---
_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: '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).'
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
- 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.
date_created: 2018-12-11T11:47:14Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:03:12Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4310/HHA.2017.v19.n2.a16
ec_funded: 1
intvolume: ' 19'
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
(H2020)
publication: Homology, Homotopy and Applications
publication_identifier:
issn:
- '15320073'
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
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: '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:
- 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'
file_name: 2017_Thesis_Nikitenko_source.zip
file_size: 2863219
relation: source_file
file_date_updated: 2020-07-14T12:47:26Z
has_accepted_license: '1'
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: '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: '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.
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.
date_created: 2018-12-11T11:51:59Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-20T09:42:40Z
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:
- ' 07477171'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 78
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: 2023-10-17T11:24:57Z
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:
- '00029890'
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: '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: '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: '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."
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: 2021-01-12T06:48:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.apnum.2016.04.005
ec_funded: 1
intvolume: ' 107'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 107
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'
...
---
_id: '1662'
abstract:
- lang: eng
text: We introduce a modification of the classic notion of intrinsic volume using
persistence moments of height functions. Evaluating the modified first intrinsic
volume on digital approximations of a compact body with smoothly embedded boundary
in Rn, we prove convergence to the first intrinsic volume of the body as the resolution
of the approximation improves. We have weaker results for the other modified intrinsic
volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional
unit ball.
acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne
Marie Svane for her comments on an early version of this paper. The second author
wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for
enlightening discussions and their kind hospitality during a visit of their department
in 2014."
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004
apa: Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence
of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016.
https://doi.org/10.1016/j.aim.2015.10.004.
ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic
volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703,
2016.
ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 287, 674–703.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press,
2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.
short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.
date_created: 2018-12-11T11:53:20Z
date_published: 2016-01-10T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '10'
ddc:
- '004'
department:
- _id: HeEd
doi: 10.1016/j.aim.2015.10.004
ec_funded: 1
file:
- access_level: open_access
checksum: f8869ec110c35c852ef6a37425374af7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:10Z
date_updated: 2020-07-14T12:45:10Z
file_id: '4928'
file_name: IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf
file_size: 248985
relation: main_file
file_date_updated: 2020-07-14T12:45:10Z
has_accepted_license: '1'
intvolume: ' 287'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 674 - 703
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '5488'
pubrep_id: '774'
quality_controlled: '1'
related_material:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Approximation and convergence of the intrinsic volume
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: 287
year: '2016'
...
---
_id: '5805'
abstract:
- lang: eng
text: Discretization of sphere in the integer space follows a particular discretization
scheme, which, in principle, conforms to some topological model. This eventually
gives rise to interesting topological properties of a discrete spherical surface,
which need to be investigated for its analytical characterization. This paper
presents some novel results on the local topological properties of the naive model
of discrete sphere. They follow from the bijection of each quadraginta octant
of naive sphere with its projection map called f -map on the corresponding functional
plane and from the characterization of certain jumps in the f-map. As an application,
we have shown how these properties can be used in designing an efficient reconstruction
algorithm for a naive spherical surface from an input voxel set when it is sparse
or noisy.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Nabhasmita
full_name: Sen, Nabhasmita
last_name: Sen
- 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: 'Sen N, Biswas R, Bhowmick P. On some local topological properties of naive
discrete sphere. In: Computational Topology in Image Context. Vol 9667.
Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23'
apa: 'Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological
properties of naive discrete sphere. In Computational Topology in Image Context
(Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23'
chicago: 'Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological
Properties of Naive Discrete Sphere.” In Computational Topology in Image Context,
9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.'
ieee: 'N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties
of naive discrete sphere,” in Computational Topology in Image Context,
vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.'
ista: 'Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of
naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol.
9667, 253–264.'
mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete
Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature,
2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.
short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context,
Springer Nature, Cham, 2016, pp. 253–264.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2019-01-08T20:44:24Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2022-01-28T08:01:22Z
day: '02'
department:
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_23
extern: '1'
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 253-264
place: Cham
publication: Computational Topology in Image Context
publication_identifier:
eisbn:
- 978-3-319-39441-1
eissn:
- 1611-3349
isbn:
- 978-3-319-39440-4
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On some local topological properties of naive discrete sphere
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9667
year: '2016'
...
---
_id: '5806'
abstract:
- lang: eng
text: Although the concept of functional plane for naive plane is studied and reported
in the literature in great detail, no similar study is yet found for naive sphere.
This article exposes the first study in this line, opening up further prospects
of analyzing the topological properties of sphere in the discrete space. We show
that each quadraginta octant Q of a naive sphere forms a bijection with its projected
pixel set on a unique coordinate plane, which thereby serves as the functional
plane of Q, and hence gives rise to merely mono-jumps during back projection.
The other two coordinate planes serve as para-functional and dia-functional planes
for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds
neither of the two. Owing to this, the quadraginta octants form symmetry groups
and subgroups with equivalent jump conditions. We also show a potential application
in generating a special class of discrete 3D circles based on back projection
and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry,
uniqueness, and bounded distance from the underlying real sphere and real plane.
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. On functionality of quadraginta octants of naive sphere
with application to circle drawing. In: Discrete Geometry for Computer Imagery.
Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20'
apa: 'Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants
of naive sphere with application to circle drawing. In Discrete Geometry for
Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta
Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry
for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.'
ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive
sphere with application to circle drawing,” in Discrete Geometry for Computer
Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.
ista: 'Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive
sphere with application to circle drawing. Discrete Geometry for Computer Imagery.
DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS,
vol. 9647, 256–267.'
mla: Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants
of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for
Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.
short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer
Nature, Cham, 2016, pp. 256–267.
conference:
end_date: 2016-04-20
location: Nantes, France
name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
start_date: 2016-04-18
date_created: 2019-01-08T20:44:37Z
date_published: 2016-04-09T00:00:00Z
date_updated: 2022-01-28T08:10:11Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/978-3-319-32360-2_20
extern: '1'
intvolume: ' 9647'
language:
- iso: eng
month: '04'
oa_version: None
page: 256-267
place: Cham
publication: Discrete Geometry for Computer Imagery
publication_identifier:
eisbn:
- 978-3-319-32360-2
isbn:
- 978-3-319-32359-6
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On functionality of quadraginta octants of naive sphere with application to
circle drawing
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9647
year: '2016'
...
---
_id: '5809'
abstract:
- lang: eng
text: A discrete spherical circle is a topologically well-connected 3D circle in
the integer space, which belongs to a discrete sphere as well as a discrete plane.
It is one of the most important 3D geometric primitives, but has not possibly
yet been studied up to its merit. This paper is a maiden exposition of some of
its elementary properties, which indicates a sense of its profound theoretical
prospects in the framework of digital geometry. We have shown how different types
of discretization can lead to forbidden and admissible classes, when one attempts
to define the discretization of a spherical circle in terms of intersection between
a discrete sphere and a discrete plane. Several fundamental theoretical results
have been presented, the algorithm for construction of discrete spherical circles
has been discussed, and some test results have been furnished to demonstrate its
practicality and usefulness.
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
- first_name: Valentin E.
full_name: Brimkov, Valentin E.
last_name: Brimkov
citation:
ama: 'Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete
spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer
Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7'
apa: 'Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity
and smoothness of discrete spherical circles. In Combinatorial image analysis
(Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7'
chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity
and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis,
9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.'
ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness
of discrete spherical circles,” in Combinatorial image analysis, vol. 9448,
Cham: Springer Nature, 2016, pp. 86–100.'
ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness
of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.'
mla: Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical
Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016,
pp. 86–100, doi:10.1007/978-3-319-26145-4_7.
short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis,
Springer Nature, Cham, 2016, pp. 86–100.
conference:
end_date: 2015-11-27
location: Kolkata, India
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2015-11-24
date_created: 2019-01-08T20:45:19Z
date_published: 2016-01-06T00:00:00Z
date_updated: 2022-01-28T08:13:03Z
day: '06'
department:
- _id: HeEd
doi: 10.1007/978-3-319-26145-4_7
extern: '1'
intvolume: ' 9448'
language:
- iso: eng
month: '01'
oa_version: None
page: 86-100
place: Cham
publication: Combinatorial image analysis
publication_identifier:
eisbn:
- 978-3-319-26145-4
eissn:
- 1611-3349
isbn:
- 978-3-319-26144-7
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the connectivity and smoothness of discrete spherical circles
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9448
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: '1360'
abstract:
- lang: eng
text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard
trajectories in convex bodies, when the length is measured with a (possibly asymmetric)
norm. We prove a lower bound for the length of the shortest closed billiard trajectory,
related to the non-symmetric Mahler problem. With this technique we are able to
give short and elementary proofs to some known results. '
acknowledgement: The first and third authors were supported by the Dynasty Foundation.
The first, second and third authors were supported by the Russian Foundation for
Basic Re- search grant 15-31-20403 (mol a ved).
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: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
- first_name: Anastasia
full_name: Sharipova, Anastasia
last_name: Sharipova
citation:
ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed
billiard trajectories in asymmetric normed spaces. Proceedings of the American
Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062
apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary
approach to closed billiard trajectories in asymmetric normed spaces. Proceedings
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062
chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova.
“Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2016. https://doi.org/10.1090/proc/13062.
ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach
to closed billiard trajectories in asymmetric normed spaces,” Proceedings of
the American Mathematical Society, vol. 144, no. 10. American Mathematical
Society, pp. 4501–4513, 2016.
ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach
to closed billiard trajectories in asymmetric normed spaces. Proceedings of the
American Mathematical Society. 144(10), 4501–4513.
mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories
in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society,
vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.
short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American
Mathematical Society 144 (2016) 4501–4513.
date_created: 2018-12-11T11:51:34Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:50:09Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
intvolume: ' 144'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.0442
month: '10'
oa: 1
oa_version: Preprint
page: 4501 - 4513
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5885'
quality_controlled: '1'
scopus_import: 1
status: public
title: Elementary approach to closed billiard trajectories in asymmetric normed spaces
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1408'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map (Formula presented.) on a compact
space K that are invariant with respect to perturbations of f. The perturbations
are arbitrary continuous maps within (Formula presented.) distance r from f for
a given (Formula presented.). The main drawback of the approach is that the computability
of well groups was shown only when (Formula presented.) or (Formula presented.).
Our contribution to the theory of well groups is twofold: on the one hand we improve
on the computability issue, but on the other hand we present a range of examples
where the well groups are incomplete invariants, that is, fail to capture certain
important robust properties of the zero set. For the first part, we identify a
computable subgroup of the well group that is obtained by cap product with the
pullback of the orientation of (Formula presented.) by f. In other words, well
groups can be algorithmically approximated from below. When f is smooth and (Formula
presented.), our approximation of the (Formula presented.)th well group is exact.
For the second part, we find examples of maps (Formula presented.) with all well
groups isomorphic but whose perturbations have different zero sets. We discuss
on a possible replacement of the well groups of vector valued maps by an invariant
of a better descriptive power and computability status.'
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. On computability and triviality of well groups. Discrete
& Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2
apa: Franek, P., & Krcál, M. (2016). On computability and triviality of well
groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.
ieee: P. Franek and M. Krcál, “On computability and triviality of well groups,”
Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164,
2016.
ista: Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete
& Computational Geometry. 56(1), 126–164.
mla: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.”
Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016,
pp. 126–64, doi:10.1007/s00454-016-9794-2.
short: P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.
date_created: 2018-12-11T11:51:51Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2023-02-23T10:02:11Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-016-9794-2
ec_funded: 1
file:
- access_level: open_access
checksum: e0da023abf6b72abd8c6a8c76740d53c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:55Z
date_updated: 2020-07-14T12:44:53Z
file_id: '4846'
file_name: IST-2016-614-v1+1_s00454-016-9794-2.pdf
file_size: 905303
relation: main_file
file_date_updated: 2020-07-14T12:44:53Z
has_accepted_license: '1'
intvolume: ' 56'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 126 - 164
project:
- _id: 25F8B9BC-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M01980
name: Robust invariants of Nonlinear Systems
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5799'
pubrep_id: '614'
quality_controlled: '1'
related_material:
record:
- id: '1510'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: On computability and triviality of well groups
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: 56
year: '2016'
...
---
_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'
...