---
_id: '6287'
abstract:
- lang: eng
text: The main objects considered in the present work are simplicial and CW-complexes
with vertices forming a random point cloud. In particular, we consider a Poisson
point process in R^n and study Delaunay and Voronoi complexes of the first and
higher orders and weighted Delaunay complexes obtained as sections of Delaunay
complexes, as well as the Čech complex. Further, we examine theDelaunay complex
of a Poisson point process on the sphere S^n, as well as of a uniform point cloud,
which is equivalent to the convex hull, providing a connection to the theory of
random polytopes. Each of the complexes in question can be endowed with a radius
function, which maps its cells to the radii of appropriately chosen circumspheres,
called the radius of the cell. Applying and developing discrete Morse theory for
these functions, joining it together with probabilistic and sometimes analytic
machinery, and developing several integral geometric tools, we aim at getting
the distributions of circumradii of typical cells. For all considered complexes,
we are able to generalize and obtain up to constants the distribution of radii
of typical intervals of all types. In low dimensions the constants can be computed
explicitly, thus providing the explicit expressions for the expected numbers of
cells. In particular, it allows to find the expected density of simplices of every
dimension for a Poisson point process in R^4, whereas the result for R^3 was known
already in 1970's.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873
apa: Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873
chicago: Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute
of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.
ieee: A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of
Science and Technology Austria, 2017.
ista: Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute
of Science and Technology Austria.
mla: Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute
of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.
short: A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science
and Technology Austria, 2017.
date_created: 2019-04-09T15:04:32Z
date_published: 2017-10-27T00:00:00Z
date_updated: 2023-09-15T12:10:34Z
day: '27'
ddc:
- '514'
- '516'
- '519'
degree_awarded: PhD
department:
- _id: HeEd
doi: 10.15479/AT:ISTA:th_873
file:
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date_created: 2019-04-09T14:54:51Z
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language:
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month: '10'
oa: 1
oa_version: Published Version
page: '86'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
pubrep_id: '873'
related_material:
record:
- id: '718'
relation: part_of_dissertation
status: public
- id: '5678'
relation: part_of_dissertation
status: public
- id: '87'
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: 'Discrete Morse theory for random complexes '
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2017'
...
---
_id: '688'
abstract:
- lang: eng
text: 'We show that the framework of topological data analysis can be extended from
metrics to general Bregman divergences, widening the scope of possible applications.
Examples are the Kullback - Leibler divergence, which is commonly used for comparing
text and images, and the Itakura - Saito divergence, popular for speech and sound.
In particular, we prove that appropriately generalized čech and Delaunay (alpha)
complexes capture the correct homotopy type, namely that of the corresponding
union of Bregman balls. Consequently, their filtrations give the correct persistence
diagram, namely the one generated by the uniformly growing Bregman balls. Moreover,
we show that unlike the metric setting, the filtration of Vietoris-Rips complexes
may fail to approximate the persistence diagram. We propose algorithms to compute
the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally
test their efficiency. Lastly, we explain their surprisingly good performance
by making a connection with discrete Morse theory. '
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: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences.
In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916.
doi:10.4230/LIPIcs.SoCG.2017.39'
apa: 'Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with
Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational
Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2017.39'
chicago: Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with
Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.
ieee: H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,”
presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia,
2017, vol. 77, pp. 391–3916.
ista: Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences.
Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.
mla: Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with
Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.
short: H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916.
conference:
end_date: 2017-07-07
location: Brisbane, Australia
name: Symposium on Computational Geometry, SoCG
start_date: 2017-07-04
date_created: 2018-12-11T11:47:56Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:09:26Z
day: '01'
ddc:
- '514'
- '516'
department:
- _id: HeEd
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2017.39
file:
- access_level: open_access
checksum: 067ab0cb3f962bae6c3af6bf0094e0f3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:03Z
date_updated: 2020-07-14T12:47:42Z
file_id: '4856'
file_name: IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf
file_size: 990546
relation: main_file
file_date_updated: 2020-07-14T12:47:42Z
has_accepted_license: '1'
intvolume: ' 77'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 391-3916
publication_identifier:
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7021'
pubrep_id: '895'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topological data analysis with Bregman divergences
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 77
year: '2017'
...
---
_id: '1022'
abstract:
- lang: eng
text: We introduce a multiscale topological description of the Megaparsec web-like
cosmic matter distribution. Betti numbers and topological persistence offer a
powerful means of describing the rich connectivity structure of the cosmic web
and of its multiscale arrangement of matter and galaxies. Emanating from algebraic
topology and Morse theory, Betti numbers and persistence diagrams represent an
extension and deepening of the cosmologically familiar topological genus measure
and the related geometric Minkowski functionals. In addition to a description
of the mathematical background, this study presents the computational procedure
for computing Betti numbers and persistence diagrams for density field filtrations.
The field may be computed starting from a discrete spatial distribution of galaxies
or simulation particles. The main emphasis of this study concerns an extensive
and systematic exploration of the imprint of different web-like morphologies and
different levels of multiscale clustering in the corresponding computed Betti
numbers and persistence diagrams. To this end, we use Voronoi clustering models
as templates for a rich variety of web-like configurations and the fractal-like
Soneira-Peebles models exemplify a range of multiscale configurations. We have
identified the clear imprint of cluster nodes, filaments, walls, and voids in
persistence diagrams, along with that of the nested hierarchy of structures in
multiscale point distributions. We conclude by outlining the potential of persistent
topology for understanding the connectivity structure of the cosmic web, in large
simulations of cosmic structure formation and in the challenging context of the
observed galaxy distribution in large galaxy surveys.
acknowledgement: Part of this work has been supported by the 7th Framework Programme
for Research of the European Commission, under FETOpen grant number 255827 (CGL
Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random
Systems via Algebraic Topology) number 320422.
article_processing_charge: No
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Bernard
full_name: Jones, Bernard
last_name: Jones
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic
web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical
Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862
apa: Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M.,
Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms
of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society.
Oxford University Press. https://doi.org/10.1093/mnras/stw2862
chicago: Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter,
Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic
Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical
Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.
ieee: P. Pranav et al., “The topology of the cosmic web in terms of persistent
Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4. Oxford University Press, pp. 4281–4310, 2017.
ista: Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B,
Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti
numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.
mla: Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent
Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.
short: P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B.
Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017)
4281–4310.
date_created: 2018-12-11T11:49:44Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-22T09:40:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/mnras/stw2862
external_id:
isi:
- '000395170200039'
intvolume: ' 465'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.04519
month: '01'
oa: 1
oa_version: Submitted Version
page: 4281 - 4310
publication: Monthly Notices of the Royal Astronomical Society
publication_identifier:
issn:
- '00358711'
publication_status: published
publisher: Oxford University Press
publist_id: '6373'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The topology of the cosmic web in terms of persistent Betti numbers
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 465
year: '2017'
...
---
_id: '1065'
abstract:
- lang: eng
text: 'We consider the problem of reachability in pushdown graphs. We study the
problem for pushdown graphs with constant treewidth. Even for pushdown graphs
with treewidth 1, for the reachability problem we establish the following: (i)
the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem
would contradict the k-clique conjecture and imply faster combinatorial algorithms
for cliques in graphs.'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- 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: Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information
Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003
apa: Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant
treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003
chicago: Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with
Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003.
ieee: K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,”
Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.
ista: Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth.
Information Processing Letters. 122, 25–29.
mla: Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant
Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp.
25–29, doi:10.1016/j.ipl.2017.02.003.
short: K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.
date_created: 2018-12-11T11:49:57Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T12:08:18Z
day: '01'
ddc:
- '000'
department:
- _id: KrCh
- _id: HeEd
doi: 10.1016/j.ipl.2017.02.003
ec_funded: 1
external_id:
isi:
- '000399506600005'
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:17Z
date_updated: 2019-10-15T07:44:51Z
file_id: '4998'
file_name: IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf
file_size: 247657
relation: main_file
file_date_updated: 2019-10-15T07:44:51Z
has_accepted_license: '1'
intvolume: ' 122'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 25 - 29
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Information Processing Letters
publication_identifier:
issn:
- '00200190'
publication_status: published
publisher: Elsevier
publist_id: '6323'
pubrep_id: '991'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pushdown reachability with constant treewidth
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 122
year: '2017'
...
---
_id: '1072'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a radius parameter, we study the Čech,
Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized
discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel
sets of generalized discrete Morse functions, we prove that the four complexes
are simple-homotopy equivalent by a sequence of simplicial collapses, which are
explicitly described by a single discrete gradient field.
acknowledgement: This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP),
by ESF under the ACAT Research Network Programme, by the Russian Government under
mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR
109 “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions
of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991
apa: Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay
complexes. Transactions of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/tran/6991
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Complexes.” Transactions of the American Mathematical Society.
American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.
ieee: U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,”
Transactions of the American Mathematical Society, vol. 369, no. 5. American
Mathematical Society, pp. 3741–3762, 2017.
ista: Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes.
Transactions of the American Mathematical Society. 369(5), 3741–3762.
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Complexes.” Transactions of the American Mathematical Society, vol. 369,
no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.
short: U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society
369 (2017) 3741–3762.
date_created: 2018-12-11T11:49:59Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2023-09-20T12:05:56Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/6991
ec_funded: 1
external_id:
arxiv:
- '1312.1231'
isi:
- '000398030400024'
intvolume: ' 369'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1312.1231
month: '05'
oa: 1
oa_version: Preprint
page: 3741 - 3762
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '6311'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Morse theory of Čech and delaunay complexes
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 369
year: '2017'
...
---
_id: '1173'
abstract:
- lang: eng
text: We introduce the Voronoi functional of a triangulation of a finite set of
points in the Euclidean plane and prove that among all geometric triangulations
of the point set, the Delaunay triangulation maximizes the functional. This result
neither extends to topological triangulations in the plane nor to geometric triangulations
in three and higher dimensions.
acknowledgement: This research is partially supported by the Russian Government under
the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by
ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by
NSF grants DMS-1101688, DMS-1400876.
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: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- 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, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is
maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910.
doi:10.1007/s00493-016-3308-y
apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The
Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica.
Springer. https://doi.org/10.1007/s00493-016-3308-y
chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko.
“The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.”
Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.
ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional
is maximized by the Delaunay triangulation in the plane,” Combinatorica,
vol. 37, no. 5. Springer, pp. 887–910, 2017.
ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional
is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5),
887–910.
mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay
Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017,
pp. 887–910, doi:10.1007/s00493-016-3308-y.
short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017)
887–910.
date_created: 2018-12-11T11:50:32Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2023-09-20T11:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
isi:
- '000418056000005'
intvolume: ' 37'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.6337
month: '10'
oa: 1
oa_version: Submitted Version
page: 887 - 910
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Combinatorica
publication_identifier:
issn:
- '02099683'
publication_status: published
publisher: Springer
publist_id: '6182'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 37
year: '2017'
...
---
_id: '1180'
abstract:
- lang: eng
text: In this article we define an algebraic vertex of a generalized polyhedron
and show that the set of algebraic vertices is the smallest set of points needed
to define the polyhedron. We prove that the indicator function of a generalized
polytope P is a linear combination of indicator functions of simplices whose vertices
are algebraic vertices of P. We also show that the indicator function of any generalized
polyhedron is a linear combination, with integer coefficients, of indicator functions
of cones with apices at algebraic vertices and line-cones. The concept of an algebraic
vertex is closely related to the Fourier–Laplace transform. We show that a point
v is an algebraic vertex of a generalized polyhedron P if and only if the tangent
cone of P, at v, has non-zero Fourier–Laplace transform.
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: Imre
full_name: Bárány, Imre
last_name: Bárány
- first_name: Sinai
full_name: Robins, Sinai
last_name: Robins
citation:
ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026
apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex
polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026
chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of
Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.
ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,”
Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.
ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 308, 627–644.
mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances
in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.
short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.
date_created: 2018-12-11T11:50:34Z
date_published: 2017-02-21T00:00:00Z
date_updated: 2023-09-20T11:21:27Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
isi:
- '000409292900015'
intvolume: ' 308'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07594
month: '02'
oa: 1
oa_version: Submitted Version
page: 627 - 644
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Advances in Mathematics
publication_identifier:
issn:
- '00018708'
publication_status: published
publisher: Academic Press
publist_id: '6173'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Algebraic vertices of non-convex polyhedra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 308
year: '2017'
...
---
_id: '481'
abstract:
- lang: eng
text: We introduce planar matchings on directed pseudo-line arrangements, which
yield a planar set of pseudo-line segments such that only matching-partners are
adjacent. By translating the planar matching problem into a corresponding stable
roommates problem we show that such matchings always exist. Using our new framework,
we establish, for the first time, a complete, rigorous definition of weighted
straight skeletons, which are based on a so-called wavefront propagation process.
We present a generalized and unified approach to treat structural changes in the
wavefront that focuses on the restoration of weak planarity by finding planar
matchings.
acknowledgement: 'Supported by NSERC and the Ross and Muriel Cheriton Fellowship.
Research supported by Austrian Science Fund (FWF): P25816-N15.'
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons.
International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229.
doi:10.1142/S0218195916600050
apa: Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted
straight skeletons. International Journal of Computational Geometry and Applications.
World Scientific Publishing. https://doi.org/10.1142/S0218195916600050
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” International Journal of Computational Geometry
and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” International Journal of Computational Geometry and Applications,
vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.
ista: Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight
skeletons. International Journal of Computational Geometry and Applications. 26(3–4),
211–229.
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
International Journal of Computational Geometry and Applications, vol.
26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.
short: T. Biedl, S. Huber, P. Palfrader, International Journal of Computational
Geometry and Applications 26 (2017) 211–229.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-04-13T00:00:00Z
date_updated: 2023-02-21T16:06:22Z
day: '13'
ddc:
- '004'
- '514'
- '516'
department:
- _id: HeEd
doi: 10.1142/S0218195916600050
file:
- access_level: open_access
checksum: f79e8558bfe4b368dfefeb8eec2e3a5e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:34Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4758'
file_name: IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf
file_size: 769296
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 26'
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 211 - 229
publication: International Journal of Computational Geometry and Applications
publication_status: published
publisher: World Scientific Publishing
publist_id: '7338'
pubrep_id: '949'
quality_controlled: '1'
related_material:
record:
- id: '10892'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Planar matchings for weighted straight skeletons
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: 26
year: '2017'
...
---
_id: '521'
abstract:
- lang: eng
text: Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y
induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful
in showing that the classical dimension raising theorems hold in large scale;
that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and
Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely
n-to-1 maps, which include the natural quotient maps via a finite group action,
and prove that they preserve the asymptotic dimension.
author:
- first_name: Kyle
full_name: Austin, Kyle
last_name: Austin
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
citation:
ama: Austin K, Virk Z. Higson compactification and dimension raising. Topology
and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005
apa: Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005
chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.
ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology
and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.
ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology
and its Applications. 215, 45–57.
mla: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.
short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:01:21Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
intvolume: ' 215'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.03954v1
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
issn:
- '01668641'
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2017'
...
---
_id: '1216'
abstract:
- lang: eng
text: 'A framework fo r extracting features in 2D transient flows, based on the
acceleration field to ensure Galilean invariance is proposed in this paper. The
minima of the acceleration magnitude (a superset of acceleration zeros) are extracted
and discriminated into vortices and saddle points, based on the spectral properties
of the velocity Jacobian. The extraction of topological features is performed
with purely combinatorial algorithms from discrete computational topology. The
feature points are prioritized with persistence, as a physically meaningful importance
measure. These feature points are tracked in time with a robust algorithm for
tracking features. Thus, a space-time hierarchy of the minima is built and vortex
merging events are detected. We apply the acceleration feature extraction strategy
to three two-dimensional shear flows: (1) an incompressible periodic cylinder
wake, (2) an incompressible planar mixing layer and (3) a weakly compressible
planar jet. The vortex-like acceleration feature points are shown to be well aligned
with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure
field and minima of λ2.'
acknowledgement: "The authors acknowledge funding of the German Re-\r\nsearch Foundation
\ (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of
\ Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther
\ funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS
\ research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence
'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM)
of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social
\ Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society
\ for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics
\ Foundation for additional support. A part of this\r\nwork was performed
using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912"
author:
- first_name: Jens
full_name: Kasten, Jens
last_name: Kasten
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Hans
full_name: Hege, Hans
last_name: Hege
- first_name: Bernd
full_name: Noack, Bernd
last_name: Noack
- first_name: Guillaume
full_name: Daviller, Guillaume
last_name: Daviller
- first_name: Marek
full_name: Morzyński, Marek
last_name: Morzyński
citation:
ama: Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady
shear flows. Archives of Mechanics. 2016;68(1):55-80.
apa: Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., &
Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives
of Mechanics. Polish Academy of Sciences Publishing House.
chicago: Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume
Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear
Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House,
2016.
ieee: J. Kasten et al., “Acceleration feature points of unsteady shear flows,”
Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing
House, pp. 55–80, 2016.
ista: Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M.
2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics.
68(1), 55–80.
mla: Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.”
Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing
House, 2016, pp. 55–80.
short: J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński,
Archives of Mechanics 68 (2016) 55–80.
date_created: 2018-12-11T11:50:46Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:09Z
day: '01'
department:
- _id: HeEd
intvolume: ' 68'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf
month: '01'
oa: 1
oa_version: Published Version
page: 55 - 80
publication: Archives of Mechanics
publication_status: published
publisher: Polish Academy of Sciences Publishing House
publist_id: '6118'
quality_controlled: '1'
scopus_import: 1
status: public
title: Acceleration feature points of unsteady shear flows
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2016'
...
---
_id: '1222'
abstract:
- lang: eng
text: We consider packings of congruent circles on a square flat torus, i.e., periodic
(w.r.t. a square lattice) planar circle packings, with the maximal circle radius.
This problem is interesting due to a practical reason—the problem of “super resolution
of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly,
for the case N=7 there are three different optimal arrangements. Our proof is
based on a computer enumeration of toroidal irreducible contact graphs.
acknowledgement: We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy
for some useful comments and remarks, and especially Thom Sulanke for modifying
surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant
DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported
by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg
State University) under RF Government Grant 11.G34.31.0026.
author:
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
citation:
ama: Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat
torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6
apa: Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles
on a square flat torus. Discrete & Computational Geometry. Springer.
https://doi.org/10.1007/s00454-015-9742-6
chicago: Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles
on a Square Flat Torus.” Discrete & Computational Geometry. Springer,
2016. https://doi.org/10.1007/s00454-015-9742-6.
ieee: O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square
flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer,
pp. 1–20, 2016.
ista: Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square
flat torus. Discrete & Computational Geometry. 55(1), 1–20.
mla: Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on
a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no.
1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.
short: O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.
date_created: 2018-12-11T11:50:48Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-015-9742-6
intvolume: ' 55'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1212.0649
month: '01'
oa: 1
oa_version: Preprint
page: 1 - 20
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '6111'
quality_controlled: '1'
scopus_import: 1
status: public
title: Optimal packings of congruent circles on a square flat torus
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2016'
...
---
_id: '1237'
abstract:
- lang: eng
text: 'Bitmap images of arbitrary dimension may be formally perceived as unions
of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology
and homology groups are well known topological invariants of such sets. Cohomological
operations, such as the cup product, provide higher-order algebraic topological
invariants, especially important for digital images of dimension higher than 3.
If such an operation is determined at the level of simplicial chains [see e.g.
González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively
computable. However, decomposing a cubical complex into a simplicial one deleteriously
affects the efficiency of such an approach. In order to avoid this overhead, a
direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015,
253-275] for the cup product in cohomology, and implemented in the ChainCon software
package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for
the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series,
1947, 290-320] directly at the level of cubical chains, and we prove the correctness
of this formula. An implementation of this formula is programmed in C++ within
the ChainCon software framework. We provide a few examples and discuss the effectiveness
of this approach. One specific application follows from the fact that Steenrod
squares yield tests for the topological extension problem: Can a given map A →
Sd to a sphere Sd be extended to a given super-complex X of A? In particular,
the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value
r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the
extension problem.'
acknowledgement: The research conducted by both authors has received funding from
the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and
no. 622033 (for P. P.).
alternative_title:
- LNCS
author:
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: 'Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667.
Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13'
apa: 'Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares
(Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image
Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13'
chicago: Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,”
9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13.
ieee: 'M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented
at the CTIC: Computational Topology in Image Context, Marseille, France, 2016,
vol. 9667, pp. 140–151.'
ista: 'Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC:
Computational Topology in Image Context, LNCS, vol. 9667, 140–151.'
mla: Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares.
Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.
short: M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2018-12-11T11:50:52Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2021-01-12T06:49:18Z
day: '02'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_13
ec_funded: 1
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 140 - 151
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication_status: published
publisher: Springer
publist_id: '6096'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computation of cubical Steenrod squares
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 9667
year: '2016'
...
---
_id: '1252'
abstract:
- lang: eng
text: We study the homomorphism induced in homology by a closed correspondence between
topological spaces, using projections from the graph of the correspondence to
its domain and codomain. We provide assumptions under which the homomorphism induced
by an outer approximation of a continuous map coincides with the homomorphism
induced in homology by the map. In contrast to more classical results we do not
require that the projection to the domain have acyclic preimages. Moreover, we
show that it is possible to retrieve correct homological information from a correspondence
even if some data is missing or perturbed. Finally, we describe an application
to combinatorial maps that are either outer approximations of continuous maps
or reconstructions of such maps from a finite set of data points.
acknowledgement: "The authors gratefully acknowledge the support of the Lorenz Center
which\r\nprovided an opportunity for us to discuss in depth the work of this paper.
Research leading to these results has received funding from Fundo Europeu de Desenvolvimento
Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade
(POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia
e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie
Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013)
under REA grant agreement no. 622033 (supporting PP). The work of the first and
third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019,
1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second
author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029),
Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Shaun
full_name: Harker, Shaun
last_name: Harker
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from
a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801.
doi:10.1090/proc/12812
apa: Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing
a map on homology from a correspondence. Proceedings of the American Mathematical
Society. American Mathematical Society. https://doi.org/10.1090/proc/12812
chicago: Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk.
“Inducing a Map on Homology from a Correspondence.” Proceedings of the American
Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.
ieee: S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on
homology from a correspondence,” Proceedings of the American Mathematical Society,
vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.
ista: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology
from a correspondence. Proceedings of the American Mathematical Society. 144(4),
1787–1801.
mla: Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings
of the American Mathematical Society, vol. 144, no. 4, American Mathematical
Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.
short: S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American
Mathematical Society 144 (2016) 1787–1801.
date_created: 2018-12-11T11:50:57Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2022-05-24T09:35:58Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/12812
ec_funded: 1
external_id:
arxiv:
- '1411.7563'
intvolume: ' 144'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.7563
month: '04'
oa: 1
oa_version: Preprint
page: 1787 - 1801
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 1088-6826
publication_status: published
publisher: American Mathematical Society
publist_id: '6075'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inducing a map on homology from a correspondence
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1254'
abstract:
- lang: eng
text: We use rigorous numerical techniques to compute a lower bound for the exponent
of expansivity outside a neighborhood of the critical point for thousands of intervals
of parameter values in the quadratic family. We first compute a radius of the
critical neighborhood outside which the map is uniformly expanding. This radius
is taken as small as possible, yet large enough for our numerical procedure to
succeed in proving that the expansivity exponent outside this neighborhood is
positive. Then, for each of the intervals, we compute a lower bound for this expansivity
exponent, valid for all the parameters in that interval. We illustrate and study
the distribution of the radii and the expansivity exponents. The results of our
computations are mathematically rigorous. The source code of the software and
the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.
acknowledgement: "AG and PP were partially supported by Abdus Salam International
Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS,
and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento
Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade
(POFC) and from the Portuguese national funds through Fundação para a Ciência e
a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions)
of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant
agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics
\ of Kyoto University for providing access\r\nto their server for conducting
\ computations for this\r\nproject."
author:
- first_name: Ali
full_name: Golmakani, Ali
last_name: Golmakani
- first_name: Stefano
full_name: Luzzatto, Stefano
last_name: Luzzatto
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical
neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124.
doi:10.1080/10586458.2015.1048011
apa: Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity
outside a critical neighborhood in the quadratic family. Experimental Mathematics.
Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011
chicago: Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity
Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics.
Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011.
ieee: A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside
a critical neighborhood in the quadratic family,” Experimental Mathematics,
vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.
ista: Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a
critical neighborhood in the quadratic family. Experimental Mathematics. 25(2),
116–124.
mla: Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood
in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor
and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.
short: A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016)
116–124.
date_created: 2018-12-11T11:50:58Z
date_published: 2016-04-02T00:00:00Z
date_updated: 2021-01-12T06:49:25Z
day: '02'
department:
- _id: HeEd
doi: 10.1080/10586458.2015.1048011
ec_funded: 1
intvolume: ' 25'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1504.00116
month: '04'
oa: 1
oa_version: Preprint
page: 116 - 124
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Experimental Mathematics
publication_status: published
publisher: Taylor and Francis
publist_id: '6071'
quality_controlled: '1'
scopus_import: 1
status: public
title: Uniform expansivity outside a critical neighborhood in the quadratic family
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2016'
...
---
_id: '1272'
abstract:
- lang: eng
text: We study different means to extend offsetting based on skeletal structures
beyond the well-known constant-radius and mitered offsets supported by Voronoi
diagrams and straight skeletons, for which the orthogonal distance of offset elements
to their respective input elements is constant and uniform over all input elements.
Our main contribution is a new geometric structure, called variable-radius Voronoi
diagram, which supports the computation of variable-radius offsets, i.e., offsets
whose distance to the input is allowed to vary along the input. We discuss properties
of this structure and sketch a prototype implementation that supports the computation
of variable-radius offsets based on this new variant of Voronoi diagrams.
acknowledgement: 'This work was supported by Austrian Science Fund (FWF): P25816-N15.'
author:
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using
skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721.
doi:10.1080/16864360.2016.1150718
apa: Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of
planar structures using skeletons. Computer-Aided Design and Applications.
Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718
chicago: Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting
of Planar Structures Using Skeletons.” Computer-Aided Design and Applications.
Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718.
ieee: M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures
using skeletons,” Computer-Aided Design and Applications, vol. 13, no.
5. Taylor and Francis, pp. 712–721, 2016.
ista: Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures
using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.
mla: Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.”
Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis,
2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.
short: M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13
(2016) 712–721.
date_created: 2018-12-11T11:51:04Z
date_published: 2016-09-02T00:00:00Z
date_updated: 2021-01-12T06:49:32Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.1080/16864360.2016.1150718
file:
- access_level: open_access
checksum: c746f3a48edb62b588d92ea5d0fd2c0e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:20Z
date_updated: 2020-07-14T12:44:42Z
file_id: '5206'
file_name: IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf
file_size: 1678369
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 13'
issue: '5'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 712 - 721
publication: Computer-Aided Design and Applications
publication_status: published
publisher: Taylor and Francis
publist_id: '6048'
pubrep_id: '694'
quality_controlled: '1'
scopus_import: 1
status: public
title: Generalized offsetting of planar structures using skeletons
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2016'
...
---
_id: '1289'
abstract:
- lang: eng
text: 'Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI)
magnifying endoscopic (ME) images of the stomach, we combine methods from image
processing, topology, geometry, and machine learning to classify patterns into
three classes: oval, tubular and irregular. Training the algorithm on a small
number of images of each type, we achieve a high rate of correct classifications.
The analysis of the learning algorithm reveals that a handful of geometric and
topological features are responsible for the overwhelming majority of decisions.'
article_processing_charge: No
author:
- first_name: Olga
full_name: Dunaeva, Olga
last_name: Dunaeva
- 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: Lukyanov, Anton
last_name: Lukyanov
- first_name: Michael
full_name: Machin, Michael
last_name: Machin
- first_name: Daria
full_name: Malkova, Daria
last_name: Malkova
- first_name: Roman
full_name: Kuvaev, Roman
last_name: Kuvaev
- first_name: Sergey
full_name: Kashin, Sergey
last_name: Kashin
citation:
ama: Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy
images with persistent homology. Pattern Recognition Letters. 2016;83(1):13-22.
doi:10.1016/j.patrec.2015.12.012
apa: Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev,
R., & Kashin, S. (2016). The classification of endoscopy images with persistent
homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2015.12.012
chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria
Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images
with Persistent Homology.” Pattern Recognition Letters. Elsevier, 2016.
https://doi.org/10.1016/j.patrec.2015.12.012.
ieee: O. Dunaeva et al., “The classification of endoscopy images with persistent
homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22,
2016.
ista: Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin
S. 2016. The classification of endoscopy images with persistent homology. Pattern
Recognition Letters. 83(1), 13–22.
mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent
Homology.” Pattern Recognition Letters, vol. 83, no. 1, Elsevier, 2016,
pp. 13–22, doi:10.1016/j.patrec.2015.12.012.
short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev,
S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.
date_created: 2018-12-11T11:51:10Z
date_published: 2016-11-01T00:00:00Z
date_updated: 2023-02-23T10:04:40Z
day: '01'
ddc:
- '004'
- '514'
department:
- _id: HeEd
doi: 10.1016/j.patrec.2015.12.012
file:
- access_level: open_access
checksum: 33458bbb8c32a339e1adeca6d5a1112d
content_type: application/pdf
creator: dernst
date_created: 2019-04-17T07:55:51Z
date_updated: 2020-07-14T12:44:42Z
file_id: '6334'
file_name: 2016-Edelsbrunner_The_classification.pdf
file_size: 1921113
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 83'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
page: 13 - 22
publication: Pattern Recognition Letters
publication_status: published
publisher: Elsevier
publist_id: '6027'
pubrep_id: '975'
quality_controlled: '1'
related_material:
record:
- id: '1568'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: The classification of endoscopy images with persistent homology
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2016'
...
---
_id: '1292'
abstract:
- lang: eng
text: We give explicit formulas and algorithms for the computation of the Thurston–Bennequin
invariant of a nullhomologous Legendrian knot on a page of a contact open book
and on Heegaard surfaces in convex position. Furthermore, we extend the results
to rationally nullhomologous knots in arbitrary 3-manifolds.
acknowledgement: "The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful
discussions and advice and Christian Evers for helpful remarks on a draft version."
author:
- first_name: Sebastian
full_name: Durst, Sebastian
last_name: Durst
- first_name: Marc
full_name: Kegel, Marc
last_name: Kegel
- first_name: Mirko D
full_name: Klukas, Mirko D
id: 34927512-F248-11E8-B48F-1D18A9856A87
last_name: Klukas
citation:
ama: Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in
open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4
apa: Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin
invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4
chicago: Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin
Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4.
ieee: S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant
in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer,
pp. 441–455, 2016.
ista: Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant
in open books. Acta Mathematica Hungarica. 150(2), 441–455.
mla: Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open
Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp.
441–55, doi:10.1007/s10474-016-0648-4.
short: S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.
date_created: 2018-12-11T11:51:11Z
date_published: 2016-12-01T00:00:00Z
date_updated: 2021-01-12T06:49:40Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10474-016-0648-4
intvolume: ' 150'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.00794
month: '12'
oa: 1
oa_version: Preprint
page: 441 - 455
publication: Acta Mathematica Hungarica
publication_status: published
publisher: Springer
publist_id: '6023'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing the Thurston–Bennequin invariant in open books
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 150
year: '2016'
...
---
_id: '1295'
abstract:
- lang: eng
text: Voronoi diagrams and Delaunay triangulations have been extensively used to
represent and compute geometric features of point configurations. We introduce
a generalization to poset diagrams and poset complexes, which contain order-k
and degree-k Voronoi diagrams and their duals as special cases. Extending a result
of Aurenhammer from 1990, we show how to construct poset diagrams as weighted
Voronoi diagrams of average balls.
acknowledgement: This work is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages.
Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030'
apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls
II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier.
https://doi.org/10.1016/j.endm.2016.09.030'
chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier,
2016. https://doi.org/10.1016/j.endm.2016.09.030.'
ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted
averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier,
pp. 169–174, 2016.'
ista: 'Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted
averages. Electronic Notes in Discrete Mathematics. 54, 169–174.'
mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol.
54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.'
short: H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics
54 (2016) 169–174.
date_created: 2018-12-11T11:51:12Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:49:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.endm.2016.09.030
ec_funded: 1
intvolume: ' 54'
language:
- iso: eng
month: '10'
oa_version: None
page: 169 - 174
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Electronic Notes in Discrete Mathematics
publication_status: published
publisher: Elsevier
publist_id: '5976'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Multiple covers with balls II: Weighted averages'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 54
year: '2016'
...
---
_id: '1330'
abstract:
- lang: eng
text: In this paper we investigate the existence of closed billiard trajectories
in not necessarily smooth convex bodies. In particular, we show that if a body
K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K
is acute (in a certain sense), then there is a closed billiard trajectory in K.
acknowledgement: Supported by People Programme (Marie Curie Actions) of the European
Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734].
Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a
ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part
by the Moebius Contest Foundation for Young Scientists, and in part by the Simons
Foundation.
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
citation:
ama: Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel
Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z
apa: Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute
angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z
chicago: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with
Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.
ieee: A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,”
Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845,
2016.
ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles.
Israel Journal of Mathematics. 216(2), 833–845.
mla: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute
Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016,
pp. 833–45, doi:10.1007/s11856-016-1429-z.
short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.
date_created: 2018-12-11T11:51:24Z
date_published: 2016-10-15T00:00:00Z
date_updated: 2021-01-12T06:49:56Z
day: '15'
department:
- _id: HeEd
doi: 10.1007/s11856-016-1429-z
ec_funded: 1
intvolume: ' 216'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1506.06014
month: '10'
oa: 1
oa_version: Preprint
page: 833 - 845
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Israel Journal of Mathematics
publication_status: published
publisher: Springer
publist_id: '5938'
quality_controlled: '1'
scopus_import: 1
status: public
title: Billiards in convex bodies with acute angles
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 216
year: '2016'
...
---
_id: '1617'
abstract:
- lang: eng
text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d
is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of
equal measure and placing a random point inside each of the N=md cubes. We prove
that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d,
where the upper bound with an unspecified constant Cd was proven earlier by Beck.
Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality
and a suitably taylored Bernstein inequality; we have reasons to believe that
the upper bound has the sharp scaling in N. Additional heuristics suggest that
jittered sampling should be able to improve known bounds on the inverse of the
star-discrepancy in the regime N≳dd. We also prove a partition principle showing
that every partition of [0,1]d combined with a jittered sampling construction
gives rise to a set whose expected squared L2-discrepancy is smaller than that
of purely random points.'
acknowledgement: We are grateful to the referee whose suggestions greatly improved
the quality and clarity of the exposition.
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Stefan
full_name: Steinerberger, Stefan
last_name: Steinerberger
citation:
ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal
of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003
apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered
sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003
chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003.
ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,”
Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.
ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling.
Journal of Complexity. 33, 199–216.
mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216,
doi:10.1016/j.jco.2015.11.003.
short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.
date_created: 2018-12-11T11:53:03Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2021-01-12T06:52:02Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.11.003
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1510.00251
month: '04'
oa: 1
oa_version: Submitted Version
page: 199 - 216
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5549'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the discrepancy of jittered sampling
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2016'
...