---
_id: '8317'
abstract:
- lang: eng
text: When can a polyomino piece of paper be folded into a unit cube? Prior work
studied tree-like polyominoes, but polyominoes with holes remain an intriguing
open problem. We present sufficient conditions for a polyomino with one or several
holes to fold into a cube, and conditions under which cube folding is impossible.
In particular, we show that all but five special “basic” holes guarantee foldability.
acknowledgement: This research was performed in part at the 33rd Bellairs Winter Workshop
on Computational Geometry. We thank all other participants for a fruitful atmosphere.
H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially
funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.
article_number: '101700'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Hugo A.
full_name: Akitaya, Hugo A.
last_name: Akitaya
- first_name: Kenneth C.
full_name: Cheung, Kenneth C.
last_name: Cheung
- first_name: Erik D.
full_name: Demaine, Erik D.
last_name: Demaine
- first_name: Martin L.
full_name: Demaine, Martin L.
last_name: Demaine
- first_name: Sándor P.
full_name: Fekete, Sándor P.
last_name: Fekete
- first_name: Linda
full_name: Kleist, Linda
last_name: Kleist
- first_name: Irina
full_name: Kostitsyna, Irina
last_name: Kostitsyna
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Klara
full_name: Mundilova, Klara
last_name: Mundilova
- first_name: Christiane
full_name: Schmidt, Christiane
last_name: Schmidt
citation:
ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes
into a cube. Computational Geometry: Theory and Applications. 2021;93.
doi:10.1016/j.comgeo.2020.101700'
apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M.
L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a
cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700'
chicago: 'Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine,
Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes
with Holes into a Cube.” Computational Geometry: Theory and Applications.
Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.'
ieee: 'O. Aichholzer et al., “Folding polyominoes with holes into a cube,”
Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.'
ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist
L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding
polyominoes with holes into a cube. Computational Geometry: Theory and Applications.
93, 101700.'
mla: 'Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational
Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.'
short: 'O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P.
Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt,
Computational Geometry: Theory and Applications 93 (2021).'
corr_author: '1'
date_created: 2020-08-30T22:01:09Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2026-04-16T09:14:31Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2020.101700
external_id:
arxiv:
- '1910.09917'
isi:
- '000579185100004'
intvolume: ' 93'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.09917v3
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: 'Computational Geometry: Theory and Applications'
publication_identifier:
eissn:
- 1879-081X
issn:
- 0925-7721
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '6989'
relation: shorter_version
status: public
scopus_import: '1'
status: public
title: Folding polyominoes with holes into a cube
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 93
year: '2021'
...
---
_id: '9296'
abstract:
- lang: eng
text: ' matching is compatible to two or more labeled point sets of size n with
labels {1,…,n} if its straight-line drawing on each of these point sets is
crossing-free. We study the maximum number of edges in a matching compatible to
two or more labeled point sets in general position in the plane. We show that
for any two labeled convex sets of n points there exists a compatible matching
with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct
compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use
probabilistic arguments to show that for any ℓ given sets of n points there
exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges.
Finally, we show that Θ(logn) copies of any set of n points are necessary and
sufficient for the existence of a labeling such that any compatible matching consists
only of a single edge.'
acknowledgement: 'A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411.
Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative
DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported
by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by
ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23
(RiSE).'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Daniel
full_name: Perz, Daniel
last_name: Perz
- first_name: Alexander
full_name: Pilz, Alexander
last_name: Pilz
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings.
In: 15th International Conference on Algorithms and Computation. Vol 12635.
Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18'
apa: 'Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D.,
Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International
Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon,
Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18'
chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada,
Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible
Matchings.” In 15th International Conference on Algorithms and Computation,
12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.
ieee: O. Aichholzer et al., “On compatible matchings,” in 15th International
Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635,
pp. 221–233.
ista: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec
J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference
on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol.
12635, 221–233.'
mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International
Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021,
pp. 221–33, doi:10.1007/978-3-030-68211-8_18.
short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz,
J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and
Computation, Springer Nature, 2021, pp. 221–233.
conference:
end_date: 2021-03-02
location: Yangon, Myanmar
name: 'WALCOM: Algorithms and Computation'
start_date: 2021-02-28
date_created: 2021-03-28T22:01:41Z
date_published: 2021-02-16T00:00:00Z
date_updated: 2026-04-16T09:18:21Z
day: '16'
department:
- _id: UlWa
- _id: HeEd
- _id: KrCh
doi: 10.1007/978-3-030-68211-8_18
ec_funded: 1
external_id:
arxiv:
- '2101.03928'
isi:
- '001435069600018'
intvolume: ' 12635'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.03928
month: '02'
oa: 1
oa_version: Preprint
page: 221-233
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
publication: 15th International Conference on Algorithms and Computation
publication_identifier:
eisbn:
- '9783030682118'
eissn:
- 1611-3349
isbn:
- '9783030682101'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11938'
relation: later_version
status: public
scopus_import: '1'
status: public
title: On compatible matchings
type: conference
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 12635
year: '2021'
...
---
_id: '9824'
abstract:
- lang: eng
text: We define a new compact coordinate system in which each integer triplet addresses
a voxel in the BCC grid, and we investigate some of its properties. We propose
a characterization of 3D discrete analytical planes with their topological features
(in the Cartesian and in the new coordinate system) such as the interrelation
between the thickness of the plane and the separability constraint we aim to obtain.
acknowledgement: 'This work has been partially supported by the Ministry of Education,
Science and Technological Development of the Republic of Serbia through the project
no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from
the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and
the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’,
Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic
grid - coordinate system and discrete analytical plane definition. In: Discrete
Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163.
doi:10.1007/978-3-030-76657-3_10'
apa: 'Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021).
Body centered cubic grid - coordinate system and discrete analytical plane definition.
In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163).
Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10'
chicago: Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and
Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical
Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63.
Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.
ieee: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered
cubic grid - coordinate system and discrete analytical plane definition,” in Discrete
Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp.
152–163.
ista: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered
cubic grid - coordinate system and discrete analytical plane definition. Discrete
Geometry and Mathematical Morphology. DGMM: International Conference on Discrete
Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.'
mla: Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete
Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology,
vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.
short: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete
Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
conference:
end_date: 2021-05-27
location: Uppsala, Sweden
name: 'DGMM: International Conference on Discrete Geometry and Mathematical Morphology'
start_date: 2021-05-24
date_created: 2021-08-08T22:01:29Z
date_published: 2021-05-16T00:00:00Z
date_updated: 2026-04-16T09:26:30Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/978-3-030-76657-3_10
ec_funded: 1
external_id:
isi:
- '001286400400010'
intvolume: ' 12708'
isi: 1
language:
- iso: eng
month: '05'
oa_version: None
page: 152-163
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: Discrete Geometry and Mathematical Morphology
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030766566'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Body centered cubic grid - coordinate system and discrete analytical plane
definition
type: conference
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 12708
year: '2021'
...
---
_id: '15064'
abstract:
- lang: eng
text: We call a continuous self-map that reveals itself through a discrete set of
point-value pairs a sampled dynamical system. Capturing the available information
with chain maps on Delaunay complexes, we use persistent homology to quantify
the evidence of recurrent behavior. We establish a sampling theorem to recover
the eigenspaces of the endomorphism on homology induced by the self-map. Using
a combinatorial gradient flow arising from the discrete Morse theory for Čech
and Delaunay complexes, we construct a chain map to transform the problem from
the natural but expensive Čech complexes to the computationally efficient Delaunay
triangulations. The fast chain map algorithm has applications beyond dynamical
systems.
acknowledgement: This research has been supported by the DFG Collaborative Research
Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant
No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant
No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding
provided by Projekt DEAL.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: U.
full_name: Bauer, U.
last_name: Bauer
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: M.
full_name: Mrozek, M.
last_name: Mrozek
citation:
ama: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow
and homology inference for self-maps. Journal of Applied and Computational
Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8
apa: Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay
gradient flow and homology inference for self-maps. Journal of Applied and
Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8
chicago: Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay
Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and
Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.
ieee: U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient
flow and homology inference for self-maps,” Journal of Applied and Computational
Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.
ista: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient
flow and homology inference for self-maps. Journal of Applied and Computational
Topology. 4(4), 455–480.
mla: Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.”
Journal of Applied and Computational Topology, vol. 4, no. 4, Springer
Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.
short: U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and
Computational Topology 4 (2020) 455–480.
date_created: 2024-03-04T10:47:49Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2024-03-04T10:54:04Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s41468-020-00058-8
file:
- access_level: open_access
checksum: eed1168b6e66cd55272c19bb7fca8a1c
content_type: application/pdf
creator: dernst
date_created: 2024-03-04T10:52:42Z
date_updated: 2024-03-04T10:52:42Z
file_id: '15065'
file_name: 2020_JourApplCompTopology_Bauer.pdf
file_size: 851190
relation: main_file
success: 1
file_date_updated: 2024-03-04T10:52:42Z
has_accepted_license: '1'
intvolume: ' 4'
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 455-480
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Čech-Delaunay gradient flow and homology inference for self-maps
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...
---
_id: '10867'
abstract:
- lang: eng
text: In this paper we find a tight estimate for Gromov’s waist of the balls in
spaces of constant curvature, deduce the estimates for the balls in Riemannian
manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar
result for normed spaces.
acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International
Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037
apa: Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical
spaces. International Mathematics Research Notices. Oxford University Press.
https://doi.org/10.1093/imrn/rny037
chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and
Spherical Spaces.” International Mathematics Research Notices. Oxford University
Press, 2020. https://doi.org/10.1093/imrn/rny037.
ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,”
International Mathematics Research Notices, vol. 2020, no. 3. Oxford University
Press, pp. 669–697, 2020.
ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces.
International Mathematics Research Notices. 2020(3), 669–697.
mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical
Spaces.” International Mathematics Research Notices, vol. 2020, no. 3,
Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.
short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020)
669–697.
date_created: 2022-03-18T11:39:30Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-24T14:19:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/imrn/rny037
external_id:
arxiv:
- '1702.07513'
isi:
- '000522852700002'
intvolume: ' 2020'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.07513
month: '02'
oa: 1
oa_version: Preprint
page: 669-697
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Waist of balls in hyperbolic and spherical spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_id: '7666'
abstract:
- lang: eng
text: Generalizing the decomposition of a connected planar graph into a tree and
a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition
of a smooth vector field. Specifically, we show that for every polyhedral complex,
K, and every dimension, p, there is a partition of the set of p-cells into a maximal
p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the
p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition
is unique, and it can be computed by a matrix reduction algorithm that also constructs
canonical bases of cycle and boundary groups.
acknowledgement: This project has received funding from the European Research Council
under the European Union’s Horizon 2020 research and innovation programme (Grant
Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative
Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant
No. I02979-N35 of the Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
citation:
ama: Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex.
Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x
apa: Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an
ordered complex. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-020-00188-x
chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases
of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature,
2020. https://doi.org/10.1007/s00454-020-00188-x.
ieee: H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,”
Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775,
2020.
ista: Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex.
Discrete and Computational Geometry. 64, 759–775.
mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of
an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer
Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.
short: H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020)
759–775.
corr_author: '1'
date_created: 2020-04-19T22:00:56Z
date_published: 2020-03-20T00:00:00Z
date_updated: 2025-04-14T07:48:36Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00188-x
ec_funded: 1
external_id:
isi:
- '000520918800001'
file:
- access_level: open_access
checksum: f8cc96e497f00c38340b5dafe0cb91d7
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T13:22:21Z
date_updated: 2020-11-20T13:22:21Z
file_id: '8786'
file_name: 2020_DiscreteCompGeo_Edelsbrunner.pdf
file_size: 701673
relation: main_file
success: 1
file_date_updated: 2020-11-20T13:22:21Z
has_accepted_license: '1'
intvolume: ' 64'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 759-775
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _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: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tri-partitions and bases of an ordered complex
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '7952'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued
smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate
an isomanifold is to consider its Piecewise-Linear (PL) approximation based on
a triangulation \U0001D4AF of the ambient space ℝ^d. In this paper, we give conditions
under which the PL-approximation of an isomanifold is topologically equivalent
to the isomanifold. The conditions are easy to satisfy in the sense that they
can always be met by taking a sufficiently fine triangulation \U0001D4AF. This
contrasts with previous results on the triangulation of manifolds where, in arbitrary
dimensions, delicate perturbations are needed to guarantee topological correctness,
which leads to strong limitations in practice. We further give a bound on the
Fréchet distance between the original isomanifold and its PL-approximation. Finally
we show analogous results for the PL-approximation of an isomanifold with boundary. "
alternative_title:
- LIPIcs
article_number: 20:1-20:18
article_processing_charge: No
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations
of isomanifolds. In: 36th International Symposium on Computational Geometry.
Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.20'
apa: 'Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness
of PL-approximations of isomanifolds. In 36th International Symposium on Computational
Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20'
chicago: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL-Approximations of Isomanifolds.” In 36th International Symposium on Computational
Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
https://doi.org/10.4230/LIPIcs.SoCG.2020.20.
ieee: J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations
of isomanifolds,” in 36th International Symposium on Computational Geometry,
Zürich, Switzerland, 2020, vol. 164.
ista: 'Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations
of isomanifolds. 36th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.'
mla: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational
Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2020, doi:10.4230/LIPIcs.SoCG.2020.20.
short: J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-06-26
location: Zürich, Switzerland
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2020-06-22
corr_author: '1'
date_created: 2020-06-09T07:24:11Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2025-04-22T13:45:17Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2020.20
ec_funded: 1
file:
- access_level: open_access
checksum: 38cbfa4f5d484d267a35d44d210df044
content_type: application/pdf
creator: dernst
date_created: 2020-06-17T10:13:34Z
date_updated: 2020-07-14T12:48:06Z
file_id: '7969'
file_name: 2020_LIPIcsSoCG_Boissonnat.pdf
file_size: 1009739
relation: main_file
file_date_updated: 2020-07-14T12:48:06Z
has_accepted_license: '1'
intvolume: ' 164'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 36th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-143-6
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '9649'
relation: later_version
status: public
scopus_import: '1'
status: public
title: The topological correctness of PL-approximations of isomanifolds
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: 164
year: '2020'
...
---
_id: '7962'
abstract:
- lang: eng
text: 'A string graph is the intersection graph of a family of continuous arcs in
the plane. The intersection graph of a family of plane convex sets is a string
graph, but not all string graphs can be obtained in this way. We prove the following
structure theorem conjectured by Janson and Uzzell: The vertex set of almost all
string graphs on n vertices can be partitioned into five cliques such that some
pair of them is not connected by any edge (n→∞). We also show that every graph
with the above property is an intersection graph of plane convex sets. As a corollary,
we obtain that almost all string graphs on n vertices are intersection graphs
of plane convex sets.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Bruce
full_name: Reed, Bruce
last_name: Reed
- first_name: Yelena
full_name: Yuditsky, Yelena
last_name: Yuditsky
citation:
ama: Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs
of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917.
doi:10.1007/s00454-020-00213-z
apa: Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are
intersection graphs of plane convex sets. Discrete and Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-020-00213-z
chicago: Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs
Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry.
Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.
ieee: J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection
graphs of plane convex sets,” Discrete and Computational Geometry, vol.
63, no. 4. Springer Nature, pp. 888–917, 2020.
ista: Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection
graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.
mla: Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane
Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer
Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z.
short: J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020)
888–917.
date_created: 2020-06-14T22:00:51Z
date_published: 2020-06-05T00:00:00Z
date_updated: 2025-04-15T07:16:56Z
day: '05'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00213-z
external_id:
arxiv:
- '1803.06710'
isi:
- '000538229000001'
intvolume: ' 63'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1803.06710
month: '06'
oa: 1
oa_version: Preprint
page: 888-917
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Almost all string graphs are intersection graphs of plane convex sets
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2020'
...
---
_id: '8163'
abstract:
- lang: eng
text: Fejes Tóth [3] studied approximations of smooth surfaces in three-space by
piecewise flat triangular meshes with a given number of vertices on the surface
that are optimal with respect to Hausdorff distance. He proves that this Hausdorff
distance decreases inversely proportional with the number of vertices of the approximating
mesh if the surface is convex. He also claims that this Hausdorff distance is
inversely proportional to the square of the number of vertices for a specific
non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by
two congruent circles. We refute this claim, and show that the asymptotic behavior
of the Hausdorff distance is linear, that is the same as for convex surfaces.
acknowledgement: "The authors are greatly indebted to Dror Atariah, Günther Rote and
John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel
Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion.
This work has been supported in part by the European Union’s Seventh Framework Programme
for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL
Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic
Foundations of Geometry Understanding in Higher Dimensions), the European Union’s
Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie
grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31."
article_processing_charge: No
article_type: original
author:
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy
of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199.
doi:10.1556/012.2020.57.2.1454
apa: Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes
Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica.
Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454
chicago: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes
Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum
Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.
ieee: G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on
the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica,
vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.
ista: Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on
the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2),
193–199.
mla: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes
Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum
Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454.
short: G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57
(2020) 193–199.
corr_author: '1'
date_created: 2020-07-24T07:09:18Z
date_published: 2020-07-24T00:00:00Z
date_updated: 2025-04-15T07:16:57Z
day: '24'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1556/012.2020.57.2.1454
ec_funded: 1
external_id:
isi:
- '000570978400005'
file:
- access_level: open_access
content_type: application/pdf
creator: mwintrae
date_created: 2020-07-24T07:09:06Z
date_updated: 2020-07-24T07:09:06Z
file_id: '8164'
file_name: 57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf
file_size: 1476072
relation: main_file
file_date_updated: 2020-07-24T07:09:06Z
has_accepted_license: '1'
intvolume: ' 57'
isi: 1
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 193-199
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: Studia Scientiarum Mathematicarum Hungarica
publication_identifier:
eissn:
- 1588-2896
issn:
- 0081-6906
publication_status: published
publisher: Akadémiai Kiadó
quality_controlled: '1'
scopus_import: '1'
status: public
title: Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
year: '2020'
...
---
_id: '8323'
article_processing_charge: No
article_type: letter_note
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
citation:
ama: Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry.
2020;64:571-574. doi:10.1007/s00454-020-00237-5
apa: Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5
chicago: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational
Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.
ieee: J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry,
vol. 64. Springer Nature, pp. 571–574, 2020.
ista: Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry.
64, 571–574.
mla: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry,
vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5.
short: J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.
corr_author: '1'
date_created: 2020-08-30T22:01:12Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2024-10-09T20:59:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00237-5
external_id:
isi:
- '000561483500001'
intvolume: ' 64'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-020-00237-5
month: '10'
oa: 1
oa_version: None
page: 571-574
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
scopus_import: '1'
status: public
title: A farewell to Ricky Pollack
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '8580'
abstract:
- lang: eng
text: We evaluate the usefulness of persistent homology in the analysis of heart
rate variability. In our approach we extract several topological descriptors characterising
datasets of RR-intervals, which are later used in classical machine learning algorithms.
By this method we are able to differentiate the group of patients with the history
of transient ischemic attack and the group of hypertensive patients.
article_number: '9158054'
article_processing_charge: No
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Beata
full_name: Graff, Beata
last_name: Graff
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Krzysztof
full_name: Narkiewicz, Krzysztof
last_name: Narkiewicz
citation:
ama: 'Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent
homology in the analysis of heart rate variability. In: 11th Conference of
the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054'
apa: 'Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application
of persistent homology in the analysis of heart rate variability. In 11th Conference
of the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054'
chicago: 'Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz.
“The Application of Persistent Homology in the Analysis of Heart Rate Variability.”
In 11th Conference of the European Study Group on Cardiovascular Oscillations:
Computation and Modelling in Physiology: New Challenges and Opportunities, .
IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.'
ieee: 'G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of
persistent homology in the analysis of heart rate variability,” in 11th Conference
of the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.'
ista: 'Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent
homology in the analysis of heart rate variability. 11th Conference of the European
Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology:
New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular
Oscillations, 9158054.'
mla: 'Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis
of Heart Rate Variability.” 11th Conference of the European Study Group on
Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges
and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.'
short: 'G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of
the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, , IEEE, 2020.'
conference:
end_date: 2020-07-15
location: Pisa, Italy
name: 'ESGCO: European Study Group on Cardiovascular Oscillations'
start_date: 2020-07-15
date_created: 2020-09-28T08:59:27Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-22T09:33:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1109/ESGCO49734.2020.9158054
external_id:
isi:
- '000621172600045'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
publication: '11th Conference of the European Study Group on Cardiovascular Oscillations:
Computation and Modelling in Physiology: New Challenges and Opportunities, '
publication_identifier:
isbn:
- '9781728157511'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: The application of persistent homology in the analysis of heart rate variability
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2020'
...
---
_id: '9156'
abstract:
- lang: eng
text: The morphometric approach [11, 14] writes the solvation free energy as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted Gaussian curvature. Together with the derivatives of the weighted
volume in [7], the weighted area in [4], and the weighted mean curvature in [1],
this yields the derivative of the morphometric expression of solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics
simulations. They also thank Patrice Koehl for the implementation of the formulas
and for his encouragement and advise along the road. Finally, they thank two anonymous
reviewers for their constructive criticism.\r\nThis project has received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 78818 Alpha). It is also partially
supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a
space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88.
doi:10.1515/cmb-2020-0101
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature
derivative of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0101
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative
of a space-filling diagram,” Computational and Mathematical Biophysics,
vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 74–88.
corr_author: '1'
date_created: 2021-02-17T15:12:44Z
date_published: 2020-07-21T00:00:00Z
date_updated: 2025-04-14T07:48:34Z
day: '21'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0101
ec_funded: 1
external_id:
arxiv:
- '1908.06777'
file:
- access_level: open_access
checksum: ca43a7440834eab6bbea29c59b56ef3a
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:33:19Z
date_updated: 2021-02-19T13:33:19Z
file_id: '9170'
file_name: 2020_CompMathBiophysics_Akopyan.pdf
file_size: 707452
relation: main_file
success: 1
file_date_updated: 2021-02-19T13:33:19Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 74-88
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: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: The weighted Gaussian curvature derivative of a space-filling diagram
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: '2020'
...
---
_id: '9157'
abstract:
- lang: eng
text: Representing an atom by a solid sphere in 3-dimensional Euclidean space, we
get the space-filling diagram of a molecule by taking the union. Molecular dynamics
simulates its motion subject to bonds and other forces, including the solvation
free energy. The morphometric approach [12, 17] writes the latter as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted mean curvature. Together with the derivatives of the weighted volume
in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this
yields the derivative of the morphometric expression of the solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of the weighted\r\ncurvature derivatives for the purpose of improving molecular
dynamics simulations and for his continued encouragement. They also thank Patrice
Koehl for the implementation of the formulas and for his encouragement and advise
along the road. Finally, they thank two anonymous reviewers for their constructive
criticism.\r\nThis project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative
Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant
no. I02979-N35 of the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling
diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0100
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of
a space-filling diagram,” Computational and Mathematical Biophysics, vol.
8, no. 1. De Gruyter, pp. 51–67, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of
a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative
of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 51–67.
corr_author: '1'
date_created: 2021-02-17T15:13:01Z
date_published: 2020-06-20T00:00:00Z
date_updated: 2025-04-14T07:48:35Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0100
ec_funded: 1
file:
- access_level: open_access
checksum: cea41de9937d07a3b927d71ee8b4e432
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:56:24Z
date_updated: 2021-02-19T13:56:24Z
file_id: '9171'
file_name: 2020_CompMathBiophysics_Akopyan2.pdf
file_size: 562359
relation: main_file
success: 1
file_date_updated: 2021-02-19T13:56:24Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 51-67
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: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted mean curvature derivative of a space-filling diagram
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: '2020'
...
---
_id: '9249'
abstract:
- lang: eng
text: Rhombic dodecahedron is a space filling polyhedron which represents the close
packing of spheres in 3D space and the Voronoi structures of the face centered
cubic (FCC) lattice. In this paper, we describe a new coordinate system where
every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid.
In order to illustrate the interest of the new coordinate system, we propose the
characterization of 3D digital plane with its topological features, such as the
interrelation between the thickness of the digital plane and the separability
constraint we aim to obtain. We also present the characterization of 3D digital
lines and study it as the intersection of multiple digital planes. Characterization
of 3D digital sphere with relevant topological features is proposed as well along
with the 48-symmetry appearing in the new coordinate system.
acknowledgement: "This work has been partially supported by the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109,
‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no.
I 02979-N35. "
article_processing_charge: No
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: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic
dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158.
doi:10.1515/mathm-2020-0106
apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital
objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and
Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106
chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital
Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and
Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.
ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects
in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications,
vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.
ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in
rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications.
4(1), 143–158.
mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical
Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp.
143–58, doi:10.1515/mathm-2020-0106.
short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology
- Theory and Applications 4 (2020) 143–158.
corr_author: '1'
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2025-04-14T07:48:35Z
day: '17'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/mathm-2020-0106
ec_funded: 1
file:
- access_level: open_access
checksum: 4a1043fa0548a725d464017fe2483ce0
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:56:37Z
date_updated: 2021-03-22T08:56:37Z
file_id: '9272'
file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf
file_size: 3668725
relation: main_file
success: 1
file_date_updated: 2021-03-22T08:56:37Z
has_accepted_license: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 143-158
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: Mathematical Morphology - Theory and Applications
publication_identifier:
issn:
- 2353-3390
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: Digital objects in rhombic dodecahedron grid
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...
---
_id: '9299'
abstract:
- lang: eng
text: We call a multigraph non-homotopic if it can be drawn in the plane in such
a way that no two edges connecting the same pair of vertices can be continuously
transformed into each other without passing through a vertex, and no loop can
be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic
multigraph on n>1 vertices can have arbitrarily many edges. We prove that the
number of crossings between the edges of a non-homotopic multigraph with n vertices
and m>4n edges is larger than cm2n for some constant c>0 , and that this
bound is tight up to a polylogarithmic factor. We also show that the lower bound
is not asymptotically sharp as n is fixed and m⟶∞ .
acknowledgement: Supported by the National Research, Development and Innovation Office,
NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional
Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant
Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant
No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full
version can be found at https://arxiv.org/abs/2006.14908.
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: Gábor
full_name: Tardos, Gábor
last_name: Tardos
- first_name: Géza
full_name: Tóth, Géza
last_name: Tóth
citation:
ama: 'Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th
International Symposium on Graph Drawing and Network Visualization. Vol 12590.
LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28'
apa: 'Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic
edges. In 28th International Symposium on Graph Drawing and Network Visualization
(Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28'
chicago: Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic
Edges.” In 28th International Symposium on Graph Drawing and Network Visualization,
12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.
ieee: J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,”
in 28th International Symposium on Graph Drawing and Network Visualization,
Virtual, Online, 2020, vol. 12590, pp. 359–371.
ista: 'Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th
International Symposium on Graph Drawing and Network Visualization. GD: Graph
Drawing and Network VisualizationLNCS vol. 12590, 359–371.'
mla: Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International
Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer
Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.
short: J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing
and Network Visualization, Springer Nature, 2020, pp. 359–371.
conference:
end_date: 2020-09-18
location: Virtual, Online
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2020-09-16
date_created: 2021-03-28T22:01:44Z
date_published: 2020-09-20T00:00:00Z
date_updated: 2025-04-15T07:16:52Z
day: '20'
department:
- _id: HeEd
doi: 10.1007/978-3-030-68766-3_28
external_id:
arxiv:
- '2006.14908'
intvolume: ' 12590'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.14908
month: '09'
oa: 1
oa_version: Preprint
page: 359-371
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: 28th International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030687656'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Crossings between non-homotopic edges
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12590
year: '2020'
...
---
_id: '74'
abstract:
- lang: eng
text: "We study the Gromov waist in the sense of t-neighborhoods for measures in
the Euclidean space, motivated by the famous theorem of Gromov about
\ the waist of radially symmetric Gaussian measures. In particular, it turns
our possible to extend Gromov’s original result to the case of not necessarily
\ radially symmetric Gaussian measure. We also provide examples of measures
having no t-neighborhood waist property, including a rather wide class\r\nof compactly
supported radially symmetric measures and their maps into the Euclidean space
of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument
\ to produce some estimates of t-neighborhoods of (weighted) volume-critical
submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic
manifolds in the complex projective space. In the appendix of this paper we provide
for reader’s convenience a more detailed explanation of the Caffarelli theorem
that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: 'Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial
non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional
Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1'
apa: Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian
measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.),
Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer
Nature. https://doi.org/10.1007/978-3-030-36020-7_1
chicago: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer
Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.
ieee: A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis,
vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.
ista: 'Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis.
vol. 2256, 1–27.'
mla: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer
Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.
short: A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects
of Functional Analysis, Springer Nature, 2020, pp. 1–27.
date_created: 2018-12-11T11:44:29Z
date_published: 2020-06-21T00:00:00Z
date_updated: 2025-07-10T11:54:33Z
day: '21'
department:
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- _id: JaMa
doi: 10.1007/978-3-030-36020-7_1
ec_funded: 1
editor:
- first_name: Bo'az
full_name: Klartag, Bo'az
last_name: Klartag
- first_name: Emanuel
full_name: Milman, Emanuel
last_name: Milman
external_id:
arxiv:
- '1808.07350'
isi:
- '000557689300003'
intvolume: ' 2256'
isi: 1
language:
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publication: Geometric Aspects of Functional Analysis
publication_identifier:
eisbn:
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eissn:
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isbn:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNM
status: public
title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2256
year: '2020'
...
---
_id: '7554'
abstract:
- lang: eng
text: Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional
weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation.
Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the
smallest empty circumscribed sphere whose center lies in the $k$-plane gives a
generalized discrete Morse function. Assuming the Voronoi tessellation is generated
by a Poisson point process in ${R}^n$, we study the expected number of simplices
in the $k$-dimensional weighted Delaunay mosaic as well as the expected number
of intervals of the Morse function, both as functions of a radius threshold. As
a by-product, we obtain a new proof for the expected number of connected components
(clumps) in a line section of a circular Boolean model in ${R}^n$.
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: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of
Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726
apa: Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics.
Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay
Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.
ieee: H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory
of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020.
ista: Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory
of Probability and its Applications. 64(4), 595–614.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.”
Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020,
pp. 595–614, doi:10.1137/S0040585X97T989726.
short: H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications
64 (2020) 595–614.
date_created: 2020-03-01T23:00:39Z
date_published: 2020-02-13T00:00:00Z
date_updated: 2025-07-10T11:54:44Z
day: '13'
department:
- _id: HeEd
doi: 10.1137/S0040585X97T989726
ec_funded: 1
external_id:
arxiv:
- '1705.08735'
isi:
- '000551393100007'
intvolume: ' 64'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/1705.08735
month: '02'
oa: 1
oa_version: Preprint
page: 595-614
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: Theory of Probability and its Applications
publication_identifier:
eissn:
- 1095-7219
issn:
- 0040-585X
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weighted Poisson–Delaunay mosaics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2020'
...
---
_id: '7567'
abstract:
- lang: eng
text: Coxeter triangulations are triangulations of Euclidean space based on a single
simplex. By this we mean that given an individual simplex we can recover the entire
triangulation of Euclidean space by inductively reflecting in the faces of the
simplex. In this paper we establish that the quality of the simplices in all Coxeter
triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate
the Delaunay property for these triangulations. Moreover, we consider an extension
of the Delaunay property, namely protection, which is a measure of non-degeneracy
of a Delaunay triangulation. In particular, one family of Coxeter triangulations
achieves the protection O(1/d2). We conjecture that both bounds are optimal for
triangulations in Euclidean space.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Aruni
full_name: Choudhary, Aruni
last_name: Choudhary
- first_name: Siargey
full_name: Kachanovich, Siargey
last_name: Kachanovich
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good
quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5
apa: Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations
have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5
chicago: Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter
Triangulations Have Good Quality.” Mathematics in Computer Science. Springer
Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.
ieee: A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations
have good quality,” Mathematics in Computer Science, vol. 14. Springer
Nature, pp. 141–176, 2020.
ista: Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have
good quality. Mathematics in Computer Science. 14, 141–176.
mla: Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics
in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5.
short: A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science
14 (2020) 141–176.
corr_author: '1'
date_created: 2020-03-05T13:30:18Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2025-04-14T07:44:03Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s11786-020-00461-5
ec_funded: 1
file:
- access_level: open_access
checksum: 1d145f3ab50ccee735983cb89236e609
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T10:18:02Z
date_updated: 2020-11-20T10:18:02Z
file_id: '8783'
file_name: 2020_MathCompScie_Choudhary.pdf
file_size: 872275
relation: main_file
success: 1
file_date_updated: 2020-11-20T10:18:02Z
has_accepted_license: '1'
intvolume: ' 14'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 141-176
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Mathematics in Computer Science
publication_identifier:
eissn:
- 1661-8289
issn:
- 1661-8270
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coxeter triangulations have good quality
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: 14
year: '2020'
...
---
_id: '9630'
abstract:
- lang: eng
text: Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms. Importantly,
instead of using the standard Euclidean distance, we look into dissimilarity measures
with information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund (FWF).
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: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0009-0009-9111-8429
citation:
ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7
apa: Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis
in information space. Journal of Computational Geometry. Carleton University.
https://doi.org/10.20382/jocg.v11i2a7
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” Journal of Computational Geometry. Carleton
University, 2020. https://doi.org/10.20382/jocg.v11i2a7.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University,
pp. 162–182, 2020.
ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
space. Journal of Computational Geometry. 11(2), 162–182.
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
Journal of Computational Geometry, vol. 11, no. 2, Carleton University,
2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.
short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
(2020) 162–182.
corr_author: '1'
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2026-04-02T14:35:31Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
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date_updated: 2021-08-11T11:55:11Z
file_id: '9882'
file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
file_size: 1449234
relation: main_file
success: 1
file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: ' 11'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
publication: Journal of Computational Geometry
publication_identifier:
eissn:
- 1920-180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 11
year: '2020'
...
---
_id: '8135'
abstract:
- lang: eng
text: Discrete Morse theory has recently lead to new developments in the theory
of random geometric complexes. This article surveys the methods and results obtained
with this new approach, and discusses some of its shortcomings. It uses simulations
to illustrate the results and to form conjectures, getting numerical estimates
for combinatorial, topological, and geometric properties of weighted and unweighted
Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes
contained in the mosaics.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreements No 78818 Alpha and No 638176). It is also partially supported
by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and
Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).
alternative_title:
- Abel Symposia
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
citation:
ama: 'Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay
mosaics and related complexes experimentally. In: Topological Data Analysis.
Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8'
apa: Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius
functions on Poisson–Delaunay mosaics and related complexes experimentally. In
Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8
chicago: Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak.
“Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.”
In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.
ieee: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions
on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological
Data Analysis, 2020, vol. 15, pp. 181–218.
ista: Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on
Poisson–Delaunay mosaics and related complexes experimentally. Topological Data
Analysis. , Abel Symposia, vol. 15, 181–218.
mla: Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics
and Related Complexes Experimentally.” Topological Data Analysis, vol.
15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.
short: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data
Analysis, Springer Nature, 2020, pp. 181–218.
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2026-04-07T12:35:47Z
day: '22'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/978-3-030-43408-3_8
ec_funded: 1
external_id:
isi:
- '001321861000008'
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creator: dernst
date_created: 2020-10-08T08:56:14Z
date_updated: 2020-10-08T08:56:14Z
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file_name: 2020-B-01-PoissonExperimentalSurvey.pdf
file_size: 2207071
relation: main_file
success: 1
file_date_updated: 2020-10-08T08:56:14Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 181-218
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2533E772-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '638176'
name: 'Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large
Scales'
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Topological Data Analysis
publication_identifier:
eissn:
- 2197-8549
isbn:
- '9783030434076'
issn:
- 2193-2808
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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record:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 15
year: '2020'
...