---
OA_place: repository
OA_type: green
_id: '21931'
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
(nonoptimal) upper bound was only obtained in 2007 by Gabrielov, Novikov, and
Shapiro, who also posed two additional interesting conjectures. 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 Conjecture 1.8 by Gabrielov, Novikov,
and Shapiro that the number of equilibria cannot exceed those of the distance
function defined by the unit point charges. Finally, we note that it is quite
possible that Maxwell's quadratic upper bound is not tight, so it is prudent to
find lower 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: e70163
article_processing_charge: No
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: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Goncalo
full_name: Oliveira, Goncalo
id: 58abbde8-f455-11eb-a497-98c8fd71b905
last_name: Oliveira
citation:
ama: Edelsbrunner H, Fillmore CD, Oliveira G. Counting equilibria of the electrostatic
potential. Proceedings of the London Mathematical Society. 2026;132(5).
doi:10.1112/plms.70163
apa: Edelsbrunner, H., Fillmore, C. D., & Oliveira, G. (2026). Counting equilibria
of the electrostatic potential. Proceedings of the London Mathematical Society.
Wiley. https://doi.org/10.1112/plms.70163
chicago: Edelsbrunner, Herbert, Christopher D Fillmore, and Goncalo Oliveira. “Counting
Equilibria of the Electrostatic Potential.” Proceedings of the London Mathematical
Society. Wiley, 2026. https://doi.org/10.1112/plms.70163.
ieee: H. Edelsbrunner, C. D. Fillmore, and G. Oliveira, “Counting equilibria of
the electrostatic potential,” Proceedings of the London Mathematical Society,
vol. 132, no. 5. Wiley, 2026.
ista: Edelsbrunner H, Fillmore CD, Oliveira G. 2026. Counting equilibria of the
electrostatic potential. Proceedings of the London Mathematical Society. 132(5),
e70163.
mla: Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.”
Proceedings of the London Mathematical Society, vol. 132, no. 5, e70163,
Wiley, 2026, doi:10.1112/plms.70163.
short: H. Edelsbrunner, C.D. Fillmore, G. Oliveira, Proceedings of the London Mathematical
Society 132 (2026).
corr_author: '1'
date_created: 2026-05-31T22:02:13Z
date_published: 2026-05-01T00:00:00Z
date_updated: 2026-07-22T06:33:54Z
day: '01'
department:
- _id: HeEd
- _id: TaHa
doi: 10.1112/plms.70163
external_id:
arxiv:
- '2501.05315'
fulldoi: https://doi.org/10.1112/plms.70163
intvolume: ' 132'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2501.05315
month: '05'
oa: 1
oa_version: Preprint
publication: Proceedings of the London Mathematical Society
publication_identifier:
eissn:
- 1460-244X
issn:
- 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
related_material:
record:
- id: '21050'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Counting equilibria of the electrostatic potential
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 132
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '20490'
abstract:
- lang: eng
text: "We study flips in hypertriangulations of planar points sets. Here a level-k
hypertriangulation of n\r\n points in the plane is a subdivision induced by the
projection of a k-hypersimplex, which is the convex hull of the barycenters of
the (k-1)-dimensional faces of the standard (n-1)-simplex. In particular, we introduce
four types of flips and prove that the level-2 hypertriangulations are connected
by these flips.\r\n"
acknowledgement: Work by all authors but the second 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 the second author is
partially supported by the Alexander von Humboldt Foundation and by the Simons Foundation
. The second author thanks Jesús A. De Loera for useful discussions on flips and
non-flips and Pavel Galashin and Alexey Balitskiy for useful discussions on plabic
graphs.
article_number: '104248'
article_processing_charge: No
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. Flips in two-dimensional
hypertriangulations. European Journal of Combinatorics. 2026;132. doi:10.1016/j.ejc.2025.104248
apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2026).
Flips in two-dimensional hypertriangulations. European Journal of Combinatorics.
Elsevier. https://doi.org/10.1016/j.ejc.2025.104248
chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and
Morteza Saghafian. “Flips in Two-Dimensional Hypertriangulations.” European
Journal of Combinatorics. Elsevier, 2026. https://doi.org/10.1016/j.ejc.2025.104248.
ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “Flips
in two-dimensional hypertriangulations,” European Journal of Combinatorics,
vol. 132. Elsevier, 2026.
ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2026. Flips in
two-dimensional hypertriangulations. European Journal of Combinatorics. 132, 104248.
mla: Edelsbrunner, Herbert, et al. “Flips in Two-Dimensional Hypertriangulations.”
European Journal of Combinatorics, vol. 132, 104248, Elsevier, 2026, doi:10.1016/j.ejc.2025.104248.
short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, European
Journal of Combinatorics 132 (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2025-10-19T22:01:31Z
date_published: 2026-02-01T00:00:00Z
date_updated: 2026-07-23T11:58:37Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.ejc.2025.104248
ec_funded: 1
external_id:
arxiv:
- '2212.11380'
isi:
- '001599061500002'
fulldoi: https://doi.org/10.1016/j.ejc.2025.104248
intvolume: ' 132'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.11380
month: '02'
oa: 1
oa_version: Preprint
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: European Journal of Combinatorics
publication_identifier:
issn:
- 0195-6698
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Flips in two-dimensional hypertriangulations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 132
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22648'
abstract:
- lang: eng
text: Bifurcation characterizes the qualitative changes in parameterized dynamical
systems and is one of the major topics in the field. In this work, we study combinatorial
bifurcations within the framework of combinatorial dynamical systems—a young but
already well-established theory. We introduce the Conley–Morse persistence barcode,
a compact algebraic descriptor of combinatorial bifurcations. This barcode captures
structural changes in a dynamical system at the level of Morse decompositions
and provides a characterization of the nature of observed transitions in terms
of the Conley index. The construction of the Conley–Morse persistence barcode
builds upon ideas from topological persistence. Specifically, we consider a persistence
module obtained from the Conley index of invariant sets indexed over a poset.
Using gentle algebras, we prove that this module decomposes into simple intervals
(bars) and compute them by adapting the zigzag persistence algorithm to our purpose.
acknowledgement: M.L. acknowledges support from the European Union’s Horizon 2020
research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 101034413. T.D. acknowledges the support of NSF funds CCF-2437030 and DMS-2301360.
The authors would like to thank the anonymous reviewers for their careful reading
of the paper. Their feedback significantly improved the quality of the article.
T.D. and M.L. would like to acknowledge many thought-provoking discussions with
Marian Mrozek on combinatorial dynamical systems and their continuations. M.S.T.
would like to thank Álvaro Sánchez for insightful discussions about representation
theory. Open access funding provided by Institute of Science and Technology (IST
Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Tamal K.
full_name: Dey, Tamal K.
last_name: Dey
- first_name: Michał
full_name: Lipiński, Michał
id: dfffb474-4317-11ee-8f5c-fe3fc95a425e
last_name: Lipiński
orcid: 0000-0001-9789-9750
- first_name: Manuel
full_name: Soriano Trigueros, Manuel
id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
last_name: Soriano Trigueros
orcid: 0000-0003-2449-1433
citation:
ama: 'Dey TK, Lipiński M, Soriano Trigueros M. Conley-Morse persistence barcode:
A homological signature of combinatorial bifurcations. Foundations of Computational
Mathematics. 2026. doi:10.1007/s10208-026-09766-6'
apa: 'Dey, T. K., Lipiński, M., & Soriano Trigueros, M. (2026). Conley-Morse
persistence barcode: A homological signature of combinatorial bifurcations. Foundations
of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-026-09766-6'
chicago: 'Dey, Tamal K., Michał Lipiński, and Manuel Soriano Trigueros. “Conley-Morse
Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” Foundations
of Computational Mathematics. Springer, 2026. https://doi.org/10.1007/s10208-026-09766-6.'
ieee: 'T. K. Dey, M. Lipiński, and M. Soriano Trigueros, “Conley-Morse persistence
barcode: A homological signature of combinatorial bifurcations,” Foundations
of Computational Mathematics. Springer, 2026.'
ista: 'Dey TK, Lipiński M, Soriano Trigueros M. 2026. Conley-Morse persistence barcode:
A homological signature of combinatorial bifurcations. Foundations of Computational
Mathematics.'
mla: 'Dey, Tamal K., et al. “Conley-Morse Persistence Barcode: A Homological Signature
of Combinatorial Bifurcations.” Foundations of Computational Mathematics,
Springer, 2026, doi:10.1007/s10208-026-09766-6.'
short: T.K. Dey, M. Lipiński, M. Soriano Trigueros, Foundations of Computational
Mathematics (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-08-05T06:11:30Z
date_published: 2026-08-04T00:00:00Z
date_updated: 2026-08-11T06:13:33Z
day: '04'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s10208-026-09766-6
ec_funded: 1
external_id:
arxiv:
- '2504.17105'
fulldoi: https://doi.org/10.1007/s10208-026-09766-6
has_accepted_license: '1'
keyword:
- Multivector field
- Conley index
- Morse decomposition
- Bifurcation
- Continuation
- Zigzag persistence
- Persistence barcode
- Gentle algebra
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10208-026-09766-6
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: epub_ahead
publisher: Springer
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: 'Conley-Morse persistence barcode: A homological signature of combinatorial
bifurcations'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '20980'
abstract:
- lang: eng
text: 'Morse decompositions partition the flows in a vector field into equivalent
structures. Given such a decomposition, one can define a further summary of its
flow structure by what is called a connection matrix. These matrices, a generalization
of Morse boundary operators from classical Morse theory, capture the connections
made by the flows among the critical structures—such as attractors, repellers,
and orbits—in a vector field. Recently, in the context of combinatorial dynamics,
an efficient persistence-like algorithm to compute connection matrices has been
proposed in Dey, Lipiński, Mrozek, and Slechta [SIAM J. Appl. Dyn. Syst., 23 (2024),
pp. 81–97]. We show that, actually, the classical persistence algorithm with exhaustive
reduction retrieves connection matrices, both simplifying the algorithm of Dey
et al. and bringing the theory of persistence closer to combinatorial dynamical
systems. We supplement this main result with an observation: the concept of persistence
as defined for scalar fields naturally adapts to Morse decompositions whose Morse
sets are filtered with a Lyapunov function. We conclude by presenting preliminary
experimental results.'
acknowledgement: "This research was supported by NSF grants DMS-2301360 and CCF-2437030
as well as from the European Union's Horizon 2020 research and innovation programme
under Marie Sk\\lodowska-Curie grant 101034413.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamal K.
full_name: Dey, Tamal K.
last_name: Dey
- first_name: Andrew
full_name: Haas, Andrew
last_name: Haas
- first_name: Michał
full_name: Lipiński, Michał
id: dfffb474-4317-11ee-8f5c-fe3fc95a425e
last_name: Lipiński
orcid: 0000-0001-9789-9750
citation:
ama: Dey TK, Haas A, Lipiński M. Computing a connection matrix and persistence efficiently
from a morse decomposition. SIAM Journal on Applied Dynamical Systems.
2026;25(1):108-130. doi:10.1137/25m1739406
apa: Dey, T. K., Haas, A., & Lipiński, M. (2026). Computing a connection matrix
and persistence efficiently from a morse decomposition. SIAM Journal on Applied
Dynamical Systems. SIAM. https://doi.org/10.1137/25m1739406
chicago: Dey, Tamal K., Andrew Haas, and Michał Lipiński. “Computing a Connection
Matrix and Persistence Efficiently from a Morse Decomposition.” SIAM Journal
on Applied Dynamical Systems. SIAM, 2026. https://doi.org/10.1137/25m1739406.
ieee: T. K. Dey, A. Haas, and M. Lipiński, “Computing a connection matrix and persistence
efficiently from a morse decomposition,” SIAM Journal on Applied Dynamical
Systems, vol. 25, no. 1. SIAM, pp. 108–130, 2026.
ista: Dey TK, Haas A, Lipiński M. 2026. Computing a connection matrix and persistence
efficiently from a morse decomposition. SIAM Journal on Applied Dynamical Systems.
25(1), 108–130.
mla: Dey, Tamal K., et al. “Computing a Connection Matrix and Persistence Efficiently
from a Morse Decomposition.” SIAM Journal on Applied Dynamical Systems,
vol. 25, no. 1, SIAM, 2026, pp. 108–30, doi:10.1137/25m1739406.
short: T.K. Dey, A. Haas, M. Lipiński, SIAM Journal on Applied Dynamical Systems
25 (2026) 108–130.
date_created: 2026-01-12T11:17:06Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-08-12T06:23:46Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1137/25m1739406
ec_funded: 1
external_id:
arxiv:
- '2502.19369'
fulldoi: https://doi.org/10.1137/25m1739406
intvolume: ' 25'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.19369
month: '01'
oa: 1
oa_version: Preprint
page: 108-130
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing a connection matrix and persistence efficiently from a morse decomposition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2026'
...
---
OA_place: publisher
OA_type: gold
_id: '22299'
abstract:
- lang: eng
text: The depth poset of a filtered Lefschetz complex reflects the dependencies
between the cancellations of different shallow birth-death pairs. Using the fast
algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for
updating the persistence diagram under transpositions in [Cohen-Steiner et al.,
2006], we give a complete case analysis of how transpositions of cells in the
filter affect the depth poset. In addition, we present statistics on the depth
poset for random point data and its sensitivity to the transpositions that occur
in random straight-line homotopies.
acknowledgement: "The authors thank Jakub Leśkiewicz and Bartosz Furmanek for discussions\r\nthat
helped improve the paper. Herbert Edelsbrunner: DFG Collaborative Research Center
TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35\r\nMichał Lipiński:
European Union’s Horizon 2020 research and innovation programme under the\r\nMarie
Skłodowska-Curie Grant Agreement No. 101034413\r\nMarian Mrozek: Polish National
Science Center under Opus Grant 2019/35/B/ST1/00874 and Opus\r\nGrant 2025/57/B/ST1/00550"
alternative_title:
- LIPIcs
article_number: 41:1-41:18
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: Michał
full_name: Lipiński, Michał
id: dfffb474-4317-11ee-8f5c-fe3fc95a425e
last_name: Lipiński
orcid: 0000-0001-9789-9750
- first_name: Marian
full_name: Mrozek, Marian
last_name: Mrozek
orcid: 0000-0002-0619-6417
- 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: Fedor
full_name: Zimin, Fedor
id: afd27eda-91c1-11f0-aad8-c6edbec24c04
last_name: Zimin
citation:
ama: 'Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. The depth
poset under transpositions in the filter. In: 42nd International Symposium
on Computational Geometry. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2026. doi:10.4230/LIPICS.SOCG.2026.41'
apa: 'Edelsbrunner, H., Lipiński, M., Mrozek, M., Soriano Trigueros, M., & Zimin,
F. (2026). The depth poset under transpositions in the filter. In 42nd International
Symposium on Computational Geometry (Vol. 367). New Brunswick, NJ, United
States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2026.41'
chicago: Edelsbrunner, Herbert, Michał Lipiński, Marian Mrozek, Manuel Soriano Trigueros,
and Fedor Zimin. “The Depth Poset under Transpositions in the Filter.” In 42nd
International Symposium on Computational Geometry, Vol. 367. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPICS.SOCG.2026.41.
ieee: H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, and F. Zimin,
“The depth poset under transpositions in the filter,” in 42nd International
Symposium on Computational Geometry, New Brunswick, NJ, United States, 2026,
vol. 367.
ista: 'Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. 2026.
The depth poset under transpositions in the filter. 42nd International Symposium
on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs,
vol. 367, 41:1-41:18.'
mla: Edelsbrunner, Herbert, et al. “The Depth Poset under Transpositions in the
Filter.” 42nd International Symposium on Computational Geometry, vol. 367,
41:1-41:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPICS.SOCG.2026.41.
short: H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, F. Zimin,
in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2026.
conference:
end_date: 2026-06-05
location: New Brunswick, NJ, United States
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2026-06-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-07-13T09:56:38Z
date_published: 2026-05-27T00:00:00Z
date_updated: 2026-08-12T09:02:56Z
day: '27'
ddc:
- '500'
department:
- _id: HeEd
- _id: GradSch
doi: 10.4230/LIPICS.SOCG.2026.41
ec_funded: 1
external_id:
arxiv:
- '2511.21961'
file:
- access_level: open_access
checksum: 9dfb96ee66985c724b499b0e5888dc8e
content_type: application/pdf
creator: dernst
date_created: 2026-07-14T06:08:05Z
date_updated: 2026-07-14T06:08:05Z
file_id: '22329'
file_name: 2026_LIPIcSSoCG_Edelsbrunner.pdf
file_size: 2902144
relation: main_file
success: 1
file_date_updated: 2026-07-14T06:08:05Z
fulldoi: https://doi.org/10.4230/LIPICS.SOCG.2026.41
has_accepted_license: '1'
intvolume: ' 367'
keyword:
- Algebraic topology
- Lefschetz complexes
- persistent homology
- vines and vineyards
- birth-death pairs
- shallow pairs
- relations
- partial orders
- transpositions
- Theory of computation → Computational geometry
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 42nd International Symposium on Computational Geometry
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959774185'
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 depth poset under transpositions in the filter
tmp:
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short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20657'
abstract:
- lang: eng
text: 'The Upper Bound Theorem for convex polytopes implies that the p-th Betti
number of the Čech complex of any set of N points in ℝ^d and any radius satisfies
β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions,
which prove that this upper bound is asymptotically tight. For example, we describe
a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number
of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of
the Čech complex at the other radius is n². '
acknowledgement: The first author is supported by the European Research Council (ERC),
grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant no. I 02979-N35. The second author is supported by the
European Research Council (ERC), grant “GeoScape” and by the Hungarian Science Foundation
(NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian
Science Fund (FWF), grant no. Z 342-N31. Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
citation:
ama: Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. Discrete
& Computational Geometry. 2026;75:597-624. doi:10.1007/s00454-025-00796-5
apa: Edelsbrunner, H., & Pach, J. (2026). Maximum Betti numbers of Čech complexes.
Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-025-00796-5
chicago: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
Discrete & Computational Geometry. Springer Nature, 2026. https://doi.org/10.1007/s00454-025-00796-5.
ieee: H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” Discrete
& Computational Geometry, vol. 75. Springer Nature, pp. 597–624, 2026.
ista: Edelsbrunner H, Pach J. 2026. Maximum Betti numbers of Čech complexes. Discrete
& Computational Geometry. 75, 597–624.
mla: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
Discrete & Computational Geometry, vol. 75, Springer Nature, 2026,
pp. 597–624, doi:10.1007/s00454-025-00796-5.
short: H. Edelsbrunner, J. Pach, Discrete & Computational Geometry 75 (2026)
597–624.
corr_author: '1'
das_tickbox: '0'
date_created: 2025-11-19T09:44:58Z
date_published: 2026-03-01T00:00:00Z
date_updated: 2026-10-02T11:48:00Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-025-00796-5
ec_funded: 1
external_id:
arxiv:
- '2310.14801'
isi:
- '001610592600001'
file:
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checksum: c17c014dbbf5be702195c737890251c8
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creator: dernst
date_created: 2026-07-27T08:11:05Z
date_updated: 2026-07-27T08:11:05Z
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file_size: 546483
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success: 1
file_date_updated: 2026-07-27T08:11:05Z
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intvolume: ' 75'
isi: 1
language:
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month: '03'
oa: 1
oa_version: Published Version
page: 597-624
project:
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call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
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call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: Discrete & Computational Geometry
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eissn:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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scopus_import: '1'
status: public
supplementarymaterial: no
title: Maximum Betti numbers of Čech complexes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 75
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '20585'
abstract:
- lang: eng
text: Motivated by applications in medical sciences, we study finite chromatic sets
in Euclidean space from a topological perspective. Based on the persistent homology
for images, kernels and cokernels, we design provably stable homological quantifiers
that describe the geometric micro- and macro-structure of how the color classes
mingle. These can be efficiently computed using chromatic variants of Delaunay
and alpha complexes, and code that does these computations is provided.
acknowledgement: "This project has received funding from the European Research\r\nCouncil
(ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund\r\n(FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR\r\n109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
alpha complexes. Foundations of Data Science. 2026;8:30-62. doi:10.3934/fods.2025003
apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (2026). Chromatic alpha complexes. Foundations of Data Science. AIMS.
https://doi.org/10.3934/fods.2025003
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “Chromatic Alpha Complexes.” Foundations of Data Science.
AIMS, 2026. https://doi.org/10.3934/fods.2025003.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“Chromatic alpha complexes,” Foundations of Data Science, vol. 8. AIMS,
pp. 30–62, 2026.
ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2026. Chromatic
alpha complexes. Foundations of Data Science. 8, 30–62.
mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” Foundations
of Data Science, vol. 8, AIMS, 2026, pp. 30–62, doi:10.3934/fods.2025003.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations
of Data Science 8 (2026) 30–62.
corr_author: '1'
date_created: 2025-11-02T23:01:33Z
date_published: 2026-03-01T00:00:00Z
date_updated: 2026-10-02T11:56:12Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.3934/fods.2025003
ec_funded: 1
external_id:
arxiv:
- '2212.03128'
fulldoi: https://doi.org/10.3934/fods.2025003
has_accepted_license: '1'
intvolume: ' 8'
keyword:
- Topological data analysis
- Delaunay mosaic
- alpha complex
- chromatic sets
- persistent homology
- kernel/image/cokernel persistent homology
- radius function
- discrete Morse theory
- exact sequences
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.03128
mathsc:
- 62R40
- 55N31
- 68T09
- 57Q70
month: '03'
oa: 1
oa_version: Preprint
page: 30-62
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Foundations of Data Science
publication_identifier:
eissn:
- 2639-8001
publication_status: published
publisher: AIMS
quality_controlled: '1'
related_material:
record:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Chromatic alpha complexes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2026'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '23087'
abstract:
- lang: eng
text: Disordered materials such as glasses are promising candidates as solid-state
electrolytes for batteries, but they tend to exhibit low ionic conductivity and
current methods for investigating and predicting the ionic conductivity of electrolyte
materials are inefficient. Here, we propose a framework that summarizes the topological
properties of the electrolyte material’s atomic structure with a weighted graph
based on periodic boundary conditions. We then compute a variation of the max-flow
algorithm, a commonly used model in continuum models of transportation and liquid
flow, on this summary and show that it is compatible with the simulated periodic
atomic structures. Using molecular dynamics simulations of various glassy solid-state
electrolyte families including both mobile lithium and sodium ions, we validate
the approach by showing a positive correlation between the area-normalized maximum
flow predicted from the static glass structures and the ionic conductivity as
obtained from the simulations, especially in the case of high-conductivity sulfide
glass electrolytes. We envision that the developed methodology, which only relies
on static atomic structure, will accelerate the discovery of highly conductive
sulfide glassy electrolytes for high-performance all-solid-state batteries.
acknowledgement: We thank the Danish e-Infrastructure Cooperation (DeiC) for access
to computational resources at Sophia and LUMI-C (DeiC-AAU-N5-202200005). This work
was supported by the Independent Research Fund Denmark (1026-00037), European Union
(ERC, NewGLASS, 101044664), and Danish Data Science Academy, which in turn is funded
by the Novo Nordisk Foundation (NNF21SA0069429) and VILLUM FONDEN (40516). Y.B.B.
acknowledges support from the Austrian Science Fund (FWF) 10.55776/ESP9584724.
article_number: '10343'
article_processing_charge: Yes
article_type: original
author:
- first_name: Matteo
full_name: Pegoraro, Matteo
last_name: Pegoraro
- first_name: Rasmus
full_name: Christensen, Rasmus
last_name: Christensen
- first_name: Søren S.
full_name: Sørensen, Søren S.
last_name: Sørensen
- first_name: Anders R.
full_name: Lindbjerg, Anders R.
last_name: Lindbjerg
- first_name: Tao
full_name: Du, Tao
last_name: Du
- first_name: Yossi
full_name: Bleile, Yossi
id: 920a7385-7995-11ef-9bfd-8c434cd8f3c2
last_name: Bleile
orcid: 0000-0002-4861-9174
- first_name: Anne Marie
full_name: Svane, Anne Marie
last_name: Svane
- first_name: Christophe A.N.
full_name: Biscio, Christophe A.N.
last_name: Biscio
- first_name: Lisbeth
full_name: Fajstrup, Lisbeth
last_name: Fajstrup
- first_name: Morten M.
full_name: Smedskjaer, Morten M.
last_name: Smedskjaer
citation:
ama: Pegoraro M, Christensen R, Sørensen SS, et al. Predicting ionic conductivity
of sulfide glass solid-state electrolytes using max-flow methodology. Nature
Communications. 2026;17. doi:10.1038/s41467-026-77363-w
apa: Pegoraro, M., Christensen, R., Sørensen, S. S., Lindbjerg, A. R., Du, T., Bokor
Bleile, Y., … Smedskjaer, M. M. (2026). Predicting ionic conductivity of sulfide
glass solid-state electrolytes using max-flow methodology. Nature Communications.
Springer Nature. https://doi.org/10.1038/s41467-026-77363-w
chicago: Pegoraro, Matteo, Rasmus Christensen, Søren S. Sørensen, Anders R. Lindbjerg,
Tao Du, Yossi Bokor Bleile, Anne Marie Svane, Christophe A.N. Biscio, Lisbeth
Fajstrup, and Morten M. Smedskjaer. “Predicting Ionic Conductivity of Sulfide
Glass Solid-State Electrolytes Using Max-Flow Methodology.” Nature Communications.
Springer Nature, 2026. https://doi.org/10.1038/s41467-026-77363-w.
ieee: M. Pegoraro et al., “Predicting ionic conductivity of sulfide glass
solid-state electrolytes using max-flow methodology,” Nature Communications,
vol. 17. Springer Nature, 2026.
ista: Pegoraro M, Christensen R, Sørensen SS, Lindbjerg AR, Du T, Bokor Bleile Y,
Svane AM, Biscio CAN, Fajstrup L, Smedskjaer MM. 2026. Predicting ionic conductivity
of sulfide glass solid-state electrolytes using max-flow methodology. Nature Communications.
17, 10343.
mla: Pegoraro, Matteo, et al. “Predicting Ionic Conductivity of Sulfide Glass Solid-State
Electrolytes Using Max-Flow Methodology.” Nature Communications, vol. 17,
10343, Springer Nature, 2026, doi:10.1038/s41467-026-77363-w.
short: M. Pegoraro, R. Christensen, S.S. Sørensen, A.R. Lindbjerg, T. Du, Y. Bokor
Bleile, A.M. Svane, C.A.N. Biscio, L. Fajstrup, M.M. Smedskjaer, Nature Communications
17 (2026).
das_tickbox: '1'
dataavailabilitystatement: All data supporting the findings of this study are available
within the article and Supplementary Information files. Source data are provided
with this paper. The developed code to perform the max-flow calculations is available
as part of the Topological Materials Analysis (ToMA) library, which is available
at Zenodo (https://doi.org/10.5281/zenodo.10781424) and Github (https://github.com/yossibokorbleile/TopologicalMaterialAnalysis),
with documentation available at https://yossi.eu/toma/. To enhance usability, we
have included a brief documentation on how to compile ToMA as well as a minimal
working example of the code together with an example trajectory directly in the
ToMA repository. LAMMPS is an open-source code available at https://lammps.sandia.gov.
date_created: 2026-10-11T22:02:03Z
date_published: 2026-09-30T00:00:00Z
date_updated: 2026-10-12T09:03:58Z
day: '30'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1038/s41467-026-77363-w
external_id:
pmid:
- '42811056'
file:
- access_level: open_access
checksum: eba760f5982a89f59664957e00c5d2d6
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date_created: 2026-10-12T09:00:06Z
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intvolume: ' 17'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 9106a876-16d5-11f0-9cad-bbf11c9952f9
grant_number: ESP 9584724
name: Quantitative Unbiased Shape Analysis with Geometry & Topology
publication: Nature Communications
publication_identifier:
eissn:
- 2041-1723
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Predicting ionic conductivity of sulfide glass solid-state electrolytes using
max-flow methodology
tmp:
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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: 17
year: '2026'
...
---
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '20867'
abstract:
- lang: eng
text: We discuss the embeddability of subspaces of the Gromov–Hausdorff space, which
consists of isometry classes of compact metric spaces endowed with the Gromov–Hausdorff
distance, into Hilbert spaces. These embeddings are particularly valuable for
applications to topological data analysis. We prove that its subspace consisting
of metric spaces with at most n points has asymptotic dimension n(n−1)∕2. Thus,
there exists a coarse embedding of that space into a Hilbert space. On the contrary,
if the number of points is not bounded, then the subspace cannot be coarsely embedded
into any uniformly convex Banach space and so, in particular, into any Hilbert
space. Furthermore, we prove that, even if we restrict to finite metric spaces
whose diameter is bounded by some constant, the subspace still cannot be bi-Lipschitz
embedded into any finite-dimensional Hilbert space. We obtain both nonembeddability
results by finding obstructions to coarse and bi-Lipschitz embeddings in families
of isometry classes of finite subsets of the real line endowed with the Euclidean–Hausdorff
distance.
acknowledgement: "The author was supported by the FWF Grant, Project number I4245-N35.
The author would like to thank Thomas Weighill for the helpful discussions around
Theorem 3.10, and Takamitsu Yamauchi for bringing to my attention the fundamental
reference [35]. Furthermore, the author\r\nis thankful for the detailed and helpful
comments of the reviewer of this manuscript."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Zava N. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces. Algebraic & Geometric Topology. 2025;25(8):5153-5174.
doi:10.2140/agt.2025.25.5153
apa: Zava, N. (2025). Coarse and bi-Lipschitz embeddability of subspaces of the
Gromov–Hausdorff space into Hilbert spaces. Algebraic & Geometric Topology.
Mathematical Sciences Publishers. https://doi.org/10.2140/agt.2025.25.5153
chicago: Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the
Gromov–Hausdorff Space into Hilbert Spaces.” Algebraic & Geometric Topology.
Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/agt.2025.25.5153.
ieee: N. Zava, “Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces,” Algebraic & Geometric Topology, vol. 25,
no. 8. Mathematical Sciences Publishers, pp. 5153–5174, 2025.
ista: Zava N. 2025. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces. Algebraic & Geometric Topology. 25(8), 5153–5174.
mla: Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff
Space into Hilbert Spaces.” Algebraic & Geometric Topology, vol. 25,
no. 8, Mathematical Sciences Publishers, 2025, pp. 5153–74, doi:10.2140/agt.2025.25.5153.
short: N. Zava, Algebraic & Geometric Topology 25 (2025) 5153–5174.
corr_author: '1'
date_created: 2025-12-29T12:09:09Z
date_published: 2025-11-20T00:00:00Z
date_updated: 2026-01-05T12:19:09Z
day: '20'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.2140/agt.2025.25.5153
external_id:
arxiv:
- '2303.04730'
file:
- access_level: open_access
checksum: 1e05b4f17a44500ae1ae1e21bc636f6a
content_type: application/pdf
creator: dernst
date_created: 2026-01-05T12:16:38Z
date_updated: 2026-01-05T12:16:38Z
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file_name: 2025_AlgebraicGeomTopology_Zava.pdf
file_size: 574389
relation: main_file
success: 1
file_date_updated: 2026-01-05T12:16:38Z
fulldoi: https://doi.org/10.2140/agt.2025.25.5153
has_accepted_license: '1'
intvolume: ' 25'
issue: '8'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 5153-5174
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I04245
name: Algebraic Footprints of Geometric Features in Homology
publication: Algebraic & Geometric Topology
publication_identifier:
eissn:
- 1472-2739
issn:
- 1472-2747
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
space into Hilbert spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '18626'
abstract:
- lang: eng
text: "The local angle property of the (order-1) Delaunay triangulations of a generic
set in R2\r\n asserts that the sum of two angles opposite a common edge is less
than π. This paper extends this property to higher order and uses it to generalize
two classic properties from order-1 to order-2: (1) among the complete level-2
hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation
lexicographically maximizes the sorted angle vector; (2) among the maximal level-2
hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation
is the only one that has the local angle property. We also use our method of establishing
(2) to give a new short proof of the angle vector optimality for the (order-1)
Delaunay triangulation. For order-1, both properties have been instrumental in
numerous applications of Delaunay triangulations, and we expect that their generalization
will make order-2 Delaunay triangulations more attractive to applications as well."
acknowledgement: Work by the first and third 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. Work by the second
author is partially supported by the Alexander von Humboldt Foundation.
article_number: '110055'
article_processing_charge: No
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: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Edelsbrunner H, Garber A, Saghafian M. Order-2 Delaunay triangulations optimize
angles. Advances in Mathematics. 2025;461. doi:10.1016/j.aim.2024.110055
apa: Edelsbrunner, H., Garber, A., & Saghafian, M. (2025). Order-2 Delaunay
triangulations optimize angles. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.110055
chicago: Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “Order-2 Delaunay
Triangulations Optimize Angles.” Advances in Mathematics. Elsevier, 2025.
https://doi.org/10.1016/j.aim.2024.110055.
ieee: H. Edelsbrunner, A. Garber, and M. Saghafian, “Order-2 Delaunay triangulations
optimize angles,” Advances in Mathematics, vol. 461. Elsevier, 2025.
ista: Edelsbrunner H, Garber A, Saghafian M. 2025. Order-2 Delaunay triangulations
optimize angles. Advances in Mathematics. 461, 110055.
mla: Edelsbrunner, Herbert, et al. “Order-2 Delaunay Triangulations Optimize Angles.”
Advances in Mathematics, vol. 461, 110055, Elsevier, 2025, doi:10.1016/j.aim.2024.110055.
short: H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
corr_author: '1'
date_created: 2024-12-08T23:01:54Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-04-15T07:16:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.aim.2024.110055
ec_funded: 1
external_id:
arxiv:
- '2310.18238'
isi:
- '001370682500001'
fulldoi: https://doi.org/10.1016/j.aim.2024.110055
intvolume: ' 461'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2310.18238
month: '02'
oa: 1
oa_version: Preprint
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: Advances in Mathematics
publication_identifier:
eissn:
- 1090-2082
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Order-2 Delaunay triangulations optimize angles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 461
year: '2025'
...
---
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
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:
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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
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doi: 10.48550/ARXIV.2501.05315
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month: '03'
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publication: arXiv
publication_status: draft
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title: Counting equilibria of the electrostatic potential
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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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has_accepted_license: '1'
intvolume: ' 73'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 490-499
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
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call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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supplementarymaterial: no
title: Average and expected distortion of Voronoi paths and scapes
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...