generalize this notion to the mid-sphere axis, which consists of all
points for which the Euclidean distance function has two interchanging saddles
that swap their partners in the pairing by persistent homology. It offers a discrete-algebraic
multi-scale approach to computing ridge-like structures on the surface. As a proof
of concept, an algorithm that computes stair-case approximations of the mid-sphere
axis is provided.
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Martin H
full_name: Thoresen, Martin H
id: 47CB1472-F248-11E8-B48F-1D18A9856A87
last_name: Thoresen
citation:
ama: 'Edelsbrunner H, Stephenson ER, Thoresen MH. The mid-sphere cousin of the medial
axis transform. In: 4th International Joint Conference on Discrete Geometry
and Mathematical Morphology. Vol 16296. Springer Nature; 2025:133-147. doi:10.1007/978-3-032-09544-2_10'
apa: 'Edelsbrunner, H., Stephenson, E. R., & Thoresen, M. H. (2025). The mid-sphere
cousin of the medial axis transform. In 4th International Joint Conference
on Discrete Geometry and Mathematical Morphology (Vol. 16296, pp. 133–147).
Groningen, The Netherlands: Springer Nature. https://doi.org/10.1007/978-3-032-09544-2_10'
chicago: Edelsbrunner, Herbert, Elizabeth R Stephenson, and Martin H Thoresen. “The
Mid-Sphere Cousin of the Medial Axis Transform.” In 4th International Joint
Conference on Discrete Geometry and Mathematical Morphology, 16296:133–47.
Springer Nature, 2025. https://doi.org/10.1007/978-3-032-09544-2_10.
ieee: H. Edelsbrunner, E. R. Stephenson, and M. H. Thoresen, “The mid-sphere cousin
of the medial axis transform,” in 4th International Joint Conference on Discrete
Geometry and Mathematical Morphology, Groningen, The Netherlands, 2025, vol.
16296, pp. 133–147.
ista: 'Edelsbrunner H, Stephenson ER, Thoresen MH. 2025. The mid-sphere cousin of the medial
axis transform. 4th International Joint Conference on Discrete Geometry and Mathematical
Morphology. DGMM: Discrete Geometry and Mathematical Morphology, LNCS, vol. 16296,
133–147.'
mla: Edelsbrunner, Herbert, et al. “The Mid-Sphere Cousin of the Medial Axis Transform.”
4th International Joint Conference on Discrete Geometry and Mathematical Morphology,
vol. 16296, Springer Nature, 2025, pp. 133–47, doi:10.1007/978-3-032-09544-2_10.
short: H. Edelsbrunner, E.R. Stephenson, M.H. Thoresen, in:, 4th International Joint
Conference on Discrete Geometry and Mathematical Morphology, Springer Nature,
2025, pp. 133–147.
conference:
end_date: 2025-11-06
location: Groningen, The Netherlands
name: 'DGMM: Discrete Geometry and Mathematical Morphology'
start_date: 2025-11-03
date_created: 2025-11-23T23:01:37Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2025-11-24T10:05:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-032-09544-2_10
external_id:
arxiv:
- '2504.14743'
intvolume: ' 16296'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2504.14743
month: '11'
oa: 1
oa_version: Preprint
page: 133-147
publication: 4th International Joint Conference on Discrete Geometry and Mathematical
Morphology
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783032095435'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The mid-sphere cousin of the medial axis transform
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16296
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '20729'
abstract:
- lang: eng
text: 'Persistence modules (defined as a sequence of vector spaces and linear maps
between them) are a key tool in topological data analysis. They are easy to interpret
and fast to compute. However, when considering persistence maps (i.e. maps between
persistence modules), these properties are lost. We propose a new invariant for
persistence maps consisting of a partial matching such that: it is easy to interpret,
it is more discriminative than the image of the persistence map, and can be calculated
with cubical complexity.'
acknowledgement: Álvaro Torras-Casas contract is funded by the French Agence Nationale
de la Recherche through the project reference ANR-22-CPJ1-0047-01. Rocio Gonzalez-Diaz
is partially funded by the European Union under grant agreement no. 101070028-2
(REXASI-PRO).
article_processing_charge: Yes (in subscription journal)
author:
- first_name: Rocio
full_name: Gonzalez-Diaz, Rocio
last_name: Gonzalez-Diaz
- first_name: Manuel
full_name: Soriano Trigueros, Manuel
id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
last_name: Soriano Trigueros
orcid: 0000-0003-2449-1433
- first_name: Alvaro
full_name: Torras-Casas, Alvaro
last_name: Torras-Casas
citation:
ama: 'Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings
for persistent homology. In: Proceedings of the 2025 International Symposium
on Symbolic and Algebraic Computation. Association for Computing Machinery;
2025:188-196. doi:10.1145/3747199.3747561'
apa: 'Gonzalez-Diaz, R., Soriano Trigueros, M., & Torras-Casas, A. (2025). Additive
partial matchings for persistent homology. In Proceedings of the 2025 International
Symposium on Symbolic and Algebraic Computation (pp. 188–196). Guanajuato,
Mexico: Association for Computing Machinery. https://doi.org/10.1145/3747199.3747561'
chicago: Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas.
“Additive Partial Matchings for Persistent Homology.” In Proceedings of the
2025 International Symposium on Symbolic and Algebraic Computation, 188–96.
Association for Computing Machinery, 2025. https://doi.org/10.1145/3747199.3747561.
ieee: R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial
matchings for persistent homology,” in Proceedings of the 2025 International
Symposium on Symbolic and Algebraic Computation, Guanajuato, Mexico, 2025,
pp. 188–196.
ista: 'Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2025. Additive partial
matchings for persistent homology. Proceedings of the 2025 International Symposium
on Symbolic and Algebraic Computation. ISSAC: International Symposium on Symbolic
and Algebraic Computation, 188–196.'
mla: Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings for Persistent Homology.”
Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation,
Association for Computing Machinery, 2025, pp. 188–96, doi:10.1145/3747199.3747561.
short: R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, in:, Proceedings
of the 2025 International Symposium on Symbolic and Algebraic Computation, Association
for Computing Machinery, 2025, pp. 188–196.
conference:
end_date: 2025-08-01
location: Guanajuato, Mexico
name: 'ISSAC: International Symposium on Symbolic and Algebraic Computation'
start_date: 2025-07-28
corr_author: '1'
date_created: 2025-12-07T23:02:01Z
date_published: 2025-11-10T00:00:00Z
date_updated: 2025-12-09T13:46:42Z
day: '10'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1145/3747199.3747561
file:
- access_level: open_access
checksum: 1c299cca165a20e2518afe4fda63dbf1
content_type: application/pdf
creator: dernst
date_created: 2025-12-09T13:43:17Z
date_updated: 2025-12-09T13:43:17Z
file_id: '20751'
file_name: 2025_ISSAC_GonzalezDiaz.pdf
file_size: 761617
relation: main_file
success: 1
file_date_updated: 2025-12-09T13:43:17Z
has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 188-196
publication: Proceedings of the 2025 International Symposium on Symbolic and Algebraic
Computation
publication_identifier:
isbn:
- '9798400720758'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Additive partial matchings for persistent homology
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '20867'
abstract:
- lang: eng
text: We discuss the embeddability of subspaces of the Gromov–Hausdorff space, which
consists of isometry classes of compact metric spaces endowed with the Gromov–Hausdorff
distance, into Hilbert spaces. These embeddings are particularly valuable for
applications to topological data analysis. We prove that its subspace consisting
of metric spaces with at most n points has asymptotic dimension n(n−1)∕2. Thus,
there exists a coarse embedding of that space into a Hilbert space. On the contrary,
if the number of points is not bounded, then the subspace cannot be coarsely embedded
into any uniformly convex Banach space and so, in particular, into any Hilbert
space. Furthermore, we prove that, even if we restrict to finite metric spaces
whose diameter is bounded by some constant, the subspace still cannot be bi-Lipschitz
embedded into any finite-dimensional Hilbert space. We obtain both nonembeddability
results by finding obstructions to coarse and bi-Lipschitz embeddings in families
of isometry classes of finite subsets of the real line endowed with the Euclidean–Hausdorff
distance.
acknowledgement: "The author was supported by the FWF Grant, Project number I4245-N35.
The author would like to thank Thomas Weighill for the helpful discussions around
Theorem 3.10, and Takamitsu Yamauchi for bringing to my attention the fundamental
reference [35]. Furthermore, the author\r\nis thankful for the detailed and helpful
comments of the reviewer of this manuscript."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Zava N. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces. Algebraic & Geometric Topology. 2025;25(8):5153-5174.
doi:10.2140/agt.2025.25.5153
apa: Zava, N. (2025). Coarse and bi-Lipschitz embeddability of subspaces of the
Gromov–Hausdorff space into Hilbert spaces. Algebraic & Geometric Topology.
Mathematical Sciences Publishers. https://doi.org/10.2140/agt.2025.25.5153
chicago: Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the
Gromov–Hausdorff Space into Hilbert Spaces.” Algebraic & Geometric Topology.
Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/agt.2025.25.5153.
ieee: N. Zava, “Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces,” Algebraic & Geometric Topology, vol. 25,
no. 8. Mathematical Sciences Publishers, pp. 5153–5174, 2025.
ista: Zava N. 2025. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces. Algebraic & Geometric Topology. 25(8), 5153–5174.
mla: Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff
Space into Hilbert Spaces.” Algebraic & Geometric Topology, vol. 25,
no. 8, Mathematical Sciences Publishers, 2025, pp. 5153–74, doi:10.2140/agt.2025.25.5153.
short: N. Zava, Algebraic & Geometric Topology 25 (2025) 5153–5174.
corr_author: '1'
date_created: 2025-12-29T12:09:09Z
date_published: 2025-11-20T00:00:00Z
date_updated: 2026-01-05T12:19:09Z
day: '20'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.2140/agt.2025.25.5153
external_id:
arxiv:
- '2303.04730'
file:
- access_level: open_access
checksum: 1e05b4f17a44500ae1ae1e21bc636f6a
content_type: application/pdf
creator: dernst
date_created: 2026-01-05T12:16:38Z
date_updated: 2026-01-05T12:16:38Z
file_id: '20943'
file_name: 2025_AlgebraicGeomTopology_Zava.pdf
file_size: 574389
relation: main_file
success: 1
file_date_updated: 2026-01-05T12:16:38Z
has_accepted_license: '1'
intvolume: ' 25'
issue: '8'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 5153-5174
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I04245
name: Algebraic Footprints of Geometric Features in Homology
publication: Algebraic & Geometric Topology
publication_identifier:
eissn:
- 1472-2739
issn:
- 1472-2747
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '17149'
abstract:
- lang: eng
text: The approximation of a circle with the edges of a fine square grid distorts
the perimeter by a factor about 4/Pi. We prove that this factor is the same on
average (in the ergodic sense) for approximations of any rectifiable curve by
the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend
the results to all dimensions, generalizing Voronoi paths to Voronoi scapes.
acknowledgement: "The authors thank Ranita Biswas and Tatiana Ezubova for the collaboration
on computational experiments that motivated the work reported in this paper. The
authors also thank Daniel Bonnema for proofreading and noticing an issue with the
original proof of Lemma 4.3.\r\nOpen access funding provided by Institute of Science
and Technology (IST Austria).\r\nThis project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund
(FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109,
‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No.
I 02979-N35."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Average and expected distortion of Voronoi paths
and scapes. Discrete & Computational Geometry. 2025;73:490-499. doi:10.1007/s00454-024-00660-y
apa: Edelsbrunner, H., & Nikitenko, A. (2025). Average and expected distortion
of Voronoi paths and scapes. Discrete & Computational Geometry. Springer
Nature. https://doi.org/10.1007/s00454-024-00660-y
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Average and Expected Distortion
of Voronoi Paths and Scapes.” Discrete & Computational Geometry. Springer
Nature, 2025. https://doi.org/10.1007/s00454-024-00660-y.
ieee: H. Edelsbrunner and A. Nikitenko, “Average and expected distortion of Voronoi
paths and scapes,” Discrete & Computational Geometry, vol. 73. Springer
Nature, pp. 490–499, 2025.
ista: Edelsbrunner H, Nikitenko A. 2025. Average and expected distortion of Voronoi
paths and scapes. Discrete & Computational Geometry. 73, 490–499.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Average and Expected Distortion
of Voronoi Paths and Scapes.” Discrete & Computational Geometry, vol.
73, Springer Nature, 2025, pp. 490–99, doi:10.1007/s00454-024-00660-y.
short: H. Edelsbrunner, A. Nikitenko, Discrete & Computational Geometry 73 (2025)
490–499.
corr_author: '1'
date_created: 2024-06-16T22:01:07Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2026-02-16T12:18:50Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-024-00660-y
ec_funded: 1
external_id:
arxiv:
- '2012.03350'
isi:
- '001238566200004'
pmid:
- '39974750'
file:
- access_level: open_access
checksum: ffb0c818222138f9f113f4bbea41e834
content_type: application/pdf
creator: dernst
date_created: 2025-04-23T07:31:32Z
date_updated: 2025-04-23T07:31:32Z
file_id: '19610'
file_name: 2025_DiscreteComputGeom_EdelsbrunnerHe.pdf
file_size: 283443
relation: main_file
success: 1
file_date_updated: 2025-04-23T07:31:32Z
has_accepted_license: '1'
intvolume: ' 73'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 490-499
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Average and expected distortion of Voronoi paths and scapes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 73
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20260'
abstract:
- lang: eng
text: The medial axis of a set consists of the points in the ambient space without
a unique closest point in the original set. Since its introduction, the medial
axis has been used extensively in many applications as a method of computing a
skeleton topologically equivalent to the original set. Unfortunately, one limiting
factor in the use of the medial axis of a smooth manifold is that it is not necessarily
topologically stable under small perturbations of the manifold. To counter these
instabilities, various prunings of the medial axis have been proposed in the computational
geometry community. Here, we examine one type of pruning, called burning. Because
of the good experimental results it was hoped that the burning method of simplifying
the medial axis would be stable. In this work, we show a simple example that dashes
such hopes. Based on Bing’s house with two rooms, we demonstrate an isotopy of
a shape where the medial axis goes from collapsible to non-collapsible. More precisely,
we consider the standard deformation retract from the closed ball to Bing’s house
with two rooms, but stop just short of the point where Bing’s house becomes two
dimensional. This way we obtain an isotopy from the 3-ball to a thickened version
of Bing’s house. Under this isotopy, the medial axis goes from collapsible to
non-collapsible. We stress that this isotopy can be made generic, in the sense
of singularity theory, as developed by Arnol’d and Thom.
acknowledgement: "We thank André Lieutier, David Letscher, Ellen Gasparovic, Kathryn
Leonard, and Tao Ju for early discussions on this work. We also thank Lu Liu, Yajie
Yan, and Tao Ju for sharing code to generate the examples. We further thank Abigail
Thompson for discussion on the conjecture and James Damon for sharing his insight
in singularity theory. We thank the reviewers for their detailed reviews, which
helped to improve the exposition.\r\nOpen access funding provided by Institute of
Science and Technology (IST Austria). Partially supported by the DFG Collaborative
Research Center TRR 109, ‘Discretization in Geometry and Dynamics’ and the European
Research Council (ERC), grant no. 788183, ‘Alpha Shape Theory Extended’. The first
author was supported in part by the National Science Foundation through grants DBI-1759807,
CCF-1907612, and CCF-2444309. The fourth author was supported by the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
grant agreement No. 754411, the Austrian science fund (FWF) M-3073, ANR grant StratMesh,
ANR-24-CE48-1899, and the welcome package from IDEX of the Université Côte d’Azur,
ANR-15-IDEX-01."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Erin Wolf
full_name: Chambers, Erin Wolf
last_name: Chambers
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Chambers EW, Fillmore CD, Stephenson ER, Wintraecken M. Burning or collapsing
the medial axis is unstable. La Matematica. 2025;4:811-828. doi:10.1007/s44007-025-00170-0
apa: Chambers, E. W., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M.
(2025). Burning or collapsing the medial axis is unstable. La Matematica.
Springer Nature. https://doi.org/10.1007/s44007-025-00170-0
chicago: Chambers, Erin Wolf, Christopher D Fillmore, Elizabeth R Stephenson, and
Mathijs Wintraecken. “Burning or Collapsing the Medial Axis Is Unstable.” La
Matematica. Springer Nature, 2025. https://doi.org/10.1007/s44007-025-00170-0.
ieee: E. W. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “Burning
or collapsing the medial axis is unstable,” La Matematica, vol. 4. Springer
Nature, pp. 811–828, 2025.
ista: Chambers EW, Fillmore CD, Stephenson ER, Wintraecken M. 2025. Burning or collapsing
the medial axis is unstable. La Matematica. 4, 811–828.
mla: Chambers, Erin Wolf, et al. “Burning or Collapsing the Medial Axis Is Unstable.”
La Matematica, vol. 4, Springer Nature, 2025, pp. 811–28, doi:10.1007/s44007-025-00170-0.
short: E.W. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, La Matematica
4 (2025) 811–828.
corr_author: '1'
date_created: 2025-08-31T22:01:33Z
date_published: 2025-12-01T00:00:00Z
date_updated: 2026-04-07T11:42:48Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s44007-025-00170-0
ec_funded: 1
file:
- access_level: open_access
checksum: e2043259194bfcdf3d74c4da8a5a853f
content_type: application/pdf
creator: dernst
date_created: 2025-12-30T07:52:58Z
date_updated: 2025-12-30T07:52:58Z
file_id: '20885'
file_name: 2025_LaMatematica_Chambers.pdf
file_size: 2678640
relation: main_file
success: 1
file_date_updated: 2025-12-30T07:52:58Z
has_accepted_license: '1'
intvolume: ' 4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 811-828
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: La Matematica
publication_identifier:
eissn:
- 2730-9657
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '21021'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Burning or collapsing the medial axis is unstable
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2025'
...
---
OA_place: publisher
_id: '18979'
abstract:
- lang: eng
text: "Topological Data Analysis (TDA) is a discipline utilizing the mathematical
field of topology to study data, most prominently collections of point sets. This
thesis summarizes three projects related to computations in TDA.\r\n\r\nThe first
one establishes a variant of TDA for chromatic point sets, where each point is
given a color. For example, we are given positions of cells within a tumor microenvironment,
and color the cancerous cells red, and the immune cells blue.\r\n\r\nThe aim is
then to give a quantitative description of how the two or more sets of points
spatially interact. Building on image, kernel and cokernel variants of persistent
homology, we suggest six-packs of persistent diagrams as such a descriptor.\r\n\r\nWe
describe a construction of a chromatic alpha complex, which enables efficient
computation of several variants of the six-packs. We give topological descriptions
of natural subcomplexes of the chromatic alpha complex, and show that the radii
of the simplices form a discrete Morse function. Finally, we provide an implementation
of the presented chromatic TDA pipeline.\r\n\r\nThe second part aims to translate
a powerful tool of sheaf theory to elementary terms using labeled matrices. The
goal is to enable their use in computational settings. We show that derived categories
of sheaves over finite posets have, up to isomorphism, unique objects---minimal
injective resolutions---and give a concrete algorithm to compute them. We further
describe simple algorithms to compute derived pushforwards and pullbacks for monotonic
maps, and their proper variants for inclusions, and demonstrate their tractability
by providing an implementation. Finally, we suggest a discrete definition of microsupport
and show desirable properties inspired by discrete Morse theory.\r\n\r\nIn the
last part, we present a collection of observations about collapses. We give a
characterization of collapsibility in terms of unitriangular submatrices of the
boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant
of the Procrustes problem. We establish relation between dual collapses and relative
Morse theory and pose several open questions. Finally, focusing on complexes embedded
in the three-dimensional Euclidean space, we describe a relation between the collapsibility
and the triviality of a polygonal knot."
acknowledgement: "The research presented in this thesis was funded with the Wittgenstein
Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative
Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian
Science Fund (FWF),\r\ngrant no. I 02979-N35.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
citation:
ama: Draganov O. Structures and computations in topological data analysis. 2025.
doi:10.15479/at:ista:18979
apa: Draganov, O. (2025). Structures and computations in topological data analysis.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18979
chicago: Draganov, Ondrej. “Structures and Computations in Topological Data Analysis.”
Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/at:ista:18979.
ieee: O. Draganov, “Structures and computations in topological data analysis,” Institute
of Science and Technology Austria, 2025.
ista: Draganov O. 2025. Structures and computations in topological data analysis.
Institute of Science and Technology Austria.
mla: Draganov, Ondrej. Structures and Computations in Topological Data Analysis.
Institute of Science and Technology Austria, 2025, doi:10.15479/at:ista:18979.
short: O. Draganov, Structures and Computations in Topological Data Analysis, Institute
of Science and Technology Austria, 2025.
corr_author: '1'
date_created: 2025-01-31T17:04:40Z
date_published: 2025-02-03T00:00:00Z
date_updated: 2026-04-07T11:47:30Z
day: '03'
ddc:
- '514'
- '004'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:18979
file:
- access_level: closed
checksum: af6567e5d35e5eb330b8925ae37f1998
content_type: application/zip
creator: odragano
date_created: 2025-01-31T16:58:30Z
date_updated: 2025-01-31T16:58:30Z
file_id: '18983'
file_name: Thesis.zip
file_size: 11899491
relation: source_file
- access_level: open_access
checksum: c3fef68e35b9dc2020b2ca6006da6343
content_type: application/pdf
creator: odragano
date_created: 2025-02-04T16:22:07Z
date_updated: 2025-02-04T16:22:07Z
file_id: '19000'
file_name: Thesis.pdf
file_size: 8857514
relation: main_file
file_date_updated: 2025-02-04T16:22:07Z
has_accepted_license: '1'
keyword:
- topological data analysis
- chromatic point set
- alpha complex
- persistent homology
- six pack
- sheaf
- microlocal discrete Morse
- injective resolution
- collapse
- knot
- discrete Morse theory
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '140'
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '15091'
relation: part_of_dissertation
status: public
- id: '18981'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Structures and computations in topological data analysis
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '21253'
abstract:
- lang: eng
text: We solve a problem of Dujmović and Wood (2007) by showing that a complete
convex geometric graph on n vertices cannot be decomposed into fewer than n -
1 star-forests, each consisting of noncrossing edges. This bound is clearly tight.
We also discuss similar questions for abstract graphs.
acknowledgement: A preliminary version of this note has been published in the proceedings
of the 31st International Symposium on Graph Drawing and Network Visualization,
Palermo, 2023. The authors would like to thank the anonymous referees for their
valuable comments.
article_number: '102186'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: János
full_name: Pach, János
last_name: Pach
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
- first_name: Patrick
full_name: Schnider, Patrick
last_name: Schnider
citation:
ama: Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests.
Computational Geometry. 2025;129. doi:10.1016/j.comgeo.2025.102186
apa: Pach, J., Saghafian, M., & Schnider, P. (2025). Decomposition of geometric
graphs into star-forests. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2025.102186
chicago: Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of
Geometric Graphs into Star-Forests.” Computational Geometry. Elsevier,
2025. https://doi.org/10.1016/j.comgeo.2025.102186.
ieee: J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs
into star-forests,” Computational Geometry, vol. 129. Elsevier, 2025.
ista: Pach J, Saghafian M, Schnider P. 2025. Decomposition of geometric graphs into
star-forests. Computational Geometry. 129, 102186.
mla: Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.”
Computational Geometry, vol. 129, 102186, Elsevier, 2025, doi:10.1016/j.comgeo.2025.102186.
short: J. Pach, M. Saghafian, P. Schnider, Computational Geometry 129 (2025).
corr_author: '1'
date_created: 2026-02-16T15:48:42Z
date_published: 2025-12-01T00:00:00Z
date_updated: 2026-04-16T09:12:36Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2025.102186
external_id:
arxiv:
- '2306.13201'
intvolume: ' 129'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.13201
month: '12'
oa: 1
oa_version: Preprint
publication: Computational Geometry
publication_identifier:
issn:
- 0925-7721
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '15012'
relation: earlier_version
status: public
status: public
title: Decomposition of geometric graphs into star-forests
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 129
year: '2025'
...
---
OA_place: repository
_id: '21050'
abstract:
- lang: eng
text: "In 1873, James C. Maxwell conjectured that the electric field generated by
$n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The
first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov
and Shapiro, who also posed two additional interesting conjectures.\r\n In this
article, we give the best upper bound known to date on the number of zeroes of
the electric field, and construct a counterexample to a conjecture of Gabrielov,
Novikov and Shapiro that the number of equilibria cannot exceed those of the distance
function defined by the unit point charges.\r\n Finally, we note that it is quite
possible that Maxwell's quadratic upper bound is not tight, so it is prudent to
find smaller bounds. Hence, we also explore examples and construct configurations
of charges achieving the highest ratios of the number of electric field zeroes
by point charges found to this day."
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Gonçalo
full_name: Olivera, Gonçalo
last_name: Olivera
citation:
ama: Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic
potential. arXiv. doi:10.48550/ARXIV.2501.05315
apa: Edelsbrunner, H., Fillmore, C. D., & Olivera, G. (n.d.). Counting equilibria
of the electrostatic potential. arXiv. https://doi.org/10.48550/ARXIV.2501.05315
chicago: Edelsbrunner, Herbert, Christopher D Fillmore, and Gonçalo Olivera. “Counting
Equilibria of the Electrostatic Potential.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2501.05315.
ieee: H. Edelsbrunner, C. D. Fillmore, and G. Olivera, “Counting equilibria of the
electrostatic potential,” arXiv. .
ista: Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic
potential. arXiv, 10.48550/ARXIV.2501.05315.
mla: Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.”
ArXiv, doi:10.48550/ARXIV.2501.05315.
short: H. Edelsbrunner, C.D. Fillmore, G. Olivera, ArXiv (n.d.).
corr_author: '1'
date_created: 2026-01-27T14:29:27Z
date_published: 2025-03-20T00:00:00Z
date_updated: 2026-06-02T09:24:17Z
day: '20'
department:
- _id: HeEd
doi: 10.48550/ARXIV.2501.05315
external_id:
arxiv:
- '2501.05315'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2501.05315
month: '03'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '21021'
relation: dissertation_contains
status: public
- id: '21931'
relation: later_version
status: public
status: public
title: Counting equilibria of the electrostatic potential
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: repository
_id: '21016'
abstract:
- lang: eng
text: Motivated by applications in chemistry, we give a homlogical definition of
tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex.
For a filtered complex, this defines a persistence module. We give a method for
identifying birth and death times using kernel persistence and a matrix reduction
algorithm for pairing birth and death times.
acknowledgement: "Y. B. B. and L. F. were funded by the Independent Research Fund
Denmark, grant\r\nnumber 1026-00037. T. H. was partially supported by the European
Research Council\r\n(ERC) Horizon 2020, grant number 788183."
article_number: '2505.17858'
article_processing_charge: No
arxiv: 1
author:
- first_name: Yossi
full_name: Bleile, Yossi
id: 920a7385-7995-11ef-9bfd-8c434cd8f3c2
last_name: Bleile
orcid: 0000-0002-4861-9174
- first_name: Lisbeth
full_name: Fajstrup, Lisbeth
last_name: Fajstrup
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Anne Marie
full_name: Svane, Anne Marie
last_name: Svane
- first_name: Søren Strandskov
full_name: Sørensen, Søren Strandskov
last_name: Sørensen
citation:
ama: Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms
using kernel persistence. arXiv. doi:10.48550/arXiv.2505.17858
apa: Bokor Bleile, Y., Fajstrup, L., Heiss, T., Svane, A. M., & Sørensen, S.
S. (n.d.). Identifying cobordisms using kernel persistence. arXiv. https://doi.org/10.48550/arXiv.2505.17858
chicago: Bokor Bleile, Yossi, Lisbeth Fajstrup, Teresa Heiss, Anne Marie Svane,
and Søren Strandskov Sørensen. “Identifying Cobordisms Using Kernel Persistence.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2505.17858.
ieee: Y. Bokor Bleile, L. Fajstrup, T. Heiss, A. M. Svane, and S. S. Sørensen, “Identifying
cobordisms using kernel persistence,” arXiv. .
ista: Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms
using kernel persistence. arXiv, 2505.17858.
mla: Bokor Bleile, Yossi, et al. “Identifying Cobordisms Using Kernel Persistence.”
ArXiv, 2505.17858, doi:10.48550/arXiv.2505.17858.
short: Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv
(n.d.).
date_created: 2026-01-20T10:12:21Z
date_published: 2025-05-23T00:00:00Z
date_updated: 2026-06-11T11:51:13Z
day: '23'
department:
- _id: HeEd
doi: 10.48550/arXiv.2505.17858
ec_funded: 1
external_id:
arxiv:
- '2505.17858'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2505.17858
month: '05'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: arXiv
publication_status: submitted
status: public
title: Identifying cobordisms using kernel persistence
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
_id: '14345'
abstract:
- lang: eng
text: For a locally finite set in R2, the order-k Brillouin tessellations form an
infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely
dense and generic, then the corresponding infinite sequences of minimum and maximum
angles are both monotonic in k. As an example, a stationary Poisson point process
in R2 is locally finite, coarsely dense, and generic with probability one. For
such a set, the distributions of angles in the Voronoi tessellations, Delaunay
mosaics, and Brillouin tessellations are independent of the order and can be derived
from the formula for angles in order-1 Delaunay mosaics given by Miles (Math.
Biosci. 6, 85–127 (1970)).
acknowledgement: Work by all authors but A. Garber is supported by the European Research
Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund
(FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109,
Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially
supported by the Alexander von Humboldt Foundation.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Garber, Alexey
last_name: Garber
- first_name: Mohadese
full_name: Ghafari, Mohadese
last_name: Ghafari
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher
order Brillouin tessellations and related tilings in the plane. Discrete and
Computational Geometry. 2024;72:29-48. doi:10.1007/s00454-023-00566-1
apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2024).
On angles in higher order Brillouin tessellations and related tilings in the plane.
Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1
chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and
Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related
Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature,
2024. https://doi.org/10.1007/s00454-023-00566-1.
ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles
in higher order Brillouin tessellations and related tilings in the plane,” Discrete
and Computational Geometry, vol. 72. Springer Nature, pp. 29–48, 2024.
ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles
in higher order Brillouin tessellations and related tilings in the plane. Discrete
and Computational Geometry. 72, 29–48.
mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations
and Related Tilings in the Plane.” Discrete and Computational Geometry,
vol. 72, Springer Nature, 2024, pp. 29–48, doi:10.1007/s00454-023-00566-1.
short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete
and Computational Geometry 72 (2024) 29–48.
corr_author: '1'
date_created: 2023-09-17T22:01:10Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-04-23T08:41:59Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00566-1
ec_funded: 1
external_id:
arxiv:
- '2204.01076'
isi:
- '001060727600004'
pmid:
- '39610762'
file:
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checksum: b207b4e00f904e8ea8a30e24f0251f79
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T09:43:19Z
date_updated: 2024-07-22T09:43:19Z
file_id: '17301'
file_name: 2024_DiscreteComputGeom_Edelsbrunner.pdf
file_size: 892019
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success: 1
file_date_updated: 2024-07-22T09:43:19Z
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intvolume: ' 72'
isi: 1
language:
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month: '07'
oa: 1
oa_version: Published Version
page: 29-48
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On angles in higher order Brillouin tessellations and related tilings in the
plane
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 72
year: '2024'
...
---
_id: '17891'
abstract:
- lang: eng
text: "Abstract\r\nMethods used in topological data analysis naturally capture higher-order
interactions in point cloud data embedded in a metric space. This methodology
was recently extended to data living in an information space, by which we mean
a space measured with an information theoretical distance. One such setting is
a finite collection of discrete probability distributions embedded in the probability
simplex measured with the relative entropy (Kullback–Leibler divergence). More
generally, one can work with a Bregman divergence parameterized by a different
notion of entropy. While theoretical algorithms exist for this setup, there is
a paucity of implementations for exploring and comparing geometric-topological
properties of various information spaces. The interest of this work is therefore
twofold. First, we propose the first robust algorithms and software for geometric
and topological data analysis in information space. Perhaps surprisingly, despite
working with Bregman divergences, our design reuses robust libraries for the Euclidean
case. Second, using the new software, we take the first steps towards understanding
the geometric-topological structure of these spaces. In particular, we compare
them with the more familiar spaces equipped with the Euclidean and Fisher metrics."
acknowledgement: We thank Anton Nikitenko for first observing that the Wrap complex
can be characterized as stated in Claim (ii) of the Wrap Complex Lemma, and Ondrej
Draganov for correcting a critical mistake in one of our formulas in Section 2.
article_number: '637'
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Edelsbrunner H, Ölsböck K, Wagner H. Understanding higher-order interactions
in information space. Entropy. 2024;26(8). doi:10.3390/e26080637
apa: Edelsbrunner, H., Ölsböck, K., & Wagner, H. (2024). Understanding higher-order
interactions in information space. Entropy. MDPI. https://doi.org/10.3390/e26080637
chicago: Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. “Understanding
Higher-Order Interactions in Information Space.” Entropy. MDPI, 2024. https://doi.org/10.3390/e26080637.
ieee: H. Edelsbrunner, K. Ölsböck, and H. Wagner, “Understanding higher-order interactions
in information space,” Entropy, vol. 26, no. 8. MDPI, 2024.
ista: Edelsbrunner H, Ölsböck K, Wagner H. 2024. Understanding higher-order interactions
in information space. Entropy. 26(8), 637.
mla: Edelsbrunner, Herbert, et al. “Understanding Higher-Order Interactions in Information
Space.” Entropy, vol. 26, no. 8, 637, MDPI, 2024, doi:10.3390/e26080637.
short: H. Edelsbrunner, K. Ölsböck, H. Wagner, Entropy 26 (2024).
date_created: 2024-09-08T22:01:11Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T09:13:44Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.3390/e26080637
external_id:
isi:
- '001305543500001'
pmid:
- '39202107'
file:
- access_level: open_access
checksum: 624a9e2c5b49d6c38b88b0f675467ba3
content_type: application/pdf
creator: dernst
date_created: 2024-09-09T09:01:12Z
date_updated: 2024-09-09T09:01:12Z
file_id: '17948'
file_name: 2024_Entropy_Edelsbrunner.pdf
file_size: 8025139
relation: main_file
success: 1
file_date_updated: 2024-09-09T09:01:12Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
pmid: 1
publication: Entropy
publication_identifier:
eissn:
- 1099-4300
publication_status: published
publisher: MDPI
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/
scopus_import: '1'
status: public
title: Understanding higher-order interactions in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 26
year: '2024'
...
---
_id: '18097'
abstract:
- lang: eng
text: "In our companion paper \"Tight bounds for the learning of homotopy à la Niyogi,
Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds\"
we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on
a sample P of an input shape \U0001D4AE (either manifold or general set with positive
reach) such that one can infer the homotopy of \U0001D4AE from the union of balls
with some radius centred at P, both in Euclidean space and in a Riemannian manifold
of bounded curvature. The construction showing the optimality of the bounds is
not straightforward. The purpose of this video is to visualize and thus elucidate
said construction in the Euclidean setting."
acknowledgement: "This research has been supported by the European Research Council
(ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF),
grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant No. I02979-N35. Mathijs Wintraecken: Supported by the
European Union’s Horizon 2020 research and innovation programme under the Marie
Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant
No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.\r\nWe
thank Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Mariette Yvinec for discussion."
alternative_title:
- LIPIcs
article_number: '87'
article_processing_charge: Yes
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Ishika
full_name: Ghosh, Ishika
id: ee449b28-344d-11ef-a6d5-9ca430e9e9ff
last_name: Ghosh
- first_name: Andre
full_name: Lieutier, Andre
last_name: Lieutier
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Attali D, Kourimska H, Fillmore CD, et al. The ultimate frontier: An optimality
construction for homotopy inference (media exposition). In: 40th International
Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.87'
apa: 'Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson,
E. R., & Wintraecken, M. (2024). The ultimate frontier: An optimality construction
for homotopy inference (media exposition). In 40th International Symposium
on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.87'
chicago: 'Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh,
Andre Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “The Ultimate
Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).”
In 40th International Symposium on Computational Geometry, Vol. 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.87.'
ieee: 'D. Attali et al., “The ultimate frontier: An optimality construction
for homotopy inference (media exposition),” in 40th International Symposium
on Computational Geometry, Athens, Greece, 2024, vol. 293.'
ista: 'Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken
M. 2024. The ultimate frontier: An optimality construction for homotopy inference
(media exposition). 40th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 293, 87.'
mla: 'Attali, Dominique, et al. “The Ultimate Frontier: An Optimality Construction
for Homotopy Inference (Media Exposition).” 40th International Symposium on
Computational Geometry, vol. 293, 87, Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.87.'
short: 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.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
corr_author: '1'
date_created: 2024-09-19T10:29:48Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2025-04-15T07:16:58Z
day: '06'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.87
ec_funded: 1
file:
- access_level: open_access
checksum: 9355c2e60b8ec285e1b22719c5b73f1a
content_type: application/pdf
creator: dernst
date_created: 2024-09-19T10:30:37Z
date_updated: 2024-09-19T10:30:37Z
file_id: '18098'
file_name: 2024_LIPICs_Attali.pdf
file_size: 3507177
relation: main_file
success: 1
file_date_updated: 2024-09-19T10:30:37Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: 'The ultimate frontier: An optimality construction for homotopy inference (media
exposition)'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...
---
OA_place: publisher
OA_type: gold
_id: '18556'
abstract:
- lang: eng
text: Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined
length of the minimum spanning trees of B and A⧵B divided by the length of the
minimum spanning tree of A. The question of the supremum, over all sets A, of
the maximum, over all subsets B, is related to the Steiner ratio, and we prove
this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional
lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin
the most difficult of these results is the upper bound for the inf-max, which
we prove by showing that the hexagonal lattice cannot have MST-ratio larger than
1.25.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, "Discretization
in Geometry and Dynamics", Austrian Science Fund (FWF), grant no. I 02979-N35.
alternative_title:
- LIPIcs
article_number: '3'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean
MST-ratio for bi-colored lattices. In: 32nd International Symposium on Graph
Drawing and Network Visualization. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.GD.2024.3'
apa: 'Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (2024). The Euclidean MST-ratio for bi-colored lattices. In 32nd International
Symposium on Graph Drawing and Network Visualization (Vol. 320). Vienna, Austria:
Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.GD.2024.3'
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In 32nd
International Symposium on Graph Drawing and Network Visualization, Vol. 320.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.GD.2024.3.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“The Euclidean MST-ratio for bi-colored lattices,” in 32nd International Symposium
on Graph Drawing and Network Visualization, Vienna, Austria, 2024, vol. 320.
ista: 'Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The
Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph
Drawing and Network Visualization. GD: Graph Drawing and Network Visualization,
LIPIcs, vol. 320, 3.'
mla: Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored
Lattices.” 32nd International Symposium on Graph Drawing and Network Visualization,
vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.GD.2024.3.
short: 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.
conference:
end_date: 2024-09-20
location: Vienna, Austria
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2024-09-18
corr_author: '1'
date_created: 2024-11-17T23:01:47Z
date_published: 2024-10-28T00:00:00Z
date_updated: 2025-12-02T13:50:50Z
day: '28'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.GD.2024.3
ec_funded: 1
external_id:
arxiv:
- '2403.10204'
isi:
- '001540278400001'
file:
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checksum: 5f9b35e115c3d375e99be78da9054cb4
content_type: application/pdf
creator: dernst
date_created: 2024-11-18T07:49:25Z
date_updated: 2024-11-18T07:49:25Z
file_id: '18560'
file_name: 2024_LIPIcs_CultreradiMontesano.pdf
file_size: 908541
relation: main_file
success: 1
file_date_updated: 2024-11-18T07:49:25Z
has_accepted_license: '1'
intvolume: ' 320'
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language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: 32nd International Symposium on Graph Drawing and Network Visualization
publication_identifier:
isbn:
- '9783959773430'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Euclidean MST-ratio for bi-colored lattices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 320
year: '2024'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18604'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a randomized
FPT-time algorithm where the parameter is the number of popular faces.'
acknowledgement: "This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. has been supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]
and by the NWO Gravitation project NETWORKS under grant no. 024.002.003. Part of
the work was done while A.W. was emplyed at Graz University of Technology. Preliminary
versions of this work have been presented at the 38th European Workshop on Computational
Geometry (EuroCG\r\n2022) in Perugia [10] and at the 31st International Symposium
on Graph Drawing and Network Visualization (GD 2023) in Isola delle Femmine [11]."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. Journal of Graph Algorithms and Applications. 2024;28(2):47-82.
doi:10.7155/jgaa.v28i2.2988
apa: De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.v28i2.2988
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in
Curve Arrangements.” Journal of Graph Algorithms and Applications. Brown
University, 2024. https://doi.org/10.7155/jgaa.v28i2.2988.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
Journal of Graph Algorithms and Applications, vol. 28, no. 2. Brown University,
pp. 47–82, 2024.
ista: De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. Journal of Graph
Algorithms and Applications. 28(2), 47–82.
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
Journal of Graph Algorithms and Applications, vol. 28, no. 2, Brown University,
2024, pp. 47–82, doi:10.7155/jgaa.v28i2.2988.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, Journal of Graph Algorithms and Applications 28 (2024) 47–82.
corr_author: '1'
date_created: 2024-12-01T23:01:54Z
date_published: 2024-11-03T00:00:00Z
date_updated: 2024-12-03T09:49:18Z
day: '03'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.7155/jgaa.v28i2.2988
external_id:
arxiv:
- '2202.12175'
file:
- access_level: open_access
checksum: be611da6f9d790dc980d6fb7283fe889
content_type: application/pdf
creator: dernst
date_created: 2024-12-03T09:45:00Z
date_updated: 2024-12-03T09:45:00Z
file_id: '18609'
file_name: 2024_JourGraphAlgorithms_deNooijer.pdf
file_size: 1582493
relation: main_file
success: 1
file_date_updated: 2024-12-03T09:45:00Z
has_accepted_license: '1'
intvolume: ' 28'
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 47-82
publication: Journal of Graph Algorithms and Applications
publication_identifier:
issn:
- 1526-1719
publication_status: published
publisher: Brown University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2024'
...
---
OA_place: publisher
OA_type: gold
_id: '18998'
abstract:
- lang: eng
text: Word embeddings represent language vocabularies as clouds of d-dimensional
points. We investigate how information is conveyed by the general shape of these
clouds, instead of representing the semantic meaning of each token. Specifically,
we use the notion of persistent homology from topological data analysis (TDA)
to measure the distances between language pairs from the shape of their unlabeled
embeddings. These distances quantify the degree of non-isometry of the embeddings.
To distinguish whether these differences are random training errors or capture
real information about the languages, we use the computed distance matrices to
construct language phylogenetic trees over 81 Indo-European languages. Careful
evaluation shows that our reconstructed trees exhibit strong and statistically-significant
similarities to the reference.
article_processing_charge: No
arxiv: 1
author:
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Steven
full_name: Skiena, Steven
last_name: Skiena
citation:
ama: 'Draganov O, Skiena S. The shape of word embeddings: Quantifying non-isometry
with topological data analysis. In: Findings of the Association for Computational
Linguistics: EMNLP 2024. Association for Computational Linguistics; 2024:12080-12099.
doi:10.18653/v1/2024.findings-emnlp.705'
apa: 'Draganov, O., & Skiena, S. (2024). The shape of word embeddings: Quantifying
non-isometry with topological data analysis. In Findings of the Association
for Computational Linguistics: EMNLP 2024 (pp. 12080–12099). Miami, FL, United
States: Association for Computational Linguistics. https://doi.org/10.18653/v1/2024.findings-emnlp.705'
chicago: 'Draganov, Ondrej, and Steven Skiena. “The Shape of Word Embeddings: Quantifying
Non-Isometry with Topological Data Analysis.” In Findings of the Association
for Computational Linguistics: EMNLP 2024, 12080–99. Association for Computational
Linguistics, 2024. https://doi.org/10.18653/v1/2024.findings-emnlp.705.'
ieee: 'O. Draganov and S. Skiena, “The shape of word embeddings: Quantifying non-isometry
with topological data analysis,” in Findings of the Association for Computational
Linguistics: EMNLP 2024, Miami, FL, United States, 2024, pp. 12080–12099.'
ista: 'Draganov O, Skiena S. 2024. The shape of word embeddings: Quantifying non-isometry
with topological data analysis. Findings of the Association for Computational
Linguistics: EMNLP 2024. EMNLP: Conference on Empirical Methods in Natural Language
Processing, 12080–12099.'
mla: 'Draganov, Ondrej, and Steven Skiena. “The Shape of Word Embeddings: Quantifying
Non-Isometry with Topological Data Analysis.” Findings of the Association for
Computational Linguistics: EMNLP 2024, Association for Computational Linguistics,
2024, pp. 12080–99, doi:10.18653/v1/2024.findings-emnlp.705.'
short: 'O. Draganov, S. Skiena, in:, Findings of the Association for Computational
Linguistics: EMNLP 2024, Association for Computational Linguistics, 2024, pp.
12080–12099.'
conference:
end_date: 2024-11-16
location: Miami, FL, United States
name: 'EMNLP: Conference on Empirical Methods in Natural Language Processing'
start_date: 2024-11-12
corr_author: '1'
date_created: 2025-02-04T16:19:28Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-02-10T08:21:37Z
day: '01'
ddc:
- '500'
department:
- _id: GradSch
- _id: HeEd
doi: 10.18653/v1/2024.findings-emnlp.705
external_id:
arxiv:
- '2404.00500'
file:
- access_level: open_access
checksum: f4416a5962194f0181ab0dc7f9ef93c0
content_type: application/pdf
creator: dernst
date_created: 2025-02-10T08:20:34Z
date_updated: 2025-02-10T08:20:34Z
file_id: '19016'
file_name: 2024_EMNLP_Draganov.pdf
file_size: 1312638
relation: main_file
success: 1
file_date_updated: 2025-02-10T08:20:34Z
has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 12080-12099
publication: 'Findings of the Association for Computational Linguistics: EMNLP 2024'
publication_status: published
publisher: Association for Computational Linguistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The shape of word embeddings: Quantifying non-isometry with topological data
analysis'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '18999'
abstract:
- lang: eng
text: Exploring the shape of point configurations has been a key driver in the evolution
of TDA (short for topological data analysis) since its infancy. This survey illustrates
the recent efforts to broaden these ideas to model spatial interactions among
multiple configurations, each distinguished by a color. It describes advances
in this area and prepares the ground for further exploration by mentioning unresolved
questions and promising research avenues while focusing on the overlap with discrete
geometry.
article_number: '2406.04102'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
topological data analysis. arXiv. doi:10.48550/ARXIV.2406.04102
apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (n.d.). Chromatic topological data analysis. arXiv. https://doi.org/10.48550/ARXIV.2406.04102
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “Chromatic Topological Data Analysis.” ArXiv, n.d.
https://doi.org/10.48550/ARXIV.2406.04102.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“Chromatic topological data analysis,” arXiv. .
ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
topological data analysis. arXiv, 2406.04102.
mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Topological Data Analysis.”
ArXiv, 2406.04102, doi:10.48550/ARXIV.2406.04102.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv
(n.d.).
corr_author: '1'
date_created: 2025-02-04T16:21:21Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2025-02-10T08:14:27Z
day: '06'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
doi: 10.48550/ARXIV.2406.04102
external_id:
arxiv:
- '2406.04102'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2406.04102
month: '06'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Chromatic topological data analysis
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14888'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a probabilistic
FPT-approach in the number of popular faces.'
acknowledgement: 'This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].
A preliminary version of this work has been presented at the 38th European Workshop
on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper,
which includes appendices but is otherwise identical, is available as a technical
report [10].'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. In: 31st International Symposium on Graph Drawing and Network
Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2'
apa: 'De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
In 31st International Symposium on Graph Drawing and Network Visualization
(Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature.
https://doi.org/10.1007/978-3-031-49275-4_2'
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve
Arrangements.” In 31st International Symposium on Graph Drawing and Network
Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
in 31st International Symposium on Graph Drawing and Network Visualization,
Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.
ista: 'De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International
Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network
Visualization, LNCS, vol. 14466, 18–33.'
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
31st International Symposium on Graph Drawing and Network Visualization,
vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network
Visualization, Springer Nature, 2024, pp. 18–33.
conference:
end_date: 2023-09-22
location: Isola delle Femmine, Palermo, Italy
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2023-09-20
date_created: 2024-01-28T23:01:43Z
date_published: 2024-01-06T00:00:00Z
date_updated: 2025-09-04T11:52:35Z
day: '06'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-031-49275-4_2
external_id:
arxiv:
- '2202.12175'
isi:
- '001207942000002'
intvolume: ' 14466'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2202.12175
month: '01'
oa: 1
oa_version: Preprint
page: 18-33
publication: 31st International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031492747'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14466
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15247'
abstract:
- lang: eng
text: Extending the notion of sunflowers, we call a family of at least two sets
an odd-sunflower if every element of the underlying set is contained in an odd
number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture,
recently proved by Naslund and Sawin, that there is a constant <2 such that every
family of subsets of an n-element set that contains no odd-sunflower consists
of at most n sets. We construct such families of size at least 1.5021n. We also
characterize minimal odd-sunflowers of triples.
acknowledgement: We are grateful to Balázs Keszegh, and to the members of the Miklós
Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib
for pointing out several important mathematical typos.
article_number: '105889'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Frankl, Peter
last_name: Frankl
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Dömötör
full_name: Pálvölgyi, Dömötör
last_name: Pálvölgyi
citation:
ama: Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. Journal of Combinatorial
Theory, Series A. 2024;206(8). doi:10.1016/j.jcta.2024.105889
apa: Frankl, P., Pach, J., & Pálvölgyi, D. (2024). Odd-sunflowers. Journal
of Combinatorial Theory, Series A. Elsevier. https://doi.org/10.1016/j.jcta.2024.105889
chicago: Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” Journal
of Combinatorial Theory, Series A. Elsevier, 2024. https://doi.org/10.1016/j.jcta.2024.105889.
ieee: P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” Journal of Combinatorial
Theory, Series A, vol. 206, no. 8. Elsevier, 2024.
ista: Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial
Theory, Series A. 206(8), 105889.
mla: Frankl, Peter, et al. “Odd-Sunflowers.” Journal of Combinatorial Theory,
Series A, vol. 206, no. 8, 105889, Elsevier, 2024, doi:10.1016/j.jcta.2024.105889.
short: P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series
A 206 (2024).
corr_author: '1'
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