---
OA_place: repository
_id: '18673'
abstract:
- lang: eng
text: "Motivated by applications to crystalline materials, we generalize the merge
tree and the related barcode of a filtered complex to the periodic setting in
Euclidean space. They are invariant under isometries, changing bases, and indeed
changing lattices. In addition, we prove stability under perturbations and provide
an algorithm that under mild geometric conditions typically satisfied by crystalline
materials takes O((n+m)logn) time, in which n and m are the numbers of vertices
and edges in the quotient complex, respectively.\r\n"
acknowledgement: "Both authors are partially supported by the European Research Council
(ERC) Horizon 2020 project\r\n‘Alpha Shape Theory Extended’, grant no. 788183. The
first author is also partially supported by the DFG\r\nCollaborative Research Center
TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund\r\n(FWF),
grant no. I 02979-N35."
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: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
citation:
ama: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv.
doi:10.48550/arXiv.2408.16575
apa: Edelsbrunner, H., & Heiss, T. (n.d.). Merge trees of periodic filtrations.
arXiv. https://doi.org/10.48550/arXiv.2408.16575
chicago: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.16575.
ieee: H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” arXiv.
.
ista: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, 10.48550/arXiv.2408.16575.
mla: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.”
ArXiv, doi:10.48550/arXiv.2408.16575.
short: H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-12-18T14:06:57Z
date_published: 2024-08-29T00:00:00Z
date_updated: 2026-04-07T12:54:09Z
day: '29'
department:
- _id: HeEd
doi: 10.48550/arXiv.2408.16575
ec_funded: 1
external_id:
arxiv:
- '2408.16575'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2408.16575
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
status: public
title: Merge trees of periodic filtrations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
_id: '18981'
abstract:
- lang: eng
text: We establish several results combining discrete Morse theory and microlocal
sheaf theory in the setting of finite posets and simplicial complexes. Our primary
tool is a computationally tractable description of the bounded derived category
of sheaves on a poset with the Alexandrov topology. We prove that each bounded
complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes)
minimal injective resolution, and we provide algorithms for computing minimal
injective resolution of an injective complex, as well as several useful functors
between derived categories of sheaves. For the constant sheaf on a simplicial
complex, we give asymptotically tight bounds on the complexity of computing the
minimal injective resolution using those algorithms. Our main result is a novel
definition of the discrete microsupport of a bounded complex of sheaves on a finite
poset. We detail several foundational properties of the discrete microsupport,
as well as a microlocal generalization of the discrete homological Morse theorem
and Morse inequalities.
acknowledgement: "This project has received funding from the European Research Council
(ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize,\r\nAustrian Science Fund (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), grant no. I 02979-N35."
article_processing_charge: No
arxiv: 1
author:
- first_name: Adam
full_name: Brown, Adam
last_name: Brown
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
citation:
ama: Brown A, Draganov O. Discrete microlocal Morse theory. arXiv. doi:10.48550/arXiv.2209.14993
apa: Brown, A., & Draganov, O. (n.d.). Discrete microlocal Morse theory. arXiv.
https://doi.org/10.48550/arXiv.2209.14993
chicago: Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2209.14993.
ieee: A. Brown and O. Draganov, “Discrete microlocal Morse theory,” arXiv.
.
ista: Brown A, Draganov O. Discrete microlocal Morse theory. arXiv, 10.48550/arXiv.2209.14993.
mla: Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” ArXiv,
doi:10.48550/arXiv.2209.14993.
short: A. Brown, O. Draganov, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-01-31T17:03:04Z
date_published: 2024-06-09T00:00:00Z
date_updated: 2026-04-07T11:47:29Z
day: '09'
department:
- _id: HeEd
doi: 10.48550/arXiv.2209.14993
ec_funded: 1
external_id:
arxiv:
- '2209.14993'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2209.14993
month: '06'
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: arXiv
publication_status: draft
related_material:
record:
- id: '20323'
relation: later_version
status: public
- id: '18979'
relation: dissertation_contains
status: public
status: public
title: Discrete microlocal Morse theory
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: publisher
OA_type: gold
_id: '18998'
abstract:
- lang: eng
text: Word embeddings represent language vocabularies as clouds of d-dimensional
points. We investigate how information is conveyed by the general shape of these
clouds, instead of representing the semantic meaning of each token. Specifically,
we use the notion of persistent homology from topological data analysis (TDA)
to measure the distances between language pairs from the shape of their unlabeled
embeddings. These distances quantify the degree of non-isometry of the embeddings.
To distinguish whether these differences are random training errors or capture
real information about the languages, we use the computed distance matrices to
construct language phylogenetic trees over 81 Indo-European languages. Careful
evaluation shows that our reconstructed trees exhibit strong and statistically-significant
similarities to the reference.
article_processing_charge: No
arxiv: 1
author:
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Steven
full_name: Skiena, Steven
last_name: Skiena
citation:
ama: 'Draganov O, Skiena S. The shape of word embeddings: Quantifying non-isometry
with topological data analysis. In: Findings of the Association for Computational
Linguistics: EMNLP 2024. Association for Computational Linguistics; 2024:12080-12099.
doi:10.18653/v1/2024.findings-emnlp.705'
apa: 'Draganov, O., & Skiena, S. (2024). The shape of word embeddings: Quantifying
non-isometry with topological data analysis. In Findings of the Association
for Computational Linguistics: EMNLP 2024 (pp. 12080–12099). Miami, FL, United
States: Association for Computational Linguistics. https://doi.org/10.18653/v1/2024.findings-emnlp.705'
chicago: 'Draganov, Ondrej, and Steven Skiena. “The Shape of Word Embeddings: Quantifying
Non-Isometry with Topological Data Analysis.” In Findings of the Association
for Computational Linguistics: EMNLP 2024, 12080–99. Association for Computational
Linguistics, 2024. https://doi.org/10.18653/v1/2024.findings-emnlp.705.'
ieee: 'O. Draganov and S. Skiena, “The shape of word embeddings: Quantifying non-isometry
with topological data analysis,” in Findings of the Association for Computational
Linguistics: EMNLP 2024, Miami, FL, United States, 2024, pp. 12080–12099.'
ista: 'Draganov O, Skiena S. 2024. The shape of word embeddings: Quantifying non-isometry
with topological data analysis. Findings of the Association for Computational
Linguistics: EMNLP 2024. EMNLP: Conference on Empirical Methods in Natural Language
Processing, 12080–12099.'
mla: 'Draganov, Ondrej, and Steven Skiena. “The Shape of Word Embeddings: Quantifying
Non-Isometry with Topological Data Analysis.” Findings of the Association for
Computational Linguistics: EMNLP 2024, Association for Computational Linguistics,
2024, pp. 12080–99, doi:10.18653/v1/2024.findings-emnlp.705.'
short: 'O. Draganov, S. Skiena, in:, Findings of the Association for Computational
Linguistics: EMNLP 2024, Association for Computational Linguistics, 2024, pp.
12080–12099.'
conference:
end_date: 2024-11-16
location: Miami, FL, United States
name: 'EMNLP: Conference on Empirical Methods in Natural Language Processing'
start_date: 2024-11-12
corr_author: '1'
date_created: 2025-02-04T16:19:28Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-02-10T08:21:37Z
day: '01'
ddc:
- '500'
department:
- _id: GradSch
- _id: HeEd
doi: 10.18653/v1/2024.findings-emnlp.705
external_id:
arxiv:
- '2404.00500'
file:
- access_level: open_access
checksum: f4416a5962194f0181ab0dc7f9ef93c0
content_type: application/pdf
creator: dernst
date_created: 2025-02-10T08:20:34Z
date_updated: 2025-02-10T08:20:34Z
file_id: '19016'
file_name: 2024_EMNLP_Draganov.pdf
file_size: 1312638
relation: main_file
success: 1
file_date_updated: 2025-02-10T08:20:34Z
has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 12080-12099
publication: 'Findings of the Association for Computational Linguistics: EMNLP 2024'
publication_status: published
publisher: Association for Computational Linguistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The shape of word embeddings: Quantifying non-isometry with topological data
analysis'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '18999'
abstract:
- lang: eng
text: Exploring the shape of point configurations has been a key driver in the evolution
of TDA (short for topological data analysis) since its infancy. This survey illustrates
the recent efforts to broaden these ideas to model spatial interactions among
multiple configurations, each distinguished by a color. It describes advances
in this area and prepares the ground for further exploration by mentioning unresolved
questions and promising research avenues while focusing on the overlap with discrete
geometry.
article_number: '2406.04102'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
topological data analysis. arXiv. doi:10.48550/ARXIV.2406.04102
apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (n.d.). Chromatic topological data analysis. arXiv. https://doi.org/10.48550/ARXIV.2406.04102
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “Chromatic Topological Data Analysis.” ArXiv, n.d.
https://doi.org/10.48550/ARXIV.2406.04102.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“Chromatic topological data analysis,” arXiv. .
ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
topological data analysis. arXiv, 2406.04102.
mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Topological Data Analysis.”
ArXiv, 2406.04102, doi:10.48550/ARXIV.2406.04102.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv
(n.d.).
corr_author: '1'
date_created: 2025-02-04T16:21:21Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2025-02-10T08:14:27Z
day: '06'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
doi: 10.48550/ARXIV.2406.04102
external_id:
arxiv:
- '2406.04102'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2406.04102
month: '06'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Chromatic topological data analysis
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '17891'
abstract:
- lang: eng
text: "Abstract\r\nMethods used in topological data analysis naturally capture higher-order
interactions in point cloud data embedded in a metric space. This methodology
was recently extended to data living in an information space, by which we mean
a space measured with an information theoretical distance. One such setting is
a finite collection of discrete probability distributions embedded in the probability
simplex measured with the relative entropy (Kullback–Leibler divergence). More
generally, one can work with a Bregman divergence parameterized by a different
notion of entropy. While theoretical algorithms exist for this setup, there is
a paucity of implementations for exploring and comparing geometric-topological
properties of various information spaces. The interest of this work is therefore
twofold. First, we propose the first robust algorithms and software for geometric
and topological data analysis in information space. Perhaps surprisingly, despite
working with Bregman divergences, our design reuses robust libraries for the Euclidean
case. Second, using the new software, we take the first steps towards understanding
the geometric-topological structure of these spaces. In particular, we compare
them with the more familiar spaces equipped with the Euclidean and Fisher metrics."
acknowledgement: We thank Anton Nikitenko for first observing that the Wrap complex
can be characterized as stated in Claim (ii) of the Wrap Complex Lemma, and Ondrej
Draganov for correcting a critical mistake in one of our formulas in Section 2.
article_number: '637'
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Edelsbrunner H, Ölsböck K, Wagner H. Understanding higher-order interactions
in information space. Entropy. 2024;26(8). doi:10.3390/e26080637
apa: Edelsbrunner, H., Ölsböck, K., & Wagner, H. (2024). Understanding higher-order
interactions in information space. Entropy. MDPI. https://doi.org/10.3390/e26080637
chicago: Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. “Understanding
Higher-Order Interactions in Information Space.” Entropy. MDPI, 2024. https://doi.org/10.3390/e26080637.
ieee: H. Edelsbrunner, K. Ölsböck, and H. Wagner, “Understanding higher-order interactions
in information space,” Entropy, vol. 26, no. 8. MDPI, 2024.
ista: Edelsbrunner H, Ölsböck K, Wagner H. 2024. Understanding higher-order interactions
in information space. Entropy. 26(8), 637.
mla: Edelsbrunner, Herbert, et al. “Understanding Higher-Order Interactions in Information
Space.” Entropy, vol. 26, no. 8, 637, MDPI, 2024, doi:10.3390/e26080637.
short: H. Edelsbrunner, K. Ölsböck, H. Wagner, Entropy 26 (2024).
date_created: 2024-09-08T22:01:11Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T09:13:44Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.3390/e26080637
external_id:
isi:
- '001305543500001'
pmid:
- '39202107'
file:
- access_level: open_access
checksum: 624a9e2c5b49d6c38b88b0f675467ba3
content_type: application/pdf
creator: dernst
date_created: 2024-09-09T09:01:12Z
date_updated: 2024-09-09T09:01:12Z
file_id: '17948'
file_name: 2024_Entropy_Edelsbrunner.pdf
file_size: 8025139
relation: main_file
success: 1
file_date_updated: 2024-09-09T09:01:12Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
pmid: 1
publication: Entropy
publication_identifier:
eissn:
- 1099-4300
publication_status: published
publisher: MDPI
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/
scopus_import: '1'
status: public
title: Understanding higher-order interactions in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 26
year: '2024'
...
---
_id: '18097'
abstract:
- lang: eng
text: "In our companion paper \"Tight bounds for the learning of homotopy à la Niyogi,
Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds\"
we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on
a sample P of an input shape \U0001D4AE (either manifold or general set with positive
reach) such that one can infer the homotopy of \U0001D4AE from the union of balls
with some radius centred at P, both in Euclidean space and in a Riemannian manifold
of bounded curvature. The construction showing the optimality of the bounds is
not straightforward. The purpose of this video is to visualize and thus elucidate
said construction in the Euclidean setting."
acknowledgement: "This research has been supported by the European Research Council
(ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF),
grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant No. I02979-N35. Mathijs Wintraecken: Supported by the
European Union’s Horizon 2020 research and innovation programme under the Marie
Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant
No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.\r\nWe
thank Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Mariette Yvinec for discussion."
alternative_title:
- LIPIcs
article_number: '87'
article_processing_charge: Yes
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Ishika
full_name: Ghosh, Ishika
id: ee449b28-344d-11ef-a6d5-9ca430e9e9ff
last_name: Ghosh
- first_name: Andre
full_name: Lieutier, Andre
last_name: Lieutier
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Attali D, Kourimska H, Fillmore CD, et al. The ultimate frontier: An optimality
construction for homotopy inference (media exposition). In: 40th International
Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.87'
apa: 'Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson,
E. R., & Wintraecken, M. (2024). The ultimate frontier: An optimality construction
for homotopy inference (media exposition). In 40th International Symposium
on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.87'
chicago: 'Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh,
Andre Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “The Ultimate
Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).”
In 40th International Symposium on Computational Geometry, Vol. 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.87.'
ieee: 'D. Attali et al., “The ultimate frontier: An optimality construction
for homotopy inference (media exposition),” in 40th International Symposium
on Computational Geometry, Athens, Greece, 2024, vol. 293.'
ista: 'Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken
M. 2024. The ultimate frontier: An optimality construction for homotopy inference
(media exposition). 40th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 293, 87.'
mla: 'Attali, Dominique, et al. “The Ultimate Frontier: An Optimality Construction
for Homotopy Inference (Media Exposition).” 40th International Symposium on
Computational Geometry, vol. 293, 87, Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.87.'
short: D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson,
M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
corr_author: '1'
date_created: 2024-09-19T10:29:48Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2025-04-15T07:16:58Z
day: '06'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.87
ec_funded: 1
file:
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checksum: 9355c2e60b8ec285e1b22719c5b73f1a
content_type: application/pdf
creator: dernst
date_created: 2024-09-19T10:30:37Z
date_updated: 2024-09-19T10:30:37Z
file_id: '18098'
file_name: 2024_LIPICs_Attali.pdf
file_size: 3507177
relation: main_file
success: 1
file_date_updated: 2024-09-19T10:30:37Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: 'The ultimate frontier: An optimality construction for homotopy inference (media
exposition)'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...
---
OA_place: publisher
_id: '18667'
abstract:
- lang: eng
text: "Many chemical and physical properties of materials are determined by the
material’s shape,\r\nfor example the size of its pores and the width of its tunnels.
This makes materials science\r\na prime application area for geometrical and topological
methods. Nevertheless many\r\nmethods in topological data analysis have not been
satisfyingly extended to the needs of\r\nmaterials science. This thesis provides
new methods and new mathematical theorems\r\ntargeted at those specific needs
by answering four different research questions. While the\r\nmotivation for each
of the research questions arises from materials science, the methods\r\nare versatile
and can be applied in different areas as well. \r\n\r\nThe first research question
is concerned with image data, for example a three-dimensional\r\ncomputed tomography
(CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies
for digital images and depending on the application either of them might be\r\nrequired.
However, software for computing the topological data analysis method persistence\r\nhomology,
usually supports only one of the two topologies. We answer the question how to\r\ncompute
persistent homology of an image with respect to one of the two topologies using\r\nsoftware
that is intended for the other topology. \r\n\r\nThe second research question
is concerned with image data as well, and asks how much\r\nof the topological
information of an image is lost when the resolution is coarsened. As\r\ncomputer
tomography scanners are more expensive the higher the resolution, it is an\r\nimportant
question in materials science to know which resolution is enough to get satisfying\r\npersistent
homology. We give theoretical bounds on the information loss based on different\r\ngeometrical
properties of the object to be scanned. In addition, we conduct experiments on\r\nsand
and stone CT image data. \r\n\r\nThe third research question is motivated by comparing
crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically,
crystalline materials are either modeled by\r\nunmanageable infinite periodic
point sets, or by one of their fundamental domains, which is\r\nunstable under
perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate
properties such that comparing the crystals can be eased by comparing the\r\nfingerprints
instead. We define the density fingerprint and prove the necessary properties.
\r\n\r\nThe fourth research question is motivated by studying the hole-structure
or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials.
A common way to deal\r\nwith periodicity is to take a fundamental domain and identify
opposite boundaries to form a\r\ntorus. However, computing persistent homology
or merge trees on that torus loses some\r\nof the information materials scientists
are interested in and is additionally not stable under\r\ncertain noise. We therefore
decorate the merge tree stemming from the torus with additional\r\ninformation
describing the density and growth rate of the periodic copies of a component\r\nwithin
a growing spherical window. We prove all desired properties, like stability and
efficient\r\ncomputability."
acknowledgement: "I was supported by the European Research Council (ERC) Horizon 2020
project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship.
In addition,\r\nI am very thankful for having been able to attend the second Workshop
for Women in\r\nComputational Topology in July 2019, funded by the Mathematical
Sciences Institute at\r\nANU, the US National Science Foundation through the award
CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association
for Women in Mathematics. Two of the\r\nprojects presented in this thesis started
there. One of them reached completion thanks to\r\nfunding from the MSRI Summer
Research in Mathematics program awarded to me and my\r\ncollaborators in 2020."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
citation:
ama: Heiss T. New methods for applying topological data analysis to materials science.
2024. doi:10.15479/at:ista:18667
apa: Heiss, T. (2024). New methods for applying topological data analysis to
materials science. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18667
chicago: Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials
Science.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18667.
ieee: T. Heiss, “New methods for applying topological data analysis to materials
science,” Institute of Science and Technology Austria, 2024.
ista: Heiss T. 2024. New methods for applying topological data analysis to materials
science. Institute of Science and Technology Austria.
mla: Heiss, Teresa. New Methods for Applying Topological Data Analysis to Materials
Science. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18667.
short: T. Heiss, New Methods for Applying Topological Data Analysis to Materials
Science, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-12-17T16:17:55Z
date_published: 2024-12-17T00:00:00Z
date_updated: 2026-07-07T13:43:27Z
day: '17'
ddc:
- '514'
- '516'
- '004'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:18667
ec_funded: 1
file:
- access_level: open_access
checksum: 247bb057aed2fba1cd4711917aaa2d77
content_type: application/pdf
creator: theiss
date_created: 2024-12-19T10:24:46Z
date_updated: 2024-12-19T10:24:46Z
file_id: '18686'
file_name: Teresa_Heiss_PhD_Thesis_final.pdf
file_size: 7752253
relation: main_file
success: 1
- access_level: closed
checksum: 9648b45c07a008ee11a07f99856a139d
content_type: application/zip
creator: theiss
date_created: 2024-12-19T10:24:50Z
date_updated: 2024-12-19T10:24:50Z
file_id: '18687'
file_name: PhD_Thesis.zip
file_size: 17197731
relation: source_file
file_date_updated: 2024-12-19T10:24:50Z
has_accepted_license: '1'
keyword:
- persistent homology
- topological data analysis
- periodic
- crystalline materials
- images
- fingerprint
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: '111'
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication_identifier:
isbn:
- 978-3-99078-052-7
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10828'
relation: part_of_dissertation
status: public
- id: '11440'
relation: part_of_dissertation
status: public
- id: '18673'
relation: part_of_dissertation
status: public
- id: '9345'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: New methods for applying topological data analysis to materials science
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: repository
_id: '15091'
abstract:
- lang: eng
text: "Motivated by applications in the medical sciences, we study finite chromatic\r\nsets
in Euclidean space from a topological perspective. Based on the persistent\r\nhomology
for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers
that describe the geometric micro- and macro-structure\r\nof how the color classes
mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay
and alpha complexes, and code that does these\r\ncomputations is provided."
article_number: '2212.03128'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
alpha complexes. arXiv. doi:10.48550/arXiv.2212.03128
apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (n.d.). Chromatic alpha complexes. arXiv. https://doi.org/10.48550/arXiv.2212.03128
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “Chromatic Alpha Complexes.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2212.03128.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“Chromatic alpha complexes,” arXiv. .
ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
alpha complexes. arXiv, 2212.03128.
mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” ArXiv,
2212.03128, doi:10.48550/arXiv.2212.03128.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv
(n.d.).
corr_author: '1'
date_created: 2024-03-08T10:13:59Z
date_published: 2024-02-07T00:00:00Z
date_updated: 2026-07-23T12:03:56Z
day: '07'
department:
- _id: HeEd
doi: 10.48550/arXiv.2212.03128
external_id:
arxiv:
- '2212.03128'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2212.03128
month: '02'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18979'
relation: dissertation_contains
status: public
- id: '15094'
relation: dissertation_contains
status: public
- id: '20585'
relation: later_version
status: public
status: public
title: Chromatic alpha 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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
_id: '17146'
abstract:
- lang: eng
text: The Upper Bound Theorem for convex polytopes implies that the p-th Betti number
of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p
= O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions,
which prove that this upper bound is asymptotically tight. For example, we describe
a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number
of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of
the Čech complex at the other radius is n². In particular, there is an arrangement
of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers
a long-standing open question in computational geometry.
acknowledgement: "The first author is supported by the European Research Council (ERC),
grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant no. {I 02979-N35.} The second author is supported by the
European Research Council (ERC), grant \"GeoScape\" and by the Hungarian Science
Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein
Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.\r\nThe authors thank Matt
Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart
for early discussions on the linked circles construction in three dimensions, and
Gábor Tardos for helpful remarks and suggestions."
alternative_title:
- LIPIcs
article_number: '53'
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: 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. In: 40th
International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.53'
apa: 'Edelsbrunner, H., & Pach, J. (2024). Maximum Betti numbers of Čech complexes.
In 40th International Symposium on Computational Geometry (Vol. 293). Athens,
Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.53'
chicago: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
In 40th International Symposium on Computational Geometry, Vol. 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.53.
ieee: H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” in
40th International Symposium on Computational Geometry, Athens, Greece,
2024, vol. 293.
ista: 'Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th
International Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, LIPIcs, vol. 293, 53.'
mla: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.”
40th International Symposium on Computational Geometry, vol. 293, 53, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.53.
short: H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-07-27T08:15:58Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.53
ec_funded: 1
external_id:
arxiv:
- '2310.14801'
file:
- access_level: open_access
checksum: 5442d44fb89d77477a87668d6e61aac9
content_type: application/pdf
creator: dernst
date_created: 2024-06-17T08:46:33Z
date_updated: 2024-06-17T08:46:33Z
file_id: '17152'
file_name: 2024_LIPICS_Edelsbrunner.pdf
file_size: 766562
relation: main_file
success: 1
file_date_updated: 2024-06-17T08:46:33Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 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: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '20657'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Maximum Betti numbers of Čech complexes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...
---
_id: '12086'
abstract:
- lang: eng
text: We present a simple algorithm for computing higher-order Delaunay mosaics
that works in Euclidean spaces of any finite dimensions. The algorithm selects
the vertices of the order-k mosaic from incrementally constructed lower-order
mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box
to construct the order-k mosaic from its vertices. Beyond this black-box, the
algorithm uses only combinatorial operations, thus facilitating easy implementation.
We extend this algorithm to compute higher-order α-shapes and provide open-source
implementations. We present experimental results for properties of higher-order
Delaunay mosaics of random point sets.
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This
project has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme, Grant No. 788183,
from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and
from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics
and alpha shapes. Algorithmica. 2023;85:277-295. doi:10.1007/s00453-022-01027-6
apa: Edelsbrunner, H., & Osang, G. F. (2023). A simple algorithm for higher-order
Delaunay mosaics and alpha shapes. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-022-01027-6
chicago: Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order
Delaunay Mosaics and Alpha Shapes.” Algorithmica. Springer Nature, 2023.
https://doi.org/10.1007/s00453-022-01027-6.
ieee: H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay
mosaics and alpha shapes,” Algorithmica, vol. 85. Springer Nature, pp.
277–295, 2023.
ista: Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay
mosaics and alpha shapes. Algorithmica. 85, 277–295.
mla: Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order
Delaunay Mosaics and Alpha Shapes.” Algorithmica, vol. 85, Springer Nature,
2023, pp. 277–95, doi:10.1007/s00453-022-01027-6.
short: H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.
corr_author: '1'
date_created: 2022-09-11T22:01:57Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2025-04-23T08:46:48Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00453-022-01027-6
ec_funded: 1
external_id:
isi:
- '000846967100001'
pmid:
- '36687803'
file:
- access_level: open_access
checksum: 71685ca5121f4c837f40c3f8eb50c915
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T10:02:48Z
date_updated: 2023-01-20T10:02:48Z
file_id: '12322'
file_name: 2023_Algorithmica_Edelsbrunner.pdf
file_size: 911017
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success: 1
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has_accepted_license: '1'
intvolume: ' 85'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 277-295
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: Algorithmica
publication_identifier:
eissn:
- 1432-0541
issn:
- 0178-4617
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A simple algorithm for higher-order Delaunay mosaics and alpha shapes
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: 85
year: '2023'
...
---
_id: '12287'
abstract:
- lang: eng
text: We present criteria for establishing a triangulation of a manifold. Given
a manifold M, a simplicial complex A, and a map H from the underlying space of
A to M, our criteria are presented in local coordinate charts for M, and ensure
that H is a homeomorphism. These criteria do not require a differentiable structure,
or even an explicit metric on M. No Delaunay property of A is assumed. The result
provides a triangulation guarantee for algorithms that construct a simplicial
complex by working in local coordinate patches. Because the criteria are easily
verified in such a setting, they are expected to be of general use.
acknowledgement: "This work has been funded by the European Research Council under
the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations
of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan
Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh
was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by
the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken
also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian
Science Fund (FWF): M-3073. A part of the results described in this paper were presented
at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science
Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Ramsay
full_name: Dyer, Ramsay
last_name: Dyer
- first_name: Arijit
full_name: Ghosh, Arijit
last_name: Ghosh
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating
general manifolds. Discrete & Computational Geometry. 2023;69:156-191.
doi:10.1007/s00454-022-00431-7
apa: Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local
criteria for triangulating general manifolds. Discrete & Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7
chicago: Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken.
“Local Criteria for Triangulating General Manifolds.” Discrete & Computational
Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7.
ieee: J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for
triangulating general manifolds,” Discrete & Computational Geometry,
vol. 69. Springer Nature, pp. 156–191, 2023.
ista: Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating
general manifolds. Discrete & Computational Geometry. 69, 156–191.
mla: Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.”
Discrete & Computational Geometry, vol. 69, Springer Nature, 2023,
pp. 156–91, doi:10.1007/s00454-022-00431-7.
short: J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational
Geometry 69 (2023) 156–191.
corr_author: '1'
date_created: 2023-01-16T10:04:06Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2025-04-14T07:44:00Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-022-00431-7
ec_funded: 1
external_id:
isi:
- '000862193600001'
file:
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checksum: 46352e0ee71e460848f88685ca852681
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T11:01:10Z
date_updated: 2023-02-02T11:01:10Z
file_id: '12488'
file_name: 2023_DiscreteCompGeometry_Boissonnat.pdf
file_size: 582850
relation: main_file
success: 1
file_date_updated: 2023-02-02T11:01:10Z
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intvolume: ' 69'
isi: 1
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Theoretical Computer Science
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 156-191
project:
- _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: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local criteria for triangulating general manifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 69
year: '2023'
...
---
_id: '12544'
abstract:
- lang: eng
text: Geometry is crucial in our efforts to comprehend the structures and dynamics
of biomolecules. For example, volume, surface area, and integrated mean and Gaussian
curvature of the union of balls representing a molecule are used to quantify its
interactions with the water surrounding it in the morphometric implicit solvent
models. The Alpha Shape theory provides an accurate and reliable method for computing
these geometric measures. In this paper, we derive homogeneous formulas for the
expressions of these measures and their derivatives with respect to the atomic
coordinates, and we provide algorithms that implement them into a new software
package, AlphaMol. The only variables in these formulas are the interatomic distances,
making them insensitive to translations and rotations. AlphaMol includes a sequential
algorithm and a parallel algorithm. In the parallel version, we partition the
atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree
algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented
by a buffer zone to account for atoms whose ball representations may partially
cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up
compared to an independent serial implementation when using 32 processors. For
instance, it takes 31 s to compute the geometric measures and derivatives of each
atom in a viral capsid with more than 26 million atoms on 32 Intel processors
running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant
computations, which ultimately limit the impact of using multiple processors.
AlphaMol is available as an OpenSource software.
acknowledgement: "P.K. acknowledges support from the University of California Multicampus
Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant
No.1760485). H.E. acknowledges support from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program, 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.\r\nOpen Access
is funded by the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Patrice
full_name: Koehl, Patrice
last_name: Koehl
- 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
citation:
ama: Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean,
and Gaussian curvatures of molecules and their derivatives. Journal of Chemical
Information and Modeling. 2023;63(3):973-985. doi:10.1021/acs.jcim.2c01346
apa: Koehl, P., Akopyan, A., & Edelsbrunner, H. (2023). Computing the volume,
surface area, mean, and Gaussian curvatures of molecules and their derivatives.
Journal of Chemical Information and Modeling. American Chemical Society.
https://doi.org/10.1021/acs.jcim.2c01346
chicago: Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the
Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.”
Journal of Chemical Information and Modeling. American Chemical Society,
2023. https://doi.org/10.1021/acs.jcim.2c01346.
ieee: P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface
area, mean, and Gaussian curvatures of molecules and their derivatives,” Journal
of Chemical Information and Modeling, vol. 63, no. 3. American Chemical Society,
pp. 973–985, 2023.
ista: Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area,
mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical
Information and Modeling. 63(3), 973–985.
mla: Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian
Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information
and Modeling, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85,
doi:10.1021/acs.jcim.2c01346.
short: P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and
Modeling 63 (2023) 973–985.
corr_author: '1'
date_created: 2023-02-12T23:00:59Z
date_published: 2023-02-13T00:00:00Z
date_updated: 2025-04-15T07:16:52Z
day: '13'
ddc:
- '510'
- '540'
department:
- _id: HeEd
doi: 10.1021/acs.jcim.2c01346
ec_funded: 1
external_id:
isi:
- '000920370700001'
pmid:
- '36638318'
file:
- access_level: open_access
checksum: 7d20562269edff1e31b9d6019d4983b0
content_type: application/pdf
creator: dernst
date_created: 2023-08-16T12:21:13Z
date_updated: 2023-08-16T12:21:13Z
file_id: '14070'
file_name: 2023_JCIM_Koehl.pdf
file_size: 8069223
relation: main_file
success: 1
file_date_updated: 2023-08-16T12:21:13Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 973-985
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: Journal of Chemical Information and Modeling
publication_identifier:
eissn:
- 1549-960X
issn:
- 1549-9596
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing the volume, surface area, mean, and Gaussian curvatures of molecules
and their derivatives
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: 63
year: '2023'
...
---
_id: '12548'
abstract:
- lang: eng
text: The limited exchange between human communities is a key factor in preventing
the spread of COVID-19. This paper introduces a digital framework that combines
an integration of real mobility data at the country scale with a series of modeling
techniques and visual capabilities that highlight mobility patterns before and
during the pandemic. The findings not only significantly exhibit mobility trends
and different degrees of similarities at regional and local levels but also provide
potential insight into the emergence of a pandemic on human behavior patterns
and their likely socio-economic impacts.
article_number: '00093'
article_processing_charge: No
author:
- first_name: Mohammad
full_name: Forghani, Mohammad
last_name: Forghani
- first_name: Christophe
full_name: Claramunt, Christophe
last_name: Claramunt
- first_name: Farid
full_name: Karimipour, Farid
id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425
last_name: Karimipour
orcid: 0000-0001-6746-4174
- first_name: Georg
full_name: Heiler, Georg
last_name: Heiler
citation:
ama: 'Forghani M, Claramunt C, Karimipour F, Heiler G. Visual analytics of mobility
network changes observed using mobile phone data during COVID-19 pandemic. In:
2022 IEEE International Conference on Data Mining Workshops. Institute
of Electrical and Electronics Engineers; 2023. doi:10.1109/icdmw58026.2022.00093'
apa: 'Forghani, M., Claramunt, C., Karimipour, F., & Heiler, G. (2023). Visual
analytics of mobility network changes observed using mobile phone data during
COVID-19 pandemic. In 2022 IEEE International Conference on Data Mining Workshops.
Orlando, FL, United States: Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/icdmw58026.2022.00093'
chicago: Forghani, Mohammad, Christophe Claramunt, Farid Karimipour, and Georg Heiler.
“Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data
during COVID-19 Pandemic.” In 2022 IEEE International Conference on Data Mining
Workshops. Institute of Electrical and Electronics Engineers, 2023. https://doi.org/10.1109/icdmw58026.2022.00093.
ieee: M. Forghani, C. Claramunt, F. Karimipour, and G. Heiler, “Visual analytics
of mobility network changes observed using mobile phone data during COVID-19 pandemic,”
in 2022 IEEE International Conference on Data Mining Workshops, Orlando,
FL, United States, 2023.
ista: 'Forghani M, Claramunt C, Karimipour F, Heiler G. 2023. Visual analytics of
mobility network changes observed using mobile phone data during COVID-19 pandemic.
2022 IEEE International Conference on Data Mining Workshops. ICDMW: Conference
on Data Mining Workshops, 00093.'
mla: Forghani, Mohammad, et al. “Visual Analytics of Mobility Network Changes Observed
Using Mobile Phone Data during COVID-19 Pandemic.” 2022 IEEE International
Conference on Data Mining Workshops, 00093, Institute of Electrical and Electronics
Engineers, 2023, doi:10.1109/icdmw58026.2022.00093.
short: M. Forghani, C. Claramunt, F. Karimipour, G. Heiler, in:, 2022 IEEE International
Conference on Data Mining Workshops, Institute of Electrical and Electronics Engineers,
2023.
conference:
end_date: 2022-12-01
location: Orlando, FL, United States
name: 'ICDMW: Conference on Data Mining Workshops'
start_date: 2022-11-28
date_created: 2023-02-14T07:56:21Z
date_published: 2023-02-08T00:00:00Z
date_updated: 2024-10-21T06:01:25Z
day: '08'
ddc:
- '600'
department:
- _id: HeEd
doi: 10.1109/icdmw58026.2022.00093
external_id:
isi:
- '000971492200145'
file:
- access_level: open_access
checksum: c253bee25e6dfe484f96662daa119cb6
content_type: application/pdf
creator: fkarimip
date_created: 2023-02-14T07:58:26Z
date_updated: 2023-02-14T07:58:26Z
file_id: '12549'
file_name: Visual Analysis_Mobility_COVID19 - SocDM2022.pdf
file_size: 1183339
relation: main_file
success: 1
file_date_updated: 2023-02-14T07:58:26Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Submitted Version
publication: 2022 IEEE International Conference on Data Mining Workshops
publication_identifier:
eisbn:
- '9798350346091'
eissn:
- 2375-9259
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visual analytics of mobility network changes observed using mobile phone data
during COVID-19 pandemic
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2023'
...
---
_id: '12709'
abstract:
- lang: eng
text: Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within
distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter
family of spaces that grow larger when r increases or k decreases, called the
multicover bifiltration. Motivated by the problem of computing the homology of
this bifiltration, we introduce two closely related combinatorial bifiltrations,
one polyhedral and the other simplicial, which are both topologically equivalent
to the multicover bifiltration and far smaller than a Čech-based model considered
in prior work of Sheehy. Our polyhedral construction is a bifiltration of the
rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using
a variant of an algorithm given by these authors as well. Using an implementation
for dimension 2 and 3, we provide experimental results. Our simplicial construction
is useful for understanding the polyhedral construction and proving its correctness.
acknowledgement: We thank the anonymous reviewers for many helpful comments and suggestions,
which led to substantial improvements of the paper. The first two authors were supported
by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first
author was partly supported by an Austrian Marshall Plan Scholarship, and by the
Brummer & Partners MathDataLab. A conference version of this paper was presented
at the 37th International Symposium on Computational Geometry (SoCG 2021). Open
access funding provided by the Royal Institute of Technology.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: René
full_name: Corbet, René
last_name: Corbet
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Michael
full_name: Lesnick, Michael
last_name: Lesnick
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration.
Discrete and Computational Geometry. 2023;70:376-405. doi:10.1007/s00454-022-00476-8
apa: Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2023). Computing the
multicover bifiltration. Discrete and Computational Geometry. Springer
Nature. https://doi.org/10.1007/s00454-022-00476-8
chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing
the Multicover Bifiltration.” Discrete and Computational Geometry. Springer
Nature, 2023. https://doi.org/10.1007/s00454-022-00476-8.
ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover
bifiltration,” Discrete and Computational Geometry, vol. 70. Springer Nature,
pp. 376–405, 2023.
ista: Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration.
Discrete and Computational Geometry. 70, 376–405.
mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and
Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8.
short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational
Geometry 70 (2023) 376–405.
date_created: 2023-03-05T23:01:06Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2025-07-10T12:01:57Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-022-00476-8
external_id:
arxiv:
- '2103.07823'
isi:
- '000936496800001'
pmid:
- '37581017'
file:
- access_level: open_access
checksum: 71ce7e59f7ee4620acc704fecca620c2
content_type: application/pdf
creator: cchlebak
date_created: 2023-03-07T14:40:14Z
date_updated: 2023-03-07T14:40:14Z
file_id: '12715'
file_name: 2023_DisCompGeo_Corbet.pdf
file_size: 1359323
relation: main_file
success: 1
file_date_updated: 2023-03-07T14:40:14Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 376-405
pmid: 1
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '9605'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Computing the multicover bifiltration
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: 70
year: '2023'
...
---
_id: '12763'
abstract:
- lang: eng
text: 'Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift
176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended
the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets
S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert
showed that sets of positive reach in Euclidean space and Riemannian manifolds
are very similar. In this paper we introduce a slight variant of Kleinjohann’s
and Bangert’s extension and quantify the similarity between sets of positive reach
in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we
bound the local feature size (a local version of the reach) of its lifting to
the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that
rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated
by the importance of the reach and local feature size to manifold learning, topological
inference, and triangulating manifolds and the fact that intrinsic approaches
circumvent the curse of dimensionality.'
acknowledgement: "We thank Eddie Aamari, David Cohen-Steiner, Isa Costantini, Fred
Chazal, Ramsay Dyer, André Lieutier, and Alef Sterk for discussion and Pierre Pansu
for encouragement. We further acknowledge the anonymous reviewers whose comments
helped improve the exposition.\r\nThe research leading to these results has received
funding from the European Research Council (ERC) under the European Union’s Seventh
Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic
Foundations of Geometry Understanding in Higher Dimensions). The first author is
further supported by the French government, through the 3IA Côte d’Azur Investments
in the Future project managed by the National Research Agency (ANR) with the reference
number ANR-19-P3IA-0002. The second author is supported by the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411 and the Austrian science fund (FWF) M-3073."
article_processing_charge: No
article_type: original
author:
- first_name: Jean Daniel
full_name: Boissonnat, Jean Daniel
last_name: Boissonnat
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat JD, Wintraecken M. The reach of subsets of manifolds. Journal
of Applied and Computational Topology. 2023;7:619-641. doi:10.1007/s41468-023-00116-x
apa: Boissonnat, J. D., & Wintraecken, M. (2023). The reach of subsets of manifolds.
Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00116-x
chicago: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets
of Manifolds.” Journal of Applied and Computational Topology. Springer
Nature, 2023. https://doi.org/10.1007/s41468-023-00116-x.
ieee: J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,”
Journal of Applied and Computational Topology, vol. 7. Springer Nature,
pp. 619–641, 2023.
ista: Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal
of Applied and Computational Topology. 7, 619–641.
mla: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of
Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer
Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x.
short: J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology
7 (2023) 619–641.
corr_author: '1'
date_created: 2023-03-26T22:01:08Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2025-04-14T07:44:01Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s41468-023-00116-x
ec_funded: 1
intvolume: ' 7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1
month: '09'
oa: 1
oa_version: Submitted Version
page: 619-641
project:
- _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: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The reach of subsets of manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2023'
...
---
_id: '12764'
abstract:
- lang: eng
text: We study a new discretization of the Gaussian curvature for polyhedral surfaces.
This discrete Gaussian curvature is defined on each conical singularity of a polyhedral
surface as the quotient of the angle defect and the area of the Voronoi cell corresponding
to the singularity. We divide polyhedral surfaces into discrete conformal classes
using a generalization of discrete conformal equivalence pioneered by Feng Luo.
We subsequently show that, in every discrete conformal class, there exists a polyhedral
surface with constant discrete Gaussian curvature. We also provide explicit examples
to demonstrate that this surface is in general not unique.
acknowledgement: Open access funding provided by the Austrian Science Fund (FWF).
This research was supported by the FWF grant, Project number I4245-N35, and by the
Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID
195170736 - TRR109.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
citation:
ama: Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and
Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2
apa: Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. Discrete
and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00484-2
chicago: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete
and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00484-2.
ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete
and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023.
ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete
and Computational Geometry. 70, 123–153.
mla: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete
and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 123–53, doi:10.1007/s00454-023-00484-2.
short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.
corr_author: '1'
date_created: 2023-03-26T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2025-04-23T08:59:15Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00484-2
external_id:
isi:
- '000948148000001'
pmid:
- '37292248'
file:
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checksum: cdbf90ba4a7ddcb190d37b9e9d4cb9d3
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T11:46:24Z
date_updated: 2023-10-04T11:46:24Z
file_id: '14396'
file_name: 2023_DiscreteGeometry_Kourimska.pdf
file_size: 1026683
relation: main_file
success: 1
file_date_updated: 2023-10-04T11:46:24Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 123-153
pmid: 1
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I04245
name: Algebraic Footprints of Geometric Features in Homology
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete yamabe problem for polyhedral surfaces
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: 70
year: '2023'
...
---
_id: '12833'
abstract:
- lang: eng
text: 'The input to the token swapping problem is a graph with vertices v1, v2,
. . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal
is to get token i to vertex vi for all i= 1, . . . , n using a minimum number
of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token
swapping on a tree, also known as “sorting with a transposition tree,” is not
known to be in P nor NP-complete. We present some partial results: 1. An optimum
swap sequence may need to perform a swap on a leaf vertex that has the correct
token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that
fixes happy leaves—as all known approximation algorithms for the problem do—has
approximation factor at least 4/3. Furthermore, the two best-known 2-approximation
algorithms have approximation factor exactly 2. 3. A generalized problem—weighted
coloured token swapping—is NP-complete on trees, but solvable in polynomial time
on paths and stars. In this version, tokens and vertices have colours, and colours
have weights. The goal is to get every token to a vertex of the same colour, and
the cost of a swap is the sum of the weights of the two tokens involved.'
acknowledgement: "This work was begun at the University of Waterloo and was partially
supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n"
article_number: '9'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ahmad
full_name: Biniaz, Ahmad
last_name: Biniaz
- first_name: Kshitij
full_name: Jain, Kshitij
last_name: Jain
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tillmann
full_name: Miltzow, Tillmann
last_name: Miltzow
- first_name: Debajyoti
full_name: Mondal, Debajyoti
last_name: Mondal
- first_name: Anurag Murty
full_name: Naredla, Anurag Murty
last_name: Naredla
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Alexi
full_name: Turcotte, Alexi
last_name: Turcotte
citation:
ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics
and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383
apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte,
A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer
Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383
chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow,
Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token
Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science.
EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383.
ieee: A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics
and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.
ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec
J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical
Computer Science. 24(2), 9.
mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and
Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383.
short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla,
J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science
24 (2023).
date_created: 2023-04-16T22:01:08Z
date_published: 2023-01-18T00:00:00Z
date_updated: 2025-01-20T14:05:09Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
- _id: HeEd
- _id: UlWa
doi: 10.46298/DMTCS.8383
external_id:
arxiv:
- '1903.06981'
file:
- access_level: open_access
checksum: 439102ea4f6e2aeefd7107dfb9ccf532
content_type: application/pdf
creator: dernst
date_created: 2023-04-17T08:10:28Z
date_updated: 2023-04-17T08:10:28Z
file_id: '12844'
file_name: 2022_DMTCS_Biniaz.pdf
file_size: 2072197
relation: main_file
success: 1
file_date_updated: 2023-04-17T08:10:28Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
publication: Discrete Mathematics and Theoretical Computer Science
publication_identifier:
eissn:
- 1365-8050
issn:
- 1462-7264
publication_status: published
publisher: EPI Sciences
quality_controlled: '1'
related_material:
record:
- id: '7950'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Token swapping on trees
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '13048'
abstract:
- lang: eng
text: In this paper we introduce a pruning of the medial axis called the (λ,α)-medial
axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff
sense under weak assumptions. More formally we prove that if K and K′ are close
in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as
metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is
1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff
distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲
dH(K,K′)1/2. These quantified stability results provide guarantees for practical
computations of medial axes from approximations. Moreover, they provide key ingredients
for studying the computability of the medial axis in the context of computable
analysis.
acknowledgement: "We are greatly indebted to Erin Chambers for posing a number of
questions that eventually led to this paper. We would also like to thank the other
organizers of the workshop on ‘Algorithms\r\nfor the medial axis’. We are also indebted
to Tatiana Ezubova for helping with the search for and translation of Russian literature.
The second author thanks all members of the Edelsbrunner and Datashape groups for
the atmosphere in which the research was conducted.\r\nThe research leading to these
results has received funding from the European Research Council (ERC) under the
European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement
No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions).
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."
article_processing_charge: No
arxiv: 1
author:
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of
the medial axis. In: Proceedings of the 55th Annual ACM Symposium on Theory
of Computing. Association for Computing Machinery; 2023:1768-1776. doi:10.1145/3564246.3585113'
apa: 'Lieutier, A., & Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff
stable subsets of the medial axis. In Proceedings of the 55th Annual ACM Symposium
on Theory of Computing (pp. 1768–1776). Orlando, FL, United States: Association
for Computing Machinery. https://doi.org/10.1145/3564246.3585113'
chicago: Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff
Stable Subsets of the Medial Axis.” In Proceedings of the 55th Annual ACM Symposium
on Theory of Computing, 1768–76. Association for Computing Machinery, 2023.
https://doi.org/10.1145/3564246.3585113.
ieee: A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets
of the medial axis,” in Proceedings of the 55th Annual ACM Symposium on Theory
of Computing, Orlando, FL, United States, 2023, pp. 1768–1776.
ista: 'Lieutier A, Wintraecken M. 2023. Hausdorff and Gromov-Hausdorff stable subsets
of the medial axis. Proceedings of the 55th Annual ACM Symposium on Theory of
Computing. STOC: Symposium on Theory of Computing, 1768–1776.'
mla: Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable
Subsets of the Medial Axis.” Proceedings of the 55th Annual ACM Symposium on
Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–76,
doi:10.1145/3564246.3585113.
short: A. Lieutier, M. Wintraecken, in:, Proceedings of the 55th Annual ACM Symposium
on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–1776.
conference:
end_date: 2023-06-23
location: Orlando, FL, United States
name: 'STOC: Symposium on Theory of Computing'
start_date: 2023-06-20
corr_author: '1'
date_created: 2023-05-22T08:02:02Z
date_published: 2023-06-02T00:00:00Z
date_updated: 2025-09-09T12:26:49Z
day: '02'
department:
- _id: HeEd
doi: 10.1145/3564246.3585113
ec_funded: 1
external_id:
arxiv:
- '2303.04014'
isi:
- '001064640700143'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2303.04014
month: '06'
oa: 1
oa_version: Preprint
page: 1768-1776
project:
- _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: Proceedings of the 55th Annual ACM Symposium on Theory of Computing
publication_identifier:
isbn:
- '9781450399135'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hausdorff and Gromov-Hausdorff stable subsets of the medial axis
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2023'
...
---
_id: '13134'
abstract:
- lang: eng
text: We propose a characterization of discrete analytical spheres, planes and lines
in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently
proposed alternative compact coordinate system, in which each integer triplet
addresses some voxel in the grid. We define spheres and planes through double
Diophantine inequalities and investigate their relevant topological features,
such as functionality or the interrelation between the thickness of the objects
and their connectivity and separation properties. We define lines as the intersection
of planes. The number of the planes (up to six) is equal to the number of the
pairs of faces of a BCC voxel that are parallel to the line.
acknowledgement: The first author has been partially supported by the Ministry of
Science, Technological Development and Innovation of the Republic of Serbia through
the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG
Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’,
Austrian Science Fund (FWF), grant no. I 02979-N35.
article_number: '109693'
article_processing_charge: No
article_type: original
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical
objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10).
doi:10.1016/j.patcog.2023.109693
apa: Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023).
Discrete analytical objects in the body-centered cubic grid. Pattern Recognition.
Elsevier. https://doi.org/10.1016/j.patcog.2023.109693
chicago: Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and
Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern
Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693.
ieee: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete
analytical objects in the body-centered cubic grid,” Pattern Recognition,
vol. 142, no. 10. Elsevier, 2023.
ista: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical
objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693.
mla: Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic
Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693.
short: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition
142 (2023).
corr_author: '1'
date_created: 2023-06-18T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2025-04-15T07:45:32Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.patcog.2023.109693
external_id:
isi:
- '001013526000001'
intvolume: ' 142'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa_version: None
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
publication: Pattern Recognition
publication_identifier:
issn:
- 0031-3203
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete analytical objects in the body-centered cubic grid
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 142
year: '2023'
...
---
_id: '13165'
abstract:
- lang: eng
text: "A graph G=(V, E) is called fully regular if for every independent set I c
V, the number of vertices in V\\I that are not connected to any element of I
depends only on the size of I. A linear ordering of the vertices of G is called
successive if for every i, the first i vertices induce a connected subgraph of
G. We give an explicit formula for the number of successive vertex orderings of
a fully regular graph.\r\nAs an application of our results, we give alternative
proofs of two theorems of Stanley and Gao & Peng, determining the number of linear
edge orderings of complete graphs and complete bipartite graphs, respectively,
with the property that the first i edges induce a connected subgraph.\r\nAs another
application, we give a simple product formula for the number of linear orderings
of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for
every i, the first i hyperedges induce a connected subgraph. We found similar
formulas for complete (non-partite) 3-uniform hypergraphs and in another closely
related case, but we managed to verify them only when the number of vertices is
small."
article_number: '105776'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Lixing
full_name: Fang, Lixing
last_name: Fang
- first_name: Hao
full_name: Huang, Hao
last_name: Huang
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Gábor
full_name: Tardos, Gábor
last_name: Tardos
- first_name: Junchi
full_name: Zuo, Junchi
last_name: Zuo
citation:
ama: Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully
regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10).
doi:10.1016/j.jcta.2023.105776
apa: Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive
vertex orderings of fully regular graphs. Journal of Combinatorial Theory.
Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776
chicago: Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive
Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory.
Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776.
ieee: L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings
of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol.
199, no. 10. Elsevier, 2023.
ista: Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings
of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776.
mla: Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.”
Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier,
2023, doi:10.1016/j.jcta.2023.105776.
short: L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory.
Series A 199 (2023).
corr_author: '1'
date_created: 2023-06-25T22:00:45Z
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