---
_id: '14888'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a probabilistic
FPT-approach in the number of popular faces.'
acknowledgement: 'This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].
A preliminary version of this work has been presented at the 38th European Workshop
on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper,
which includes appendices but is otherwise identical, is available as a technical
report [10].'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. In: 31st International Symposium on Graph Drawing and Network
Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2'
apa: 'De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
In 31st International Symposium on Graph Drawing and Network Visualization
(Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature.
https://doi.org/10.1007/978-3-031-49275-4_2'
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve
Arrangements.” In 31st International Symposium on Graph Drawing and Network
Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
in 31st International Symposium on Graph Drawing and Network Visualization,
Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.
ista: 'De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International
Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network
Visualization, LNCS, vol. 14466, 18–33.'
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
31st International Symposium on Graph Drawing and Network Visualization,
vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network
Visualization, Springer Nature, 2024, pp. 18–33.
conference:
end_date: 2023-09-22
location: Isola delle Femmine, Palermo, Italy
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2023-09-20
date_created: 2024-01-28T23:01:43Z
date_published: 2024-01-06T00:00:00Z
date_updated: 2025-09-04T11:52:35Z
day: '06'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-031-49275-4_2
external_id:
arxiv:
- '2202.12175'
isi:
- '001207942000002'
intvolume: ' 14466'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2202.12175
month: '01'
oa: 1
oa_version: Preprint
page: 18-33
publication: 31st International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031492747'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14466
year: '2024'
...
---
_id: '15012'
abstract:
- lang: eng
text: We solve a problem of Dujmović and Wood (2007) by showing that a complete
convex geometric graph on n vertices cannot be decomposed into fewer than n-1
star-forests, each consisting of noncrossing edges. This bound is clearly tight.
We also discuss similar questions for abstract graphs.
acknowledgement: János Pach’s Research partially supported by European Research Council
(ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH),
grant K-131529. Work by Morteza Saghafian is partially supported by the European
Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian
Science Fund (FWF), grant No. Z 342-N31.
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
- first_name: Patrick
full_name: Schnider, Patrick
last_name: Schnider
citation:
ama: 'Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests.
In: 31st International Symposium on Graph Drawing and Network Visualization.
Vol 14465. Springer Nature; 2024:339-346. doi:10.1007/978-3-031-49272-3_23'
apa: 'Pach, J., Saghafian, M., & Schnider, P. (2024). Decomposition of geometric
graphs into star-forests. In 31st International Symposium on Graph Drawing
and Network Visualization (Vol. 14465, pp. 339–346). Isola delle Femmine,
Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49272-3_23'
chicago: Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric
Graphs into Star-Forests.” In 31st International Symposium on Graph Drawing
and Network Visualization, 14465:339–46. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49272-3_23.
ieee: J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs
into star-forests,” in 31st International Symposium on Graph Drawing and Network
Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp.
339–346.
ista: 'Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs
into star-forests. 31st International Symposium on Graph Drawing and Network Visualization.
GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.'
mla: Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.”
31st International Symposium on Graph Drawing and Network Visualization,
vol. 14465, Springer Nature, 2024, pp. 339–46, doi:10.1007/978-3-031-49272-3_23.
short: J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on
Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.
conference:
end_date: 2023-09-22
location: Isola delle Femmine, Palermo, Italy
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2023-09-20
date_created: 2024-02-18T23:01:03Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2026-04-16T09:12:37Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-031-49272-3_23
ec_funded: 1
external_id:
arxiv:
- '2306.13201'
isi:
- '001207939600023'
intvolume: ' 14465'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.13201
month: '01'
oa: 1
oa_version: Preprint
page: 339-346
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
publication: 31st International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eisbn:
- '9783031492723'
eissn:
- 1611-3349
isbn:
- '9783031492716'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '21253'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Decomposition of geometric graphs into star-forests
type: conference
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 14465
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: 2026-04-07T12:58:47Z
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: '20585'
relation: later_version
status: public
- id: '18979'
relation: dissertation_contains
status: public
- id: '15094'
relation: dissertation_contains
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: '15093'
abstract:
- lang: eng
text: We present a dynamic data structure for maintaining the persistent homology
of a time series of real numbers. The data structure supports local operations,
including the insertion and deletion of an item and the cutting and concatenating
of lists, each in time O(log n + k), in which n counts the critical items and
k the changes in the augmented persistence diagram. To achieve this, we design
a tailor-made tree structure with an unconventional representation, referred to
as banana tree, which may be useful in its own right.
acknowledgement: The first and second authors are funded by the European Research Council under the
European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha
Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31,
and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The
third author received funding by the European Research Council under the European
Union’s Horizon 2020research and innovation programme, ERC grant no. 101019564, “The Design of Modern Fully Dynamic DataStructures
(MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize
with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant
no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. The
fourth author is funded by the Vienna Graduate School on Computational Optimization,
FWF project no. W1260-N35.
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: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Lara
full_name: Ost, Lara
last_name: Ost
citation:
ama: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining
the persistent homology of time series. In: Woodruff DP, ed. Proceedings of
the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society
for Industrial and Applied Mathematics; 2024:243-295. doi:10.1137/1.9781611977912.11'
apa: 'Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., & Ost, L.
(2024). Dynamically maintaining the persistent homology of time series. In D.
P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete
Algorithms (SODA) (pp. 243–295). Alexandria, VA, USA: Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.11'
chicago: Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika Henzinger,
and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.”
In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms
(SODA), edited by David P. Woodruff, 243–95. Society for Industrial and Applied
Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.11.
ieee: S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically
maintaining the persistent homology of time series,” in Proceedings of the
2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Alexandria,
VA, USA, 2024, pp. 243–295.
ista: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. 2024. Dynamically
maintaining the persistent homology of time series. Proceedings of the 2024 Annual
ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete
Algorithms, 243–295.'
mla: Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent
Homology of Time Series.” Proceedings of the 2024 Annual ACM-SIAM Symposium
on Discrete Algorithms (SODA), edited by David P. Woodruff, Society for Industrial
and Applied Mathematics, 2024, pp. 243–95, doi:10.1137/1.9781611977912.11.
short: S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, L. Ost, in:, D.P.
Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete
Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.
conference:
end_date: 2024-01-10
location: Alexandria, VA, USA
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2024-01-07
corr_author: '1'
date_created: 2024-03-08T10:27:39Z
date_published: 2024-01-04T00:00:00Z
date_updated: 2026-04-07T12:58:47Z
day: '04'
department:
- _id: HeEd
- _id: MoHe
doi: 10.1137/1.9781611977912.11
ec_funded: 1
editor:
- first_name: David P.
full_name: Woodruff, David P.
last_name: Woodruff
external_id:
arxiv:
- '2311.01115'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2311.01115
month: '01'
oa: 1
oa_version: Preprint
page: 243 - 295
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: bd9ca328-d553-11ed-ba76-dc4f890cfe62
call_identifier: H2020
grant_number: '101019564'
name: The design and evaluation of modern fully dynamic data structures
- _id: 34def286-11ca-11ed-8bc3-da5948e1613c
grant_number: Z00422
name: Efficient algorithms
- _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe
grant_number: P33775
name: Fast Algorithms for a Reactive Network Layer
publication: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms
(SODA)
publication_identifier:
eisbn:
- '9781611977912'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Dynamically maintaining the persistent homology of time series
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: publisher
_id: '15094'
abstract:
- lang: eng
text: "Point sets, geometric networks, and arrangements of hyperplanes are fundamental
objects in\r\ndiscrete geometry that have captivated mathematicians for centuries,
if not millennia. This\r\nthesis seeks to cast new light on these structures by
illustrating specific instances where a\r\ntopological perspective, specifically
through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt
first glance, the topology of these geometric objects might seem uneventful: point
sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition
of Rd, which\r\nis a contractible space, and the topology of a network primarily
involves the enumeration\r\nof connected components and cycles within the network.
However, beneath this apparent\r\nsimplicity, there lies an array of intriguing
structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused
on three case studies, each addressing one of the mentioned objects, this work\r\nwill
showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry,
algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
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
citation:
ama: Cultrera di Montesano S. Persistence and Morse theory for discrete geometric
structures. 2024. doi:10.15479/at:ista:15094
apa: Cultrera di Montesano, S. (2024). Persistence and Morse theory for discrete
geometric structures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15094
chicago: Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete
Geometric Structures.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15094.
ieee: S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric
structures,” Institute of Science and Technology Austria, 2024.
ista: Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric
structures. Institute of Science and Technology Austria.
mla: Cultrera di Montesano, Sebastiano. Persistence and Morse Theory for Discrete
Geometric Structures. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15094.
short: S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric
Structures, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-03-08T15:28:10Z
date_published: 2024-03-08T00:00:00Z
date_updated: 2026-04-07T12:58:48Z
day: '08'
ddc:
- '514'
- '500'
- '516'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:15094
ec_funded: 1
file:
- access_level: open_access
checksum: 1e468bfa42a7dcf04d89f4dadc621c87
content_type: application/pdf
creator: scultrer
date_created: 2024-03-14T08:55:07Z
date_updated: 2024-03-14T08:55:07Z
file_id: '15112'
file_name: Thesis Sebastiano.pdf
file_size: 4106872
relation: main_file
success: 1
- access_level: closed
checksum: bcbd213490f5a7e68855a092bbce93f1
content_type: application/zip
creator: scultrer
date_created: 2024-03-14T08:56:24Z
date_updated: 2024-03-14T14:14:35Z
file_id: '15113'
file_name: Thesis (1).zip
file_size: 4746234
relation: source_file
file_date_updated: 2024-03-14T14:14:35Z
has_accepted_license: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: '108'
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: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '15091'
relation: part_of_dissertation
status: public
- id: '11660'
relation: part_of_dissertation
status: public
- id: '15090'
relation: part_of_dissertation
status: public
- id: '15093'
relation: part_of_dissertation
status: public
- id: '13182'
relation: part_of_dissertation
status: public
- id: '11658'
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: Persistence and Morse theory for discrete geometric structures
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15247'
abstract:
- lang: eng
text: Extending the notion of sunflowers, we call a family of at least two sets
an odd-sunflower if every element of the underlying set is contained in an odd
number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture,
recently proved by Naslund and Sawin, that there is a constant <2 such that every
family of subsets of an n-element set that contains no odd-sunflower consists
of at most n sets. We construct such families of size at least 1.5021n. We also
characterize minimal odd-sunflowers of triples.
acknowledgement: We are grateful to Balázs Keszegh, and to the members of the Miklós
Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib
for pointing out several important mathematical typos.
article_number: '105889'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Frankl, Peter
last_name: Frankl
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Dömötör
full_name: Pálvölgyi, Dömötör
last_name: Pálvölgyi
citation:
ama: Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. Journal of Combinatorial
Theory, Series A. 2024;206(8). doi:10.1016/j.jcta.2024.105889
apa: Frankl, P., Pach, J., & Pálvölgyi, D. (2024). Odd-sunflowers. Journal
of Combinatorial Theory, Series A. Elsevier. https://doi.org/10.1016/j.jcta.2024.105889
chicago: Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” Journal
of Combinatorial Theory, Series A. Elsevier, 2024. https://doi.org/10.1016/j.jcta.2024.105889.
ieee: P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” Journal of Combinatorial
Theory, Series A, vol. 206, no. 8. Elsevier, 2024.
ista: Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial
Theory, Series A. 206(8), 105889.
mla: Frankl, Peter, et al. “Odd-Sunflowers.” Journal of Combinatorial Theory,
Series A, vol. 206, no. 8, 105889, Elsevier, 2024, doi:10.1016/j.jcta.2024.105889.
short: P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series
A 206 (2024).
corr_author: '1'
date_created: 2024-03-31T22:01:11Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-04T13:20:39Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jcta.2024.105889
external_id:
arxiv:
- '2310.16701'
isi:
- '001217739200001'
file:
- access_level: open_access
checksum: ffc29d65e712849f0d31009271e06a63
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:37:20Z
date_updated: 2025-01-09T08:37:20Z
file_id: '18791'
file_name: 2024_JourCombiTheoryA_Frankl.pdf
file_size: 366029
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:37:20Z
has_accepted_license: '1'
intvolume: ' 206'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Combinatorial Theory, Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Odd-sunflowers
tmp:
image: /images/cc_by_nc.png
legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
short: CC BY-NC (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 206
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15380'
abstract:
- lang: eng
text: The depth of a cell in an arrangement of n (non-vertical) great-spheres in
Sd is the number of great-spheres that pass above the cell. We prove Euler-type
relations, which imply extensions of the classic Dehn–Sommerville relations for
convex polytopes to sublevel sets of the depth function, and we use the relations
to extend the expressions for the number of faces of neighborly polytopes to the
number of cells of levels in neighborly arrangements.
acknowledgement: "The authors thank Uli Wagner and Emo Welzl for comments on an earlier
version of this paper, and for pointing out related work in the prior literature.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria). 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: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- 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
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements:
Dehn–Sommerville–Euler relations with applications. Journal of Applied and
Computational Topology. 2024;8:557-578. doi:10.1007/s41468-024-00173-w'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications.
Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-024-00173-w'
chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations
with Applications.” Journal of Applied and Computational Topology. Springer
Nature, 2024. https://doi.org/10.1007/s41468-024-00173-w.'
ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth
in arrangements: Dehn–Sommerville–Euler relations with applications,” Journal
of Applied and Computational Topology, vol. 8. Springer Nature, pp. 557–578,
2024.'
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth
in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of
Applied and Computational Topology. 8, 557–578.'
mla: 'Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations
with Applications.” Journal of Applied and Computational Topology, vol.
8, Springer Nature, 2024, pp. 557–78, doi:10.1007/s41468-024-00173-w.'
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal
of Applied and Computational Topology 8 (2024) 557–578.
corr_author: '1'
date_created: 2024-05-12T22:01:03Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-05-14T09:27:57Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s41468-024-00173-w
ec_funded: 1
external_id:
pmid:
- '39308789'
file:
- access_level: open_access
checksum: 0ee15c1493a6413cf356ab2f32c81a9e
content_type: application/pdf
creator: dernst
date_created: 2025-04-23T08:01:36Z
date_updated: 2025-04-23T08:01:36Z
file_id: '19612'
file_name: 2024_JourApplCompTopo_BiswasRa.pdf
file_size: 522831
relation: main_file
success: 1
file_date_updated: 2025-04-23T08:01:36Z
has_accepted_license: '1'
intvolume: ' 8'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 557-578
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 Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11658'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: 'Depth in arrangements: Dehn–Sommerville–Euler relations with applications'
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: 8
year: '2024'
...
---
_id: '17144'
abstract:
- lang: eng
text: "We prove that the medial axis of closed sets is Hausdorff stable in the following
sense: Let \U0001D4AE ⊆ ℝ^d be a fixed closed set that contains a bounding sphere.
That is, the bounding sphere is part of the set \U0001D4AE. Consider the space
of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant.
The map from this space of diffeomorphisms (endowed with a Banach norm) to the
space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping
a diffeomorphism F to the closure of the medial axis of F(\U0001D4AE), is Lipschitz.
This extends a previous stability result of Chazal and Soufflet on the stability
of the medial axis of C² manifolds under C² ambient diffeomorphisms."
acknowledgement: "This research has been supported by the European Research Council
(ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF),
grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant No. I 02979-N35.\r\nSupported by the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and
the welcome package from IDEX of the Université Cô d'Azur.\r\nWe are greatly indebted
to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher
Fillmore, and Elizabeth Stephenson for early discussions and all members of the
Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape
team (Inria) for the atmosphere in which this research was conducted."
alternative_title:
- LIPIcs
article_number: '69'
article_processing_charge: No
arxiv: 1
author:
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded
set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms.
In: 40th International Symposium on Computational Geometry. Vol 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.69'
apa: 'Kourimska, H., Lieutier, A., & Wintraecken, M. (2024). The medial axis
of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance
Under ambient diffeomorphisms. In 40th International Symposium on Computational
Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für
Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.69'
chicago: Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis
of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance
Under Ambient Diffeomorphisms.” In 40th International Symposium on Computational
Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
https://doi.org/10.4230/LIPIcs.SoCG.2024.69.
ieee: H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed
bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient
diffeomorphisms,” in 40th International Symposium on Computational Geometry,
Athens, Greece, 2024, vol. 293.
ista: 'Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed
bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient
diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 293, 69.'
mla: Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz
Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.”
40th International Symposium on Computational Geometry, vol. 293, 69, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.69.
short: H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium
on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2024.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-04-15T07:16:58Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.69
ec_funded: 1
external_id:
arxiv:
- '2212.01118'
file:
- access_level: open_access
checksum: b40ff456c19294adb5d9613fcfd751c6
content_type: application/pdf
creator: dernst
date_created: 2024-06-17T08:33:40Z
date_updated: 2024-06-17T08:33:40Z
file_id: '17150'
file_name: 2024_LIPICS_Kourimska.pdf
file_size: 1612558
relation: main_file
success: 1
file_date_updated: 2024-06-17T08:33:40Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: The medial axis of any closed bounded set Is Lipschitz stable with respect
to the Hausdorff distance Under ambient diffeomorphisms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...
---
_id: '17145'
abstract:
- lang: eng
text: Grid peeling is the process of repeatedly removing the convex hull vertices
of the grid points that lie inside a given convex curve. It has been conjectured
that, for a more and more refined grid, grid peeling converges to a continuous
process, the affine curve-shortening flow, which deforms the curve based on the
curvature. We prove this conjecture for one class of curves, parabolas with a
vertical axis, and we determine the value of the constant factor in the formula
that relates the two processes.
acknowledgement: Part of this work was done while G.R. enjoyed the hospitality of
the Institute of Science and Technology Austria (ISTA) as a visiting professor during
his sabbatical in the winter semester 2022/23.
alternative_title:
- LIPIcs
article_number: '76'
article_processing_charge: No
arxiv: 1
author:
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
- first_name: Moritz
full_name: Rüber, Moritz
last_name: Rüber
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: 40th International
Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.76'
apa: 'Rote, G., Rüber, M., & Saghafian, M. (2024). Grid peeling of parabolas.
In 40th International Symposium on Computational Geometry (Vol. 293). Athens,
Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.76'
chicago: Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.”
In 40th International Symposium on Computational Geometry, Vol. 293. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.76.
ieee: G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in 40th
International Symposium on Computational Geometry, Athens, Greece, 2024, vol.
293.
ista: 'Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International
Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry,
LIPIcs, vol. 293, 76.'
mla: Rote, Günter, et al. “Grid Peeling of Parabolas.” 40th International Symposium
on Computational Geometry, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.76.
short: G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2024-06-17T08:41:56Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.76
external_id:
arxiv:
- '2402.15787'
file:
- access_level: open_access
checksum: fbad1de06383a6b7e8a1cb3e8c7205ce
content_type: application/pdf
creator: dernst
date_created: 2024-06-17T08:40:04Z
date_updated: 2024-06-17T08:40:04Z
file_id: '17151'
file_name: 2024_LIPICS_Rote.pdf
file_size: 1430896
relation: main_file
success: 1
file_date_updated: 2024-06-17T08:40:04Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Grid peeling of parabolas
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...
---
_id: '17146'
abstract:
- lang: eng
text: The Upper Bound Theorem for convex polytopes implies that the p-th Betti number
of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p
= O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions,
which prove that this upper bound is asymptotically tight. For example, we describe
a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number
of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of
the Čech complex at the other radius is n². In particular, there is an arrangement
of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers
a long-standing open question in computational geometry.
acknowledgement: "The first author is supported by the European Research Council (ERC),
grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant no. {I 02979-N35.} The second author is supported by the
European Research Council (ERC), grant \"GeoScape\" and by the Hungarian Science
Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein
Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.\r\nThe authors thank Matt
Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart
for early discussions on the linked circles construction in three dimensions, and
Gábor Tardos for helpful remarks and suggestions."
alternative_title:
- 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: 2025-12-01T15:19:20Z
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: '17170'
abstract:
- lang: eng
text: "In this article we extend and strengthen the seminal work by Niyogi, Smale,
and Weinberger on the learning of the homotopy type from a sample of an underlying
space. In their work, Niyogi, Smale, and Weinberger studied samples of C² manifolds
with positive reach embedded in ℝ^d. We extend their results in the following
ways: - As the ambient space we consider both ℝ^d and Riemannian manifolds with
lower bounded sectional curvature. - In both types of ambient spaces, we study
sets of positive reach - a significantly more general setting than C² manifolds
- as well as general manifolds of positive reach. - The sample P of a set (or
a manifold) \U0001D4AE of positive reach may be noisy. We work with two one-sided
Hausdorff distances - ε and δ - between P and \U0001D4AE. We provide tight bounds
in terms of ε and δ, that guarantee that there exists a parameter r such that
the union of balls of radius r centred at the sample P deformation-retracts to
\U0001D4AE. We exhibit their tightness by an explicit construction. We carefully
distinguish the roles of δ and ε. This is not only essential to achieve tight
bounds, but also sensible in practical situations, since it allows one to adapt
the bound according to sample density and the amount of noise present in the sample
separately."
acknowledgement: "This research has been supported by the European Research Council
(ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF),
grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian
Science Fund (FWF), grant No. I 02979-N35.\r\nWintraecken, Mathijs: Supported by
the European Union’s Horizon 2020 research and innovation programme under the Marie
Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant
No. M-3073, and the welcome package from IDEX of the Université Côte d'Azur."
alternative_title:
- LIPIcs
article_processing_charge: No
arxiv: 1
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Ishika
full_name: Ghosh, Ishika
id: ee449b28-344d-11ef-a6d5-9ca430e9e9ff
last_name: Ghosh
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Attali D, Kourimska H, Fillmore CD, et al. Tight bounds for the learning of
homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and
of Riemannian manifolds. In: 40th International Symposium on Computational
Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024:11:1-11:19.
doi:10.4230/LIPIcs.SoCG.2024.11'
apa: 'Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson,
E. R., & Wintraecken, M. (2024). Tight bounds for the learning of homotopy
à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian
manifolds. In 40th International Symposium on Computational Geometry (Vol.
293, p. 11:1-11:19). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2024.11'
chicago: Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh,
André Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “Tight Bounds
for the Learning of Homotopy à La Niyogi, Smale, and Weinberger for Subsets of
Euclidean Spaces and of Riemannian Manifolds.” In 40th International Symposium
on Computational Geometry, 293:11:1-11:19. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.11.
ieee: D. Attali et al., “Tight bounds for the learning of homotopy à la Niyogi,
Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds,”
in 40th International Symposium on Computational Geometry, Athens, Greece,
2024, vol. 293, p. 11:1-11:19.
ista: 'Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken
M. 2024. Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger
for subsets of euclidean spaces and of Riemannian manifolds. 40th International
Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry,
LIPIcs, vol. 293, 11:1-11:19.'
mla: Attali, Dominique, et al. “Tight Bounds for the Learning of Homotopy à La Niyogi,
Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds.”
40th International Symposium on Computational Geometry, vol. 293, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19, doi:10.4230/LIPIcs.SoCG.2024.11.
short: D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson,
M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
date_created: 2024-06-25T11:45:58Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2025-04-15T07:16:57Z
day: '06'
ddc:
- '516'
department:
- _id: GradSch
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.11
ec_funded: 1
external_id:
arxiv:
- '2206.10485'
file:
- access_level: open_access
checksum: 6a2ddc8b51aa58f197a8b294750f1f8d
content_type: application/pdf
creator: cfillmor
date_created: 2024-06-25T11:47:26Z
date_updated: 2024-06-25T11:47:26Z
file_id: '17171'
file_name: LIPIcs.SoCG.2024.11.pdf
file_size: 20886142
relation: main_file
success: 1
file_date_updated: 2024-06-25T11:47:26Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 11:1-11:19
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: 40th International Symposium on Computational Geometry
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959773164'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger
for subsets of euclidean spaces and of Riemannian manifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...
---
_id: '17190'
abstract:
- lang: eng
text: "For a locally finite set, \U0001D434⊆ℝ\U0001D451\r\n, the \U0001D458\r\nth
Brillouin zone of \U0001D44E∈\U0001D434\r\n is the region of points \U0001D465∈ℝ\U0001D451\r\n
for which ‖\U0001D465−\U0001D44E‖\r\n is the \U0001D458\r\nth smallest among the
Euclidean distances between \U0001D465\r\n and the points in \U0001D434\r\n. If
\U0001D434\r\n is a lattice, the \U0001D458\r\nth Brillouin zones of the points
in \U0001D434\r\n are translates of each other, and together they tile space.
Depending on the value of \U0001D458\r\n, they express medium- or long-range order
in the set. We study fundamental geometric and combinatorial properties of Brillouin
zones, focusing on the integer lattice and its perturbations. Our results include
the stability of a Brillouin zone under perturbations, a linear upper bound on
the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of
the maximum volume of a chamber to zero for the integer lattice."
acknowledgement: The second author is partially supported by the Alexander von Humboldt
Foundation. The sixth author is supported by the European Union's Horizon 2020 research
and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and
by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European
Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science
Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109,
Austrian Science Fund (FWF) grant I 02979-N35.
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: Ghafaris, Mohadese
last_name: Ghafaris
- 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: Saghafiant, Morteza
last_name: Saghafiant
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M.
Brillouin zones of integer lattices and their perturbations. SIAM Journal on
Discrete Mathematics. 2024;38(2):1784-1807. doi:10.1137/22M1489071
apa: Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., &
Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations.
SIAM Journal on Discrete Mathematics. Society for Industrial and Applied
Mathematics. https://doi.org/10.1137/22M1489071
chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss,
Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices
and Their Perturbations.” SIAM Journal on Discrete Mathematics. Society
for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/22M1489071.
ieee: H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken,
“Brillouin zones of integer lattices and their perturbations,” SIAM Journal
on Discrete Mathematics, vol. 38, no. 2. Society for Industrial and Applied
Mathematics, pp. 1784–1807, 2024.
ista: Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M.
2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal
on Discrete Mathematics. 38(2), 1784–1807.
mla: Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their
Perturbations.” SIAM Journal on Discrete Mathematics, vol. 38, no. 2, Society
for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:10.1137/22M1489071.
short: H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken,
SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.
corr_author: '1'
date_created: 2024-06-30T22:01:05Z
date_published: 2024-06-07T00:00:00Z
date_updated: 2025-09-08T08:06:04Z
day: '07'
department:
- _id: HeEd
doi: 10.1137/22M1489071
ec_funded: 1
external_id:
arxiv:
- '2204.01077'
isi:
- '001292728600001'
intvolume: ' 38'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2204.01077
month: '06'
oa: 1
oa_version: Preprint
page: 1784-1807
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
- _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: SIAM Journal on Discrete Mathematics
publication_identifier:
issn:
- 0895-4801
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Brillouin zones of integer lattices and their perturbations
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 38
year: '2024'
...
---
OA_place: publisher
OA_type: gold
_id: '18556'
abstract:
- lang: eng
text: Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined
length of the minimum spanning trees of B and A⧵B divided by the length of the
minimum spanning tree of A. The question of the supremum, over all sets A, of
the maximum, over all subsets B, is related to the Steiner ratio, and we prove
this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional
lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin
the most difficult of these results is the upper bound for the inf-max, which
we prove by showing that the hexagonal lattice cannot have MST-ratio larger than
1.25.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, "Discretization
in Geometry and Dynamics", Austrian Science Fund (FWF), grant no. I 02979-N35.
alternative_title:
- LIPIcs
article_number: '3'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean
MST-ratio for bi-colored lattices. In: 32nd International Symposium on Graph
Drawing and Network Visualization. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.GD.2024.3'
apa: 'Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (2024). The Euclidean MST-ratio for bi-colored lattices. In 32nd International
Symposium on Graph Drawing and Network Visualization (Vol. 320). Vienna, Austria:
Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.GD.2024.3'
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In 32nd
International Symposium on Graph Drawing and Network Visualization, Vol. 320.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.GD.2024.3.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“The Euclidean MST-ratio for bi-colored lattices,” in 32nd International Symposium
on Graph Drawing and Network Visualization, Vienna, Austria, 2024, vol. 320.
ista: 'Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The
Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph
Drawing and Network Visualization. GD: Graph Drawing and Network Visualization,
LIPIcs, vol. 320, 3.'
mla: Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored
Lattices.” 32nd International Symposium on Graph Drawing and Network Visualization,
vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.GD.2024.3.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:,
32nd International Symposium on Graph Drawing and Network Visualization, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
conference:
end_date: 2024-09-20
location: Vienna, Austria
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2024-09-18
corr_author: '1'
date_created: 2024-11-17T23:01:47Z
date_published: 2024-10-28T00:00:00Z
date_updated: 2025-12-02T13:50:50Z
day: '28'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.GD.2024.3
ec_funded: 1
external_id:
arxiv:
- '2403.10204'
isi:
- '001540278400001'
file:
- access_level: open_access
checksum: 5f9b35e115c3d375e99be78da9054cb4
content_type: application/pdf
creator: dernst
date_created: 2024-11-18T07:49:25Z
date_updated: 2024-11-18T07:49:25Z
file_id: '18560'
file_name: 2024_LIPIcs_CultreradiMontesano.pdf
file_size: 908541
relation: main_file
success: 1
file_date_updated: 2024-11-18T07:49:25Z
has_accepted_license: '1'
intvolume: ' 320'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: 32nd International Symposium on Graph Drawing and Network Visualization
publication_identifier:
isbn:
- '9783959773430'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Euclidean MST-ratio for bi-colored lattices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 320
year: '2024'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18604'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a randomized
FPT-time algorithm where the parameter is the number of popular faces.'
acknowledgement: "This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. has been supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]
and by the NWO Gravitation project NETWORKS under grant no. 024.002.003. Part of
the work was done while A.W. was emplyed at Graz University of Technology. Preliminary
versions of this work have been presented at the 38th European Workshop on Computational
Geometry (EuroCG\r\n2022) in Perugia [10] and at the 31st International Symposium
on Graph Drawing and Network Visualization (GD 2023) in Isola delle Femmine [11]."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. Journal of Graph Algorithms and Applications. 2024;28(2):47-82.
doi:10.7155/jgaa.v28i2.2988
apa: De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.v28i2.2988
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in
Curve Arrangements.” Journal of Graph Algorithms and Applications. Brown
University, 2024. https://doi.org/10.7155/jgaa.v28i2.2988.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
Journal of Graph Algorithms and Applications, vol. 28, no. 2. Brown University,
pp. 47–82, 2024.
ista: De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. Journal of Graph
Algorithms and Applications. 28(2), 47–82.
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
Journal of Graph Algorithms and Applications, vol. 28, no. 2, Brown University,
2024, pp. 47–82, doi:10.7155/jgaa.v28i2.2988.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, Journal of Graph Algorithms and Applications 28 (2024) 47–82.
corr_author: '1'
date_created: 2024-12-01T23:01:54Z
date_published: 2024-11-03T00:00:00Z
date_updated: 2024-12-03T09:49:18Z
day: '03'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.7155/jgaa.v28i2.2988
external_id:
arxiv:
- '2202.12175'
file:
- access_level: open_access
checksum: be611da6f9d790dc980d6fb7283fe889
content_type: application/pdf
creator: dernst
date_created: 2024-12-03T09:45:00Z
date_updated: 2024-12-03T09:45:00Z
file_id: '18609'
file_name: 2024_JourGraphAlgorithms_deNooijer.pdf
file_size: 1582493
relation: main_file
success: 1
file_date_updated: 2024-12-03T09:45:00Z
has_accepted_license: '1'
intvolume: ' 28'
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 47-82
publication: Journal of Graph Algorithms and Applications
publication_identifier:
issn:
- 1526-1719
publication_status: published
publisher: Brown University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2024'
...
---
OA_place: publisher
_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: 2026-04-07T12:54:10Z
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: '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
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'
...