---
_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
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: '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:
- access_level: open_access
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:
- id: '187'
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: '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: '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
external_id:
isi:
- '000678124900050'
pmid:
- '34292957'
file:
- access_level: open_access
checksum: 0277aa155d5db1febd2cb384768bba5f
content_type: application/pdf
creator: asandaue
date_created: 2021-08-09T09:25:41Z
date_updated: 2021-08-09T09:25:41Z
file_id: '9832'
file_name: 2021_PLoSONE_Graff.pdf
file_size: 2706919
relation: main_file
success: 1
file_date_updated: 2021-08-09T09:25:41Z
has_accepted_license: '1'
intvolume: ' 16'
isi: 1
issue: '7'
language:
- 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: '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
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:
- access_level: open_access
checksum: 3514382e3a1eb87fa6c61ad622874415
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:55:10Z
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: '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: '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
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: '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: '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:
- '000700090000001'
pmid:
- '34569592'
file:
- access_level: open_access
checksum: b4da0c420530295e61b153960f6cb350
content_type: application/pdf
creator: dernst
date_created: 2023-10-03T09:21:42Z
date_updated: 2023-10-03T09:21:42Z
file_id: '14385'
file_name: 2021_SoftMatter_acceptedversion_Osang.pdf
file_size: 4678788
relation: main_file
success: 1
file_date_updated: 2023-10-03T09:21:42Z
has_accepted_license: '1'
intvolume: ' 17'
isi: 1
issue: '40'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Submitted Version
page: 9107-9115
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: 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: '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
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'
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intvolume: ' 189'
language:
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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: '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: '8338'
abstract:
- lang: eng
text: Canonical parametrisations of classical confocal coordinate systems are introduced
and exploited to construct non-planar analogues of incircular (IC) nets on individual
quadrics and systems of confocal quadrics. Intimate connections with classical
deformations of quadrics that are isometric along asymptotic lines and circular
cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces
of Blaschke type generated by asymptotic and characteristic lines that are diagonally
related to lines of curvature is proved theoretically and established constructively.
Appropriate samplings (grids) of these webs lead to three-dimensional extensions
of non-planar IC nets. Three-dimensional octahedral grids composed of planes and
spatially extending (checkerboard) IC-nets are shown to arise in connection with
systems of confocal quadrics in Minkowski space. In this context, the Laguerre
geometric notion of conical octahedral grids of planes is introduced. The latter
generalise the octahedral grids derived from systems of confocal quadrics in Minkowski
space. An explicit construction of conical octahedral grids is presented. The
results are accompanied by various illustrations which are based on the explicit
formulae provided by the theory.
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by
the Australian Research Council (DP1401000851). A.V.A. was also supported by the
European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (Grant Agreement No. 78818 Alpha).
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexander I.
full_name: Bobenko, Alexander I.
last_name: Bobenko
- first_name: Wolfgang K.
full_name: Schief, Wolfgang K.
last_name: Schief
- first_name: Jan
full_name: Techter, Jan
last_name: Techter
citation:
ama: Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal)
quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976.
doi:10.1007/s00454-020-00240-w
apa: Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually
diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w
chicago: Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter.
“On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete
and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w.
ieee: A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal
nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational
Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.
ista: Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets
on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry.
66, 938–976.
mla: Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics
and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66,
Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.
short: A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational
Geometry 66 (2021) 938–976.
date_created: 2020-09-06T22:01:13Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-03-07T14:51:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00240-w
ec_funded: 1
external_id:
arxiv:
- '1908.00856'
isi:
- '000564488500002'
intvolume: ' 66'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1908.00856
month: '10'
oa: 1
oa_version: Preprint
page: 938-976
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2021'
...
---
_id: '8248'
abstract:
- lang: eng
text: 'We consider the following setting: suppose that we are given a manifold M
in Rd with positive reach. Moreover assume that we have an embedded simplical
complex A without boundary, whose vertex set lies on the manifold, is sufficiently
dense and such that all simplices in A have sufficient quality. We prove that
if, locally, interiors of the projection of the simplices onto the tangent space
do not intersect, then A is a triangulation of the manifold, that is, they are
homeomorphic.'
acknowledgement: "Open access funding provided by the Institute of Science and Technology
(IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015),
India.\r\nThis 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 is supported by Ramanujan
Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding
from the European Union’s Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie Grant Agreement No. 754411."
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: Ramsay
full_name: Dyer, Ramsay
last_name: Dyer
- first_name: Arijit
full_name: Ghosh, Arijit
last_name: Ghosh
- first_name: Andre
full_name: Lieutier, Andre
last_name: Lieutier
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions
for triangulating submanifolds of Euclidean space. Discrete and Computational
Geometry. 2021;66:666-686. doi:10.1007/s00454-020-00233-9
apa: Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M.
(2021). Local conditions for triangulating submanifolds of Euclidean space. Discrete
and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00233-9
chicago: Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and
Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean
Space.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00233-9.
ieee: J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local
conditions for triangulating submanifolds of Euclidean space,” Discrete and
Computational Geometry, vol. 66. Springer Nature, pp. 666–686, 2021.
ista: Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions
for triangulating submanifolds of Euclidean space. Discrete and Computational
Geometry. 66, 666–686.
mla: Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds
of Euclidean Space.” Discrete and Computational Geometry, vol. 66, Springer
Nature, 2021, pp. 666–86, doi:10.1007/s00454-020-00233-9.
short: J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete
and Computational Geometry 66 (2021) 666–686.
date_created: 2020-08-11T07:11:51Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2024-03-07T14:54:59Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00233-9
ec_funded: 1
external_id:
isi:
- '000558119300001'
has_accepted_license: '1'
intvolume: ' 66'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-020-00233-9
month: '09'
oa: 1
oa_version: Published Version
page: 666-686
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local conditions for triangulating submanifolds of Euclidean space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2021'
...
---
_id: '7905'
abstract:
- lang: eng
text: We investigate a sheaf-theoretic interpretation of stratification learning
from geometric and topological perspectives. Our main result is the construction
of stratification learning algorithms framed in terms of a sheaf on a partially
ordered set with the Alexandroff topology. We prove that the resulting decomposition
is the unique minimal stratification for which the strata are homogeneous and
the given sheaf is constructible. In particular, when we choose to work with the
local homology sheaf, our algorithm gives an alternative to the local homology
transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM
Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the
cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2),
195–222, 2020). Additionally, we give examples of stratifications based on the
geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018),
illustrating how the sheaf-theoretic approach can be used to study stratifications
from both topological and geometric perspectives. This approach also points toward
future applications of sheaf theory in the study of topological data analysis
by illustrating the utility of the language of sheaf theory in generalizing existing
algorithms.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375.
The authors would like to thank the anonymous referees for their insightful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Bei
full_name: Wang, Bei
last_name: Wang
citation:
ama: Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and
topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198.
doi:10.1007/s00454-020-00206-y
apa: Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from
geometric and topological perspectives. Discrete and Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-020-00206-y
chicago: Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from
Geometric and Topological Perspectives.” Discrete and Computational Geometry.
Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y.
ieee: A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric
and topological perspectives,” Discrete and Computational Geometry, vol.
65. Springer Nature, pp. 1166–1198, 2021.
ista: Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric
and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.
mla: Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric
and Topological Perspectives.” Discrete and Computational Geometry, vol.
65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y.
short: A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.
date_created: 2020-05-30T10:26:04Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2024-03-07T15:01:58Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00206-y
external_id:
arxiv:
- '1712.07734'
isi:
- '000536324700001'
file:
- access_level: open_access
checksum: 487a84ea5841b75f04f66d7ebd71b67e
content_type: application/pdf
creator: dernst
date_created: 2020-11-25T09:06:41Z
date_updated: 2020-11-25T09:06:41Z
file_id: '8803'
file_name: 2020_DiscreteCompGeometry_Brown.pdf
file_size: 1013730
relation: main_file
success: 1
file_date_updated: 2020-11-25T09:06:41Z
has_accepted_license: '1'
intvolume: ' 65'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1166-1198
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sheaf-theoretic stratification learning from geometric and topological perspectives
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 65
year: '2021'
...
---
_id: '7567'
abstract:
- lang: eng
text: Coxeter triangulations are triangulations of Euclidean space based on a single
simplex. By this we mean that given an individual simplex we can recover the entire
triangulation of Euclidean space by inductively reflecting in the faces of the
simplex. In this paper we establish that the quality of the simplices in all Coxeter
triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate
the Delaunay property for these triangulations. Moreover, we consider an extension
of the Delaunay property, namely protection, which is a measure of non-degeneracy
of a Delaunay triangulation. In particular, one family of Coxeter triangulations
achieves the protection O(1/d2). We conjecture that both bounds are optimal for
triangulations in Euclidean space.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Aruni
full_name: Choudhary, Aruni
last_name: Choudhary
- first_name: Siargey
full_name: Kachanovich, Siargey
last_name: Kachanovich
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good
quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5
apa: Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations
have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5
chicago: Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter
Triangulations Have Good Quality.” Mathematics in Computer Science. Springer
Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.
ieee: A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations
have good quality,” Mathematics in Computer Science, vol. 14. Springer
Nature, pp. 141–176, 2020.
ista: Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have
good quality. Mathematics in Computer Science. 14, 141–176.
mla: Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics
in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5.
short: A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science
14 (2020) 141–176.
date_created: 2020-03-05T13:30:18Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2021-01-12T08:14:13Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s11786-020-00461-5
ec_funded: 1
file:
- access_level: open_access
checksum: 1d145f3ab50ccee735983cb89236e609
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T10:18:02Z
date_updated: 2020-11-20T10:18:02Z
file_id: '8783'
file_name: 2020_MathCompScie_Choudhary.pdf
file_size: 872275
relation: main_file
success: 1
file_date_updated: 2020-11-20T10:18:02Z
has_accepted_license: '1'
intvolume: ' 14'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 141-176
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Mathematics in Computer Science
publication_identifier:
eissn:
- 1661-8289
issn:
- 1661-8270
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coxeter triangulations have good quality
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2020'
...
---
_id: '8135'
abstract:
- lang: eng
text: Discrete Morse theory has recently lead to new developments in the theory
of random geometric complexes. This article surveys the methods and results obtained
with this new approach, and discusses some of its shortcomings. It uses simulations
to illustrate the results and to form conjectures, getting numerical estimates
for combinatorial, topological, and geometric properties of weighted and unweighted
Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes
contained in the mosaics.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreements No 78818 Alpha and No 638176). It is also partially supported
by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and
Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).
alternative_title:
- Abel Symposia
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
citation:
ama: 'Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay
mosaics and related complexes experimentally. In: Topological Data Analysis.
Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8'
apa: Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius
functions on Poisson–Delaunay mosaics and related complexes experimentally. In
Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8
chicago: Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak.
“Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.”
In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.
ieee: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions
on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological
Data Analysis, 2020, vol. 15, pp. 181–218.
ista: Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on
Poisson–Delaunay mosaics and related complexes experimentally. Topological Data
Analysis. , Abel Symposia, vol. 15, 181–218.
mla: Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics
and Related Complexes Experimentally.” Topological Data Analysis, vol.
15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.
short: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data
Analysis, Springer Nature, 2020, pp. 181–218.
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2021-01-12T08:17:06Z
day: '22'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/978-3-030-43408-3_8
ec_funded: 1
file:
- access_level: open_access
checksum: 7b5e0de10675d787a2ddb2091370b8d8
content_type: application/pdf
creator: dernst
date_created: 2020-10-08T08:56:14Z
date_updated: 2020-10-08T08:56:14Z
file_id: '8628'
file_name: 2020-B-01-PoissonExperimentalSurvey.pdf
file_size: 2207071
relation: main_file
success: 1
file_date_updated: 2020-10-08T08:56:14Z
has_accepted_license: '1'
intvolume: ' 15'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 181-218
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2533E772-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '638176'
name: Efficient Simulation of Natural Phenomena at Extremely Large Scales
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Topological Data Analysis
publication_identifier:
eissn:
- '21978549'
isbn:
- '9783030434076'
issn:
- '21932808'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2020'
...
---
_id: '9249'
abstract:
- lang: eng
text: Rhombic dodecahedron is a space filling polyhedron which represents the close
packing of spheres in 3D space and the Voronoi structures of the face centered
cubic (FCC) lattice. In this paper, we describe a new coordinate system where
every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid.
In order to illustrate the interest of the new coordinate system, we propose the
characterization of 3D digital plane with its topological features, such as the
interrelation between the thickness of the digital plane and the separability
constraint we aim to obtain. We also present the characterization of 3D digital
lines and study it as the intersection of multiple digital planes. Characterization
of 3D digital sphere with relevant topological features is proposed as well along
with the 48-symmetry appearing in the new coordinate system.
acknowledgement: "This work has been partially supported by the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109,
‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no.
I 02979-N35. "
article_processing_charge: No
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic
dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158.
doi:10.1515/mathm-2020-0106
apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital
objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and
Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106
chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital
Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and
Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.
ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects
in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications,
vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.
ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in
rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications.
4(1), 143–158.
mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical
Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp.
143–58, doi:10.1515/mathm-2020-0106.
short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology
- Theory and Applications 4 (2020) 143–158.
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2021-03-22T09:01:50Z
day: '17'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/mathm-2020-0106
ec_funded: 1
file:
- access_level: open_access
checksum: 4a1043fa0548a725d464017fe2483ce0
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:56:37Z
date_updated: 2021-03-22T08:56:37Z
file_id: '9272'
file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf
file_size: 3668725
relation: main_file
success: 1
file_date_updated: 2021-03-22T08:56:37Z
has_accepted_license: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 143-158
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Mathematical Morphology - Theory and Applications
publication_identifier:
issn:
- 2353-3390
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: Digital objects in rhombic dodecahedron grid
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...
---
_id: '9299'
abstract:
- lang: eng
text: We call a multigraph non-homotopic if it can be drawn in the plane in such
a way that no two edges connecting the same pair of vertices can be continuously
transformed into each other without passing through a vertex, and no loop can
be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic
multigraph on n>1 vertices can have arbitrarily many edges. We prove that the
number of crossings between the edges of a non-homotopic multigraph with n vertices
and m>4n edges is larger than cm2n for some constant c>0 , and that this
bound is tight up to a polylogarithmic factor. We also show that the lower bound
is not asymptotically sharp as n is fixed and m⟶∞ .
acknowledgement: Supported by the National Research, Development and Innovation Office,
NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional
Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant
Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant
No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full
version can be found at https://arxiv.org/abs/2006.14908.
article_processing_charge: No
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Gábor
full_name: Tardos, Gábor
last_name: Tardos
- first_name: Géza
full_name: Tóth, Géza
last_name: Tóth
citation:
ama: 'Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th
International Symposium on Graph Drawing and Network Visualization. Vol 12590.
LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28'
apa: 'Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic
edges. In 28th International Symposium on Graph Drawing and Network Visualization
(Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28'
chicago: Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic
Edges.” In 28th International Symposium on Graph Drawing and Network Visualization,
12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.
ieee: J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,”
in 28th International Symposium on Graph Drawing and Network Visualization,
Virtual, Online, 2020, vol. 12590, pp. 359–371.
ista: 'Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th
International Symposium on Graph Drawing and Network Visualization. GD: Graph
Drawing and Network VisualizationLNCS vol. 12590, 359–371.'
mla: Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International
Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer
Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.
short: J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing
and Network Visualization, Springer Nature, 2020, pp. 359–371.
conference:
end_date: 2020-09-18
location: Virtual, Online
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2020-09-16
date_created: 2021-03-28T22:01:44Z
date_published: 2020-09-20T00:00:00Z
date_updated: 2021-04-06T11:32:32Z
day: '20'
department:
- _id: HeEd
doi: 10.1007/978-3-030-68766-3_28
external_id:
arxiv:
- '2006.14908'
intvolume: ' 12590'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.14908
month: '09'
oa: 1
oa_version: Preprint
page: 359-371
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: 28th International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030687656'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Crossings between non-homotopic edges
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12590
year: '2020'
...
---
_id: '9630'
abstract:
- lang: eng
text: Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms. Importantly,
instead of using the standard Euclidean distance, we look into dissimilarity measures
with information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7
apa: Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis
in information space. Journal of Computational Geometry. Carleton University.
https://doi.org/10.20382/jocg.v11i2a7
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” Journal of Computational Geometry. Carleton
University, 2020. https://doi.org/10.20382/jocg.v11i2a7.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University,
pp. 162–182, 2020.
ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
space. Journal of Computational Geometry. 11(2), 162–182.
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
Journal of Computational Geometry, vol. 11, no. 2, Carleton University,
2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.
short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
(2020) 162–182.
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2021-08-11T12:26:34Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
file:
- access_level: open_access
checksum: f02d0b2b3838e7891a6c417fc34ffdcd
content_type: application/pdf
creator: asandaue
date_created: 2021-08-11T11:55:11Z
date_updated: 2021-08-11T11:55:11Z
file_id: '9882'
file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
file_size: 1449234
relation: main_file
success: 1
file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: ' 11'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Journal of Computational Geometry
publication_identifier:
eissn:
- 1920180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 11
year: '2020'
...
---
_id: '8538'
abstract:
- lang: eng
text: We prove some recent experimental observations of Dan Reznik concerning periodic
billiard orbits in ellipses. For example, the sum of cosines of the angles of
a periodic billiard polygon remains constant in the 1-parameter family of such
polygons (that exist due to the Poncelet porism). In our proofs, we use geometric
and complex analytic methods.
acknowledgement: " This paper would not be written if not for Dan Reznik’s curiosity
and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller
for interesting discussions. It is a pleasure to thank the Mathematical Institute
of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy
for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality.
AA was supported by European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported
by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR
191."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Richard
full_name: Schwartz, Richard
last_name: Schwartz
- first_name: Serge
full_name: Tabachnikov, Serge
last_name: Tabachnikov
citation:
ama: Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European
Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9
apa: Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses
revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9
chicago: Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in
Ellipses Revisited.” European Journal of Mathematics. Springer Nature,
2020. https://doi.org/10.1007/s40879-020-00426-9.
ieee: A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,”
European Journal of Mathematics. Springer Nature, 2020.
ista: Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited.
European Journal of Mathematics.
mla: Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal
of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.
short: A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics
(2020).
date_created: 2020-09-20T22:01:38Z
date_published: 2020-09-09T00:00:00Z
date_updated: 2021-12-02T15:10:17Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00426-9
ec_funded: 1
external_id:
arxiv:
- '2001.02934'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.02934
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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: Billiards in ellipses revisited
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '7952'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued
smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate
an isomanifold is to consider its Piecewise-Linear (PL) approximation based on
a triangulation \U0001D4AF of the ambient space ℝ^d. In this paper, we give conditions
under which the PL-approximation of an isomanifold is topologically equivalent
to the isomanifold. The conditions are easy to satisfy in the sense that they
can always be met by taking a sufficiently fine triangulation \U0001D4AF. This
contrasts with previous results on the triangulation of manifolds where, in arbitrary
dimensions, delicate perturbations are needed to guarantee topological correctness,
which leads to strong limitations in practice. We further give a bound on the
Fréchet distance between the original isomanifold and its PL-approximation. Finally
we show analogous results for the PL-approximation of an isomanifold with boundary. "
alternative_title:
- LIPIcs
article_number: 20:1-20:18
article_processing_charge: No
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations
of isomanifolds. In: 36th International Symposium on Computational Geometry.
Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.20'
apa: 'Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness
of PL-approximations of isomanifolds. In 36th International Symposium on Computational
Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20'
chicago: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL-Approximations of Isomanifolds.” In 36th International Symposium on Computational
Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
https://doi.org/10.4230/LIPIcs.SoCG.2020.20.
ieee: J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations
of isomanifolds,” in 36th International Symposium on Computational Geometry,
Zürich, Switzerland, 2020, vol. 164.
ista: 'Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations
of isomanifolds. 36th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.'
mla: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational
Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2020, doi:10.4230/LIPIcs.SoCG.2020.20.
short: J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-06-26
location: Zürich, Switzerland
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2020-06-22
date_created: 2020-06-09T07:24:11Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-02T06:49:16Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2020.20
ec_funded: 1
file:
- access_level: open_access
checksum: 38cbfa4f5d484d267a35d44d210df044
content_type: application/pdf
creator: dernst
date_created: 2020-06-17T10:13:34Z
date_updated: 2020-07-14T12:48:06Z
file_id: '7969'
file_name: 2020_LIPIcsSoCG_Boissonnat.pdf
file_size: 1009739
relation: main_file
file_date_updated: 2020-07-14T12:48:06Z
has_accepted_license: '1'
intvolume: ' 164'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 36th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-143-6
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '9649'
relation: later_version
status: public
scopus_import: '1'
status: public
title: The topological correctness of PL-approximations of isomanifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 164
year: '2020'
...
---
_id: '74'
abstract:
- lang: eng
text: "We study the Gromov waist in the sense of t-neighborhoods for measures in
the Euclidean space, motivated by the famous theorem of Gromov about
\ the waist of radially symmetric Gaussian measures. In particular, it turns
our possible to extend Gromov’s original result to the case of not necessarily
\ radially symmetric Gaussian measure. We also provide examples of measures
having no t-neighborhood waist property, including a rather wide class\r\nof compactly
supported radially symmetric measures and their maps into the Euclidean space
of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument
\ to produce some estimates of t-neighborhoods of (weighted) volume-critical
submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic
manifolds in the complex projective space. In the appendix of this paper we provide
for reader’s convenience a more detailed explanation of the Caffarelli theorem
that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: 'Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial
non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional
Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1'
apa: Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian
measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.),
Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer
Nature. https://doi.org/10.1007/978-3-030-36020-7_1
chicago: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer
Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.
ieee: A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis,
vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.
ista: 'Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis.
vol. 2256, 1–27.'
mla: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer
Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.
short: A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects
of Functional Analysis, Springer Nature, 2020, pp. 1–27.
date_created: 2018-12-11T11:44:29Z
date_published: 2020-06-21T00:00:00Z
date_updated: 2023-08-17T13:48:31Z
day: '21'
department:
- _id: HeEd
- _id: JaMa
doi: 10.1007/978-3-030-36020-7_1
ec_funded: 1
editor:
- first_name: Bo'az
full_name: Klartag, Bo'az
last_name: Klartag
- first_name: Emanuel
full_name: Milman, Emanuel
last_name: Milman
external_id:
arxiv:
- '1808.07350'
isi:
- '000557689300003'
intvolume: ' 2256'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.07350
month: '06'
oa: 1
oa_version: Preprint
page: 1-27
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Geometric Aspects of Functional Analysis
publication_identifier:
eisbn:
- '9783030360207'
eissn:
- '16179692'
isbn:
- '9783030360191'
issn:
- '00758434'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNM
status: public
title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
type: book_chapter
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2256
year: '2020'
...
---
_id: '7554'
abstract:
- lang: eng
text: Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional
weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation.
Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the
smallest empty circumscribed sphere whose center lies in the $k$-plane gives a
generalized discrete Morse function. Assuming the Voronoi tessellation is generated
by a Poisson point process in ${R}^n$, we study the expected number of simplices
in the $k$-dimensional weighted Delaunay mosaic as well as the expected number
of intervals of the Morse function, both as functions of a radius threshold. As
a by-product, we obtain a new proof for the expected number of connected components
(clumps) in a line section of a circular Boolean model in ${R}^n$.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of
Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726
apa: Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics.
Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay
Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.
ieee: H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory
of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020.
ista: Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory
of Probability and its Applications. 64(4), 595–614.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.”
Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020,
pp. 595–614, doi:10.1137/S0040585X97T989726.
short: H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications
64 (2020) 595–614.
date_created: 2020-03-01T23:00:39Z
date_published: 2020-02-13T00:00:00Z
date_updated: 2023-08-18T06:45:48Z
day: '13'
department:
- _id: HeEd
doi: 10.1137/S0040585X97T989726
ec_funded: 1
external_id:
arxiv:
- '1705.08735'
isi:
- '000551393100007'
intvolume: ' 64'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.08735
month: '02'
oa: 1
oa_version: Preprint
page: 595-614
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Theory of Probability and its Applications
publication_identifier:
eissn:
- '10957219'
issn:
- 0040585X
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weighted Poisson–Delaunay mosaics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '7666'
abstract:
- lang: eng
text: Generalizing the decomposition of a connected planar graph into a tree and
a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition
of a smooth vector field. Specifically, we show that for every polyhedral complex,
K, and every dimension, p, there is a partition of the set of p-cells into a maximal
p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the
p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition
is unique, and it can be computed by a matrix reduction algorithm that also constructs
canonical bases of cycle and boundary groups.
acknowledgement: This project has received funding from the European Research Council
under the European Union’s Horizon 2020 research and innovation programme (Grant
Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative
Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant
No. I02979-N35 of the Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
citation:
ama: Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex.
Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x
apa: Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an
ordered complex. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-020-00188-x
chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases
of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature,
2020. https://doi.org/10.1007/s00454-020-00188-x.
ieee: H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,”
Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775,
2020.
ista: Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex.
Discrete and Computational Geometry. 64, 759–775.
mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of
an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer
Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.
short: H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020)
759–775.
date_created: 2020-04-19T22:00:56Z
date_published: 2020-03-20T00:00:00Z
date_updated: 2023-08-21T06:13:48Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00188-x
ec_funded: 1
external_id:
isi:
- '000520918800001'
file:
- access_level: open_access
checksum: f8cc96e497f00c38340b5dafe0cb91d7
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T13:22:21Z
date_updated: 2020-11-20T13:22:21Z
file_id: '8786'
file_name: 2020_DiscreteCompGeo_Edelsbrunner.pdf
file_size: 701673
relation: main_file
success: 1
file_date_updated: 2020-11-20T13:22:21Z
has_accepted_license: '1'
intvolume: ' 64'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 759-775
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tri-partitions and bases of an ordered complex
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '7962'
abstract:
- lang: eng
text: 'A string graph is the intersection graph of a family of continuous arcs in
the plane. The intersection graph of a family of plane convex sets is a string
graph, but not all string graphs can be obtained in this way. We prove the following
structure theorem conjectured by Janson and Uzzell: The vertex set of almost all
string graphs on n vertices can be partitioned into five cliques such that some
pair of them is not connected by any edge (n→∞). We also show that every graph
with the above property is an intersection graph of plane convex sets. As a corollary,
we obtain that almost all string graphs on n vertices are intersection graphs
of plane convex sets.'
article_processing_charge: No
article_type: original
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Bruce
full_name: Reed, Bruce
last_name: Reed
- first_name: Yelena
full_name: Yuditsky, Yelena
last_name: Yuditsky
citation:
ama: Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs
of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917.
doi:10.1007/s00454-020-00213-z
apa: Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are
intersection graphs of plane convex sets. Discrete and Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-020-00213-z
chicago: Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs
Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry.
Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.
ieee: J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection
graphs of plane convex sets,” Discrete and Computational Geometry, vol.
63, no. 4. Springer Nature, pp. 888–917, 2020.
ista: Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection
graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.
mla: Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane
Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer
Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z.
short: J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020)
888–917.
date_created: 2020-06-14T22:00:51Z
date_published: 2020-06-05T00:00:00Z
date_updated: 2023-08-21T08:49:18Z
day: '05'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00213-z
external_id:
arxiv:
- '1803.06710'
isi:
- '000538229000001'
intvolume: ' 63'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1803.06710
month: '06'
oa: 1
oa_version: Preprint
page: 888-917
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Almost all string graphs are intersection graphs of plane convex sets
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2020'
...
---
_id: '8323'
article_processing_charge: No
article_type: letter_note
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
citation:
ama: Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry.
2020;64:571-574. doi:10.1007/s00454-020-00237-5
apa: Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5
chicago: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational
Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.
ieee: J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry,
vol. 64. Springer Nature, pp. 571–574, 2020.
ista: Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry.
64, 571–574.
mla: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry,
vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5.
short: J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.
date_created: 2020-08-30T22:01:12Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T09:05:04Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00237-5
external_id:
isi:
- '000561483500001'
intvolume: ' 64'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-020-00237-5
month: '10'
oa: 1
oa_version: None
page: 571-574
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
scopus_import: '1'
status: public
title: A farewell to Ricky Pollack
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '8580'
abstract:
- lang: eng
text: We evaluate the usefulness of persistent homology in the analysis of heart
rate variability. In our approach we extract several topological descriptors characterising
datasets of RR-intervals, which are later used in classical machine learning algorithms.
By this method we are able to differentiate the group of patients with the history
of transient ischemic attack and the group of hypertensive patients.
article_number: '9158054'
article_processing_charge: No
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Beata
full_name: Graff, Beata
last_name: Graff
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Krzysztof
full_name: Narkiewicz, Krzysztof
last_name: Narkiewicz
citation:
ama: 'Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent
homology in the analysis of heart rate variability. In: 11th Conference of
the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054'
apa: 'Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application
of persistent homology in the analysis of heart rate variability. In 11th Conference
of the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054'
chicago: 'Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz.
“The Application of Persistent Homology in the Analysis of Heart Rate Variability.”
In 11th Conference of the European Study Group on Cardiovascular Oscillations:
Computation and Modelling in Physiology: New Challenges and Opportunities, .
IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.'
ieee: 'G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of
persistent homology in the analysis of heart rate variability,” in 11th Conference
of the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.'
ista: 'Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent
homology in the analysis of heart rate variability. 11th Conference of the European
Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology:
New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular
Oscillations, 9158054.'
mla: 'Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis
of Heart Rate Variability.” 11th Conference of the European Study Group on
Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges
and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.'
short: 'G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of
the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, , IEEE, 2020.'
conference:
end_date: 2020-07-15
location: Pisa, Italy
name: 'ESGCO: European Study Group on Cardiovascular Oscillations'
start_date: 2020-07-15
date_created: 2020-09-28T08:59:27Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-22T09:33:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1109/ESGCO49734.2020.9158054
external_id:
isi:
- '000621172600045'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
publication: '11th Conference of the European Study Group on Cardiovascular Oscillations:
Computation and Modelling in Physiology: New Challenges and Opportunities, '
publication_identifier:
isbn:
- '9781728157511'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: The application of persistent homology in the analysis of heart rate variability
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2020'
...
---
_id: '10867'
abstract:
- lang: eng
text: In this paper we find a tight estimate for Gromov’s waist of the balls in
spaces of constant curvature, deduce the estimates for the balls in Riemannian
manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar
result for normed spaces.
acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.'
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International
Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037
apa: Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical
spaces. International Mathematics Research Notices. Oxford University Press.
https://doi.org/10.1093/imrn/rny037
chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and
Spherical Spaces.” International Mathematics Research Notices. Oxford University
Press, 2020. https://doi.org/10.1093/imrn/rny037.
ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,”
International Mathematics Research Notices, vol. 2020, no. 3. Oxford University
Press, pp. 669–697, 2020.
ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces.
International Mathematics Research Notices. 2020(3), 669–697.
mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical
Spaces.” International Mathematics Research Notices, vol. 2020, no. 3,
Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.
short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020)
669–697.
date_created: 2022-03-18T11:39:30Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-24T14:19:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/imrn/rny037
external_id:
arxiv:
- '1702.07513'
isi:
- '000522852700002'
intvolume: ' 2020'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.07513
month: '02'
oa: 1
oa_version: Preprint
page: 669-697
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Waist of balls in hyperbolic and spherical spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_id: '7460'
abstract:
- lang: eng
text: "Many methods for the reconstruction of shapes from sets of points produce
ordered simplicial complexes, which are collections of vertices, edges, triangles,
and their higher-dimensional analogues, called simplices, in which every simplex
gets assigned a real value measuring its size. This thesis studies ordered simplicial
complexes, with a focus on their topology, which reflects the connectedness of
the represented shapes and the presence of holes. We are interested both in understanding
better the structure of these complexes, as well as in developing algorithms for
applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure
for a simplex is the radius of the smallest empty circumsphere. Based on it, we
revisit Alpha and Wrap complexes and experimentally determine their probabilistic
properties for random data. Also, we prove the existence of tri-partitions, propose
algorithms to open and close holes, and extend the concepts from Euclidean to
Bregman geometries."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
citation:
ama: Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460
apa: Ölsböck, K. (2020). The hole system of triangulated shapes. Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460
chicago: Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute
of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.
ieee: K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science
and Technology Austria, 2020.
ista: Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science
and Technology Austria.
mla: Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute
of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460.
short: K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science
and Technology Austria, 2020.
date_created: 2020-02-06T14:56:53Z
date_published: 2020-02-10T00:00:00Z
date_updated: 2023-09-07T13:15:30Z
day: '10'
ddc:
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:7460
file:
- access_level: open_access
checksum: 1df9f8c530b443c0e63a3f2e4fde412e
content_type: application/pdf
creator: koelsboe
date_created: 2020-02-06T14:43:54Z
date_updated: 2020-07-14T12:47:58Z
file_id: '7461'
file_name: thesis_ist-final_noack.pdf
file_size: 76195184
relation: main_file
- access_level: closed
checksum: 7a52383c812b0be64d3826546509e5a4
content_type: application/x-zip-compressed
creator: koelsboe
date_created: 2020-02-06T14:52:45Z
date_updated: 2020-07-14T12:47:58Z
description: latex source files, figures
file_id: '7462'
file_name: latex-files.zip
file_size: 122103715
relation: source_file
file_date_updated: 2020-07-14T12:47:58Z
has_accepted_license: '1'
keyword:
- shape reconstruction
- hole manipulation
- ordered complexes
- Alpha complex
- Wrap complex
- computational topology
- Bregman geometry
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '02'
oa: 1
oa_version: Published Version
page: '155'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '6608'
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: The hole system of triangulated shapes
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2020'
...
---
_id: '7944'
abstract:
- lang: eng
text: "This thesis considers two examples of reconfiguration problems: flipping
edges in edge-labelled triangulations of planar point sets and swapping labelled
tokens placed on vertices of a graph. In both cases the studied structures – all
the triangulations of a given point set or all token placements on a given graph
– can be thought of as vertices of the so-called reconfiguration graph, in which
two vertices are adjacent if the corresponding structures differ by a single elementary
operation – by a flip of a diagonal in a triangulation or by a swap of tokens
on adjacent vertices, respectively. We study the reconfiguration of one instance
of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor
triangulations of point sets in which each edge has a unique label and a flip
transfers the label from the removed edge to the new edge, we prove a polynomial-time
testable condition, called the Orbit Theorem, that characterizes when two triangulations
of the same point set lie in the same connected component of the reconfiguration
graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot.
We additionally provide a polynomial time algorithm that computes a reconfiguring
flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties
of a certain high-dimensional cell complex that has the usual reconfiguration
graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph,
we make partial progress on the problem of finding shortest reconfiguration sequences.
We disprove the so-called Happy Leaf Conjecture and demonstrate the importance
of swapping tokens that are already placed at the correct vertices. We also prove
that a generalization of the problem to weighted coloured token swapping is NP-hard
on trees but solvable in polynomial time on paths and stars."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
citation:
ama: Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944
apa: Masárová, Z. (2020). Reconfiguration problems. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944
chicago: Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and
Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.
ieee: Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology
Austria, 2020.
ista: Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology
Austria.
mla: Masárová, Zuzana. Reconfiguration Problems. Institute of Science and
Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.
short: Z. Masárová, Reconfiguration Problems, Institute of Science and Technology
Austria, 2020.
date_created: 2020-06-08T00:49:46Z
date_published: 2020-06-09T00:00:00Z
date_updated: 2023-09-07T13:17:37Z
day: '09'
ddc:
- '516'
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: UlWa
doi: 10.15479/AT:ISTA:7944
file:
- access_level: open_access
checksum: df688bc5a82b50baee0b99d25fc7b7f0
content_type: application/pdf
creator: zmasarov
date_created: 2020-06-08T00:34:00Z
date_updated: 2020-07-14T12:48:05Z
file_id: '7945'
file_name: THESIS_Zuzka_Masarova.pdf
file_size: 13661779
relation: main_file
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checksum: 45341a35b8f5529c74010b7af43ac188
content_type: application/zip
creator: zmasarov
date_created: 2020-06-08T00:35:30Z
date_updated: 2020-07-14T12:48:05Z
file_id: '7946'
file_name: THESIS_Zuzka_Masarova_SOURCE_FILES.zip
file_size: 32184006
relation: source_file
file_date_updated: 2020-07-14T12:48:05Z
has_accepted_license: '1'
keyword:
- reconfiguration
- reconfiguration graph
- triangulations
- flip
- constrained triangulations
- shellability
- piecewise-linear balls
- token swapping
- trees
- coloured weighted token swapping
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: '160'
publication_identifier:
isbn:
- 978-3-99078-005-3
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '7950'
relation: part_of_dissertation
status: public
- id: '5986'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Reconfiguration problems
tmp:
image: /images/cc_by_sa.png
legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
BY-SA 4.0)
short: CC BY-SA (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2020'
...
---
_id: '8703'
abstract:
- lang: eng
text: 'Even though Delaunay originally introduced his famous triangulations in the
case of infinite point sets with translational periodicity, a software that computes
such triangulations in the general case is not yet available, to the best of our
knowledge. Combining and generalizing previous work, we present a practical algorithm
for computing such triangulations. The algorithm has been implemented and experiments
show that its performance is as good as the one of the CGAL package, which is
restricted to cubic periodicity. '
alternative_title:
- LIPIcs
article_number: '75'
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
- first_name: Mael
full_name: Rouxel-Labbé, Mael
last_name: Rouxel-Labbé
- first_name: Monique
full_name: Teillaud, Monique
last_name: Teillaud
citation:
ama: 'Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay
triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75'
apa: 'Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL
periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms
(Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für
Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75'
chicago: Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing
CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on
Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
https://doi.org/10.4230/LIPIcs.ESA.2020.75.
ieee: G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic
Delaunay triangulations,” in 28th Annual European Symposium on Algorithms,
Virtual, Online; Pisa, Italy, 2020, vol. 173.
ista: 'Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay
triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European
Symposium on Algorithms, LIPIcs, vol. 173, 75.'
mla: Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.”
28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75.
short: G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium
on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-09-09
location: Virtual, Online; Pisa, Italy
name: 'ESA: Annual European Symposium on Algorithms'
start_date: 2020-09-07
date_created: 2020-10-25T23:01:18Z
date_published: 2020-08-26T00:00:00Z
date_updated: 2023-09-07T13:29:00Z
day: '26'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.ESA.2020.75
ec_funded: 1
file:
- access_level: open_access
checksum: fe0f7c49a99ed870c671b911e10d5496
content_type: application/pdf
creator: cziletti
date_created: 2020-10-27T14:31:52Z
date_updated: 2020-10-27T14:31:52Z
file_id: '8712'
file_name: 2020_LIPIcs_Osang.pdf
file_size: 733291
relation: main_file
success: 1
file_date_updated: 2020-10-27T14:31:52Z
has_accepted_license: '1'
intvolume: ' 173'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: 28th Annual European Symposium on Algorithms
publication_identifier:
isbn:
- '9783959771627'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '9056'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Generalizing CGAL periodic Delaunay triangulations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 173
year: '2020'
...
---
_id: '8163'
abstract:
- lang: eng
text: Fejes Tóth [3] studied approximations of smooth surfaces in three-space by
piecewise flat triangular meshes with a given number of vertices on the surface
that are optimal with respect to Hausdorff distance. He proves that this Hausdorff
distance decreases inversely proportional with the number of vertices of the approximating
mesh if the surface is convex. He also claims that this Hausdorff distance is
inversely proportional to the square of the number of vertices for a specific
non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by
two congruent circles. We refute this claim, and show that the asymptotic behavior
of the Hausdorff distance is linear, that is the same as for convex surfaces.
acknowledgement: "The authors are greatly indebted to Dror Atariah, Günther Rote and
John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel
Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion.
This work has been supported in part by the European Union’s Seventh Framework Programme
for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL
Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic
Foundations of Geometry Understanding in Higher Dimensions), the European Union’s
Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie
grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31."
article_processing_charge: No
article_type: original
author:
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy
of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199.
doi:10.1556/012.2020.57.2.1454
apa: Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes
Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica.
Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454
chicago: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes
Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum
Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.
ieee: G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on
the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica,
vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.
ista: Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on
the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2),
193–199.
mla: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes
Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum
Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454.
short: G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57
(2020) 193–199.
date_created: 2020-07-24T07:09:18Z
date_published: 2020-07-24T00:00:00Z
date_updated: 2023-10-10T13:05:27Z
day: '24'
ddc:
- '510'
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ec_funded: 1
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- '000570978400005'
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call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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call_identifier: FWF
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name: The Wittgenstein Prize
publication: Studia Scientiarum Mathematicarum Hungarica
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issn:
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title: Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes
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...
---
_id: '9157'
abstract:
- lang: eng
text: Representing an atom by a solid sphere in 3-dimensional Euclidean space, we
get the space-filling diagram of a molecule by taking the union. Molecular dynamics
simulates its motion subject to bonds and other forces, including the solvation
free energy. The morphometric approach [12, 17] writes the latter as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted mean curvature. Together with the derivatives of the weighted volume
in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this
yields the derivative of the morphometric expression of the solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of the weighted\r\ncurvature derivatives for the purpose of improving molecular
dynamics simulations and for his continued encouragement. They also thank Patrice
Koehl for the implementation of the formulas and for his encouragement and advise
along the road. Finally, they thank two anonymous reviewers for their constructive
criticism.\r\nThis project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative
Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant
no. I02979-N35 of the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling
diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0100
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of
a space-filling diagram,” Computational and Mathematical Biophysics, vol.
8, no. 1. De Gruyter, pp. 51–67, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of
a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative
of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 51–67.
date_created: 2021-02-17T15:13:01Z
date_published: 2020-06-20T00:00:00Z
date_updated: 2023-10-17T12:34:51Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0100
ec_funded: 1
file:
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checksum: cea41de9937d07a3b927d71ee8b4e432
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:56:24Z
date_updated: 2021-02-19T13:56:24Z
file_id: '9171'
file_name: 2020_CompMathBiophysics_Akopyan2.pdf
file_size: 562359
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file_date_updated: 2021-02-19T13:56:24Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 51-67
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted mean curvature derivative of a space-filling diagram
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image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2020'
...
---
_id: '9156'
abstract:
- lang: eng
text: The morphometric approach [11, 14] writes the solvation free energy as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted Gaussian curvature. Together with the derivatives of the weighted
volume in [7], the weighted area in [4], and the weighted mean curvature in [1],
this yields the derivative of the morphometric expression of solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics
simulations. They also thank Patrice Koehl for the implementation of the formulas
and for his encouragement and advise along the road. Finally, they thank two anonymous
reviewers for their constructive criticism.\r\nThis project has received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 78818 Alpha). It is also partially
supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a
space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88.
doi:10.1515/cmb-2020-0101
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature
derivative of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0101
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative
of a space-filling diagram,” Computational and Mathematical Biophysics,
vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 74–88.
date_created: 2021-02-17T15:12:44Z
date_published: 2020-07-21T00:00:00Z
date_updated: 2023-10-17T12:35:10Z
day: '21'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0101
ec_funded: 1
external_id:
arxiv:
- '1908.06777'
file:
- access_level: open_access
checksum: ca43a7440834eab6bbea29c59b56ef3a
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creator: dernst
date_created: 2021-02-19T13:33:19Z
date_updated: 2021-02-19T13:33:19Z
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file_name: 2020_CompMathBiophysics_Akopyan.pdf
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file_date_updated: 2021-02-19T13:33:19Z
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issue: '1'
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month: '07'
oa: 1
oa_version: Published Version
page: 74-88
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted Gaussian curvature derivative of a space-filling diagram
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2020'
...
---
_id: '15064'
abstract:
- lang: eng
text: We call a continuous self-map that reveals itself through a discrete set of
point-value pairs a sampled dynamical system. Capturing the available information
with chain maps on Delaunay complexes, we use persistent homology to quantify
the evidence of recurrent behavior. We establish a sampling theorem to recover
the eigenspaces of the endomorphism on homology induced by the self-map. Using
a combinatorial gradient flow arising from the discrete Morse theory for Čech
and Delaunay complexes, we construct a chain map to transform the problem from
the natural but expensive Čech complexes to the computationally efficient Delaunay
triangulations. The fast chain map algorithm has applications beyond dynamical
systems.
acknowledgement: This research has been supported by the DFG Collaborative Research
Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant
No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant
No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding
provided by Projekt DEAL.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: U.
full_name: Bauer, U.
last_name: Bauer
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: M.
full_name: Mrozek, M.
last_name: Mrozek
citation:
ama: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow
and homology inference for self-maps. Journal of Applied and Computational
Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8
apa: Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay
gradient flow and homology inference for self-maps. Journal of Applied and
Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8
chicago: Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay
Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and
Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.
ieee: U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient
flow and homology inference for self-maps,” Journal of Applied and Computational
Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.
ista: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient
flow and homology inference for self-maps. Journal of Applied and Computational
Topology. 4(4), 455–480.
mla: Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.”
Journal of Applied and Computational Topology, vol. 4, no. 4, Springer
Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.
short: U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and
Computational Topology 4 (2020) 455–480.
date_created: 2024-03-04T10:47:49Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2024-03-04T10:54:04Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s41468-020-00058-8
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checksum: eed1168b6e66cd55272c19bb7fca8a1c
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creator: dernst
date_created: 2024-03-04T10:52:42Z
date_updated: 2024-03-04T10:52:42Z
file_id: '15065'
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file_size: 851190
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success: 1
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intvolume: ' 4'
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 455-480
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Čech-Delaunay gradient flow and homology inference for self-maps
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...
---
_id: '6515'
abstract:
- lang: eng
text: We give non-degeneracy criteria for Riemannian simplices based on simplices
in spaces of constant sectional curvature. It extends previous work on Riemannian
simplices, where we developed Riemannian simplices with respect to Euclidean reference
simplices. The criteria we give in this article are in terms of quality measures
for spaces of constant curvature that we develop here. We see that simplices in
spaces that have nearly constant curvature, are already non-degenerate under very
weak quality demands. This is of importance because it allows for sampling of
Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature.
author:
- first_name: Ramsay
full_name: Dyer, Ramsay
last_name: Dyer
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature.
Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9
apa: Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces
of constant curvature. Journal of Computational Geometry . Carleton University.
https://doi.org/10.20382/jocg.v10i1a9
chicago: Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled
on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton
University, 2019. https://doi.org/10.20382/jocg.v10i1a9.
ieee: R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant
curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton
University, pp. 223–256, 2019.
ista: Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant
curvature. Journal of Computational Geometry . 10(1), 223–256.
mla: Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.”
Journal of Computational Geometry , vol. 10, no. 1, Carleton University,
2019, pp. 223–256, doi:10.20382/jocg.v10i1a9.
short: R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10
(2019) 223–256.
date_created: 2019-06-03T09:35:33Z
date_published: 2019-07-01T00:00:00Z
date_updated: 2021-01-12T08:07:50Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.20382/jocg.v10i1a9
ec_funded: 1
file:
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checksum: 57b4df2f16a74eb499734ec8ee240178
content_type: application/pdf
creator: mwintrae
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date_updated: 2020-07-14T12:47:32Z
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relation: main_file
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intvolume: ' 10'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 223–256
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'Journal of Computational Geometry '
publication_identifier:
issn:
- 1920-180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: 1
status: public
title: Simplices modelled on spaces of constant curvature
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '2019'
...
---
_id: '6628'
abstract:
- lang: eng
text: Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces
in Euclidean space by piecewise flat triangular meshes with a given number
of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this
Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and
d is the dimension of Euclidean space. Moreover the pro-portionality constant
can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In
this short note, we prove the extrinsic nature of this constant for manifolds
of sufficiently high codimension. We do so by constructing an family of isometric
embeddings of the flat torus in Euclidean space.
author:
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of
optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational
Geometry. ; 2019:275-279.'
apa: Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff
distance of optimal triangulations of manifolds. In The 31st Canadian Conference
in Computational Geometry (pp. 275–279). Edmonton, Canada.
chicago: Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff
Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference
in Computational Geometry, 275–79, 2019.
ieee: G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance
of optimal triangulations of manifolds,” in The 31st Canadian Conference in
Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.
ista: 'Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance
of optimal triangulations of manifolds. The 31st Canadian Conference in Computational
Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.'
mla: Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff
Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference
in Computational Geometry, 2019, pp. 275–79.
short: G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational
Geometry, 2019, pp. 275–279.
conference:
end_date: 2019-08-10
location: Edmonton, Canada
name: 'CCCG: Canadian Conference in Computational Geometry'
start_date: 2019-08-08
date_created: 2019-07-12T08:34:57Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2021-01-12T08:08:16Z
day: '01'
ddc:
- '004'
department:
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: ceabd152cfa55170d57763f9c6c60a53
content_type: application/pdf
creator: mwintrae
date_created: 2019-07-12T08:32:46Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6629'
file_name: IntrinsicExtrinsicCCCG2019.pdf
file_size: 321176
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 275-279
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: The 31st Canadian Conference in Computational Geometry
publication_status: published
quality_controlled: '1'
scopus_import: 1
status: public
title: The extrinsic nature of the Hausdorff distance of optimal triangulations of
manifolds
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '6648'
abstract:
- lang: eng
text: "Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms.
Importantly, instead of using the standard Euclidean distance, we look into dissimilarity
measures with information-theoretic justification, and we develop the theory\r\nneeded
for applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context."
alternative_title:
- LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. In: 35th International Symposium on Computational Geometry. Vol
129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31'
apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis
in information space. In 35th International Symposium on Computational Geometry
(Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31'
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” In 35th International Symposium on Computational
Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” in 35th International Symposium on Computational Geometry, Portland,
OR, United States, 2019, vol. 129, p. 31:1-31:14.
ista: 'Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information
space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium
on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.'
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
35th International Symposium on Computational Geometry, vol. 129, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31.
short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on
Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019,
p. 31:1-31:14.
conference:
end_date: 2019-06-21
location: Portland, OR, United States
name: 'SoCG 2019: Symposium on Computational Geometry'
start_date: 2019-06-18
date_created: 2019-07-17T10:36:09Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2021-01-12T08:08:23Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPICS.SOCG.2019.31
external_id:
arxiv:
- '1903.08510'
file:
- access_level: open_access
checksum: 8ec8720730d4c789bf7b06540f1c29f4
content_type: application/pdf
creator: dernst
date_created: 2019-07-24T06:40:01Z
date_updated: 2020-07-14T12:47:35Z
file_id: '6666'
file_name: 2019_LIPICS_Edelsbrunner.pdf
file_size: 1355179
relation: main_file
file_date_updated: 2020-07-14T12:47:35Z
has_accepted_license: '1'
intvolume: ' 129'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 31:1-31:14
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: 35th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959771047'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: 1
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 129
year: '2019'
...
---
_id: '6989'
abstract:
- lang: eng
text: 'When can a polyomino piece of paper be folded into a unit cube? Prior work
studied tree-like polyominoes, but polyominoes with holes remain an intriguing
open problem. We present sufficient conditions for a polyomino with hole(s) to
fold into a cube, and conditions under which cube folding is impossible. In particular,
we show that all but five special simple holes guarantee foldability. '
acknowledgement: This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank
all other participants for a fruitful atmosphere.
article_processing_charge: No
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Hugo A
full_name: Akitaya, Hugo A
last_name: Akitaya
- first_name: Kenneth C
full_name: Cheung, Kenneth C
last_name: Cheung
- first_name: Erik D
full_name: Demaine, Erik D
last_name: Demaine
- first_name: Martin L
full_name: Demaine, Martin L
last_name: Demaine
- first_name: Sandor P
full_name: Fekete, Sandor P
last_name: Fekete
- first_name: Linda
full_name: Kleist, Linda
last_name: Kleist
- first_name: Irina
full_name: Kostitsyna, Irina
last_name: Kostitsyna
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Klara
full_name: Mundilova, Klara
last_name: Mundilova
- first_name: Christiane
full_name: Schmidt, Christiane
last_name: Schmidt
citation:
ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes
into a cube. In: Proceedings of the 31st Canadian Conference on Computational
Geometry. Canadian Conference on Computational Geometry; 2019:164-170.'
apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M.
L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a
cube. In Proceedings of the 31st Canadian Conference on Computational Geometry
(pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.'
chicago: Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin
L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes
into a Cube.” In Proceedings of the 31st Canadian Conference on Computational
Geometry, 164–70. Canadian Conference on Computational Geometry, 2019.
ieee: O. Aichholzer et al., “Folding polyominoes with holes into a cube,”
in Proceedings of the 31st Canadian Conference on Computational Geometry,
Edmonton, Canada, 2019, pp. 164–170.
ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist
L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding
polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference
on Computational Geometry. CCCG: Canadian Conference in Computational Geometry,
164–170.'
mla: Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings
of the 31st Canadian Conference on Computational Geometry, Canadian Conference
on Computational Geometry, 2019, pp. 164–70.
short: O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P.
Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt,
in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian
Conference on Computational Geometry, 2019, pp. 164–170.
conference:
end_date: 2019-08-10
location: Edmonton, Canada
name: 'CCCG: Canadian Conference in Computational Geometry'
start_date: 2019-08-08
date_created: 2019-11-04T16:46:11Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2023-08-04T10:57:42Z
day: '01'
department:
- _id: HeEd
external_id:
arxiv:
- '1910.09917'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://cccg.ca/proceedings/2019/proceedings.pdf
month: '08'
oa: 1
oa_version: Published Version
page: 164-170
publication: Proceedings of the 31st Canadian Conference on Computational Geometry
publication_status: published
publisher: Canadian Conference on Computational Geometry
quality_controlled: '1'
related_material:
record:
- id: '8317'
relation: extended_version
status: public
scopus_import: '1'
status: public
title: Folding polyominoes with holes into a cube
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
year: '2019'
...
---
_id: '6671'
abstract:
- lang: eng
text: 'In this paper we discuss three results. The first two concern general sets
of positive reach: we first characterize the reach of a closed set by means of
a bound on the metric distortion between the distance measured in the ambient
Euclidean space and the shortest path distance measured in the set. Secondly,
we prove that the intersection of a ball with radius less than the reach with
the set is geodesically convex, meaning that the shortest path between any two
points in the intersection lies itself in the intersection. For our third result
we focus on manifolds with positive reach and give a bound on the angle between
tangent spaces at two different points in terms of the reach and the distance
between the two points.'
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: André
full_name: Lieutier, André
last_name: Lieutier
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic
convexity and the variation of tangent spaces. Journal of Applied and Computational
Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8
apa: Boissonnat, J.-D., Lieutier, A., & Wintraecken, M. (2019). The reach, metric
distortion, geodesic convexity and the variation of tangent spaces. Journal
of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8
chicago: Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The
Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.”
Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8.
ieee: J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion,
geodesic convexity and the variation of tangent spaces,” Journal of Applied
and Computational Topology, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.
ista: Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion,
geodesic convexity and the variation of tangent spaces. Journal of Applied and
Computational Topology. 3(1–2), 29–58.
mla: Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity
and the Variation of Tangent Spaces.” Journal of Applied and Computational
Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8.
short: J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational
Topology 3 (2019) 29–58.
date_created: 2019-07-24T08:37:29Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-08-22T12:37:47Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s41468-019-00029-8
ec_funded: 1
file:
- access_level: open_access
checksum: a5b244db9f751221409cf09c97ee0935
content_type: application/pdf
creator: dernst
date_created: 2019-07-31T08:09:56Z
date_updated: 2020-07-14T12:47:36Z
file_id: '6741'
file_name: 2019_JournAppliedComputTopol_Boissonnat.pdf
file_size: 2215157
relation: main_file
file_date_updated: 2020-07-14T12:47:36Z
has_accepted_license: '1'
intvolume: ' 3'
issue: 1-2
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 29–58
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: The reach, metric distortion, geodesic convexity and the variation of tangent
spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2019'
...
---
_id: '6050'
abstract:
- lang: eng
text: 'We answer a question of David Hilbert: given two circles it is not possible
in general to construct their centers using only a straightedge. On the other
hand, we give infinitely many families of pairs of circles for which such construction
is possible. '
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Fedorov, Roman
last_name: Fedorov
citation:
ama: Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of
the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240
apa: Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge.
Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240
chicago: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.
ieee: A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings
of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.
ista: Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings
of the American Mathematical Society. 147, 91–102.
mla: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society, vol. 147, AMS, 2019,
pp. 91–102, doi:10.1090/proc/14240.
short: A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society
147 (2019) 91–102.
date_created: 2019-02-24T22:59:19Z
date_published: 2019-01-01T00:00:00Z
date_updated: 2023-08-24T14:48:59Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/14240
external_id:
arxiv:
- '1709.02562'
isi:
- '000450363900008'
intvolume: ' 147'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.02562
month: '01'
oa: 1
oa_version: Preprint
page: 91-102
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: Two circles and only a straightedge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 147
year: '2019'
...
---
_id: '6634'
abstract:
- lang: eng
text: In this paper we prove several new results around Gromov's waist theorem.
We give a simple proof of Vaaler's theorem on sections of the unit cube using
the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective
spaces, flat tori, convex bodies in Euclidean space; and establish waist-type
results in terms of the Hausdorff measure.
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alfredo
full_name: Hubard, Alfredo
last_name: Hubard
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different
spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490.
doi:10.12775/TMNA.2019.008
apa: Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for
the waists of different spaces. Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008
chicago: Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds
for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.
ieee: A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists
of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53,
no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.
ista: Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists
of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.
mla: Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different
Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka
Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.
short: A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis
53 (2019) 457–490.
date_created: 2019-07-14T21:59:19Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-08-29T06:32:48Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2019.008
ec_funded: 1
external_id:
arxiv:
- '1612.06926'
isi:
- '000472541600004'
intvolume: ' 53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.06926
month: '06'
oa: 1
oa_version: Preprint
page: 457-490
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Akademicka Platforma Czasopism
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower and upper bounds for the waists of different spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2019'
...
---
_id: '6756'
abstract:
- lang: eng
text: "We study the topology generated by the temperature fluctuations of the cosmic
microwave background (CMB) radiation, as quantified by the number of components
and holes, formally given by the Betti numbers, in the growing excursion sets.
We compare CMB maps observed by the Planck satellite with a thousand simulated
maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations.
The comparison is multi-scale, being performed on a sequence of degraded maps
with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over
\U0001D54A2 is incomplete due to obfuscation effects by bright point sources and
other extended foreground objects like our own galaxy. To deal with such situations,
where analysis in the presence of “masks” is of importance, we introduce the concept
of relative homology. The parametric χ2-test shows differences between observations
and simulations, yielding p-values at percent to less than permil levels roughly
between 2 and 7°, with the difference in the number of components and holes peaking
at more than 3σ sporadically at these scales. The highest observed deviation between
the observations and simulations for b0 and b1 is approximately between 3σ and
4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler
characteristic at 3.66° in the literature, computed from independent measurements
of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave
Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler
characteristic is phenomenologically related to the strongly anomalous behaviour
of components and holes, or the zeroth and first Betti numbers, respectively.
Further, since these topological descriptors show consistent anomalous behaviour
over independent measurements of Planck and WMAP, instrumental and systematic
errors may be an unlikely source. These are also the scales at which the observed
maps exhibit low variance compared to the simulations, and approximately the range
of scales at which the power spectrum exhibits a dip with respect to the theoretical
model. Non-parametric tests show even stronger differences at almost all scales.
Crucially, Gaussian simulations based on power-spectrum matching the characteristics
of the observed dipped power spectrum are not able to resolve the anomaly. Understanding
the origin of the anomalies in the CMB, whether cosmological in nature or arising
due to late-time effects, is an extremely challenging task. Regardless, beyond
the trivial possibility that this may still be a manifestation of an extreme Gaussian
case, these observations, along with the super-horizon scales involved, may motivate
the study of primordial non-Gaussianity. Alternative scenarios worth exploring
may be models with non-trivial topology, including topological defect models."
article_number: A163
article_processing_charge: No
article_type: original
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Robert J.
full_name: Adler, Robert J.
last_name: Adler
- first_name: Thomas
full_name: Buchert, Thomas
last_name: Buchert
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Bernard J.T.
full_name: Jones, Bernard J.T.
last_name: Jones
- first_name: Armin
full_name: Schwartzman, Armin
last_name: Schwartzman
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
citation:
ama: Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature
fluctuations in the cosmic microwave background. Astronomy and Astrophysics.
2019;627. doi:10.1051/0004-6361/201834916
apa: Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman,
A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations
in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences.
https://doi.org/10.1051/0004-6361/201834916
chicago: Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner,
Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert.
“Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.”
Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.
ieee: P. Pranav et al., “Unexpected topology of the temperature fluctuations
in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627.
EDP Sciences, 2019.
ista: Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner
H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations
in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.
mla: Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations
in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627,
A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.
short: P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman,
H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).
date_created: 2019-08-04T21:59:18Z
date_published: 2019-07-17T00:00:00Z
date_updated: 2023-08-29T07:01:48Z
day: '17'
ddc:
- '520'
- '530'
department:
- _id: HeEd
doi: 10.1051/0004-6361/201834916
external_id:
arxiv:
- '1812.07678'
isi:
- '000475839300003'
file:
- access_level: open_access
checksum: 83b9209ed9eefbdcefd89019c5a97805
content_type: application/pdf
creator: dernst
date_created: 2019-08-05T08:08:59Z
date_updated: 2020-07-14T12:47:39Z
file_id: '6766'
file_name: 2019_AstronomyAstrophysics_Pranav.pdf
file_size: 14420451
relation: main_file
file_date_updated: 2020-07-14T12:47:39Z
has_accepted_license: '1'
intvolume: ' 627'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 265683E4-B435-11E9-9278-68D0E5697425
grant_number: M62909-18-1-2038
name: Toward Computational Information Topology
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Astronomy and Astrophysics
publication_identifier:
eissn:
- '14320746'
issn:
- '00046361'
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Unexpected topology of the temperature fluctuations in the cosmic microwave
background
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: 627
year: '2019'
...
---
_id: '6793'
abstract:
- lang: eng
text: The Regge symmetry is a set of remarkable relations between two tetrahedra
whose edge lengths are related in a simple fashion. It was first discovered as
a consequence of an asymptotic formula in mathematical physics. Here, we give
a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic
geometry.
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Ivan
full_name: Izmestiev, Ivan
last_name: Izmestiev
citation:
ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli
formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775.
doi:10.1112/blms.12276
apa: Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics,
and the Schläfli formula. Bulletin of the London Mathematical Society.
London Mathematical Society. https://doi.org/10.1112/blms.12276
chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society.
London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.
ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the
Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51,
no. 5. London Mathematical Society, pp. 765–775, 2019.
ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the
Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.
mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society,
vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.
short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51
(2019) 765–775.
date_created: 2019-08-11T21:59:23Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-29T07:08:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12276
ec_funded: 1
external_id:
arxiv:
- '1903.04929'
isi:
- '000478560200001'
intvolume: ' 51'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.04929
month: '10'
oa: 1
oa_version: Preprint
page: 765-775
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- '14692120'
issn:
- '00246093'
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Regge symmetry, confocal conics, and the Schläfli formula
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 51
year: '2019'
...
---
_id: '6828'
abstract:
- lang: eng
text: In this paper we construct a family of exact functors from the category of
Whittaker modules of the simple complex Lie algebra of type to the category of
finite-dimensional modules of the graded affine Hecke algebra of type . Using
results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors
map standard modules to standard modules (or zero) and simple modules to simple
modules (or zero). Moreover, we show that each simple module of the graded affine
Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker
category contains the BGG category as a full subcategory, our results generalize
results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between
finite-dimensional representations of and representations of the symmetric group
.
article_processing_charge: No
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
citation:
ama: Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027
apa: Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal
of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027
chicago: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal
of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.
ieee: A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra,
vol. 538. Elsevier, pp. 261–289, 2019.
ista: Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
538, 261–289.
mla: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of
Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.
short: A. Brown, Journal of Algebra 538 (2019) 261–289.
date_created: 2019-08-22T07:54:13Z
date_published: 2019-11-15T00:00:00Z
date_updated: 2023-08-29T07:11:47Z
day: '15'
department:
- _id: HeEd
doi: 10.1016/j.jalgebra.2019.07.027
external_id:
arxiv:
- '1805.04676'
isi:
- '000487176300011'
intvolume: ' 538'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.04676
month: '11'
oa: 1
oa_version: Preprint
page: 261-289
publication: Journal of Algebra
publication_identifier:
issn:
- 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Arakawa-Suzuki functors for Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 538
year: '2019'
...
---
_id: '7216'
abstract:
- lang: eng
text: 'We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system
to label a stream of noisy observations of transit vehicle trajectories with the
transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently
to large transit networks, our system first retrieves a small set of candidate
routes from a geometrically indexed data structure, then applies a fine-grained
scoring step to choose the best match. Given that real-time data remains unavailable
for the majority of the world’s transit agencies, these inferences can help feed
a real-time map of a transit system’s trips, infer transit trip delays in real
time, or measure and correct noisy transit tracking data. This system can run
on vehicle observations from a variety of sources that don’t attach route information
to vehicle observations, such as public imagery streams or user-contributed transit
vehicle sightings.We abstract away the specifics of the sensing system and demonstrate
the effectiveness of our system on a "semisynthetic" dataset of all New York City
buses, where we simulate sensed trajectories by starting with fully labeled vehicle
trajectories reported via the GTFS-Realtime protocol, removing the transit route
IDs, and perturbing locations with synthetic noise. Using just the geometric shapes
of the trajectories, we demonstrate that our system converges on the correct route
ID within a few minutes, even after a vehicle switches from serving one trip to
the next.'
article_number: '8917514'
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
- first_name: James
full_name: Cook, James
last_name: Cook
- first_name: Alex
full_name: Fabrikant, Alex
last_name: Fabrikant
- first_name: Marco
full_name: Gruteser, Marco
last_name: Gruteser
citation:
ama: 'Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching
of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent
Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514'
apa: 'Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL:
Real-time matching of transit vehicle trajectories to transit routes at scale.
In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New
Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514'
chicago: 'Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL:
Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.”
In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019.
https://doi.org/10.1109/ITSC.2019.8917514.'
ieee: 'G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time
matching of transit vehicle trajectories to transit routes at scale,” in 2019
IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand,
2019.'
ista: 'Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching
of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent
Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference,
8917514.'
mla: 'Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle
Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation
Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.'
short: G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent
Transportation Systems Conference, IEEE, 2019.
conference:
end_date: 2019-10-30
location: Auckland, New Zealand
name: 'ITSC: Intelligent Transportation Systems Conference'
start_date: 2019-10-27
date_created: 2019-12-29T23:00:47Z
date_published: 2019-11-28T00:00:00Z
date_updated: 2023-09-06T14:50:28Z
day: '28'
department:
- _id: HeEd
doi: 10.1109/ITSC.2019.8917514
external_id:
isi:
- '000521238102050'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
publication: 2019 IEEE Intelligent Transportation Systems Conference
publication_identifier:
isbn:
- '9781538670248'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'LiveTraVeL: Real-time matching of transit vehicle trajectories to transit
routes at scale'
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...
---
_id: '5678'
abstract:
- lang: eng
text: "The order-k Voronoi tessellation of a locally finite set \U0001D44B⊆ℝ\U0001D45B
decomposes ℝ\U0001D45B into convex domains whose points have the same k nearest
neighbors in X. Assuming X is a stationary Poisson point process, we give explicit
formulas for the expected number and total area of faces of a given dimension
per unit volume of space. We also develop a relaxed version of discrete Morse
theory and generalize by counting only faces, for which the k nearest points in
X are within a given distance threshold."
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
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete
and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2
apa: Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order
k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of
Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.
ieee: H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete
and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.
ista: Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete
and Computational Geometry. 62(4), 865–878.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order
K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019,
pp. 865–878, doi:10.1007/s00454-018-0049-2.
short: H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019)
865–878.
date_created: 2018-12-16T22:59:20Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2023-09-07T12:07:12Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-018-0049-2
ec_funded: 1
external_id:
arxiv:
- '1709.09380'
isi:
- '000494042900008'
file:
- access_level: open_access
checksum: f9d00e166efaccb5a76bbcbb4dcea3b4
content_type: application/pdf
creator: dernst
date_created: 2019-02-06T10:10:46Z
date_updated: 2020-07-14T12:47:10Z
file_id: '5932'
file_name: 2018_DiscreteCompGeometry_Edelsbrunner.pdf
file_size: 599339
relation: main_file
file_date_updated: 2020-07-14T12:47:10Z
has_accepted_license: '1'
intvolume: ' 62'
isi: 1
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 865–878
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Poisson–Delaunay Mosaics 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 62
year: '2019'
...
---
_id: '6608'
abstract:
- lang: eng
text: We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner
and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete
application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha
complex, and we use the persistence diagram of the distance function to guide
the hole opening and closing operations. The dependences between the holes define
a partial order on the cells in K that characterizes what can and what cannot
be constructed using the operations. The relations in this partial order reveal
structural information about the underlying filtration of complexes beyond what
is expressed by the persistence diagram.
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: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
citation:
ama: Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer
Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003
apa: Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered
complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003
chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in
an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.
ieee: H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,”
Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.
ista: Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex.
Computer Aided Geometric Design. 73, 1–15.
mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an
Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019,
pp. 1–15, doi:10.1016/j.cagd.2019.06.003.
short: H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.
date_created: 2019-07-07T21:59:20Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2023-09-07T13:15:29Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.cagd.2019.06.003
ec_funded: 1
external_id:
isi:
- '000485207800001'
file:
- access_level: open_access
checksum: 7c99be505dc7533257d42eb1830cef04
content_type: application/pdf
creator: kschuh
date_created: 2019-07-08T15:24:26Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6624'
file_name: Elsevier_2019_Edelsbrunner.pdf
file_size: 2665013
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: ' 73'
isi: 1
language:
- iso: eng
month: '08'
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: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Computer Aided Geometric Design
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '7460'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Holes and dependences in an ordered complex
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 73
year: '2019'
...
---
_id: '7950'
abstract:
- lang: eng
text: "The input to the token swapping problem is a graph with vertices v1, v2,
. . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The
goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number
of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token
swapping on a tree, also known as “sorting with a transposition tree,” is not
known to be in P nor NP-complete. We present some partial results:\r\n1. An
optimum swap sequence may need to perform a swap on a leaf vertex that has the
correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any
algorithm that fixes happy leaves—as all known approximation algorithms for the
problem do—has approximation factor at least 4/3. Furthermore, the two best-known
2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized
problem—weighted coloured token swapping—is NP-complete on trees, but solvable
in polynomial time on paths and stars. In this version, tokens and vertices
\ have colours, and colours have weights. The goal is to get every
token to a vertex of the same colour, and the cost of a swap is the sum of the
weights of the two tokens involved."
article_number: '1903.06981'
article_processing_charge: No
author:
- first_name: Ahmad
full_name: Biniaz, Ahmad
last_name: Biniaz
- first_name: Kshitij
full_name: Jain, Kshitij
last_name: Jain
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tillmann
full_name: Miltzow, Tillmann
last_name: Miltzow
- first_name: Debajyoti
full_name: Mondal, Debajyoti
last_name: Mondal
- first_name: Anurag Murty
full_name: Naredla, Anurag Murty
last_name: Naredla
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Alexi
full_name: Turcotte, Alexi
last_name: Turcotte
citation:
ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.
apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte,
A. (n.d.). Token swapping on trees. arXiv.
chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow,
Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token
Swapping on Trees.” ArXiv, n.d.
ieee: A. Biniaz et al., “Token swapping on trees,” arXiv. .
ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec
J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.
mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.
short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla,
J. Tkadlec, A. Turcotte, ArXiv (n.d.).
date_created: 2020-06-08T12:25:25Z
date_published: 2019-03-16T00:00:00Z
date_updated: 2024-01-04T12:42:08Z
day: '16'
department:
- _id: HeEd
- _id: UlWa
- _id: KrCh
external_id:
arxiv:
- '1903.06981'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.06981
month: '03'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '7944'
relation: dissertation_contains
status: public
- id: '12833'
relation: later_version
status: public
status: public
title: Token swapping on trees
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '188'
abstract:
- lang: eng
text: Smallest enclosing spheres of finite point sets are central to methods in
topological data analysis. Focusing on Bregman divergences to measure dissimilarity,
we prove bounds on the location of the center of a smallest enclosing sphere.
These bounds depend on the range of radii for which Bregman balls are convex.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund
alternative_title:
- Leibniz International Proceedings in Information, LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff
points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35'
apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres
and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at
the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35'
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing
Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.
ieee: 'H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and
Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational
Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.'
ista: 'Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff
points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz
International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.'
mla: Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points
in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.
short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2018, p. 35:1-35:13.
conference:
end_date: 2018-06-14
location: Budapest, Hungary
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2018-06-11
date_created: 2018-12-11T11:45:05Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2021-01-12T06:53:48Z
day: '11'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2018.35
file:
- access_level: open_access
checksum: 7509403803b3ac1aee94bbc2ad293d21
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:31:31Z
date_updated: 2020-07-14T12:45:20Z
file_id: '5724'
file_name: 2018_LIPIcs_Edelsbrunner.pdf
file_size: 489080
relation: main_file
file_date_updated: 2020-07-14T12:45:20Z
has_accepted_license: '1'
intvolume: ' 99'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 35:1 - 35:13
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7733'
quality_controlled: '1'
scopus_import: 1
status: public
title: Smallest enclosing spheres and Chernoff points in Bregman geometry
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 99
year: '2018'
...