---
_id: '5678'
abstract:
- lang: eng
text: "The order-k Voronoi tessellation of a locally finite set \U0001D44B⊆ℝ\U0001D45B
decomposes ℝ\U0001D45B into convex domains whose points have the same k nearest
neighbors in X. Assuming X is a stationary Poisson point process, we give explicit
formulas for the expected number and total area of faces of a given dimension
per unit volume of space. We also develop a relaxed version of discrete Morse
theory and generalize by counting only faces, for which the k nearest points in
X are within a given distance threshold."
article_processing_charge: Yes (via OA deal)
article_type: original
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
citation:
ama: Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete
and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2
apa: Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order
k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of
Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.
ieee: H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete
and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.
ista: Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete
and Computational Geometry. 62(4), 865–878.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order
K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019,
pp. 865–878, doi:10.1007/s00454-018-0049-2.
short: H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019)
865–878.
corr_author: '1'
date_created: 2018-12-16T22:59:20Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2026-04-08T14:19:30Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-018-0049-2
ec_funded: 1
external_id:
arxiv:
- '1709.09380'
isi:
- '000494042900008'
file:
- access_level: open_access
checksum: f9d00e166efaccb5a76bbcbb4dcea3b4
content_type: application/pdf
creator: dernst
date_created: 2019-02-06T10:10:46Z
date_updated: 2020-07-14T12:47:10Z
file_id: '5932'
file_name: 2018_DiscreteCompGeometry_Edelsbrunner.pdf
file_size: 599339
relation: main_file
file_date_updated: 2020-07-14T12:47:10Z
has_accepted_license: '1'
intvolume: ' 62'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 865–878
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Poisson–Delaunay Mosaics of Order k
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 62
year: '2019'
...
---
_id: '6989'
abstract:
- lang: eng
text: 'When can a polyomino piece of paper be folded into a unit cube? Prior work
studied tree-like polyominoes, but polyominoes with holes remain an intriguing
open problem. We present sufficient conditions for a polyomino with hole(s) to
fold into a cube, and conditions under which cube folding is impossible. In particular,
we show that all but five special simple holes guarantee foldability. '
acknowledgement: This research was performed in part at the 33rd Bellairs Winter Workshop
on Computational Geometry. We thank all other participants for a fruitful atmosphere.
article_processing_charge: No
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Hugo A
full_name: Akitaya, Hugo A
last_name: Akitaya
- first_name: Kenneth C
full_name: Cheung, Kenneth C
last_name: Cheung
- first_name: Erik D
full_name: Demaine, Erik D
last_name: Demaine
- first_name: Martin L
full_name: Demaine, Martin L
last_name: Demaine
- first_name: Sandor P
full_name: Fekete, Sandor P
last_name: Fekete
- first_name: Linda
full_name: Kleist, Linda
last_name: Kleist
- first_name: Irina
full_name: Kostitsyna, Irina
last_name: Kostitsyna
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Klara
full_name: Mundilova, Klara
last_name: Mundilova
- first_name: Christiane
full_name: Schmidt, Christiane
last_name: Schmidt
citation:
ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes
into a cube. In: Proceedings of the 31st Canadian Conference on Computational
Geometry. Canadian Conference on Computational Geometry; 2019:164-170.'
apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M.
L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a
cube. In Proceedings of the 31st Canadian Conference on Computational Geometry
(pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.'
chicago: Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin
L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes
into a Cube.” In Proceedings of the 31st Canadian Conference on Computational
Geometry, 164–70. Canadian Conference on Computational Geometry, 2019.
ieee: O. Aichholzer et al., “Folding polyominoes with holes into a cube,”
in Proceedings of the 31st Canadian Conference on Computational Geometry,
Edmonton, Canada, 2019, pp. 164–170.
ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist
L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding
polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference
on Computational Geometry. CCCG: Canadian Conference in Computational Geometry,
164–170.'
mla: Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings
of the 31st Canadian Conference on Computational Geometry, Canadian Conference
on Computational Geometry, 2019, pp. 164–70.
short: O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P.
Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt,
in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian
Conference on Computational Geometry, 2019, pp. 164–170.
conference:
end_date: 2019-08-10
location: Edmonton, Canada
name: 'CCCG: Canadian Conference in Computational Geometry'
start_date: 2019-08-08
date_created: 2019-11-04T16:46:11Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2026-04-16T09:14:30Z
day: '01'
department:
- _id: HeEd
external_id:
arxiv:
- '1910.09917'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://sites.ualberta.ca/~cccg2019/cccg2019_proceedings.pdf
month: '08'
oa: 1
oa_version: Published Version
page: 164-170
publication: Proceedings of the 31st Canadian Conference on Computational Geometry
publication_status: published
publisher: Canadian Conference on Computational Geometry
quality_controlled: '1'
related_material:
record:
- id: '8317'
relation: extended_version
status: public
scopus_import: '1'
status: public
title: Folding polyominoes with holes into a cube
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '188'
abstract:
- lang: eng
text: Smallest enclosing spheres of finite point sets are central to methods in
topological data analysis. Focusing on Bregman divergences to measure dissimilarity,
we prove bounds on the location of the center of a smallest enclosing sphere.
These bounds depend on the range of radii for which Bregman balls are convex.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund
alternative_title:
- Leibniz International Proceedings in Information, LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff
points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35'
apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres
and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at
the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35'
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing
Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.
ieee: 'H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and
Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational
Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.'
ista: 'Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff
points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz
International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.'
mla: Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points
in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.
short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2018, p. 35:1-35:13.
conference:
end_date: 2018-06-14
location: Budapest, Hungary
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2018-06-11
date_created: 2018-12-11T11:45:05Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2021-01-12T06:53:48Z
day: '11'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2018.35
file:
- access_level: open_access
checksum: 7509403803b3ac1aee94bbc2ad293d21
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:31:31Z
date_updated: 2020-07-14T12:45:20Z
file_id: '5724'
file_name: 2018_LIPIcs_Edelsbrunner.pdf
file_size: 489080
relation: main_file
file_date_updated: 2020-07-14T12:45:20Z
has_accepted_license: '1'
intvolume: ' 99'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 35:1 - 35:13
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7733'
quality_controlled: '1'
scopus_import: 1
status: public
title: Smallest enclosing spheres and Chernoff points in Bregman geometry
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 99
year: '2018'
...
---
_id: '193'
abstract:
- lang: eng
text: 'We show attacks on five data-independent memory-hard functions (iMHF) that
were submitted to the password hashing competition (PHC). Informally, an MHF is
a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly
lower hardware and/or energy cost than evaluating a single instance on a standard
single-core architecture. Data-independent means the memory access pattern of
the function is independent of the input; this makes iMHFs harder to construct
than data-dependent ones, but the latter can be attacked by various side-channel
attacks. Following [Alwen-Blocki''16], we capture the evaluation of an iMHF as
a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of
this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC.
Ideally, one would like the complexity of a DAG underlying an iMHF to be as close
to quadratic in the number of nodes of the graph as possible. Instead, we show
that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2,
TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show
that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have
exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial
property of each underlying DAG (called its depth-robustness. By establishing
upper bounds on this property we are then able to apply the general technique
of [Alwen-Block''16] for analyzing the hardware costs of an iMHF.'
acknowledgement: Leonid Reyzin was supported in part by IST Austria and by US NSF
grants 1012910, 1012798, and 1422965; this research was performed while he was visiting
IST Austria.
article_processing_charge: No
author:
- first_name: Joel F
full_name: Alwen, Joel F
id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87
last_name: Alwen
- first_name: Peter
full_name: Gazi, Peter
last_name: Gazi
- first_name: Chethan
full_name: Kamath Hosdurg, Chethan
id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87
last_name: Kamath Hosdurg
- first_name: Karen
full_name: Klein, Karen
id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87
last_name: Klein
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
- first_name: Lenoid
full_name: Reyzin, Lenoid
last_name: Reyzin
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
- first_name: Michal
full_name: Rybar, Michal
id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87
last_name: Rybar
citation:
ama: 'Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data
independent password hashing functions. In: Proceedings of the 2018 on Asia
Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534'
apa: 'Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak,
K. Z., … Rybar, M. (2018). On the memory hardness of data independent password
hashing functions. In Proceedings of the 2018 on Asia Conference on Computer
and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534'
chicago: Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F
Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar.
“On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings
of the 2018 on Asia Conference on Computer and Communication Security, 51–65.
ACM, 2018. https://doi.org/10.1145/3196494.3196534.
ieee: J. F. Alwen et al., “On the memory hardness of data independent password
hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.
ista: 'Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin
L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password
hashing functions. Proceedings of the 2018 on Asia Conference on Computer and
Communication Security. ASIACCS: Asia Conference on Computer and Communications
Security , 51–65.'
mla: Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password
Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.
short: J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak,
L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference
on Computer and Communication Security, ACM, 2018, pp. 51–65.
conference:
end_date: 2018-06-08
location: Incheon, Republic of Korea
name: 'ASIACCS: Asia Conference on Computer and Communications Security '
start_date: 2018-06-04
date_created: 2018-12-11T11:45:07Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2024-11-04T13:52:29Z
day: '01'
department:
- _id: KrPi
- _id: HeEd
- _id: VlKo
doi: 10.1145/3196494.3196534
ec_funded: 1
external_id:
isi:
- '000516620100005'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2016/783
month: '06'
oa: 1
oa_version: Submitted Version
page: 51 - 65
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: 258AA5B2-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '682815'
name: Teaching Old Crypto New Tricks
publication: Proceedings of the 2018 on Asia Conference on Computer and Communication
Security
publication_status: published
publisher: ACM
publist_id: '7723'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the memory hardness of data independent password hashing functions
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
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: '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.'
corr_author: '1'
date_created: 2018-12-11T11:46:59Z
date_published: 2018-03-01T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
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: 2025-04-15T06:50:24Z
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: '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.
corr_author: '1'
date_created: 2018-12-11T11:47:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2025-04-15T06:50:29Z
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: '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.
corr_author: '1'
date_created: 2018-12-11T11:46:19Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2025-07-10T11:52:35Z
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:
- 1631-073X
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 356
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
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: 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.
corr_author: '1'
date_created: 2018-12-11T11:46:35Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2025-06-04T08:06:10Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/7292
ec_funded: 1
external_id:
arxiv:
- '1602.04637'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 370
year: '2018'
...
---
_id: '187'
abstract:
- lang: eng
text: 'Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and
r consists of all points in ℝd that have k or more points of X within distance
r. We consider two filtrations - one in scale obtained by fixing k and increasing
r, and the other in depth obtained by fixing r and decreasing k - and we compute
the persistence diagrams of both. While standard methods suffice for the filtration
in scale, we need novel geometric and topological concepts for the filtration
in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal
integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module
from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. '
acknowledgement: This work is partially supported by the DFG Collaborative Research
Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35
of the Austrian Science Fund (FWF).
alternative_title:
- LIPIcs
article_number: '34'
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: 'Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls.
In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34'
apa: 'Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of
Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry,
Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34'
chicago: Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence
of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34.
ieee: 'H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean
balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest,
Hungary, 2018, vol. 99.'
ista: 'Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean
balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.'
mla: Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of
Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018, doi:10.4230/LIPIcs.SoCG.2018.34.
short: H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, 2018.
conference:
end_date: 2018-06-14
location: Budapest, Hungary
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2018-06-11
date_created: 2018-12-11T11:45:05Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2026-04-08T07:01:29Z
day: '11'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2018.34
file:
- access_level: open_access
checksum: d8c0533ad0018eb4ed1077475eb8fc18
content_type: application/pdf
creator: dernst
date_created: 2018-12-18T09:27:22Z
date_updated: 2020-07-14T12:45:19Z
file_id: '5738'
file_name: 2018_LIPIcs_Edelsbrunner_Osang.pdf
file_size: 528018
relation: main_file
file_date_updated: 2020-07-14T12:45:19Z
has_accepted_license: '1'
intvolume: ' 99'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7732'
quality_controlled: '1'
related_material:
record:
- id: '9317'
relation: later_version
status: public
- id: '9056'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: The multi-cover persistence of Euclidean balls
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 99
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
orcid: 0000-0002-7840-5062
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).
corr_author: '1'
date_created: 2019-04-30T06:09:57Z
date_published: 2018-05-31T00:00:00Z
date_updated: 2026-04-08T07:25:54Z
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'
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file_name: 2018_ForumMahtematics_Akopyan.pdf
file_size: 249246
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intvolume: ' 6'
isi: 1
language:
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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: '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
orcid: 0000-0002-7840-5062
- 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).
corr_author: '1'
date_created: 2018-12-11T11:44:30Z
date_published: 2018-09-13T00:00:00Z
date_updated: 2026-04-08T07:25:54Z
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'
...
---
OA_place: publisher
_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.
corr_author: '1'
date_created: 2018-12-11T11:45:10Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2026-04-08T14:04:03Z
day: '11'
ddc:
- '514'
- '516'
degree_awarded: PhD
department:
- _id: HeEd
doi: 10.15479/AT:ISTA:th_1026
file:
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checksum: dd699303623e96d1478a6ae07210dd05
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has_accepted_license: '1'
language:
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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: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2018'
...
---
_id: '87'
abstract:
- lang: eng
text: Using the geodesic distance on the n-dimensional sphere, we study the expected
radius function of the Delaunay mosaic of a random set of points. Specifically,
we consider the partition of the mosaic into intervals of the radius function
and determine the expected number of intervals whose radii are less than or equal
to a given threshold. We find that the expectations are essentially the same as
for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the
points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to
the boundary complex of the convex hull in Rn+1, so we also get the expected number
of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in
Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric
to the standard n-simplex equipped with the Fisher information metric. It follows
that the latter space has similar stochastic properties as the n-dimensional Euclidean
space. Our results are therefore relevant in information geometry and in population
genetics.
article_processing_charge: No
article_type: original
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
citation:
ama: Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius
functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238.
doi:10.1214/18-AAP1389
apa: Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have
similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes
Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied
Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.
ieee: H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar
radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability,
vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.
ista: Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar
radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5),
3215–3238.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have
Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability,
vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.
short: H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.
date_created: 2018-12-11T11:44:33Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2026-04-08T14:19:30Z
day: '01'
department:
- _id: HeEd
doi: 10.1214/18-AAP1389
external_id:
arxiv:
- '1705.02870'
isi:
- '000442893500018'
intvolume: ' 28'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.02870
month: '10'
oa: 1
oa_version: Preprint
page: 3215 - 3238
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Annals of Applied Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7967'
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Random inscribed polytopes have similar radius functions as Poisson-Delaunay
mosaics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...
---
_id: '312'
abstract:
- lang: eng
text: Motivated by biological questions, we study configurations of equal spheres
that neither pack nor cover. Placing their centers on a lattice, we define the
soft density of the configuration by penalizing multiple overlaps. Considering
the 1-parameter family of diagonally distorted 3-dimensional integer lattices,
we show that the soft density is maximized at the FCC lattice.
acknowledgement: This work was partially supported by the DFG Collaborative Research
Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35
of the Austrian Science Fund (FWF).
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft
sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201
apa: Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC
lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial
and Applied Mathematics . https://doi.org/10.1137/16M1097201
chicago: Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the
FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for
Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.
ieee: H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice
for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society
for Industrial and Applied Mathematics , pp. 750–782, 2018.
ista: Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice
for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.
mla: Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC
Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1,
Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.
short: H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.
date_created: 2018-12-11T11:45:46Z
date_published: 2018-03-29T00:00:00Z
date_updated: 2026-04-16T09:53:02Z
day: '29'
department:
- _id: HeEd
doi: 10.1137/16M1097201
external_id:
isi:
- '000428958900038'
intvolume: ' 32'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 750 - 782
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: SIAM J Discrete Math
publication_identifier:
issn:
- 0895-4801
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7553'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the optimality of the FCC lattice for soft sphere packing
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 32
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.
corr_author: '1'
date_created: 2018-12-11T11:49:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2026-05-20T10:19:33Z
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:
- 1432-0444
issn:
- 0179-5376
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2018'
...
---
_id: '1173'
abstract:
- lang: eng
text: We introduce the Voronoi functional of a triangulation of a finite set of
points in the Euclidean plane and prove that among all geometric triangulations
of the point set, the Delaunay triangulation maximizes the functional. This result
neither extends to topological triangulations in the plane nor to geometric triangulations
in three and higher dimensions.
acknowledgement: This research is partially supported by the Russian Government under
the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by
ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by
NSF grants DMS-1101688, DMS-1400876.
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is
maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910.
doi:10.1007/s00493-016-3308-y
apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The
Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica.
Springer. https://doi.org/10.1007/s00493-016-3308-y
chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko.
“The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.”
Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.
ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional
is maximized by the Delaunay triangulation in the plane,” Combinatorica,
vol. 37, no. 5. Springer, pp. 887–910, 2017.
ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional
is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5),
887–910.
mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay
Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017,
pp. 887–910, doi:10.1007/s00493-016-3308-y.
short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017)
887–910.
date_created: 2018-12-11T11:50:32Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2025-06-04T08:44:44Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
arxiv:
- '1411.6337'
isi:
- '000418056000005'
intvolume: ' 37'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.6337
month: '10'
oa: 1
oa_version: Submitted Version
page: 887 - 910
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Combinatorica
publication_identifier:
issn:
- 0209-9683
publication_status: published
publisher: Springer
publist_id: '6182'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2017'
...
---
_id: '1180'
abstract:
- lang: eng
text: In this article we define an algebraic vertex of a generalized polyhedron
and show that the set of algebraic vertices is the smallest set of points needed
to define the polyhedron. We prove that the indicator function of a generalized
polytope P is a linear combination of indicator functions of simplices whose vertices
are algebraic vertices of P. We also show that the indicator function of any generalized
polyhedron is a linear combination, with integer coefficients, of indicator functions
of cones with apices at algebraic vertices and line-cones. The concept of an algebraic
vertex is closely related to the Fourier–Laplace transform. We show that a point
v is an algebraic vertex of a generalized polyhedron P if and only if the tangent
cone of P, at v, has non-zero Fourier–Laplace transform.
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Imre
full_name: Bárány, Imre
last_name: Bárány
- first_name: Sinai
full_name: Robins, Sinai
last_name: Robins
citation:
ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026
apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex
polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026
chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of
Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.
ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,”
Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.
ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 308, 627–644.
mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances
in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.
short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.
date_created: 2018-12-11T11:50:34Z
date_published: 2017-02-21T00:00:00Z
date_updated: 2025-06-04T08:45:48Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
arxiv:
- '1508.07594'
isi:
- '000409292900015'
intvolume: ' 308'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07594
month: '02'
oa: 1
oa_version: Submitted Version
page: 627 - 644
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Academic Press
publist_id: '6173'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Algebraic vertices of non-convex polyhedra
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 308
year: '2017'
...
---
OA_type: free access
_id: '1433'
abstract:
- lang: eng
text: Phat is an open-source C. ++ library for the computation of persistent homology
by matrix reduction, targeted towards developers of software for topological data
analysis. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. We provide numerous
different reduction strategies as well as data types to store and manipulate the
boundary matrix. We compare the different combinations through extensive experimental
evaluation and identify optimization techniques that work well in practical situations.
We also compare our software with various other publicly available libraries for
persistent homology.
acknowledgement: Michael Kerber acknowledges support by the Max Planck Center for
Visual Computing and Communications (FKZ-01IMC01 and FKZ-01IM10001). Ulrich Bauer,
Jan Reininghaus, and Hubert Wagner acknowledge support by the EU Project TOPOSYS
(FP7-ICT-318493-STREP).
article_processing_charge: No
article_type: original
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
last_name: Bauer
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Jan
full_name: Reininghaus, Jan
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms
toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008
apa: Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent
homology algorithms toolbox. Journal of Symbolic Computation. Academic
Press. https://doi.org/10.1016/j.jsc.2016.03.008
chicago: Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat
- Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation.
Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.
ieee: U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology
algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic
Press, pp. 76–90, 2017.
ista: Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology
algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.
mla: Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal
of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.
short: U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation
78 (2017) 76–90.
corr_author: '1'
date_created: 2018-12-11T11:51:59Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-10-01T07:39:51Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jsc.2016.03.008
ec_funded: 1
external_id:
isi:
- '000384396000005'
intvolume: ' 78'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jsc.2016.03.008
month: '01'
oa: 1
oa_version: Published Version
page: 76 - 90
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Journal of Symbolic Computation
publication_identifier:
issn:
- ' 0747-7171'
publication_status: published
publisher: Academic Press
publist_id: '5765'
quality_controlled: '1'
related_material:
record:
- id: '10894'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Phat - Persistent homology algorithms toolbox
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 78
year: '2017'
...