---
_id: '8773'
abstract:
- lang: eng
text: Let g be a complex semisimple Lie algebra. We give a classification of contravariant
forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We
prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose
dimension is given by the cardinality of the Weyl group of g. We also describe
a procedure for parabolically inducing contravariant forms. As a corollary, we
deduce the existence of the Shapovalov form on a Verma module, and provide a formula
for the dimension of the space of contravariant forms on the degenerate Whittaker
modules M(χ,η) introduced by McDowell.
acknowledgement: "We would like to thank Peter Trapa for useful discussions, and Dragan
Milicic and Arun Ram for valuable feedback on the structure of the paper. The first
author acknowledges the support of the European Unions Horizon 2020 research and
innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411.
The second author is\r\nsupported by the National Science Foundation Award No. 1803059."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Anna
full_name: Romanov, Anna
last_name: Romanov
citation:
ama: Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205
apa: Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules.
Proceedings of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/proc/15205
chicago: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2021. https://doi.org/10.1090/proc/15205.
ieee: A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings
of the American Mathematical Society, vol. 149, no. 1. American Mathematical
Society, pp. 37–52, 2021.
ista: Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 149(1), 37–52.
mla: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
Proceedings of the American Mathematical Society, vol. 149, no. 1, American
Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.
short: A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149
(2021) 37–52.
date_created: 2020-11-19T10:17:40Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T11:11:47Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/15205
ec_funded: 1
external_id:
arxiv:
- '1910.08286'
isi:
- '000600416300004'
intvolume: ' 149'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08286
month: '01'
oa: 1
oa_version: Preprint
page: 37-52
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: Contravariant forms on Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 149
year: '2021'
...
---
_id: '8940'
abstract:
- lang: eng
text: We quantise Whitney’s construction to prove the existence of a triangulation
for any C^2 manifold, so that we get an algorithm with explicit bounds. We also
give a new elementary proof, which is completely geometric.
acknowledgement: This work has been funded by the European Research Council under
the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations
of Geometric Understanding in Higher Dimensions). The third author also received
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding
provided by the Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- 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: 'Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds:
An elementary and quantified version of Whitney’s method. Discrete & Computational
Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8'
apa: 'Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating
submanifolds: An elementary and quantified version of Whitney’s method. Discrete
& Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8'
chicago: 'Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken.
“Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s
Method.” Discrete & Computational Geometry. Springer Nature, 2021.
https://doi.org/10.1007/s00454-020-00250-8.'
ieee: 'J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds:
An elementary and quantified version of Whitney’s method,” Discrete & Computational
Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.'
ista: 'Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds:
An elementary and quantified version of Whitney’s method. Discrete & Computational
Geometry. 66(1), 386–434.'
mla: 'Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary
and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry,
vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.'
short: J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational
Geometry 66 (2021) 386–434.
date_created: 2020-12-12T11:07:02Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2023-09-05T15:02:40Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00250-8
ec_funded: 1
external_id:
isi:
- '000597770300001'
file:
- access_level: open_access
checksum: c848986091e56699dc12de85adb1e39c
content_type: application/pdf
creator: kschuh
date_created: 2021-08-06T09:52:29Z
date_updated: 2021-08-06T09:52:29Z
file_id: '9795'
file_name: 2021_DescreteCompGeopmetry_Boissonnat.pdf
file_size: 983307
relation: main_file
success: 1
file_date_updated: 2021-08-06T09:52:29Z
has_accepted_license: '1'
intvolume: ' 66'
isi: 1
issue: '1'
keyword:
- Theoretical Computer Science
- Computational Theory and Mathematics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 386-434
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: 'Triangulating submanifolds: An elementary and quantified version of Whitney’s
method'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 66
year: '2021'
...
---
_id: '9056'
abstract:
- lang: eng
text: "In this thesis we study persistence of multi-covers of Euclidean balls and
the geometric structures underlying their computation, in particular Delaunay
mosaics and Voronoi tessellations. The k-fold cover for some discrete input point
set consists of the space where at least k balls of radius r around the input
points overlap. Persistence is a notion that captures, in some sense, the topology
of the shape underlying the input. While persistence is usually computed for the
union of balls, the k-fold cover is of interest as it captures local density,\r\nand
thus might approximate the shape of the input better if the input data is noisy.
To compute persistence of these k-fold covers, we need a discretization that is
provided by higher-order Delaunay mosaics. We present and implement a simple and
efficient algorithm for the computation of higher-order Delaunay mosaics, and
use it to give experimental results for their combinatorial properties. The algorithm
makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order
Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the
tiling, we also obtain higher-order α-shapes as slices. These allow us to compute
persistence of the multi-covers for varying radius r; the computation for varying
k is less straight-foward and involves the rhomboid tiling directly. We apply
our algorithms to experimental sphere packings to shed light on their structural
properties. Finally, inspired by periodic structures in packings and materials,
we propose and implement an algorithm for periodic Delaunay triangulations to
be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss
the implications on persistence for periodic data sets."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056
apa: Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute
of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056
chicago: Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute
of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.
ieee: G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of
Science and Technology Austria, Klosterneuburg, 2021.
ista: 'Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg:
Institute of Science and Technology Austria.'
mla: Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute
of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.
short: G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science
and Technology Austria, 2021.
date_created: 2021-02-02T14:11:06Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-07T13:29:01Z
day: '01'
ddc:
- '006'
- '514'
- '516'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:9056
file:
- access_level: closed
checksum: bcf27986147cab0533b6abadd74e7629
content_type: application/zip
creator: patrickd
date_created: 2021-02-02T14:09:25Z
date_updated: 2021-02-03T10:37:28Z
file_id: '9063'
file_name: thesis_source.zip
file_size: 13446994
relation: source_file
- access_level: open_access
checksum: 9cc8af266579a464385bbe2aff6af606
content_type: application/pdf
creator: patrickd
date_created: 2021-02-02T14:09:18Z
date_updated: 2021-02-02T14:09:18Z
file_id: '9064'
file_name: thesis_pdfA2b.pdf
file_size: 5210329
relation: main_file
success: 1
file_date_updated: 2021-02-03T10:37:28Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '134'
place: Klosterneuburg
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '187'
relation: part_of_dissertation
status: public
- id: '8703'
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: Multi-cover persistence and Delaunay mosaics
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '9111'
abstract:
- lang: eng
text: 'We study the probabilistic convergence between the mapper graph and the Reeb
graph of a topological space X equipped with a continuous function f:X→R. We first
give a categorification of the mapper graph and the Reeb graph by interpreting
them in terms of cosheaves and stratified covers of the real line R. We then introduce
a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium
on point-based graphics, 2007), referred to as the enhanced mapper graph, and
demonstrate that such a construction approximates the Reeb graph of (X,f) when
it is applied to points randomly sampled from a probability density function concentrated
on (X,f). Our techniques are based on the interleaving distance of constructible
cosheaves and topological estimation via kernel density estimates. Following Munch
and Wang (In: 32nd international symposium on computational geometry, volume 51
of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany,
pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible
R-space (with a fixed open cover), approximates the Reeb graph of the same space.
We then construct an isomorphism between the mapper of (X,f) to the mapper of
a super-level set of a probability density function concentrated on (X,f). Finally,
building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b),
we show that, with high probability, we can recover the mapper of the super-level
set given a sufficiently large sample. Our work is the first to consider the mapper
construction using the theory of cosheaves in a probabilistic setting. It is part
of an ongoing effort to combine sheaf theory, probability, and statistics, to
support topological data analysis with random data.'
acknowledgement: "AB was supported in part by the European Union’s Horizon 2020 research
and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No.
754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation,
Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was
supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like
to thank the Institute for Mathematics and its Applications for hosting a workshop
titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen
Access funding provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Omer
full_name: Bobrowski, Omer
last_name: Bobrowski
- first_name: Elizabeth
full_name: Munch, Elizabeth
last_name: Munch
- first_name: Bei
full_name: Wang, Bei
last_name: Wang
citation:
ama: Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability
of random mapper graphs. Journal of Applied and Computational Topology.
2021;5(1):99-140. doi:10.1007/s41468-020-00063-x
apa: Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence
and stability of random mapper graphs. Journal of Applied and Computational
Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x
chicago: Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic
Convergence and Stability of Random Mapper Graphs.” Journal of Applied and
Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.
ieee: A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence
and stability of random mapper graphs,” Journal of Applied and Computational
Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.
ista: Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and
stability of random mapper graphs. Journal of Applied and Computational Topology.
5(1), 99–140.
mla: Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper
Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1,
Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x.
short: A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational
Topology 5 (2021) 99–140.
date_created: 2021-02-11T14:41:02Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-09-05T15:37:56Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s41468-020-00063-x
ec_funded: 1
external_id:
arxiv:
- '1909.03488'
file:
- access_level: open_access
checksum: 3f02e9d47c428484733da0f588a3c069
content_type: application/pdf
creator: dernst
date_created: 2021-02-11T14:43:59Z
date_updated: 2021-02-11T14:43:59Z
file_id: '9112'
file_name: 2020_JourApplCompTopology_Brown.pdf
file_size: 2090265
relation: main_file
success: 1
file_date_updated: 2021-02-11T14:43:59Z
has_accepted_license: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 99-140
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Probabilistic convergence and stability of random mapper graphs
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 5
year: '2021'
...
---
_id: '9253'
abstract:
- lang: eng
text: In March 2020, the Austrian government introduced a widespread lock-down in
response to the COVID-19 pandemic. Based on subjective impressions and anecdotal
evidence, Austrian public and private life came to a sudden halt. Here we assess
the effect of the lock-down quantitatively for all regions in Austria and present
an analysis of daily changes of human mobility throughout Austria using near-real-time
anonymized mobile phone data. We describe an efficient data aggregation pipeline
and analyze the mobility by quantifying mobile-phone traffic at specific point
of interests (POIs), analyzing individual trajectories and investigating the cluster
structure of the origin-destination graph. We found a reduction of commuters at
Viennese metro stations of over 80% and the number of devices with a radius of
gyration of less than 500 m almost doubled. The results of studying crowd-movement
behavior highlight considerable changes in the structure of mobility networks,
revealed by a higher modularity and an increase from 12 to 20 detected communities.
We demonstrate the relevance of mobility data for epidemiological studies by showing
a significant correlation of the outflow from the town of Ischgl (an early COVID-19
hotspot) and the reported COVID-19 cases with an 8-day time lag. This research
indicates that mobile phone usage data permits the moment-by-moment quantification
of mobility behavior for a whole country. We emphasize the need to improve the
availability of such data in anonymized form to empower rapid response to combat
COVID-19 and future pandemics.
article_processing_charge: No
arxiv: 1
author:
- first_name: Georg
full_name: Heiler, Georg
last_name: Heiler
- first_name: Tobias
full_name: Reisch, Tobias
last_name: Reisch
- first_name: Jan
full_name: Hurt, Jan
last_name: Hurt
- first_name: Mohammad
full_name: Forghani, Mohammad
last_name: Forghani
- first_name: Aida
full_name: Omani, Aida
last_name: Omani
- first_name: Allan
full_name: Hanbury, Allan
last_name: Hanbury
- first_name: Farid
full_name: Karimipour, Farid
id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425
last_name: Karimipour
orcid: 0000-0001-6746-4174
citation:
ama: 'Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed
using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International
Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374'
apa: 'Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., &
Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone
data during COVID-19 pandemic. In 2020 IEEE International Conference on Big
Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374'
chicago: Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani,
Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using
Mobile Phone Data during COVID-19 Pandemic.” In 2020 IEEE International Conference
on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374.
ieee: G. Heiler et al., “Country-wide mobility changes observed using mobile
phone data during COVID-19 pandemic,” in 2020 IEEE International Conference
on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132.
ista: 'Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F.
2021. Country-wide mobility changes observed using mobile phone data during COVID-19
pandemic. 2020 IEEE International Conference on Big Data. Big Data: International
Conference on Big Data, 3123–3132.'
mla: Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile
Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on
Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374.
short: G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour,
in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132.
conference:
end_date: 2020-12-13
location: Atlanta, GA, United States
name: 'Big Data: International Conference on Big Data'
start_date: 2020-12-10
date_created: 2021-03-21T11:34:07Z
date_published: 2021-03-19T00:00:00Z
date_updated: 2023-08-07T14:00:13Z
day: '19'
department:
- _id: HeEd
doi: 10.1109/bigdata50022.2020.9378374
external_id:
arxiv:
- '2008.10064'
isi:
- '000662554703032'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2008.10064
month: '03'
oa: 1
oa_version: Preprint
page: 3123-3132
publication: 2020 IEEE International Conference on Big Data
publication_identifier:
isbn:
- '9781728162515'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Country-wide mobility changes observed using mobile phone data during COVID-19
pandemic
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
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: 2023-02-21T16:33:44Z
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'
intvolume: ' 12635'
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: The Wittgenstein Prize
- _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:
eissn:
- '16113349'
isbn:
- '9783030682101'
issn:
- '03029743'
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 12635
year: '2021'
...
---
_id: '9317'
abstract:
- lang: eng
text: Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r
consists of all points in Rd that have k or more points of X within distance r.
We consider two filtrations—one in scale obtained by fixing k and increasing r,
and the other in depth obtained by fixing r and decreasing k—and we compute the
persistence diagrams of both. While standard methods suffice for the filtration
in scale, we need novel geometric and topological concepts for the filtration
in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal
integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module
of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.
acknowledgement: "This 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), and by the DFG Collaborative Research Center
TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35
of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute
of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
citation:
ama: Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete
and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9
apa: Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of
Euclidean balls. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-021-00281-9
chicago: Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence
of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature,
2021. https://doi.org/10.1007/s00454-021-00281-9.
ieee: H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean
balls,” Discrete and Computational Geometry, vol. 65. Springer Nature,
pp. 1296–1313, 2021.
ista: Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls.
Discrete and Computational Geometry. 65, 1296–1313.
mla: Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of
Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer
Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9.
short: H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021)
1296–1313.
date_created: 2021-04-11T22:01:15Z
date_published: 2021-03-31T00:00:00Z
date_updated: 2023-08-07T14:35:44Z
day: '31'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-021-00281-9
ec_funded: 1
external_id:
isi:
- '000635460400001'
file:
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checksum: 59b4e1e827e494209bcb4aae22e1d347
content_type: application/pdf
creator: cchlebak
date_created: 2021-12-01T10:56:53Z
date_updated: 2021-12-01T10:56:53Z
file_id: '10394'
file_name: 2021_DisCompGeo_Edelsbrunner_Osang.pdf
file_size: 677704
relation: main_file
success: 1
file_date_updated: 2021-12-01T10:56:53Z
has_accepted_license: '1'
intvolume: ' 65'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1296–1313
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 and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The multi-cover persistence of Euclidean balls
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: 65
year: '2021'
...
---
_id: '9345'
abstract:
- lang: eng
text: Modeling a crystal as a periodic point set, we present a fingerprint consisting
of density functionsthat facilitates the efficient search for new materials and
material properties. We prove invarianceunder isometries, continuity, and completeness
in the generic case, which are necessary featuresfor the reliable comparison of
crystals. The proof of continuity integrates methods from discretegeometry and
lattice theory, while the proof of generic completeness combines techniques fromgeometry
with analysis. The fingerprint has a fast algorithm based on Brillouin zones and
relatedinclusion-exclusion formulae. We have implemented the algorithm and describe
its application tocrystal structure prediction.
acknowledgement: The authors thank Janos Pach for insightful discussions on the topic
of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned
in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.
alternative_title:
- LIPIcs
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: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Vitaliy
full_name: ' Kurlin , Vitaliy'
last_name: ' Kurlin '
- first_name: Philip
full_name: Smith, Philip
last_name: Smith
- 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, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint
of a periodic point set. In: 37th International Symposium on Computational
Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik;
2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32'
apa: 'Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M.
(2021). The density fingerprint of a periodic point set. In 37th International
Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16).
Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32'
chicago: Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and
Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th
International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32.
ieee: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The
density fingerprint of a periodic point set,” in 37th International Symposium
on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.
ista: 'Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density
fingerprint of a periodic point set. 37th International Symposium on Computational
Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol.
189, 32:1-32:16.'
mla: Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point
Set.” 37th International Symposium on Computational Geometry (SoCG 2021),
vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16,
doi:10.4230/LIPIcs.SoCG.2021.32.
short: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th
International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.
conference:
end_date: 2021-06-11
location: Virtual
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-04-22T08:09:58Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T13:55:40Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.32
ec_funded: 1
file:
- access_level: open_access
checksum: 1787baef1523d6d93753b90d0c109a6d
content_type: application/pdf
creator: mwintrae
date_created: 2021-04-22T08:08:14Z
date_updated: 2021-04-22T08:08:14Z
file_id: '9346'
file_name: df_socg_final_version.pdf
file_size: 3117435
relation: main_file
success: 1
file_date_updated: 2021-04-22T08:08:14Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 32:1-32:16
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 25C5A090-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00312
name: The Wittgenstein Prize
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry (SoCG 2021)
publication_identifier:
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: The density fingerprint of a periodic point set
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9441'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate
multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension
of the manifold. A natural way to approximate a smooth isomanifold M is to consider
its Piecewise-Linear (PL) approximation M̂ based on a triangulation \U0001D4AF
of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace
isomanifolds from a given starting point. The algorithm works for arbitrary dimensions
n and d, and any precision D. Our main result is that, when f (or M) has bounded
complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and
unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂
is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation
of isomanifolds of bounded complexity in time polynomial in d. Combining this
algorithm with dimensionality reduction techniques, the dependency on d in the
size of M̂ can be completely removed with high probability. We also show that
the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds.
The algorithm for isomanifolds with boundary has been implemented and experimental
results are reported, showing that it is practical and can handle cases that are
far ahead of the state-of-the-art. "
acknowledgement: We thank Dominique Attali, Guilherme de Fonseca, Arijit Ghosh, Vincent
Pilaud and Aurélien Alvarez for their comments and suggestions. We also acknowledge
the reviewers.
alternative_title:
- LIPIcs
article_processing_charge: No
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- 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: 'Boissonnat J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in
time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: 37th
International Symposium on Computational Geometry (SoCG 2021). Vol 189. Leibniz
International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:10.4230/LIPIcs.SoCG.2021.17'
apa: 'Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Tracing
isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations.
In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol.
189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für
Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.17'
chicago: 'Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken.
“Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn
Triangulations.” In 37th International Symposium on Computational Geometry
(SoCG 2021), 189:17:1-17:16. Leibniz International Proceedings in Informatics
(LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.17.'
ieee: J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds
in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,”
in 37th International Symposium on Computational Geometry (SoCG 2021),
Virtual, 2021, vol. 189, p. 17:1-17:16.
ista: 'Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Tracing isomanifolds
in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. 37th
International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium
on Computational GeometryLeibniz International Proceedings in Informatics (LIPIcs),
LIPIcs, vol. 189, 17:1-17:16.'
mla: Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial
in d Using Coxeter-Freudenthal-Kuhn Triangulations.” 37th International Symposium
on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021, p. 17:1-17:16, doi:10.4230/LIPIcs.SoCG.2021.17.
short: J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, in:, 37th International
Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, Dagstuhl, Germany, 2021, p. 17:1-17:16.
conference:
end_date: 2021-06-11
location: Virtual
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-02T10:10:55Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-10-10T07:34:34Z
day: '02'
ddc:
- '005'
- '516'
- '514'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.17
ec_funded: 1
file:
- access_level: open_access
checksum: c322aa48d5d35a35877896cc565705b6
content_type: application/pdf
creator: mwintrae
date_created: 2021-06-02T10:22:33Z
date_updated: 2021-06-02T10:22:33Z
file_id: '9442'
file_name: LIPIcs-SoCG-2021-17.pdf
file_size: 1972902
relation: main_file
success: 1
file_date_updated: 2021-06-02T10:22:33Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 17:1-17:16
place: Dagstuhl, Germany
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry (SoCG 2021)
publication_identifier:
isbn:
- 978-3-95977-184-9
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '12960'
relation: later_version
status: public
series_title: Leibniz International Proceedings in Informatics (LIPIcs)
status: public
title: Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn
triangulations
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9465'
abstract:
- lang: eng
text: "Given a locally finite set \U0001D44B⊆ℝ\U0001D451 and an integer \U0001D458≥0,
we consider the function \U0001D430\U0001D458:Del\U0001D458(\U0001D44B)→ℝ on the
dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion
of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf
Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett
114:76–83, 2014). While this function is not necessarily generalized discrete
Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete
Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that
its increments can be meaningfully classified into critical and non-critical steps.
This result extends to the case of weighted points and sheds light on k-fold covers
with balls in Euclidean space."
article_number: '15'
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: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
citation:
ama: Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order
k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4
apa: Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay
mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4
chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the
Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021.
https://doi.org/10.1007/s00022-021-00577-4.
ieee: H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic
of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021.
ista: Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic
of order k. Journal of Geometry. 112(1), 15.
mla: Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal
of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4.
short: H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).
date_created: 2021-06-06T22:01:29Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2022-05-12T11:41:45Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00022-021-00577-4
file:
- access_level: open_access
checksum: e52a832f1def52a2b23d21bcc09e646f
content_type: application/pdf
creator: kschuh
date_created: 2021-06-11T13:16:26Z
date_updated: 2021-06-11T13:16:26Z
file_id: '9544'
file_name: 2021_Geometry_Edelsbrunner.pdf
file_size: 694706
relation: main_file
success: 1
file_date_updated: 2021-06-11T13:16:26Z
has_accepted_license: '1'
intvolume: ' 112'
issue: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Geometry
publication_identifier:
eissn:
- '14208997'
issn:
- '00472468'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A step in the Delaunay mosaic of order k
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: 112
year: '2021'
...
---
_id: '9602'
abstract:
- lang: eng
text: "An ordered graph is a graph with a linear ordering on its vertex set. We
prove that for every positive integer k, there exists a constant ck > 0 such that
any ordered graph G on n vertices with the property that neither G nor its complement
contains an induced monotone path of size k, has either a clique or an independent
set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and
Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea
of the above paper was to show that any unordered graph on n vertices that does
not contain an induced path of size k, and whose maximum degree is at most c(k)n
for some small c(k) > 0, contains two disjoint linear size subsets with no edge
between them. This approach fails for ordered graphs, because the analogous statement
is false for k ≥ 3, by a construction of Fox. We provide some further examples
showing that this statement also fails for ordered graphs avoiding other ordered
trees."
acknowledgement: We would like to thank the anonymous referees for their useful comments
and suggestions. János Pach is partially supported by Austrian Science Fund (FWF)
grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially
supported by Swiss National Science Foundation grant no. 200021_196965, and thanks
the support of MIPT Moscow. Both authors are partially supported by The Russian
Government in the framework of MegaGrant no. 075-15-2019-1926.
article_processing_charge: No
article_type: original
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: István
full_name: Tomon, István
last_name: Tomon
citation:
ama: Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. Journal of
Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004
apa: Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths.
Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004
chicago: Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone
Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004.
ieee: J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal
of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021.
ista: Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal
of Combinatorial Theory. Series B. 151, 21–37.
mla: Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.”
Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp.
21–37, doi:10.1016/j.jctb.2021.05.004.
short: J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.
date_created: 2021-06-27T22:01:47Z
date_published: 2021-06-09T00:00:00Z
date_updated: 2023-08-10T13:38:00Z
day: '09'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jctb.2021.05.004
external_id:
isi:
- '000702280800002'
file:
- access_level: open_access
checksum: 15fbc9064cd9d1c777ac0043b78c8f12
content_type: application/pdf
creator: asandaue
date_created: 2021-06-28T13:33:23Z
date_updated: 2021-06-28T13:33:23Z
file_id: '9612'
file_name: 2021_JournalOfCombinatorialTheory_Pach.pdf
file_size: 418168
relation: main_file
success: 1
file_date_updated: 2021-06-28T13:33:23Z
has_accepted_license: '1'
intvolume: ' 151'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 21-37
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Journal of Combinatorial Theory. Series B
publication_identifier:
issn:
- 0095-8956
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Erdős-Hajnal-type results for monotone paths
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: 151
year: '2021'
...
---
_id: '9604'
abstract:
- lang: eng
text: Generalizing Lee’s inductive argument for counting the cells of higher order
Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse
theoretic quantities for piecewise constant functions on planar arrangements.
Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number
of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for
1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s
first k-1 sublevel sets. We get similar expressions for the vertices, edges, and
polygons of the order-k Voronoi tessellation.
alternative_title:
- LIPIcs
article_number: '16'
article_processing_charge: No
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
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells
of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz
International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with
morse theory. In Leibniz International Proceedings in Informatics (Vol.
189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16'
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3
with Morse Theory.” In Leibniz International Proceedings in Informatics,
Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory,” in
Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz
International Proceedings in Informatics. SoCG: International Symposium on Computational
Geometry, LIPIcs, vol. 189, 16.'
mla: Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in
ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics,
vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:,
Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021.
conference:
end_date: 2021-06-11
location: Online
name: 'SoCG: International Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-27T22:01:48Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T14:02:28Z
day: '02'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.16
ec_funded: 1
file:
- access_level: open_access
checksum: 22b11a719018b22ecba2471b51f2eb40
content_type: application/pdf
creator: asandaue
date_created: 2021-06-28T13:11:39Z
date_updated: 2021-06-28T13:11:39Z
file_id: '9611'
file_name: 2021_LIPIcs_Biswas.pdf
file_size: 727817
relation: main_file
success: 1
file_date_updated: 2021-06-28T13:11:39Z
has_accepted_license: '1'
intvolume: ' 189'
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: The Wittgenstein Prize
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- '9783959771849'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting cells of order-k voronoi tessellations in ℝ3 with 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: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9605'
abstract:
- lang: eng
text: 'Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within
distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter
family of spaces that grow larger when r increases or k decreases, called the
multicover bifiltration. Motivated by the problem of computing the homology of
this bifiltration, we introduce two closely related combinatorial bifiltrations,
one polyhedral and the other simplicial, which are both topologically equivalent
to the multicover bifiltration and far smaller than a Čech-based model considered
in prior work of Sheehy. Our polyhedral construction is a bifiltration of the
rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using
a variant of an algorithm given by these authors as well. Using an implementation
for dimension 2 and 3, we provide experimental results. Our simplicial construction
is useful for understanding the polyhedral construction and proving its correctness. '
acknowledgement: The authors want to thank the reviewers for many helpful comments
and suggestions.
alternative_title:
- LIPIcs
article_number: '27'
article_processing_charge: No
arxiv: 1
author:
- first_name: René
full_name: Corbet, René
last_name: Corbet
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Michael
full_name: Lesnick, Michael
last_name: Lesnick
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: 'Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration.
In: Leibniz International Proceedings in Informatics. Vol 189. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27'
apa: 'Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing
the multicover bifiltration. In Leibniz International Proceedings in Informatics
(Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27'
chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing
the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics,
Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27.
ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover
bifiltration,” in Leibniz International Proceedings in Informatics, Online,
2021, vol. 189.
ista: 'Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration.
Leibniz International Proceedings in Informatics. SoCG: International Symposium
on Computational Geometry, LIPIcs, vol. 189, 27.'
mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International
Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27.
short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International
Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2021.
conference:
end_date: 2021-06-11
location: Online
name: 'SoCG: International Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-27T22:01:49Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-10-04T12:03:39Z
day: '02'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.27
external_id:
arxiv:
- '2103.07823'
file:
- access_level: open_access
checksum: 0de217501e7ba8b267d58deed0d51761
content_type: application/pdf
creator: cziletti
date_created: 2021-06-28T12:40:47Z
date_updated: 2021-06-28T12:40:47Z
file_id: '9610'
file_name: 2021_LIPIcs_Corbet.pdf
file_size: '1367983'
relation: main_file
success: 1
file_date_updated: 2021-06-28T12:40:47Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- '9783959771849'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
link:
- relation: extended_version
url: https://arxiv.org/abs/2103.07823
record:
- id: '12709'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Computing the multicover bifiltration
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '10071'
alternative_title:
- Early Career
article_processing_charge: No
article_type: letter_note
author:
- first_name: Henry
full_name: Adams, Henry
last_name: Adams
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Sarah
full_name: Percival, Sarah
last_name: Percival
- first_name: Lori
full_name: Ziegelmeier, Lori
last_name: Ziegelmeier
citation:
ama: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon.
Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349
apa: Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021).
How to tutorial-a-thon. Notices of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/noti2349
chicago: Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier.
“How to Tutorial-a-Thon.” Notices of the American Mathematical Society.
American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.
ieee: H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to
tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68,
no. 9. American Mathematical Society, pp. 1511–1514, 2021.
ista: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon.
Notices of the American Mathematical Society. 68(9), 1511–1514.
mla: Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical
Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14,
doi:10.1090/noti2349.
short: H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of
the American Mathematical Society 68 (2021) 1511–1514.
date_created: 2021-10-03T22:01:22Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2021-12-03T07:31:26Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/noti2349
intvolume: ' 68'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ams.org/notices/
month: '10'
oa: 1
oa_version: Published Version
page: 1511-1514
publication: Notices of the American Mathematical Society
publication_identifier:
eissn:
- 1088-9477
issn:
- 0002-9920
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to tutorial-a-thon
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 68
year: '2021'
...
---
_id: '10204'
abstract:
- lang: eng
text: Two common representations of close packings of identical spheres consisting
of hexagonal layers, called Barlow stackings, appear abundantly in minerals and
metals. These motifs, however, occupy an identical portion of space and bear identical
first-order topological signatures as measured by persistent homology. Here we
present a novel method based on k-fold covers that unambiguously distinguishes
between these patterns. Moreover, our approach provides topological evidence that
the FCC motif is the more stable of the two in the context of evolving experimental
sphere packings during the transition from disordered to an ordered state. We
conclude that our approach can be generalised to distinguish between various Barlow
stackings manifested in minerals and metals.
acknowledgement: MS acknowledges the support by Australian Research Council funding
through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour
and N. Francois for their input and valuable discussions. 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 and from the Wittgenstein
Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.
article_processing_charge: No
article_type: original
author:
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mohammad
full_name: Saadatfar, Mohammad
last_name: Saadatfar
citation:
ama: Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability
of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115.
doi:10.1039/d1sm00774b
apa: Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures
and stability of hexagonal close packing and Barlow stackings. Soft Matter.
Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b
chicago: Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological
Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft
Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b.
ieee: G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and
stability of hexagonal close packing and Barlow stackings,” Soft Matter,
vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.
ista: Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability
of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115.
mla: Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal
Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal
Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b.
short: G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.
date_created: 2021-10-31T23:01:30Z
date_published: 2021-10-20T00:00:00Z
date_updated: 2023-10-03T09:24:27Z
day: '20'
ddc:
- '540'
department:
- _id: HeEd
doi: 10.1039/d1sm00774b
ec_funded: 1
external_id:
isi:
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pmid:
- '34569592'
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month: '10'
oa: 1
oa_version: Submitted Version
page: 9107-9115
pmid: 1
project:
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call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Soft Matter
publication_identifier:
eissn:
- 1744-6848
issn:
- 1744-683X
publication_status: published
publisher: 'Royal Society of Chemistry '
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological signatures and stability of hexagonal close packing and Barlow
stackings
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 17
year: '2021'
...
---
_id: '10222'
abstract:
- lang: eng
text: Consider a random set of points on the unit sphere in ℝd, which can be either
uniformly sampled or a Poisson point process. Its convex hull is a random inscribed
polytope, whose boundary approximates the sphere. We focus on the case d = 3,
for which there are elementary proofs and fascinating formulas for metric properties.
In particular, we study the fraction of acute facets, the expected intrinsic volumes,
the total edge length, and the distance to a fixed point. Finally we generalize
the results to the ellipsoid with homeoid density.
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.\r\nWe
are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and
for directing us to relevant references. We also thank to Anton Mellit for a useful
discussion on Bessel functions."
article_processing_charge: Yes (via OA deal)
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
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed
in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459
apa: Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random
polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and
Francis. https://doi.org/10.1080/10586458.2021.1980459
chicago: Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty
of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics.
Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459.
ieee: A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes
inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis,
pp. 1–15, 2021.
ista: Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes
inscribed in the 2-sphere. Experimental Mathematics., 1–15.
mla: Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.”
Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459.
short: A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021)
1–15.
date_created: 2021-11-07T23:01:25Z
date_published: 2021-10-25T00:00:00Z
date_updated: 2023-08-14T11:57:07Z
day: '25'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1080/10586458.2021.1980459
ec_funded: 1
external_id:
arxiv:
- '2007.07783'
isi:
- '000710893500001'
file:
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creator: dernst
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date_updated: 2023-08-14T11:55:10Z
file_id: '14053'
file_name: 2023_ExperimentalMath_Akopyan.pdf
file_size: 1966019
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:55:10Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1-15
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: The Wittgenstein Prize
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Experimental Mathematics
publication_identifier:
eissn:
- 1944-950X
issn:
- 1058-6458
publication_status: published
publisher: Taylor and Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: The beauty of random polytopes inscribed in the 2-sphere
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '10367'
abstract:
- lang: eng
text: How information is created, shared and consumed has changed rapidly in recent
decades, in part thanks to new social platforms and technologies on the web. With
ever-larger amounts of unstructured and limited labels, organizing and reconciling
information from different sources and modalities is a central challenge in machine
learning. This cutting-edge tutorial aims to introduce the multimodal entailment
task, which can be useful for detecting semantic alignments when a single modality
alone does not suffice for a whole content understanding. Starting with a brief
overview of natural language processing, computer vision, structured data and
neural graph learning, we lay the foundations for the multimodal sections to follow.
We then discuss recent multimodal learning literature covering visual, audio and
language streams, and explore case studies focusing on tasks which require fine-grained
understanding of visual and linguistic semantics question answering, veracity
and hatred classification. Finally, we introduce a new dataset for recognizing
multimodal entailment, exploring it in a hands-on collaborative section. Overall,
this tutorial gives an overview of multimodal learning, introduces a multimodal
entailment dataset, and encourages future research in the topic.
acknowledgement: "We would like to thank Abby Schantz, Abe Ittycheriah, Aliaksei Severyn,
Allan Heydon, Aly\r\nGrealish, Andrey Vlasov, Arkaitz Zubiaga, Ashwin Kakarla, Chen
Sun, Clayton Williams, Cong\r\nYu, Cordelia Schmid, Da-Cheng Juan, Dan Finnie, Dani
Valevski, Daniel Rocha, David Price, David Sklar, Devi Krishna, Elena Kochkina,
Enrique Alfonseca, Franc¸oise Beaufays, Isabelle Augenstein, Jialu Liu, John Cantwell,
John Palowitch, Jordan Boyd-Graber, Lei Shi, Luis Valente, Maria Voitovich, Mehmet
Aktuna, Mogan Brown, Mor Naaman, Natalia P, Nidhi Hebbar, Pete Aykroyd, Rahul Sukthankar,
Richa Dixit, Steve Pucci, Tania Bedrax-Weiss, Tobias Kaufmann, Tom Boulos, Tu Tsao,
Vladimir Chtchetkine, Yair Kurzion, Yifan Xu and Zach Hynes."
article_processing_charge: No
author:
- first_name: Cesar
full_name: Ilharco, Cesar
last_name: Ilharco
- first_name: Afsaneh
full_name: Shirazi, Afsaneh
last_name: Shirazi
- first_name: Arjun
full_name: Gopalan, Arjun
last_name: Gopalan
- first_name: Arsha
full_name: Nagrani, Arsha
last_name: Nagrani
- first_name: Blaž
full_name: Bratanič, Blaž
last_name: Bratanič
- first_name: Chris
full_name: Bregler, Chris
last_name: Bregler
- first_name: Christina
full_name: Liu, Christina
last_name: Liu
- first_name: Felipe
full_name: Ferreira, Felipe
last_name: Ferreira
- first_name: Gabriek
full_name: Barcik, Gabriek
last_name: Barcik
- first_name: Gabriel
full_name: Ilharco, Gabriel
last_name: Ilharco
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
- first_name: Jannis
full_name: Bulian, Jannis
last_name: Bulian
- first_name: Jared
full_name: Frank, Jared
last_name: Frank
- first_name: Lucas
full_name: Smaira, Lucas
last_name: Smaira
- first_name: Qin
full_name: Cao, Qin
last_name: Cao
- first_name: Ricardo
full_name: Marino, Ricardo
last_name: Marino
- first_name: Roma
full_name: Patel, Roma
last_name: Patel
- first_name: Thomas
full_name: Leung, Thomas
last_name: Leung
- first_name: Vaiva
full_name: Imbrasaite, Vaiva
last_name: Imbrasaite
citation:
ama: 'Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment.
In: 59th Annual Meeting of the Association for Computational Linguistics and
the 11th International Joint Conference on Natural Language Processing, Tutorial
Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6'
apa: 'Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler,
C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual
Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30).
Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6'
chicago: Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič,
Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th
Annual Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30.
Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6.
ieee: C. Ilharco et al., “Recognizing multimodal entailment,” in 59th
Annual Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok,
Thailand, 2021, pp. 29–30.
ista: 'Ilharco C, Shirazi A, Gopalan A, Nagrani A, Bratanič B, Bregler C, Liu C,
Ferreira F, Barcik G, Ilharco G, Osang GF, Bulian J, Frank J, Smaira L, Cao Q,
Marino R, Patel R, Leung T, Imbrasaite V. 2021. Recognizing multimodal entailment.
59th Annual Meeting of the Association for Computational Linguistics and the 11th
International Joint Conference on Natural Language Processing, Tutorial Abstracts.
ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference
on Natural Language Processing, 29–30.'
mla: Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual
Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, Association
for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6.
short: C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler,
C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L.
Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual
Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, Association
for Computational Linguistics, 2021, pp. 29–30.
conference:
end_date: 2021-08-06
location: Bangkok, Thailand
name: 'ACL: Association for Computational Linguistics ; IJCNLP: International Joint
Conference on Natural Language Processing'
start_date: 2021-08-01
date_created: 2021-11-28T23:01:30Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2022-01-26T14:26:36Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.18653/v1/2021.acl-tutorials.6
file:
- access_level: open_access
checksum: b14052a025a6ecf675bdfe51db98c0d7
content_type: application/pdf
creator: cchlebak
date_created: 2021-11-29T08:41:00Z
date_updated: 2021-11-29T08:41:00Z
file_id: '10368'
file_name: 2021_ACL_Ilharco.pdf
file_size: 1227703
relation: main_file
success: 1
file_date_updated: 2021-11-29T08:41:00Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://aclanthology.org/2021.acl-tutorials.6/
month: '08'
oa: 1
oa_version: Published Version
page: 29-30
publication: 59th Annual Meeting of the Association for Computational Linguistics
and the 11th International Joint Conference on Natural Language Processing, Tutorial
Abstracts
publication_identifier:
isbn:
- 9-781-9540-8557-2
publication_status: published
publisher: Association for Computational Linguistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Recognizing multimodal entailment
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '10608'
abstract:
- lang: eng
text: We consider infinite-dimensional properties in coarse geometry for hyperspaces
consisting of finite subsets of metric spaces with the Hausdorff metric. We see
that several infinite-dimensional properties are preserved by taking the hyperspace
of subsets with at most n points. On the other hand, we prove that, if a metric
space contains a sequence of long intervals coarsely, then its hyperspace of finite
subsets is not coarsely embeddable into any uniformly convex Banach space. As
a corollary, the hyperspace of finite subsets of the real line is not coarsely
embeddable into any uniformly convex Banach space. It is also shown that every
(not necessarily bounded geometry) metric space with straight finite decomposition
complexity has metric sparsification property.
acknowledgement: We would like to thank the referees for their careful reading and
the comments that improved our work. The third named author would like to thank
the Division of Mathematics, Physics and Earth Sciences of the Graduate School of
Science and Engineering of Ehime University and the second named author for hosting
his visit in June 2018. Open access funding provided by Institute of Science and
Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Thomas
full_name: Weighill, Thomas
last_name: Weighill
- first_name: Takamitsu
full_name: Yamauchi, Takamitsu
last_name: Yamauchi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
citation:
ama: Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3
apa: Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality
of hyperspaces of finite subsets. European Journal of Mathematics. Springer
Nature. https://doi.org/10.1007/s40879-021-00515-3
chicago: Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality
of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer
Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3.
ieee: T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of
hyperspaces of finite subsets,” European Journal of Mathematics. Springer
Nature, 2021.
ista: Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics.
mla: Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of
Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021,
doi:10.1007/s40879-021-00515-3.
short: T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).
date_created: 2022-01-09T23:01:27Z
date_published: 2021-12-30T00:00:00Z
date_updated: 2022-01-10T08:36:55Z
day: '30'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s40879-021-00515-3
file:
- access_level: open_access
checksum: c435dcfa1ad3aadc5cdd7366bc7f4e98
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-10T08:33:22Z
date_updated: 2022-01-10T08:33:22Z
file_id: '10610'
file_name: 2021_EuJournalMath_Weighill.pdf
file_size: 384908
relation: main_file
success: 1
file_date_updated: 2022-01-10T08:33:22Z
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse infinite-dimensionality of hyperspaces of finite subsets
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '9821'
abstract:
- lang: eng
text: Heart rate variability (hrv) is a physiological phenomenon of the variation
in the length of the time interval between consecutive heartbeats. In many cases
it could be an indicator of the development of pathological states. The classical
approach to the analysis of hrv includes time domain methods and frequency domain
methods. However, attempts are still being made to define new and more effective
hrv assessment tools. Persistent homology is a novel data analysis tool developed
in the recent decades that is rooted at algebraic topology. The Topological Data
Analysis (TDA) approach focuses on examining the shape of the data in terms of
connectedness and holes, and has recently proved to be very effective in various
fields of research. In this paper we propose the use of persistent homology to
the hrv analysis. We recall selected topological descriptors used in the literature
and we introduce some new topological descriptors that reflect the specificity
of hrv, and we discuss their relation to the standard hrv measures. In particular,
we show that this novel approach provides a collection of indices that might be
at least as useful as the classical parameters in differentiating between series
of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering
from a stroke episode.
acknowledgement: We express our gratitude to the anonymous referees who provided constructive
comments that helped us improve the quality of the paper.
article_number: e0253851
article_processing_charge: Yes
article_type: original
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Beata
full_name: Graff, Beata
last_name: Graff
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Dariusz
full_name: Gąsecki, Dariusz
last_name: Gąsecki
- first_name: Krzysztof
full_name: Narkiewicz, Krzysztof
last_name: Narkiewicz
citation:
ama: Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent
homology as a new method of the assessment of heart rate variability. PLoS
ONE. 2021;16(7). doi:10.1371/journal.pone.0253851
apa: Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz,
K. (2021). Persistent homology as a new method of the assessment of heart rate
variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851
chicago: Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz
Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the
Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science,
2021. https://doi.org/10.1371/journal.pone.0253851.
ieee: G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz,
“Persistent homology as a new method of the assessment of heart rate variability,”
PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.
ista: Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021.
Persistent homology as a new method of the assessment of heart rate variability.
PLoS ONE. 16(7), e0253851.
mla: Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment
of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public
Library of Science, 2021, doi:10.1371/journal.pone.0253851.
short: G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz,
PLoS ONE 16 (2021).
date_created: 2021-08-08T22:01:28Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2023-08-10T14:21:42Z
day: '01'
ddc:
- '006'
department:
- _id: HeEd
doi: 10.1371/journal.pone.0253851
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creator: asandaue
date_created: 2021-08-09T09:25:41Z
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file_name: 2021_PLoSONE_Graff.pdf
file_size: 2706919
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- iso: eng
month: '07'
oa: 1
oa_version: Published Version
pmid: 1
publication: PLoS ONE
publication_identifier:
eissn:
- '19326203'
publication_status: published
publisher: Public Library of Science
quality_controlled: '1'
scopus_import: '1'
status: public
title: Persistent homology as a new method of the assessment of heart rate variability
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: 16
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: 2022-05-31T06:58:21Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/978-3-030-76657-3_10
ec_funded: 1
intvolume: ' 12708'
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:
- '16113349'
isbn:
- '9783030766566'
issn:
- '03029743'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12708
year: '2021'
...