---
_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
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.'
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: '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: 2023-09-13T09:13:12Z
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: '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: 2023-09-13T09:34:38Z
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:
- '08954801'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 32
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
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'
...