---
_id: '201'
abstract:
- lang: eng
text: 'We describe arrangements of three-dimensional spheres from a geometrical
and topological point of view. Real data (fitting this setup) often consist of
soft spheres which show certain degree of deformation while strongly packing against
each other. In this context, we answer the following questions: If we model a
soft packing of spheres by hard spheres that are allowed to overlap, can we measure
the volume in the overlapped areas? Can we be more specific about the overlap
volume, i.e. quantify how much volume is there covered exactly twice, three times,
or k times? What would be a good optimization criteria that rule the arrangement
of soft spheres while making a good use of the available space? Fixing a particular
criterion, what would be the optimal sphere configuration? The first result of
this thesis are short formulas for the computation of volumes covered by at least
k of the balls. The formulas exploit information contained in the order-k Voronoi
diagrams and its closely related Level-k complex. The used complexes lead to a
natural generalization into poset diagrams, a theoretical formalism that contains
the order-k and degree-k diagrams as special cases. In parallel, we define different
criteria to determine what could be considered an optimal arrangement from a geometrical
point of view. Fixing a criterion, we find optimal soft packing configurations
in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools
from computational topology on real physical data, to show the potentials of higher-order
diagrams in the description of melting crystals. The results of the experiments
leaves us with an open window to apply the theories developed in this thesis in
real applications.'
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026
apa: Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026
chicago: Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science
and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026.
ieee: M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology
Austria, 2018.
ista: Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and
Technology Austria.
mla: Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science
and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.
short: M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology
Austria, 2018.
date_created: 2018-12-11T11:45:10Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2023-09-07T12:25:32Z
day: '11'
ddc:
- '514'
- '516'
degree_awarded: PhD
department:
- _id: HeEd
doi: 10.15479/AT:ISTA:th_1026
file:
- access_level: closed
checksum: dd699303623e96d1478a6ae07210dd05
content_type: application/zip
creator: kschuh
date_created: 2019-02-05T07:43:31Z
date_updated: 2020-07-14T12:45:24Z
file_id: '5918'
file_name: IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip
file_size: 11827713
relation: source_file
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checksum: ba163849a190d2b41d66fef0e4983294
content_type: application/pdf
creator: kschuh
date_created: 2019-02-05T07:43:45Z
date_updated: 2020-07-14T12:45:24Z
file_id: '5919'
file_name: IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf
file_size: 4783846
relation: main_file
file_date_updated: 2020-07-14T12:45:24Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: '171'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '7712'
pubrep_id: '1026'
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: Multiple covers with balls
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '692'
abstract:
- lang: eng
text: We consider families of confocal conics and two pencils of Apollonian circles
having the same foci. We will show that these families of curves generate trivial
3-webs and find the exact formulas describing them.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
citation:
ama: Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata.
2018;194(1):55-64. doi:10.1007/s10711-017-0265-6
apa: Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae
Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6
chicago: Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae
Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.
ieee: A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae
Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.
ista: Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae
Dedicata. 194(1), 55–64.
mla: Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae
Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6.
short: A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.
date_created: 2018-12-11T11:47:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-08T11:40:29Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s10711-017-0265-6
ec_funded: 1
external_id:
isi:
- '000431418800004'
file:
- access_level: open_access
checksum: 1febcfc1266486053a069e3425ea3713
content_type: application/pdf
creator: kschuh
date_created: 2020-01-03T11:35:08Z
date_updated: 2020-07-14T12:47:44Z
file_id: '7222'
file_name: 2018_Springer_Akopyan.pdf
file_size: 1140860
relation: main_file
file_date_updated: 2020-07-14T12:47:44Z
has_accepted_license: '1'
intvolume: ' 194'
isi: 1
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 55 - 64
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Geometriae Dedicata
publication_status: published
publisher: Springer
publist_id: '7014'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 3-Webs generated by confocal conics and circles
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 194
year: '2018'
...
---
_id: '75'
abstract:
- lang: eng
text: We prove that any convex body in the plane can be partitioned into m convex
parts of equal areas and perimeters for any integer m≥2; this result was previously
known for prime powers m=pk. We also give a higher-dimensional generalization.
article_number: '1804.03057'
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: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number
of pieces. 2018. doi:10.48550/arXiv.1804.03057
apa: Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions
into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057
chicago: Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions
into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.
ieee: A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary
number of pieces.” arXiv, 2018.
ista: Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary
number of pieces. 1804.03057.
mla: Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of
Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.
short: A. Akopyan, S. Avvakumov, R. Karasev, (2018).
date_created: 2018-12-11T11:44:30Z
date_published: 2018-09-13T00:00:00Z
date_updated: 2023-12-18T10:51:02Z
day: '13'
department:
- _id: HeEd
- _id: JaMa
doi: 10.48550/arXiv.1804.03057
ec_funded: 1
external_id:
arxiv:
- '1804.03057'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.03057
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication_status: published
publisher: arXiv
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Convex fair partitions into arbitrary number of pieces
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '458'
abstract:
- lang: eng
text: We consider congruences of straight lines in a plane with the combinatorics
of the square grid, with all elementary quadrilaterals possessing an incircle.
It is shown that all the vertices of such nets (we call them incircular or IC-nets)
lie on confocal conics. Our main new results are on checkerboard IC-nets in the
plane. These are congruences of straight lines in the plane with the combinatorics
of the square grid, combinatorially colored as a checkerboard, such that all black
coordinate quadrilaterals possess inscribed circles. We show how this larger class
of IC-nets appears quite naturally in Laguerre geometry of oriented planes and
spheres and leads to new remarkable incidence theorems. Most of our results are
valid in hyperbolic and spherical geometries as well. We present also generalizations
in spaces of higher dimension, called checkerboard IS-nets. The construction of
these nets is based on a new 9 inspheres incidence theorem.
acknowledgement: DFG Collaborative Research Center TRR 109 “Discretization in Geometry
and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh
Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]
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: Alexander
full_name: Bobenko, Alexander
last_name: Bobenko
citation:
ama: Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions
of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292
apa: Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics.
Transactions of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/tran/7292
chicago: Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal
Conics.” Transactions of the American Mathematical Society. American Mathematical
Society, 2018. https://doi.org/10.1090/tran/7292.
ieee: A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions
of the American Mathematical Society, vol. 370, no. 4. American Mathematical
Society, pp. 2825–2854, 2018.
ista: Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions
of the American Mathematical Society. 370(4), 2825–2854.
mla: Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.”
Transactions of the American Mathematical Society, vol. 370, no. 4, American
Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292.
short: A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society
370 (2018) 2825–2854.
date_created: 2018-12-11T11:46:35Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-11T14:19:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/7292
ec_funded: 1
external_id:
isi:
- '000423197800019'
intvolume: ' 370'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.04637
month: '04'
oa: 1
oa_version: Preprint
page: 2825 - 2854
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '7363'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Incircular nets and confocal conics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 370
year: '2018'
...
---
_id: '530'
abstract:
- lang: eng
text: Inclusion–exclusion is an effective method for computing the volume of a union
of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion
formulas for the subset of Rn covered by at least k balls in a finite set. We
implement two of the formulas in dimension n=3 and report on results obtained
with our software.
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: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion.
Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014'
apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls
I: Inclusion–exclusion. Computational Geometry: Theory and Applications.
Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014'
chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications.
Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.'
ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,”
Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp.
119–133, 2018.'
ista: 'Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion.
Computational Geometry: Theory and Applications. 68, 119–133.'
mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications,
vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.'
short: 'H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications
68 (2018) 119–133.'
date_created: 2018-12-11T11:46:59Z
date_published: 2018-03-01T00:00:00Z
date_updated: 2023-09-13T08:59:00Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2017.06.014
ec_funded: 1
external_id:
isi:
- '000415778300010'
file:
- access_level: open_access
checksum: 1c8d58cd489a66cd3e2064c1141c8c5e
content_type: application/pdf
creator: dernst
date_created: 2019-02-12T06:47:52Z
date_updated: 2020-07-14T12:46:38Z
file_id: '5953'
file_name: 2018_Edelsbrunner.pdf
file_size: 708357
relation: main_file
file_date_updated: 2020-07-14T12:46:38Z
has_accepted_license: '1'
intvolume: ' 68'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Preprint
page: 119 - 133
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '7289'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple covers with balls I: Inclusion–exclusion'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 68
year: '2018'
...
---
_id: '58'
abstract:
- lang: eng
text: 'Inside a two-dimensional region (``cake""), there are m nonoverlapping
tiles of a certain kind (``toppings""). We want to expand the toppings
while keeping them nonoverlapping, and possibly add some blank pieces of the same
``certain kind,"" such that the entire cake is covered. How many blanks
must we add? We study this question in several cases: (1) The cake and toppings
are general polygons. (2) The cake and toppings are convex figures. (3) The cake
and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear
polygon and the toppings are axis-parallel rectangles. In all four cases, we provide
tight bounds on the number of blanks.'
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: Erel
full_name: Segal Halevi, Erel
last_name: Segal Halevi
citation:
ama: Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM
Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X
apa: Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements.
SIAM Journal on Discrete Mathematics. Society for Industrial and Applied
Mathematics . https://doi.org/10.1137/16M110407X
chicago: Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal
Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial
and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X.
ieee: A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,”
SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial
and Applied Mathematics , pp. 2242–2257, 2018.
ista: Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements.
SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.
mla: Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.”
SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial
and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.
short: A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018)
2242–2257.
date_created: 2018-12-11T11:44:24Z
date_published: 2018-09-06T00:00:00Z
date_updated: 2023-09-11T12:48:39Z
day: '06'
department:
- _id: HeEd
doi: 10.1137/16M110407X
ec_funded: 1
external_id:
arxiv:
- '1604.00960'
isi:
- '000450810500036'
intvolume: ' 32'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.00960
month: '09'
oa: 1
oa_version: Preprint
page: 2242 - 2257
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: SIAM Journal on Discrete Mathematics
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7996'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting blanks in polygonal arrangements
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 32
year: '2018'
...
---
_id: '6355'
abstract:
- lang: eng
text: We prove that any cyclic quadrilateral can be inscribed in any closed convex
C1-curve. The smoothness condition is not required if the quadrilateral is a
rectangle.
article_number: e7
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: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
citation:
ama: Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed
convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7
apa: Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed
in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2018.7
chicago: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be
Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma.
Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.
ieee: A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge
University Press, 2018.
ista: Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.
mla: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed
in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6,
e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.
short: A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).
date_created: 2019-04-30T06:09:57Z
date_published: 2018-05-31T00:00:00Z
date_updated: 2023-09-19T14:50:12Z
day: '31'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
- _id: JaMa
doi: 10.1017/fms.2018.7
ec_funded: 1
external_id:
arxiv:
- '1712.10205'
isi:
- '000433915500001'
file:
- access_level: open_access
checksum: 5a71b24ba712a3eb2e46165a38fbc30a
content_type: application/pdf
creator: dernst
date_created: 2019-04-30T06:14:58Z
date_updated: 2020-07-14T12:47:28Z
file_id: '6356'
file_name: 2018_ForumMahtematics_Akopyan.pdf
file_size: 249246
relation: main_file
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month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 6
year: '2018'
...
---
_id: '106'
abstract:
- lang: eng
text: The goal of this article is to introduce the reader to the theory of intrinsic
geometry of convex surfaces. We illustrate the power of the tools by proving a
theorem on convex surfaces containing an arbitrarily long closed simple geodesic.
Let us remind ourselves that a curve in a surface is called geodesic if every
sufficiently short arc of the curve is length minimizing; if, in addition, it
has no self-intersections, we call it simple geodesic. A tetrahedron with equal
opposite edges is called isosceles. The axiomatic method of Alexandrov geometry
allows us to work with the metrics of convex surfaces directly, without approximating
it first by a smooth or polyhedral metric. Such approximations destroy the closed
geodesics on the surface; therefore it is difficult (if at all possible) to apply
approximations in the proof of our theorem. On the other hand, a proof in the
smooth or polyhedral case usually admits a translation into Alexandrov’s language;
such translation makes the result more general. In fact, our proof resembles a
translation of the proof given by Protasov. Note that the main theorem implies
in particular that a smooth convex surface does not have arbitrarily long simple
closed geodesics. However we do not know a proof of this corollary that is essentially
simpler than the one presented below.
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: Anton
full_name: Petrunin, Anton
last_name: Petrunin
citation:
ama: Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer.
2018;40(3):26-31. doi:10.1007/s00283-018-9795-5
apa: Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces.
Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5
chicago: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.”
Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.
ieee: A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical
Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.
ista: Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical
Intelligencer. 40(3), 26–31.
mla: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.”
Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31,
doi:10.1007/s00283-018-9795-5.
short: A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.
date_created: 2018-12-11T11:44:40Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-13T08:49:16Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00283-018-9795-5
external_id:
arxiv:
- '1702.05172'
isi:
- '000444141200005'
intvolume: ' 40'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.05172
month: '09'
oa: 1
oa_version: Preprint
page: 26 - 31
publication: Mathematical Intelligencer
publication_status: published
publisher: Springer
publist_id: '7948'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Long geodesics on convex surfaces
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 40
year: '2018'
...
---
_id: '1064'
abstract:
- lang: eng
text: 'In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by
P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it
is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot
be separated into two subfamilies by a straight line disjoint from the disks.
In this note we show that essentially the same idea may work for different analogues
and generalizations of their result. In particular, we prove the following: Given
a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety
coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate
of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane
disjoint from the homothets.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Mikhail
full_name: Grigorev, Mikhail
last_name: Grigorev
citation:
ama: Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W.
Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009.
doi:10.1007/s00454-017-9883-x
apa: Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering
theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry.
Springer. https://doi.org/10.1007/s00454-017-9883-x
chicago: Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle
Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational
Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.
ieee: A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem
by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry,
vol. 59, no. 4. Springer, pp. 1001–1009, 2018.
ista: Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by
A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.
mla: Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and
R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer,
2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.
short: A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry
59 (2018) 1001–1009.
date_created: 2018-12-11T11:49:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-20T12:08:51Z
day: '01'
ddc:
- '516'
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-017-9883-x
ec_funded: 1
external_id:
isi:
- '000432205500011'
file:
- access_level: open_access
content_type: application/pdf
creator: dernst
date_created: 2019-01-18T09:27:36Z
date_updated: 2019-01-18T09:27:36Z
file_id: '5844'
file_name: 2018_DiscreteComp_Akopyan.pdf
file_size: 482518
relation: main_file
success: 1
file_date_updated: 2019-01-18T09:27:36Z
has_accepted_license: '1'
intvolume: ' 59'
isi: 1
issue: '4'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1001-1009
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer
publist_id: '6324'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the circle covering theorem by A.W. Goodman and R.E. Goodman
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 59
year: '2018'
...
---
_id: '409'
abstract:
- lang: eng
text: We give a simple proof of T. Stehling's result [4], whereby in any normal
tiling of the plane with convex polygons with number of sides not less than six,
all tiles except a finite number are hexagons.
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
citation:
ama: Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus
Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005
apa: Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes
Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005
chicago: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes
Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005.
ieee: A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes
Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.
ista: Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes
Rendus Mathematique. 356(4), 412–414.
mla: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes
Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.
short: A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.
date_created: 2018-12-11T11:46:19Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-13T09:34:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.crma.2018.03.005
external_id:
arxiv:
- '1805.01652'
isi:
- '000430402700009'
intvolume: ' 356'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.01652
month: '04'
oa: 1
oa_version: Preprint
page: 412-414
publication: Comptes Rendus Mathematique
publication_identifier:
issn:
- 1631073X
publication_status: published
publisher: Elsevier
publist_id: '7420'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the number of non-hexagons in a planar tiling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 356
year: '2018'
...
---
_id: '1072'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a radius parameter, we study the Čech,
Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized
discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel
sets of generalized discrete Morse functions, we prove that the four complexes
are simple-homotopy equivalent by a sequence of simplicial collapses, which are
explicitly described by a single discrete gradient field.
acknowledgement: This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP),
by ESF under the ACAT Research Network Programme, by the Russian Government under
mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR
109 “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions
of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991
apa: Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay
complexes. Transactions of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/tran/6991
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Complexes.” Transactions of the American Mathematical Society.
American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.
ieee: U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,”
Transactions of the American Mathematical Society, vol. 369, no. 5. American
Mathematical Society, pp. 3741–3762, 2017.
ista: Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes.
Transactions of the American Mathematical Society. 369(5), 3741–3762.
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Complexes.” Transactions of the American Mathematical Society, vol. 369,
no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.
short: U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society
369 (2017) 3741–3762.
date_created: 2018-12-11T11:49:59Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2023-09-20T12:05:56Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/6991
ec_funded: 1
external_id:
arxiv:
- '1312.1231'
isi:
- '000398030400024'
intvolume: ' 369'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1312.1231
month: '05'
oa: 1
oa_version: Preprint
page: 3741 - 3762
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '6311'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Morse theory of Čech and delaunay complexes
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 369
year: '2017'
...
---
_id: '1173'
abstract:
- lang: eng
text: We introduce the Voronoi functional of a triangulation of a finite set of
points in the Euclidean plane and prove that among all geometric triangulations
of the point set, the Delaunay triangulation maximizes the functional. This result
neither extends to topological triangulations in the plane nor to geometric triangulations
in three and higher dimensions.
acknowledgement: This research is partially supported by the Russian Government under
the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by
ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by
NSF grants DMS-1101688, DMS-1400876.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is
maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910.
doi:10.1007/s00493-016-3308-y
apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The
Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica.
Springer. https://doi.org/10.1007/s00493-016-3308-y
chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko.
“The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.”
Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.
ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional
is maximized by the Delaunay triangulation in the plane,” Combinatorica,
vol. 37, no. 5. Springer, pp. 887–910, 2017.
ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional
is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5),
887–910.
mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay
Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017,
pp. 887–910, doi:10.1007/s00493-016-3308-y.
short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017)
887–910.
date_created: 2018-12-11T11:50:32Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2023-09-20T11:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
isi:
- '000418056000005'
intvolume: ' 37'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.6337
month: '10'
oa: 1
oa_version: Submitted Version
page: 887 - 910
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Combinatorica
publication_identifier:
issn:
- '02099683'
publication_status: published
publisher: Springer
publist_id: '6182'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 37
year: '2017'
...
---
_id: '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
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
date_created: 2018-12-11T11:48:45Z
date_published: 2017-07-28T00:00:00Z
date_updated: 2023-09-26T16:10:03Z
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:
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:
- '03029743'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
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: 2023-09-26T15:50:52Z
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: '688'
abstract:
- lang: eng
text: 'We show that the framework of topological data analysis can be extended from
metrics to general Bregman divergences, widening the scope of possible applications.
Examples are the Kullback - Leibler divergence, which is commonly used for comparing
text and images, and the Itakura - Saito divergence, popular for speech and sound.
In particular, we prove that appropriately generalized čech and Delaunay (alpha)
complexes capture the correct homotopy type, namely that of the corresponding
union of Bregman balls. Consequently, their filtrations give the correct persistence
diagram, namely the one generated by the uniformly growing Bregman balls. Moreover,
we show that unlike the metric setting, the filtration of Vietoris-Rips complexes
may fail to approximate the persistence diagram. We propose algorithms to compute
the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally
test their efficiency. Lastly, we explain their surprisingly good performance
by making a connection with discrete Morse theory. '
alternative_title:
- LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences.
In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916.
doi:10.4230/LIPIcs.SoCG.2017.39'
apa: 'Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with
Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational
Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2017.39'
chicago: Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with
Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.
ieee: H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,”
presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia,
2017, vol. 77, pp. 391–3916.
ista: Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences.
Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.
mla: Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with
Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.
short: H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916.
conference:
end_date: 2017-07-07
location: Brisbane, Australia
name: Symposium on Computational Geometry, SoCG
start_date: 2017-07-04
date_created: 2018-12-11T11:47:56Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:09:26Z
day: '01'
ddc:
- '514'
- '516'
department:
- _id: HeEd
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2017.39
file:
- access_level: open_access
checksum: 067ab0cb3f962bae6c3af6bf0094e0f3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:03Z
date_updated: 2020-07-14T12:47:42Z
file_id: '4856'
file_name: IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf
file_size: 990546
relation: main_file
file_date_updated: 2020-07-14T12:47:42Z
has_accepted_license: '1'
intvolume: ' 77'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 391-3916
publication_identifier:
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7021'
pubrep_id: '895'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topological data analysis with Bregman divergences
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 77
year: '2017'
...
---
_id: '707'
abstract:
- lang: eng
text: We answer a question of M. Gromov on the waist of the unit ball.
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-Blackwell. 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-Blackwell,
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-Blackwell,
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-Blackwell,
2017, pp. 690–93, doi:10.1112/blms.12062.
short: A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017)
690–693.
date_created: 2018-12-11T11:48:02Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12062
ec_funded: 1
intvolume: ' 49'
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:
- '00246093'
publication_status: published
publisher: Wiley-Blackwell
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 49
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.
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: 2023-09-07T12:07:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1017/apr.2017.20
ec_funded: 1
external_id:
arxiv:
- '1607.05915'
intvolume: ' 49'
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:
- '00018678'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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.
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:53:01Z
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:
- '01668641'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 231
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.
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title: Planar matchings for weighted straight skeletons
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