---
_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
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: 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: 2025-06-04T08:44:44Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
arxiv:
- '1411.6337'
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:
- 0209-9683
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: 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: 2025-06-04T08:45:48Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
arxiv:
- '1508.07594'
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:
- 0001-8708
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 308
year: '2017'
...
---
OA_type: free access
_id: '1433'
abstract:
- lang: eng
text: Phat is an open-source C. ++ library for the computation of persistent homology
by matrix reduction, targeted towards developers of software for topological data
analysis. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. We provide numerous
different reduction strategies as well as data types to store and manipulate the
boundary matrix. We compare the different combinations through extensive experimental
evaluation and identify optimization techniques that work well in practical situations.
We also compare our software with various other publicly available libraries for
persistent homology.
acknowledgement: Michael Kerber acknowledges support by the Max Planck Center for
Visual Computing and Communications (FKZ-01IMC01 and FKZ-01IM10001). Ulrich Bauer,
Jan Reininghaus, and Hubert Wagner acknowledge support by the EU Project TOPOSYS
(FP7-ICT-318493-STREP).
article_processing_charge: No
article_type: original
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
last_name: Bauer
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Jan
full_name: Reininghaus, Jan
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms
toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008
apa: Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent
homology algorithms toolbox. Journal of Symbolic Computation. Academic
Press. https://doi.org/10.1016/j.jsc.2016.03.008
chicago: Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat
- Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation.
Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.
ieee: U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology
algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic
Press, pp. 76–90, 2017.
ista: Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology
algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.
mla: Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal
of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.
short: U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation
78 (2017) 76–90.
corr_author: '1'
date_created: 2018-12-11T11:51:59Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-10-01T07:39:51Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jsc.2016.03.008
ec_funded: 1
external_id:
isi:
- '000384396000005'
intvolume: ' 78'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jsc.2016.03.008
month: '01'
oa: 1
oa_version: Published Version
page: 76 - 90
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Journal of Symbolic Computation
publication_identifier:
issn:
- ' 0747-7171'
publication_status: published
publisher: Academic Press
publist_id: '5765'
quality_controlled: '1'
related_material:
record:
- id: '10894'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Phat - Persistent homology algorithms toolbox
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 78
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: 2025-07-10T11:49:53Z
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:
- 0020-0190
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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: 2025-04-15T08:37:54Z
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: '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
arxiv: 1
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: 2025-06-04T08:10:31Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/mnras/stw2862
external_id:
arxiv:
- '1608.04519'
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:
- 0035-8711
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 465
year: '2017'
...
---
_id: '833'
abstract:
- lang: eng
text: We present an efficient algorithm to compute Euler characteristic curves of
gray scale images of arbitrary dimension. In various applications the Euler characteristic
curve is used as a descriptor of an image. Our algorithm is the first streaming
algorithm for Euler characteristic curves. The usage of streaming removes the
necessity to store the entire image in RAM. Experiments show that our implementation
handles terabyte scale images on commodity hardware. Due to lock-free parallelism,
it scales well with the number of processor cores. Additionally, we put the concept
of the Euler characteristic curve in the wider context of computational topology.
In particular, we explain the connection with persistence diagrams.
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of
multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer;
2017:397-409. doi:10.1007/978-3-319-64689-3_32'
apa: 'Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic
curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger
(Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of
Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32'
chicago: Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden,
and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32.
ieee: 'T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves
of multidimensional images,” presented at the CAIP: Computer Analysis of Images
and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.'
ista: 'Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves
of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS,
vol. 10424, 397–409.'
mla: Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol.
10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.
short: T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer,
2017, pp. 397–409.
conference:
end_date: 2017-08-24
location: Ystad, Sweden
name: 'CAIP: Computer Analysis of Images and Patterns'
start_date: 2017-08-22
corr_author: '1'
date_created: 2018-12-11T11:48:45Z
date_published: 2017-07-28T00:00:00Z
date_updated: 2025-06-04T09:54:22Z
day: '28'
department:
- _id: HeEd
doi: 10.1007/978-3-319-64689-3_32
editor:
- first_name: Michael
full_name: Felsberg, Michael
last_name: Felsberg
- first_name: Anders
full_name: Heyden, Anders
last_name: Heyden
- first_name: Norbert
full_name: Krüger, Norbert
last_name: Krüger
external_id:
arxiv:
- '1705.02045'
isi:
- '000432085900032'
intvolume: ' 10424'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.02045
month: '07'
oa: 1
oa_version: Submitted Version
page: 397 - 409
publication_identifier:
issn:
- 0302-9743
publication_status: published
publisher: Springer
publist_id: '6815'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Streaming algorithm for Euler characteristic curves of multidimensional images
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10424
year: '2017'
...
---
_id: '836'
abstract:
- lang: eng
text: Recent research has examined how to study the topological features of a continuous
self-map by means of the persistence of the eigenspaces, for given eigenvalues,
of the endomorphism induced in homology over a field. This raised the question
of how to select dynamically significant eigenvalues. The present paper aims to
answer this question, giving an algorithm that computes the persistence of eigenspaces
for every eigenvalue simultaneously, also expressing said eigenspaces as direct
sums of “finite” and “singular” subspaces.
alternative_title:
- PROMS
article_processing_charge: No
author:
- first_name: Marc
full_name: Ethier, Marc
last_name: Ethier
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Marian
full_name: Mrozek, Marian
last_name: Mrozek
citation:
ama: 'Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the
Kronecker canonical form. In: Special Sessions in Applications of Computer
Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8'
apa: 'Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of
self-maps with the Kronecker canonical form. In Special Sessions in Applications
of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8'
chicago: Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues
of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications
of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8.
ieee: M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps
with the Kronecker canonical form,” in Special Sessions in Applications of
Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136.
ista: 'Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with
the Kronecker canonical form. Special Sessions in Applications of Computer Algebra.
ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.'
mla: Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical
Form.” Special Sessions in Applications of Computer Algebra, vol. 198,
Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.
short: M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications
of Computer Algebra, Springer, 2017, pp. 119–136.
conference:
end_date: 2015-07-23
location: Kalamata, Greece
name: 'ACA: Applications of Computer Algebra'
start_date: 2015-07-20
date_created: 2018-12-11T11:48:46Z
date_published: 2017-07-27T00:00:00Z
date_updated: 2025-04-15T08:37:55Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-56932-1_8
ec_funded: 1
external_id:
isi:
- '000434088200008'
intvolume: ' 198'
isi: 1
language:
- iso: eng
month: '07'
oa_version: None
page: 119 - 136
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Special Sessions in Applications of Computer Algebra
publication_identifier:
isbn:
- 978-331956930-7
publication_status: published
publisher: Springer
publist_id: '6812'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finding eigenvalues of self-maps with the Kronecker canonical form
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 198
year: '2017'
...
---
_id: '84'
abstract:
- lang: eng
text: The advent of high-throughput technologies and the concurrent advances in
information sciences have led to a data revolution in biology. This revolution
is most significant in molecular biology, with an increase in the number and scale
of the “omics” projects over the last decade. Genomics projects, for example,
have produced impressive advances in our knowledge of the information concealed
into genomes, from the many genes that encode for the proteins that are responsible
for most if not all cellular functions, to the noncoding regions that are now
known to provide regulatory functions. Proteomics initiatives help to decipher
the role of post-translation modifications on the protein structures and provide
maps of protein-protein interactions, while functional genomics is the field that
attempts to make use of the data produced by these projects to understand protein
functions. The biggest challenge today is to assimilate the wealth of information
provided by these initiatives into a conceptual framework that will help us decipher
life. For example, the current views of the relationship between protein structure
and function remain fragmented. We know of their sequences, more and more about
their structures, we have information on their biological activities, but we have
difficulties connecting this dotted line into an informed whole. We lack the experimental
and computational tools for directly studying protein structure, function, and
dynamics at the molecular and supra-molecular levels. In this chapter, we review
some of the current developments in building the computational tools that are
needed, focusing on the role that geometry and topology play in these efforts.
One of our goals is to raise the general awareness about the importance of geometric
methods in elucidating the mysterious foundations of our very existence. Another
goal is the broadening of what we consider a geometric algorithm. There is plenty
of valuable no-man’s-land between combinatorial and numerical algorithms, and
it seems opportune to explore this land with a computational-geometric frame of
mind.
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: Patrice
full_name: Koehl, Patrice
last_name: Koehl
citation:
ama: 'Edelsbrunner H, Koehl P. Computational topology for structural molecular biology.
In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational
Geometry, Third Edition. Handbook of Discrete and Computational Geometry.
Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601'
apa: Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural
molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook
of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor
& Francis. https://doi.org/10.1201/9781315119601
chicago: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural
Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third
Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35.
Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601.
ieee: H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular
biology,” in Handbook of Discrete and Computational Geometry, Third Edition,
C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.
ista: 'Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular
biology. In: Handbook of Discrete and Computational Geometry, Third Edition. ,
1709–1735.'
mla: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural
Molecular Biology.” Handbook of Discrete and Computational Geometry, Third
Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35,
doi:10.1201/9781315119601.
short: H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.),
Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis,
2017, pp. 1709–1735.
date_created: 2018-12-11T11:44:32Z
date_published: 2017-11-09T00:00:00Z
date_updated: 2023-10-16T11:15:22Z
day: '09'
department:
- _id: HeEd
doi: 10.1201/9781315119601
editor:
- first_name: Csaba
full_name: Toth, Csaba
last_name: Toth
- first_name: Joseph
full_name: O'Rourke, Joseph
last_name: O'Rourke
- first_name: Jacob
full_name: Goodman, Jacob
last_name: Goodman
language:
- iso: eng
month: '11'
oa_version: None
page: 1709 - 1735
publication: Handbook of Discrete and Computational Geometry, Third Edition
publication_identifier:
eisbn:
- '9781498711425'
publication_status: published
publisher: Taylor & Francis
publist_id: '7970'
quality_controlled: '1'
scopus_import: '1'
series_title: Handbook of Discrete and Computational Geometry
status: public
title: Computational topology for structural molecular biology
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...
---
_id: '909'
abstract:
- lang: eng
text: We study the lengths of curves passing through a fixed number of points on
the boundary of a convex shape in the plane. We show that, for any convex shape
K, there exist four points on the boundary of K such that the length of any curve
passing through these points is at least half of the perimeter of K. It is also
shown that the same statement does not remain valid with the additional constraint
that the points are extreme points of K. Moreover, the factor ½ cannot
be achieved with any fixed number of extreme points. We conclude the paper with
a few other inequalities related to the perimeter of a convex shape.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Vladislav
full_name: Vysotsky, Vladislav
last_name: Vysotsky
citation:
ama: Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points
of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596.
doi:10.4169/amer.math.monthly.124.7.588
apa: Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through
boundary points of a planar convex shape. The American Mathematical Monthly.
Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588
chicago: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.
ieee: A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary
points of a planar convex shape,” The American Mathematical Monthly, vol.
124, no. 7. Mathematical Association of America, pp. 588–596, 2017.
ista: Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary
points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.
mla: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96,
doi:10.4169/amer.math.monthly.124.7.588.
short: A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.
date_created: 2018-12-11T11:49:09Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-07-10T12:01:35Z
day: '01'
department:
- _id: HeEd
doi: 10.4169/amer.math.monthly.124.7.588
ec_funded: 1
external_id:
arxiv:
- '1605.07997'
isi:
- '000413947300002'
intvolume: ' 124'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.07997
month: '01'
oa: 1
oa_version: Submitted Version
page: 588 - 596
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: The American Mathematical Monthly
publication_identifier:
issn:
- 0002-9890
publication_status: published
publisher: Mathematical Association of America
publist_id: '6534'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the lengths of curves passing through boundary points of a planar convex
shape
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 124
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.
corr_author: '1'
date_created: 2018-12-11T11:46:43Z
date_published: 2017-04-13T00:00:00Z
date_updated: 2025-09-29T13:22:54Z
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.
article_processing_charge: No
arxiv: 1
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.
corr_author: '1'
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-09-18T09:47:04Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
external_id:
arxiv:
- '1608.03954'
isi:
- '000390501400005'
intvolume: ' 215'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.03954
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
issn:
- 0166-8641
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 215
year: '2017'
...
---
_id: '568'
abstract:
- lang: eng
text: 'We study robust properties of zero sets of continuous maps f: X → ℝn. Formally,
we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets
of all continuous maps g closer to f than r in the max-norm. All of these sets
are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined
by A and an element of a certain cohomotopy group which (by a recent result) is
computable whenever the dimension of X is at most 2n - 3. By considering all r
> 0 simultaneously, the pointed cohomotopy groups form a persistence module-a
structure leading to persistence diagrams as in the case of persistent homology
or well groups. Eventually, we get a descriptor of persistent robust properties
of zero sets that has better descriptive power (Theorem A) and better computability
status (Theorem B) than the established well diagrams. Moreover, if we endow every
point of each zero set with gradients of the perturbation, the robust description
of the zero sets by elements of cohomotopy groups is in some sense the best possible
(Theorem C).'
article_processing_charge: No
arxiv: 1
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
orcid: 0000-0001-8878-8397
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications.
2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16
apa: Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology,
Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16
chicago: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology,
Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.
ieee: P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy
and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.
ista: Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and
Applications. 19(2), 313–342.
mla: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy
and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.
short: P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.
corr_author: '1'
date_created: 2018-12-11T11:47:14Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-09-11T07:41:51Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4310/HHA.2017.v19.n2.a16
ec_funded: 1
external_id:
arxiv:
- '1507.04310'
isi:
- '000440749400010'
intvolume: ' 19'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1507.04310
month: '01'
oa: 1
oa_version: Submitted Version
page: 313 - 342
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 2590DB08-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '701309'
name: Atomic Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes
publication: Homology, Homotopy and Applications
publication_identifier:
issn:
- 1532-0073
publication_status: published
publisher: International Press
publist_id: '7246'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Persistence of zero sets
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 19
year: '2017'
...
---
_id: '5803'
abstract:
- lang: eng
text: Different distance metrics produce Voronoi diagrams with different properties.
It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi
diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions.
In this paper, we first show that this metric produces a persistent VD on the
2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly
approximates the corresponding VD on the 2D real plane. Next, we show that on
a 3D digital plane D, the Euclidean metric spanning over its voxel set does not
guarantee a digital VD which is persistent with the real-space VD. As a solution,
we introduce a novel concept of functional-plane-convexity, which is ensured by
the Euclidean metric spanning over the pedal set of D. Necessary proofs and some
visual result have been provided to adjudge the merit and usefulness of the proposed
concept.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital
plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature;
2017:93-104. doi:10.1007/978-3-319-59108-7_8'
apa: 'Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi
diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256,
pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi
Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104.
Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.'
ieee: 'R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on
3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer
Nature, 2017, pp. 93–104.'
ista: 'Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on
3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.'
mla: Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram
on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer
Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.
short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature,
Cham, 2017, pp. 93–104.
conference:
end_date: 2017-06-21
location: Plovdiv, Bulgaria
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2017-06-19
date_created: 2019-01-08T20:42:56Z
date_published: 2017-05-17T00:00:00Z
date_updated: 2022-01-28T07:48:24Z
day: '17'
department:
- _id: HeEd
doi: 10.1007/978-3-319-59108-7_8
extern: '1'
intvolume: ' 10256'
language:
- iso: eng
month: '05'
oa_version: None
page: 93-104
place: Cham
publication: Combinatorial image analysis
publication_identifier:
isbn:
- 978-3-319-59107-0
- 978-3-319-59108-7
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Construction of persistent Voronoi diagram on 3D digital plane
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10256
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
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: 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
corr_author: '1'
date_created: 2018-12-11T11:47:56Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2025-07-10T11:53:56Z
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:
- 1868-8969
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 77
year: '2017'
...
---
_id: '707'
abstract:
- lang: eng
text: We answer a question of M. Gromov on the waist of the unit ball.
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin
of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062
apa: Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the
ball . Bulletin of the London Mathematical Society. Wiley. https://doi.org/10.1112/blms.12062
chicago: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of
the Ball .” Bulletin of the London Mathematical Society. Wiley, 2017. https://doi.org/10.1112/blms.12062.
ieee: A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,”
Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley, pp.
690–693, 2017.
ista: Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin
of the London Mathematical Society. 49(4), 690–693.
mla: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the
Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley,
2017, pp. 690–93, doi:10.1112/blms.12062.
short: A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017)
690–693.
corr_author: '1'
date_created: 2018-12-11T11:48:02Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2025-09-10T11:04:43Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12062
ec_funded: 1
external_id:
arxiv:
- '1608.06279'
isi:
- '000407045900012'
intvolume: ' 49'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.06279
month: '08'
oa: 1
oa_version: Preprint
page: 690 - 693
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Bulletin of the London Mathematical Society
publication_identifier:
issn:
- 0024-6093
publication_status: published
publisher: Wiley
publist_id: '6982'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'A tight estimate for the waist of the ball '
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 49
year: '2017'
...
---
OA_place: publisher
_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.
corr_author: '1'
date_created: 2019-04-09T15:04:32Z
date_published: 2017-10-27T00:00:00Z
date_updated: 2026-04-08T14:19:31Z
day: '27'
ddc:
- '514'
- '516'
- '519'
degree_awarded: PhD
department:
- _id: HeEd
doi: 10.15479/AT:ISTA:th_873
file:
- access_level: open_access
checksum: ece7e598a2f060b263c2febf7f3fe7f9
content_type: application/pdf
creator: dernst
date_created: 2019-04-09T14:54:51Z
date_updated: 2020-07-14T12:47:26Z
file_id: '6289'
file_name: 2017_Thesis_Nikitenko.pdf
file_size: 2324870
relation: main_file
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checksum: 99b7ad76e317efd447af60f91e29b49b
content_type: application/zip
creator: dernst
date_created: 2019-04-09T14:54:51Z
date_updated: 2020-07-14T12:47:26Z
file_id: '6290'
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language:
- iso: eng
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: '87'
relation: part_of_dissertation
status: public
- id: '5678'
relation: part_of_dissertation
status: public
- id: '718'
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2017'
...
---
_id: '718'
abstract:
- lang: eng
text: Mapping every simplex in the Delaunay mosaic of a discrete point set to the
radius of the smallest empty circumsphere gives a generalized discrete Morse function.
Choosing the points from a Poisson point process in ℝ n , we study the expected
number of simplices in the Delaunay mosaic as well as the expected number of critical
simplices and nonsingular intervals in the corresponding generalized discrete
gradient. Observing connections with other probabilistic models, we obtain precise
expressions for the expected numbers in low dimensions. In particular, we obtain
the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions
n ≤ 4.
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
- first_name: Matthias
full_name: Reitzner, Matthias
last_name: Reitzner
citation:
ama: Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability.
2017;49(3):745-767. doi:10.1017/apr.2017.20
apa: Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes
of poisson Delaunay mosaics and their discrete Morse functions. Advances in
Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20
chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected
Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances
in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.
ieee: H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson
Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability,
vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.
ista: Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3),
745–767.
mla: Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and
Their Discrete Morse Functions.” Advances in Applied Probability, vol.
49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.
short: H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability
49 (2017) 745–767.
date_created: 2018-12-11T11:48:07Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2026-04-08T14:19:30Z
day: '01'
department:
- _id: HeEd
doi: 10.1017/apr.2017.20
ec_funded: 1
external_id:
arxiv:
- '1607.05915'
isi:
- '000416417500004'
intvolume: ' 49'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1607.05915
month: '09'
oa: 1
oa_version: Preprint
page: 745 - 767
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Advances in Applied Probability
publication_identifier:
issn:
- 0001-8678
publication_status: published
publisher: Cambridge University Press
publist_id: '6962'
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 49
year: '2017'
...
---
_id: '737'
abstract:
- lang: eng
text: We generalize Brazas’ topology on the fundamental group to the whole universal
path space X˜ i.e., to the set of homotopy classes of all based paths. We develop
basic properties of the new notion and provide a complete comparison of the obtained
topology with the established topologies, in particular with the Lasso topology
and the CO topology, i.e., the topology that is induced by the compact-open topology.
It turns out that the new topology is the finest topology contained in the CO
topology, for which the action of the fundamental group on the universal path
space is a continuous group action.
article_processing_charge: No
author:
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Andreas
full_name: Zastrow, Andreas
last_name: Zastrow
citation:
ama: Virk Z, Zastrow A. A new topology on the universal path space. Topology
and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015
apa: Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015
chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.
ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology
and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.
ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology
and its Applications. 231, 186–196.
mla: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.”
Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.
short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
corr_author: '1'
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2026-04-16T10:04:39Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2017.09.015
external_id:
isi:
- '000413889100012'
intvolume: ' 231'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 186 - 196
publication: Topology and its Applications
publication_identifier:
issn:
- 0166-8641
publication_status: published
publisher: Elsevier
publist_id: '6930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new topology on the universal path space
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 231
year: '2017'
...
---
_id: '1149'
abstract:
- lang: eng
text: 'We study the usefulness of two most prominent publicly available rigorous
ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other
based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable
of handling entire sets of initial conditions and provide tight rigorous outer
enclosures of the images under a time-T map. We conduct extensive benchmark computations
using the well-known Lorenz system, and compare the computation time against the
final accuracy achieved. We also discuss the effect of a few technical parameters,
such as the order of the numerical integration method, the value of T, and the
phase space resolution. We conclude that COSY may provide more precise results
due to its ability of avoiding the variable dependency problem. However, the overall
cost of computations conducted using CAPD is typically lower, especially when
intervals of parameters are involved. Moreover, access to COSY is limited (registration
required) and the rigorous ODE integrators are not publicly available, while CAPD
is an open source free software project. Therefore, we recommend the latter integrator
for this kind of computations. Nevertheless, proper choice of the various integration
parameters turns out to be of even greater importance than the choice of the integrator
itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.'
acknowledgement: "MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9,
and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially
supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry
of Education, Science, Technology, Culture and Sports, Japan. KM was supported by
NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR
and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part
of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch 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);
from the People Programme (Marie Curie Actions) of the European Union's Seventh
Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from
the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department
of Mathematics of Kyoto University for making their server available for conducting
the computations described in the paper, and to the reviewers for helpful comments
that contributed towards increasing the quality of the paper."
article_processing_charge: No
author:
- first_name: Tomoyuki
full_name: Miyaji, Tomoyuki
last_name: Miyaji
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Marcio
full_name: Gameiro, Marcio
last_name: Gameiro
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
citation:
ama: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous
ODE integrators for multi scale set oriented computations. Applied Numerical
Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005
apa: Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016).
A study of rigorous ODE integrators for multi scale set oriented computations.
Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005
chicago: Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and
Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set
Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016.
https://doi.org/10.1016/j.apnum.2016.04.005.
ieee: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study
of rigorous ODE integrators for multi scale set oriented computations,” Applied
Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.
ista: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of
rigorous ODE integrators for multi scale set oriented computations. Applied Numerical
Mathematics. 107, 34–47.
mla: Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale
Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier,
2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.
short: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical
Mathematics 107 (2016) 34–47.
date_created: 2018-12-11T11:50:25Z
date_published: 2016-09-01T00:00:00Z
date_updated: 2025-09-22T09:58:16Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.apnum.2016.04.005
ec_funded: 1
external_id:
isi:
- '000378447000003'
intvolume: ' 107'
isi: 1
language:
- iso: eng
month: '09'
oa_version: None
page: 34 - 47
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Applied Numerical Mathematics
publication_status: published
publisher: Elsevier
publist_id: '6209'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A study of rigorous ODE integrators for multi scale set oriented computations
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 107
year: '2016'
...