---
OA_type: closed access
_id: '19937'
abstract:
- lang: eng
text: Simplets are elementary units within simplicial complexes and are fundamental
for analyzing the structure of simplicial complexes. Previous efforts have mainly
focused on accurately counting or approximating the number of simplets rather
than studying their frequencies. However, analyzing simplet frequencies is more
practical for large-scale simplicial complexes. This paper introduces the Simplet
Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies
in simplicial complexes. Additionally, we provide a bound on the sample complexity
required to approximate the SFD vector using any uniform sampling-based algorithm
accurately. We extend the definition of simplet frequency distribution to encompass
simplices, allowing for the analysis of simplet frequencies within simplices of
simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and
the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex.
Furthermore, we present a bound on the sample complexity required for accurately
approximating the SDV and SDC for a set of simplices using any uniform sampling-based
algorithm. We also introduce algorithms for approximating SFD, geometric SFD,
SDV, and SDC. We also validate the theoretical bounds with experiments on random
simplicial complexes and demonstrate the practical application through a case
study.
acknowledgement: "The authors would like to thank the anonymous reviewers for their
valuable comments and suggestions, which improved this paper.\r\nWork by the first
and fourth authors is partially 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."
article_number: '122425'
article_processing_charge: No
article_type: original
author:
- first_name: Mohammad
full_name: Mahini, Mohammad
last_name: Mahini
- first_name: Hamid
full_name: Beigy, Hamid
last_name: Beigy
- first_name: Salman
full_name: Qadami, Salman
last_name: Qadami
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Mahini M, Beigy H, Qadami S, Saghafian M. Simplet-based signatures and approximation
in simplicial complexes: Frequency, degree, and centrality. Information Sciences.
2025;719(11). doi:10.1016/j.ins.2025.122425'
apa: 'Mahini, M., Beigy, H., Qadami, S., & Saghafian, M. (2025). Simplet-based
signatures and approximation in simplicial complexes: Frequency, degree, and centrality.
Information Sciences. Elsevier. https://doi.org/10.1016/j.ins.2025.122425'
chicago: 'Mahini, Mohammad, Hamid Beigy, Salman Qadami, and Morteza Saghafian. “Simplet-Based
Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.”
Information Sciences. Elsevier, 2025. https://doi.org/10.1016/j.ins.2025.122425.'
ieee: 'M. Mahini, H. Beigy, S. Qadami, and M. Saghafian, “Simplet-based signatures
and approximation in simplicial complexes: Frequency, degree, and centrality,”
Information Sciences, vol. 719, no. 11. Elsevier, 2025.'
ista: 'Mahini M, Beigy H, Qadami S, Saghafian M. 2025. Simplet-based signatures
and approximation in simplicial complexes: Frequency, degree, and centrality.
Information Sciences. 719(11), 122425.'
mla: 'Mahini, Mohammad, et al. “Simplet-Based Signatures and Approximation in Simplicial
Complexes: Frequency, Degree, and Centrality.” Information Sciences, vol.
719, no. 11, 122425, Elsevier, 2025, doi:10.1016/j.ins.2025.122425.'
short: M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).
corr_author: '1'
date_created: 2025-06-30T08:48:48Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2025-12-30T09:05:32Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.ins.2025.122425
ec_funded: 1
external_id:
isi:
- '001516170500002'
fulldoi: https://doi.org/10.1016/j.ins.2025.122425
intvolume: ' 719'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa_version: None
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: Information Sciences
publication_identifier:
issn:
- 0020-0255
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Simplet-based signatures and approximation in simplicial complexes: Frequency,
degree, and centrality'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 719
year: '2025'
...
---
OA_place: publisher
OA_type: gold
_id: '20005'
abstract:
- lang: eng
text: "We generalize a classical result by Boris Delaunay that introduced Delaunay
triangulations. In particular, we prove that for a locally finite and coarsely
dense generic point set A in ℝ^d, every generic point of ℝ^d belongs to exactly
binom(d+k,d) simplices whose vertices belong to A and whose circumspheres enclose
exactly k points of A. We extend this result to the cases in which the points
are weighted, and when A contains only finitely many points in ℝ^d or in \U0001D54A^d.
Furthermore, we use the result to give a new geometric proof for the fact that
volumes of hypersimplices are Eulerian numbers."
acknowledgement: "Herbert Edelsbrunner: partially supported by the Wittgenstein Prize,
Austrian Science\r\nFund (FWF), grant no. Z 342-N31, and by the DFG Collaborative
Research Center TRR 109,\r\nAustrian Science Fund (FWF), grant no. I 02979-N35.\r\nAlexey
Garber: partially supported by the Simons Foundation.\r\nMorteza Saghafian: partially
supported by the Wittgenstein Prize, Austrian Science Fund (FWF),\r\ngrant no. Z
342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund
(FWF), grant no. I 02979-N35"
alternative_title:
- LIPIcs
article_number: '43'
article_processing_charge: Yes
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: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Edelsbrunner H, Garber A, Saghafian M. On spheres with k points inside. In:
41st International Symposium on Computational Geometry. Vol 332. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.SoCG.2025.43'
apa: 'Edelsbrunner, H., Garber, A., & Saghafian, M. (2025). On spheres with
k points inside. In 41st International Symposium on Computational Geometry
(Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2025.43'
chicago: Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “On Spheres
with k Points Inside.” In 41st International Symposium on Computational Geometry,
Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SoCG.2025.43.
ieee: H. Edelsbrunner, A. Garber, and M. Saghafian, “On spheres with k points inside,”
in 41st International Symposium on Computational Geometry, Kanazawa, Japan,
2025, vol. 332.
ista: 'Edelsbrunner H, Garber A, Saghafian M. 2025. On spheres with k points inside.
41st International Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, LIPIcs, vol. 332, 43.'
mla: Edelsbrunner, Herbert, et al. “On Spheres with k Points Inside.” 41st International
Symposium on Computational Geometry, vol. 332, 43, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2025, doi:10.4230/LIPIcs.SoCG.2025.43.
short: H. Edelsbrunner, A. Garber, M. Saghafian, in:, 41st International Symposium
on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2025.
conference:
end_date: 2025-06-27
location: Kanazawa, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2025-06-23
corr_author: '1'
date_created: 2025-07-13T22:01:22Z
date_published: 2025-06-20T00:00:00Z
date_updated: 2025-07-14T07:26:14Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2025.43
external_id:
arxiv:
- '2410.21204'
file:
- access_level: open_access
checksum: b5313ed8575ea87913c71a6e3c7513c8
content_type: application/pdf
creator: dernst
date_created: 2025-07-14T07:24:22Z
date_updated: 2025-07-14T07:24:22Z
file_id: '20016'
file_name: 2025_LIPIcs.SoCG_Edelsbrunner.pdf
file_size: 661893
relation: main_file
success: 1
file_date_updated: 2025-07-14T07:24:22Z
fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2025.43
has_accepted_license: '1'
intvolume: ' 332'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
project:
- _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: 41st International Symposium on Computational Geometry
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959773706'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: On spheres with k points inside
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: 332
year: '2025'
...
---
OA_place: publisher
OA_type: gold
_id: '20006'
abstract:
- lang: eng
text: In numerous fields, dynamic time series data require continuous updates, necessitating
efficient data processing techniques for accurate analysis. This paper examines
the banana tree data structure, specifically designed to efficiently maintain
the multi-scale topological descriptor commonly known as persistent homology for
dynamically changing time series data. We implement this data structure and conduct
an experimental study to assess its properties and runtime for update operations.
Our findings indicate that banana trees are highly effective with unbiased random
data, outperforming state-of-the-art static algorithms in these scenarios. Additionally,
our results show that real-world time series share structural properties with
unbiased random walks, suggesting potential practical utility for our implementation.
acknowledgement: "Lara Ost: Supported by the Vienna Graduate School on Computational
Optimization\r\n(VGSCO), FWF project no. W1260-N35.\r\nSebastiano Cultrera di Montesano:
Supported by the Eric and Wendy Schmidt Center at the Broad Institute of MIT and
Harvard.\r\nHerbert Edelsbrunner: Partially supported by the Wittgenstein Prize,
FWF grant no. Z 342-N31,\r\nand by the DFG Collaborative Research Center TRR 109,
FWF grant no. I 02979-N35."
alternative_title:
- LIPIcs
article_number: '71'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Lara
full_name: Ost, Lara
last_name: Ost
- 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: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Ost L, Cultrera di Montesano S, Edelsbrunner H. Banana trees for the persistence
in time series experimentally. In: 41st International Symposium on Computational
Geometry. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025.
doi:10.4230/LIPIcs.SoCG.2025.71'
apa: 'Ost, L., Cultrera di Montesano, S., & Edelsbrunner, H. (2025). Banana
trees for the persistence in time series experimentally. In 41st International
Symposium on Computational Geometry (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2025.71'
chicago: Ost, Lara, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner.
“Banana Trees for the Persistence in Time Series Experimentally.” In 41st International
Symposium on Computational Geometry, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SoCG.2025.71.
ieee: L. Ost, S. Cultrera di Montesano, and H. Edelsbrunner, “Banana trees for the
persistence in time series experimentally,” in 41st International Symposium
on Computational Geometry, Kanazawa, Japan, 2025, vol. 332.
ista: 'Ost L, Cultrera di Montesano S, Edelsbrunner H. 2025. Banana trees for the
persistence in time series experimentally. 41st International Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 71.'
mla: Ost, Lara, et al. “Banana Trees for the Persistence in Time Series Experimentally.”
41st International Symposium on Computational Geometry, vol. 332, 71, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.SoCG.2025.71.
short: L. Ost, S. Cultrera di Montesano, H. Edelsbrunner, in:, 41st International
Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2025.
conference:
end_date: 2025-06-27
location: Kanazawa, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2025-06-23
corr_author: '1'
date_created: 2025-07-13T22:01:22Z
date_published: 2025-06-20T00:00:00Z
date_updated: 2025-12-30T11:04:33Z
day: '20'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2025.71
external_id:
arxiv:
- '2405.17920'
file:
- access_level: open_access
checksum: 3a4a7a707a56e0cfdf51428782dee55a
content_type: application/pdf
creator: dernst
date_created: 2025-07-14T08:23:38Z
date_updated: 2025-07-14T08:23:38Z
file_id: '20017'
file_name: 2025_LIPIcs.SoCG_Ost.pdf
file_size: 834623
relation: main_file
success: 1
file_date_updated: 2025-07-14T08:23:38Z
fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2025.71
has_accepted_license: '1'
intvolume: ' 332'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 9B9290DE-BA93-11EA-9121-9846C619BF3A
grant_number: W1260-N35
name: Vienna Graduate School on Computational Optimization
- _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: 41st International Symposium on Computational Geometry
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959773706'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/laraost/BananaPersist
scopus_import: '1'
status: public
title: Banana trees for the persistence in time series experimentally
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: 332
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
fulldoi: https://doi.org/10.1007/s44007-025-00170-0
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'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20293'
abstract:
- lang: eng
text: Motivated by questions arising at the intersection of information theory and
geometry, we compare two dissimilarity measures between finite categorical distributions.
One is the well-known Jensen–Shannon divergence, which is easy to compute and
whose square root is a proper metric. The other is what we call the minmax divergence,
which is harder to compute. Just like the Jensen–Shannon divergence, it arises
naturally from the Kullback–Leibler divergence. The main contribution of this
paper is a proof showing that the minmax divergence can be tightly approximated
by the Jensen–Shannon divergence. The bounds suggest that the square root of the
minmax divergence is a metric, and we prove that this is indeed true in the one-dimensional
case. The general case remains open. Finally, we consider analogous questions
in the context of another Bregman divergence and the corresponding Burbea–Rao
(Jensen–Bregman) divergence.
acknowledgement: "This research received partial funding from the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, the\r\nWittgenstein Prize, Austrian Science Fund (FWF),
grant no. Z 342-N31, the DFG Collaborative\r\nResearch Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35, and
the 2022 Google Research Scholar Award for project ‘Algorithms for Topological Analysis
of Neural Networks’. The APC was waived."
article_number: '854'
article_processing_charge: Yes
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Akopyan A, Edelsbrunner H, Virk Z, Wagner H. Tight bounds between the Jensen–Shannon
divergence and the minmax divergence. Entropy. 2025;27(8). doi:10.3390/e27080854
apa: Akopyan, A., Edelsbrunner, H., Virk, Z., & Wagner, H. (2025). Tight bounds
between the Jensen–Shannon divergence and the minmax divergence. Entropy.
MDPI. https://doi.org/10.3390/e27080854
chicago: Akopyan, Arseniy, Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. “Tight
Bounds between the Jensen–Shannon Divergence and the Minmax Divergence.” Entropy.
MDPI, 2025. https://doi.org/10.3390/e27080854.
ieee: A. Akopyan, H. Edelsbrunner, Z. Virk, and H. Wagner, “Tight bounds between
the Jensen–Shannon divergence and the minmax divergence,” Entropy, vol.
27, no. 8. MDPI, 2025.
ista: Akopyan A, Edelsbrunner H, Virk Z, Wagner H. 2025. Tight bounds between the
Jensen–Shannon divergence and the minmax divergence. Entropy. 27(8), 854.
mla: Akopyan, Arseniy, et al. “Tight Bounds between the Jensen–Shannon Divergence
and the Minmax Divergence.” Entropy, vol. 27, no. 8, 854, MDPI, 2025, doi:10.3390/e27080854.
short: A. Akopyan, H. Edelsbrunner, Z. Virk, H. Wagner, Entropy 27 (2025).
corr_author: '1'
date_created: 2025-09-07T22:01:33Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-09-30T14:32:31Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.3390/e27080854
ec_funded: 1
external_id:
isi:
- '001557476000001'
pmid:
- '40870326'
file:
- access_level: open_access
checksum: 65c5399c4015d9c8abb8c7a96f3d7836
content_type: application/pdf
creator: dernst
date_created: 2025-09-08T07:55:48Z
date_updated: 2025-09-08T07:55:48Z
file_id: '20309'
file_name: 2025_Entropy_Akopyan.pdf
file_size: 379340
relation: main_file
success: 1
file_date_updated: 2025-09-08T07:55:48Z
fulldoi: https://doi.org/10.3390/e27080854
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
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: Entropy
publication_identifier:
eissn:
- 1099-4300
publication_status: published
publisher: MDPI
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tight bounds between the Jensen–Shannon divergence and the minmax divergence
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: 27
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'
fulldoi: https://doi.org/10.1007/978-3-032-09544-2_10
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
fulldoi: https://doi.org/10.1145/3747199.3747561
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: repository
OA_type: green
_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.).
das_tickbox: '1'
date_created: 2026-01-20T10:12:21Z
date_published: 2025-05-23T00:00:00Z
date_updated: 2026-07-22T06:33:07Z
day: '23'
department:
- _id: HeEd
doi: 10.48550/arXiv.2505.17858
ec_funded: 1
external_id:
arxiv:
- '2505.17858'
fulldoi: https://doi.org/10.48550/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'
...
---
OA_place: repository
OA_type: green
_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_number: '2501.05315'
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, 2501.05315.
mla: Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.”
ArXiv, 2501.05315, doi:10.48550/ARXIV.2501.05315.
short: H. Edelsbrunner, C.D. Fillmore, G. Olivera, ArXiv (n.d.).
corr_author: '1'
das_tickbox: '1'
date_created: 2026-01-27T14:29:27Z
date_published: 2025-03-20T00:00:00Z
date_updated: 2026-07-22T06:33:55Z
day: '20'
department:
- _id: HeEd
doi: 10.48550/ARXIV.2501.05315
external_id:
arxiv:
- '2501.05315'
fulldoi: https://doi.org/10.48550/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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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'
das_tickbox: '0'
date_created: 2024-06-16T22:01:07Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2026-10-02T11:48:46Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-024-00660-y
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arxiv:
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call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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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'
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status: public
supplementarymaterial: no
title: Average and expected distortion of Voronoi paths and scapes
tmp:
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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
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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: 2026-10-02T11:50:58Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2025.102186
external_id:
arxiv:
- '2306.13201'
fulldoi: https://doi.org/10.1016/j.comgeo.2025.102186
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url: https://doi.org/10.48550/arXiv.2306.13201
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publication: Computational Geometry
publication_identifier:
issn:
- 0925-7721
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
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title: Decomposition of geometric graphs into star-forests
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user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 129
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: 2026-10-02T11:57:00Z
day: '03'
ddc:
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- '004'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:18979
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fulldoi: https://doi.org/10.15479/at:ista:18979
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
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type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20323'
abstract:
- lang: eng
text: We establish several results combining discrete Morse theory and microlocal
sheaf theory in the setting of finite posets and simplicial complexes. Our primary
tool is a computationally tractable description of the bounded derived category
of sheaves on a poset with the Alexandrov topology. We prove that each bounded
complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes)
minimal injective resolution, and we provide algorithms for computing minimal
injective resolution of an injective complex, as well as several useful functors
between derived categories of sheaves. For the constant sheaf on a simplicial
complex, we give asymptotically tight bounds on the complexity of computing the
minimal injective resolution using those algorithms. Our main result is a novel
definition of the discrete microsupport of a bounded complex of sheaves on a finite
poset. We detail several foundational properties of the discrete microsupport,
as well as a microlocal generalization of the discrete homological Morse theorem
and Morse inequalities.
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. Z342-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_number: '108068'
article_processing_charge: Yes (via OA deal)
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arxiv: 1
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
citation:
ama: Brown A, Draganov O. Discrete microlocal Morse theory. Journal of Pure and
Applied Algebra. 2025;229(10). doi:10.1016/j.jpaa.2025.108068
apa: Brown, A., & Draganov, O. (2025). Discrete microlocal Morse theory. Journal
of Pure and Applied Algebra. Elsevier. https://doi.org/10.1016/j.jpaa.2025.108068
chicago: Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” Journal
of Pure and Applied Algebra. Elsevier, 2025. https://doi.org/10.1016/j.jpaa.2025.108068.
ieee: A. Brown and O. Draganov, “Discrete microlocal Morse theory,” Journal of
Pure and Applied Algebra, vol. 229, no. 10. Elsevier, 2025.
ista: Brown A, Draganov O. 2025. Discrete microlocal Morse theory. Journal of Pure
and Applied Algebra. 229(10), 108068.
mla: Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” Journal
of Pure and Applied Algebra, vol. 229, no. 10, 108068, Elsevier, 2025, doi:10.1016/j.jpaa.2025.108068.
short: A. Brown, O. Draganov, Journal of Pure and Applied Algebra 229 (2025).
corr_author: '1'
date_created: 2025-09-10T05:40:09Z
date_published: 2025-10-01T00:00:00Z
date_updated: 2026-10-02T11:57:00Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jpaa.2025.108068
ec_funded: 1
external_id:
arxiv:
- '2209.14993'
file:
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issue: '10'
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: Journal of Pure and Applied Algebra
publication_identifier:
issn:
- 0022-4049
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
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- id: '18981'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Discrete microlocal Morse theory
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: 229
year: '2025'
...
---
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
fulldoi: https://doi.org/10.18653/v1/2024.findings-emnlp.705
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'
fulldoi: https://doi.org/10.48550/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: '17170'
abstract:
- lang: eng
text: "In this article we extend and strengthen the seminal work by Niyogi, Smale,
and Weinberger on the learning of the homotopy type from a sample of an underlying
space. In their work, Niyogi, Smale, and Weinberger studied samples of C² manifolds
with positive reach embedded in ℝ^d. We extend their results in the following
ways: - As the ambient space we consider both ℝ^d and Riemannian manifolds with
lower bounded sectional curvature. - In both types of ambient spaces, we study
sets of positive reach - a significantly more general setting than C² manifolds
- as well as general manifolds of positive reach. - The sample P of a set (or
a manifold) \U0001D4AE of positive reach may be noisy. We work with two one-sided
Hausdorff distances - ε and δ - between P and \U0001D4AE. We provide tight bounds
in terms of ε and δ, that guarantee that there exists a parameter r such that
the union of balls of radius r centred at the sample P deformation-retracts to
\U0001D4AE. We exhibit their tightness by an explicit construction. We carefully
distinguish the roles of δ and ε. This is not only essential to achieve tight
bounds, but also sensible in practical situations, since it allows one to adapt
the bound according to sample density and the amount of noise present in the sample
separately."
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. I 02979-N35.\r\nWintraecken, Mathijs: 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."
alternative_title:
- LIPIcs
article_processing_charge: No
arxiv: 1
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: André
full_name: Lieutier, André
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. Tight bounds for the learning of
homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and
of Riemannian manifolds. In: 40th International Symposium on Computational
Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024:11:1-11:19.
doi:10.4230/LIPIcs.SoCG.2024.11'
apa: 'Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson,
E. R., & Wintraecken, M. (2024). Tight bounds for the learning of homotopy
à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian
manifolds. In 40th International Symposium on Computational Geometry (Vol.
293, p. 11:1-11:19). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2024.11'
chicago: Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh,
André Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “Tight Bounds
for the Learning of Homotopy à La Niyogi, Smale, and Weinberger for Subsets of
Euclidean Spaces and of Riemannian Manifolds.” In 40th International Symposium
on Computational Geometry, 293:11:1-11:19. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.11.
ieee: D. Attali et al., “Tight bounds for the learning of homotopy à la Niyogi,
Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds,”
in 40th International Symposium on Computational Geometry, Athens, Greece,
2024, vol. 293, p. 11:1-11:19.
ista: 'Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken
M. 2024. Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger
for subsets of euclidean spaces and of Riemannian manifolds. 40th International
Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry,
LIPIcs, vol. 293, 11:1-11:19.'
mla: Attali, Dominique, et al. “Tight Bounds for the Learning of Homotopy à La Niyogi,
Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds.”
40th International Symposium on Computational Geometry, vol. 293, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19, doi:10.4230/LIPIcs.SoCG.2024.11.
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, p. 11:1-11:19.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
das_tickbox: '0'
date_created: 2024-06-25T11:45:58Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2026-10-02T11:23:43Z
day: '06'
ddc:
- '516'
department:
- _id: GradSch
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.11
ec_funded: 1
external_id:
arxiv:
- '2206.10485'
file:
- access_level: open_access
checksum: 6a2ddc8b51aa58f197a8b294750f1f8d
content_type: application/pdf
creator: cfillmor
date_created: 2024-06-25T11:47:26Z
date_updated: 2024-06-25T11:47:26Z
file_id: '17171'
file_name: LIPIcs.SoCG.2024.11.pdf
file_size: 20886142
relation: main_file
success: 1
file_date_updated: 2024-06-25T11:47:26Z
fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.11
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 11:1-11:19
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: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _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:
eissn:
- 1868-8969
isbn:
- '9783959773164'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger
for subsets of euclidean spaces and of Riemannian manifolds
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 293
year: '2024'
...
---
_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'
das_tickbox: '0'
date_created: 2023-09-17T22:01:10Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2026-10-02T11:45:50Z
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:
- access_level: open_access
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
relation: main_file
success: 1
file_date_updated: 2024-07-22T09:43:19Z
fulldoi: https://doi.org/10.1007/s00454-023-00566-1
has_accepted_license: '1'
intvolume: ' 72'
isi: 1
language:
- iso: eng
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'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 72
year: '2024'
...
---
_id: '17144'
abstract:
- lang: eng
text: "We prove that the medial axis of closed sets is Hausdorff stable in the following
sense: Let \U0001D4AE ⊆ ℝ^d be a fixed closed set that contains a bounding sphere.
That is, the bounding sphere is part of the set \U0001D4AE. Consider the space
of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant.
The map from this space of diffeomorphisms (endowed with a Banach norm) to the
space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping
a diffeomorphism F to the closure of the medial axis of F(\U0001D4AE), is Lipschitz.
This extends a previous stability result of Chazal and Soufflet on the stability
of the medial axis of C² manifolds under C² ambient diffeomorphisms."
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. I 02979-N35.\r\nSupported 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 Cô d'Azur.\r\nWe are greatly indebted
to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher
Fillmore, and Elizabeth Stephenson for early discussions and all members of the
Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape
team (Inria) for the atmosphere in which this research was conducted."
alternative_title:
- LIPIcs
article_number: '69'
article_processing_charge: No
arxiv: 1
author:
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded
set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms.
In: 40th International Symposium on Computational Geometry. Vol 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.69'
apa: 'Kourimska, H., Lieutier, A., & Wintraecken, M. (2024). The medial axis
of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance
Under ambient diffeomorphisms. In 40th International Symposium on Computational
Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für
Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.69'
chicago: Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis
of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance
Under Ambient Diffeomorphisms.” In 40th International Symposium on Computational
Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
https://doi.org/10.4230/LIPIcs.SoCG.2024.69.
ieee: H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed
bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient
diffeomorphisms,” in 40th International Symposium on Computational Geometry,
Athens, Greece, 2024, vol. 293.
ista: 'Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed
bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient
diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 293, 69.'
mla: Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz
Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.”
40th International Symposium on Computational Geometry, vol. 293, 69, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.69.
short: H. Kourimska, A. Lieutier, 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'
das_tickbox: '0'
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-10-02T11:46:39Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.69
ec_funded: 1
external_id:
arxiv:
- '2212.01118'
file:
- access_level: open_access
checksum: b40ff456c19294adb5d9613fcfd751c6
content_type: application/pdf
creator: dernst
date_created: 2024-06-17T08:33:40Z
date_updated: 2024-06-17T08:33:40Z
file_id: '17150'
file_name: 2024_LIPICS_Kourimska.pdf
file_size: 1612558
relation: main_file
success: 1
file_date_updated: 2024-06-17T08:33:40Z
fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.69
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'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: The medial axis of any closed bounded set Is Lipschitz stable with respect
to the Hausdorff distance Under ambient diffeomorphisms
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 293
year: '2024'
...
---
_id: '17146'
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. In particular, there is an arrangement
of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers
a long-standing open question in computational geometry.
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.\r\nThe authors thank Matt
Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart
for early discussions on the linked circles construction in three dimensions, and
Gábor Tardos for helpful remarks and suggestions."
alternative_title:
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citation:
ama: 'Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. In: 40th
International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.53'
apa: 'Edelsbrunner, H., & Pach, J. (2024). Maximum Betti numbers of Čech complexes.
In 40th International Symposium on Computational Geometry (Vol. 293). Athens,
Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.53'
chicago: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
In 40th International Symposium on Computational Geometry, Vol. 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.53.
ieee: H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” in
40th International Symposium on Computational Geometry, Athens, Greece,
2024, vol. 293.
ista: 'Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th
International Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, LIPIcs, vol. 293, 53.'
mla: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
40th International Symposium on Computational Geometry, vol. 293, 53, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.53.
short: H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
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publication: 40th International Symposium on Computational Geometry
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---
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abstract:
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text: Grid peeling is the process of repeatedly removing the convex hull vertices
of the grid points that lie inside a given convex curve. It has been conjectured
that, for a more and more refined grid, grid peeling converges to a continuous
process, the affine curve-shortening flow, which deforms the curve based on the
curvature. We prove this conjecture for one class of curves, parabolas with a
vertical axis, and we determine the value of the constant factor in the formula
that relates the two processes.
acknowledgement: Part of this work was done while G.R. enjoyed the hospitality of
the Institute of Science and Technology Austria (ISTA) as a visiting professor during
his sabbatical in the winter semester 2022/23.
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article_number: '76'
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author:
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full_name: Rote, Günter
last_name: Rote
- first_name: Moritz
full_name: Rüber, Moritz
last_name: Rüber
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: 40th International
Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.76'
apa: 'Rote, G., Rüber, M., & Saghafian, M. (2024). Grid peeling of parabolas.
In 40th International Symposium on Computational Geometry (Vol. 293). Athens,
Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.76'
chicago: Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.”
In 40th International Symposium on Computational Geometry, Vol. 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.76.
ieee: G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in 40th
International Symposium on Computational Geometry, Athens, Greece, 2024, vol.
293.
ista: 'Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International
Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry,
LIPIcs, vol. 293, 76.'
mla: Rote, Günter, et al. “Grid Peeling of Parabolas.” 40th International Symposium
on Computational Geometry, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.76.
short: G. Rote, M. Rüber, M. Saghafian, 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
das_tickbox: '0'
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-10-02T11:47:18Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.76
external_id:
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file_date_updated: 2024-06-17T08:40:04Z
fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.76
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intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
researchdata_availability: no
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status: public
supplementarymaterial: no
title: Grid peeling of parabolas
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)
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user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 293
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...