---
_id: '12544'
abstract:
- lang: eng
text: Geometry is crucial in our efforts to comprehend the structures and dynamics
of biomolecules. For example, volume, surface area, and integrated mean and Gaussian
curvature of the union of balls representing a molecule are used to quantify its
interactions with the water surrounding it in the morphometric implicit solvent
models. The Alpha Shape theory provides an accurate and reliable method for computing
these geometric measures. In this paper, we derive homogeneous formulas for the
expressions of these measures and their derivatives with respect to the atomic
coordinates, and we provide algorithms that implement them into a new software
package, AlphaMol. The only variables in these formulas are the interatomic distances,
making them insensitive to translations and rotations. AlphaMol includes a sequential
algorithm and a parallel algorithm. In the parallel version, we partition the
atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree
algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented
by a buffer zone to account for atoms whose ball representations may partially
cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up
compared to an independent serial implementation when using 32 processors. For
instance, it takes 31 s to compute the geometric measures and derivatives of each
atom in a viral capsid with more than 26 million atoms on 32 Intel processors
running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant
computations, which ultimately limit the impact of using multiple processors.
AlphaMol is available as an OpenSource software.
acknowledgement: "P.K. acknowledges support from the University of California Multicampus
Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant
No.1760485). H.E. acknowledges support from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program, Grant No.
788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31,
and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.\r\nOpen Access
is funded by the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Patrice
full_name: Koehl, Patrice
last_name: Koehl
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean,
and Gaussian curvatures of molecules and their derivatives. Journal of Chemical
Information and Modeling. 2023;63(3):973-985. doi:10.1021/acs.jcim.2c01346
apa: Koehl, P., Akopyan, A., & Edelsbrunner, H. (2023). Computing the volume,
surface area, mean, and Gaussian curvatures of molecules and their derivatives.
Journal of Chemical Information and Modeling. American Chemical Society.
https://doi.org/10.1021/acs.jcim.2c01346
chicago: Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the
Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.”
Journal of Chemical Information and Modeling. American Chemical Society,
2023. https://doi.org/10.1021/acs.jcim.2c01346.
ieee: P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface
area, mean, and Gaussian curvatures of molecules and their derivatives,” Journal
of Chemical Information and Modeling, vol. 63, no. 3. American Chemical Society,
pp. 973–985, 2023.
ista: Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area,
mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical
Information and Modeling. 63(3), 973–985.
mla: Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian
Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information
and Modeling, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85,
doi:10.1021/acs.jcim.2c01346.
short: P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and
Modeling 63 (2023) 973–985.
date_created: 2023-02-12T23:00:59Z
date_published: 2023-02-13T00:00:00Z
date_updated: 2023-08-16T12:22:07Z
day: '13'
ddc:
- '510'
- '540'
department:
- _id: HeEd
doi: 10.1021/acs.jcim.2c01346
ec_funded: 1
external_id:
isi:
- '000920370700001'
pmid:
- '36638318'
file:
- access_level: open_access
checksum: 7d20562269edff1e31b9d6019d4983b0
content_type: application/pdf
creator: dernst
date_created: 2023-08-16T12:21:13Z
date_updated: 2023-08-16T12:21:13Z
file_id: '14070'
file_name: 2023_JCIM_Koehl.pdf
file_size: 8069223
relation: main_file
success: 1
file_date_updated: 2023-08-16T12:21:13Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 973-985
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Journal of Chemical Information and Modeling
publication_identifier:
eissn:
- 1549-960X
issn:
- 1549-9596
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing the volume, surface area, mean, and Gaussian curvatures of molecules
and their derivatives
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: 63
year: '2023'
...
---
_id: '7791'
abstract:
- lang: eng
text: Extending a result of Milena Radnovic and Serge Tabachnikov, we establish
conditionsfor two different non-symmetric norms to define the same billiard reflection
law.
acknowledgement: AA was supported by European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818
Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4
and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169.
Open access funding provided by Institute of Science and Technology (IST Austria).
The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful
discussions.
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: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. When different norms lead to same billiard trajectories?
European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0
apa: Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard
trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0
chicago: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same
Billiard Trajectories?” European Journal of Mathematics. Springer Nature,
2022. https://doi.org/10.1007/s40879-020-00405-0.
ieee: A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,”
European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312,
2022.
ista: Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories?
European Journal of Mathematics. 8(4), 1309–1312.
mla: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard
Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer
Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0.
short: A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.
date_created: 2020-05-03T22:00:48Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2024-02-22T15:58:42Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00405-0
ec_funded: 1
external_id:
arxiv:
- '1912.12685'
file:
- access_level: open_access
checksum: f53e71fd03744075adcd0b8fc1b8423d
content_type: application/pdf
creator: dernst
date_created: 2020-05-04T10:33:42Z
date_updated: 2020-07-14T12:48:03Z
file_id: '7796'
file_name: 2020_EuropMathematics_Akopyan.pdf
file_size: 263926
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1309 - 1312
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: When different norms lead to same billiard trajectories?
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2022'
...
---
_id: '10222'
abstract:
- lang: eng
text: Consider a random set of points on the unit sphere in ℝd, which can be either
uniformly sampled or a Poisson point process. Its convex hull is a random inscribed
polytope, whose boundary approximates the sphere. We focus on the case d = 3,
for which there are elementary proofs and fascinating formulas for metric properties.
In particular, we study the fraction of acute facets, the expected intrinsic volumes,
the total edge length, and the distance to a fixed point. Finally we generalize
the results to the ellipsoid with homeoid density.
acknowledgement: "This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.\r\nWe
are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and
for directing us to relevant references. We also thank to Anton Mellit for a useful
discussion on Bessel functions."
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: 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: Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed
in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459
apa: Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random
polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and
Francis. https://doi.org/10.1080/10586458.2021.1980459
chicago: Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty
of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics.
Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459.
ieee: A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes
inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis,
pp. 1–15, 2021.
ista: Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes
inscribed in the 2-sphere. Experimental Mathematics., 1–15.
mla: Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.”
Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459.
short: A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021)
1–15.
date_created: 2021-11-07T23:01:25Z
date_published: 2021-10-25T00:00:00Z
date_updated: 2023-08-14T11:57:07Z
day: '25'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1080/10586458.2021.1980459
ec_funded: 1
external_id:
arxiv:
- '2007.07783'
isi:
- '000710893500001'
file:
- access_level: open_access
checksum: 3514382e3a1eb87fa6c61ad622874415
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:55:10Z
date_updated: 2023-08-14T11:55:10Z
file_id: '14053'
file_name: 2023_ExperimentalMath_Akopyan.pdf
file_size: 1966019
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:55:10Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1-15
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Experimental Mathematics
publication_identifier:
eissn:
- 1944-950X
issn:
- 1058-6458
publication_status: published
publisher: Taylor and Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: The beauty of random polytopes inscribed in the 2-sphere
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
year: '2021'
...
---
_id: '8338'
abstract:
- lang: eng
text: Canonical parametrisations of classical confocal coordinate systems are introduced
and exploited to construct non-planar analogues of incircular (IC) nets on individual
quadrics and systems of confocal quadrics. Intimate connections with classical
deformations of quadrics that are isometric along asymptotic lines and circular
cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces
of Blaschke type generated by asymptotic and characteristic lines that are diagonally
related to lines of curvature is proved theoretically and established constructively.
Appropriate samplings (grids) of these webs lead to three-dimensional extensions
of non-planar IC nets. Three-dimensional octahedral grids composed of planes and
spatially extending (checkerboard) IC-nets are shown to arise in connection with
systems of confocal quadrics in Minkowski space. In this context, the Laguerre
geometric notion of conical octahedral grids of planes is introduced. The latter
generalise the octahedral grids derived from systems of confocal quadrics in Minkowski
space. An explicit construction of conical octahedral grids is presented. The
results are accompanied by various illustrations which are based on the explicit
formulae provided by the theory.
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by
the Australian Research Council (DP1401000851). A.V.A. was also supported by the
European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (Grant Agreement No. 78818 Alpha).
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
- first_name: Alexander I.
full_name: Bobenko, Alexander I.
last_name: Bobenko
- first_name: Wolfgang K.
full_name: Schief, Wolfgang K.
last_name: Schief
- first_name: Jan
full_name: Techter, Jan
last_name: Techter
citation:
ama: Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal)
quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976.
doi:10.1007/s00454-020-00240-w
apa: Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually
diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w
chicago: Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter.
“On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete
and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w.
ieee: A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal
nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational
Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.
ista: Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets
on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry.
66, 938–976.
mla: Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics
and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66,
Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.
short: A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational
Geometry 66 (2021) 938–976.
date_created: 2020-09-06T22:01:13Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-03-07T14:51:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00240-w
ec_funded: 1
external_id:
arxiv:
- '1908.00856'
isi:
- '000564488500002'
intvolume: ' 66'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1908.00856
month: '10'
oa: 1
oa_version: Preprint
page: 938-976
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2021'
...
---
_id: '8538'
abstract:
- lang: eng
text: We prove some recent experimental observations of Dan Reznik concerning periodic
billiard orbits in ellipses. For example, the sum of cosines of the angles of
a periodic billiard polygon remains constant in the 1-parameter family of such
polygons (that exist due to the Poncelet porism). In our proofs, we use geometric
and complex analytic methods.
acknowledgement: " This paper would not be written if not for Dan Reznik’s curiosity
and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller
for interesting discussions. It is a pleasure to thank the Mathematical Institute
of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy
for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality.
AA was supported by European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported
by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR
191."
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
- first_name: Richard
full_name: Schwartz, Richard
last_name: Schwartz
- first_name: Serge
full_name: Tabachnikov, Serge
last_name: Tabachnikov
citation:
ama: Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European
Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9
apa: Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses
revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9
chicago: Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in
Ellipses Revisited.” European Journal of Mathematics. Springer Nature,
2020. https://doi.org/10.1007/s40879-020-00426-9.
ieee: A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,”
European Journal of Mathematics. Springer Nature, 2020.
ista: Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited.
European Journal of Mathematics.
mla: Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal
of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.
short: A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics
(2020).
date_created: 2020-09-20T22:01:38Z
date_published: 2020-09-09T00:00:00Z
date_updated: 2021-12-02T15:10:17Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00426-9
ec_funded: 1
external_id:
arxiv:
- '2001.02934'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.02934
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Billiards in ellipses revisited
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '74'
abstract:
- lang: eng
text: "We study the Gromov waist in the sense of t-neighborhoods for measures in
the Euclidean space, motivated by the famous theorem of Gromov about
\ the waist of radially symmetric Gaussian measures. In particular, it turns
our possible to extend Gromov’s original result to the case of not necessarily
\ radially symmetric Gaussian measure. We also provide examples of measures
having no t-neighborhood waist property, including a rather wide class\r\nof compactly
supported radially symmetric measures and their maps into the Euclidean space
of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument
\ to produce some estimates of t-neighborhoods of (weighted) volume-critical
submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic
manifolds in the complex projective space. In the appendix of this paper we provide
for reader’s convenience a more detailed explanation of the Caffarelli theorem
that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."
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: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: 'Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial
non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional
Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1'
apa: Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian
measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.),
Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer
Nature. https://doi.org/10.1007/978-3-030-36020-7_1
chicago: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer
Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.
ieee: A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis,
vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.
ista: 'Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis.
vol. 2256, 1–27.'
mla: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer
Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.
short: A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects
of Functional Analysis, Springer Nature, 2020, pp. 1–27.
date_created: 2018-12-11T11:44:29Z
date_published: 2020-06-21T00:00:00Z
date_updated: 2023-08-17T13:48:31Z
day: '21'
department:
- _id: HeEd
- _id: JaMa
doi: 10.1007/978-3-030-36020-7_1
ec_funded: 1
editor:
- first_name: Bo'az
full_name: Klartag, Bo'az
last_name: Klartag
- first_name: Emanuel
full_name: Milman, Emanuel
last_name: Milman
external_id:
arxiv:
- '1808.07350'
isi:
- '000557689300003'
intvolume: ' 2256'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.07350
month: '06'
oa: 1
oa_version: Preprint
page: 1-27
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Geometric Aspects of Functional Analysis
publication_identifier:
eisbn:
- '9783030360207'
eissn:
- '16179692'
isbn:
- '9783030360191'
issn:
- '00758434'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNM
status: public
title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
type: book_chapter
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2256
year: '2020'
...
---
_id: '10867'
abstract:
- lang: eng
text: In this paper we find a tight estimate for Gromov’s waist of the balls in
spaces of constant curvature, deduce the estimates for the balls in Riemannian
manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar
result for normed spaces.
acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.'
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
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International
Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037
apa: Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical
spaces. International Mathematics Research Notices. Oxford University Press.
https://doi.org/10.1093/imrn/rny037
chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and
Spherical Spaces.” International Mathematics Research Notices. Oxford University
Press, 2020. https://doi.org/10.1093/imrn/rny037.
ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,”
International Mathematics Research Notices, vol. 2020, no. 3. Oxford University
Press, pp. 669–697, 2020.
ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces.
International Mathematics Research Notices. 2020(3), 669–697.
mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical
Spaces.” International Mathematics Research Notices, vol. 2020, no. 3,
Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.
short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020)
669–697.
date_created: 2022-03-18T11:39:30Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-24T14:19:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/imrn/rny037
external_id:
arxiv:
- '1702.07513'
isi:
- '000522852700002'
intvolume: ' 2020'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.07513
month: '02'
oa: 1
oa_version: Preprint
page: 669-697
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Waist of balls in hyperbolic and spherical spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_id: '9157'
abstract:
- lang: eng
text: Representing an atom by a solid sphere in 3-dimensional Euclidean space, we
get the space-filling diagram of a molecule by taking the union. Molecular dynamics
simulates its motion subject to bonds and other forces, including the solvation
free energy. The morphometric approach [12, 17] writes the latter as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted mean curvature. Together with the derivatives of the weighted volume
in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this
yields the derivative of the morphometric expression of the solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of the weighted\r\ncurvature derivatives for the purpose of improving molecular
dynamics simulations and for his continued encouragement. They also thank Patrice
Koehl for the implementation of the formulas and for his encouragement and advise
along the road. Finally, they thank two anonymous reviewers for their constructive
criticism.\r\nThis project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 78818 Alpha). It is also 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)."
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
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling
diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0100
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of
a space-filling diagram,” Computational and Mathematical Biophysics, vol.
8, no. 1. De Gruyter, pp. 51–67, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of
a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative
of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 51–67.
date_created: 2021-02-17T15:13:01Z
date_published: 2020-06-20T00:00:00Z
date_updated: 2023-10-17T12:34:51Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0100
ec_funded: 1
file:
- access_level: open_access
checksum: cea41de9937d07a3b927d71ee8b4e432
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:56:24Z
date_updated: 2021-02-19T13:56:24Z
file_id: '9171'
file_name: 2020_CompMathBiophysics_Akopyan2.pdf
file_size: 562359
relation: main_file
success: 1
file_date_updated: 2021-02-19T13:56:24Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 51-67
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
publication: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted mean curvature derivative of a space-filling diagram
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: 8
year: '2020'
...
---
_id: '9156'
abstract:
- lang: eng
text: The morphometric approach [11, 14] writes the solvation free energy as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted Gaussian curvature. Together with the derivatives of the weighted
volume in [7], the weighted area in [4], and the weighted mean curvature in [1],
this yields the derivative of the morphometric expression of solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics
simulations. They also thank Patrice Koehl for the implementation of the formulas
and for his encouragement and advise along the road. Finally, they thank two anonymous
reviewers for their constructive criticism.\r\nThis project has received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 78818 Alpha). It is also 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)."
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
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a
space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88.
doi:10.1515/cmb-2020-0101
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature
derivative of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0101
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative
of a space-filling diagram,” Computational and Mathematical Biophysics,
vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 74–88.
date_created: 2021-02-17T15:12:44Z
date_published: 2020-07-21T00:00:00Z
date_updated: 2023-10-17T12:35:10Z
day: '21'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0101
ec_funded: 1
external_id:
arxiv:
- '1908.06777'
file:
- access_level: open_access
checksum: ca43a7440834eab6bbea29c59b56ef3a
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:33:19Z
date_updated: 2021-02-19T13:33:19Z
file_id: '9170'
file_name: 2020_CompMathBiophysics_Akopyan.pdf
file_size: 707452
relation: main_file
success: 1
file_date_updated: 2021-02-19T13:33:19Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 74-88
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
publication: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted Gaussian curvature derivative of a space-filling diagram
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: 8
year: '2020'
...
---
_id: '6050'
abstract:
- lang: eng
text: 'We answer a question of David Hilbert: given two circles it is not possible
in general to construct their centers using only a straightedge. On the other
hand, we give infinitely many families of pairs of circles for which such construction
is possible. '
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: Roman
full_name: Fedorov, Roman
last_name: Fedorov
citation:
ama: Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of
the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240
apa: Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge.
Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240
chicago: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.
ieee: A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings
of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.
ista: Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings
of the American Mathematical Society. 147, 91–102.
mla: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society, vol. 147, AMS, 2019,
pp. 91–102, doi:10.1090/proc/14240.
short: A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society
147 (2019) 91–102.
date_created: 2019-02-24T22:59:19Z
date_published: 2019-01-01T00:00:00Z
date_updated: 2023-08-24T14:48:59Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/14240
external_id:
arxiv:
- '1709.02562'
isi:
- '000450363900008'
intvolume: ' 147'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.02562
month: '01'
oa: 1
oa_version: Preprint
page: 91-102
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: Two circles and only a straightedge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 147
year: '2019'
...
---
_id: '6419'
abstract:
- lang: eng
text: Characterizing the fitness landscape, a representation of fitness for a large
set of genotypes, is key to understanding how genetic information is interpreted
to create functional organisms. Here we determined the evolutionarily-relevant
segment of the fitness landscape of His3, a gene coding for an enzyme in the histidine
synthesis pathway, focusing on combinations of amino acid states found at orthologous
sites of extant species. Just 15% of amino acids found in yeast His3 orthologues
were always neutral while the impact on fitness of the remaining 85% depended
on the genetic background. Furthermore, at 67% of sites, amino acid replacements
were under sign epistasis, having both strongly positive and negative effect in
different genetic backgrounds. 46% of sites were under reciprocal sign epistasis.
The fitness impact of amino acid replacements was influenced by only a few genetic
backgrounds but involved interaction of multiple sites, shaping a rugged fitness
landscape in which many of the shortest paths between highly fit genotypes are
inaccessible.
article_number: e1008079
article_processing_charge: No
author:
- first_name: Victoria
full_name: Pokusaeva, Victoria
id: 3184041C-F248-11E8-B48F-1D18A9856A87
last_name: Pokusaeva
orcid: 0000-0001-7660-444X
- first_name: Dinara R.
full_name: Usmanova, Dinara R.
last_name: Usmanova
- first_name: Ekaterina V.
full_name: Putintseva, Ekaterina V.
last_name: Putintseva
- first_name: Lorena
full_name: Espinar, Lorena
last_name: Espinar
- first_name: Karen
full_name: Sarkisyan, Karen
id: 39A7BF80-F248-11E8-B48F-1D18A9856A87
last_name: Sarkisyan
orcid: 0000-0002-5375-6341
- first_name: Alexander S.
full_name: Mishin, Alexander S.
last_name: Mishin
- first_name: Natalya S.
full_name: Bogatyreva, Natalya S.
last_name: Bogatyreva
- first_name: Dmitry
full_name: Ivankov, Dmitry
id: 49FF1036-F248-11E8-B48F-1D18A9856A87
last_name: Ivankov
- 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: Inna S.
full_name: Povolotskaya, Inna S.
last_name: Povolotskaya
- first_name: Guillaume J.
full_name: Filion, Guillaume J.
last_name: Filion
- first_name: Lucas B.
full_name: Carey, Lucas B.
last_name: Carey
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
citation:
ama: Pokusaeva V, Usmanova DR, Putintseva EV, et al. An experimental assay of the
interactions of amino acids from orthologous sequences shaping a complex fitness
landscape. PLoS Genetics. 2019;15(4). doi:10.1371/journal.pgen.1008079
apa: Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan,
K., Mishin, A. S., … Kondrashov, F. (2019). An experimental assay of the interactions
of amino acids from orthologous sequences shaping a complex fitness landscape.
PLoS Genetics. Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079
chicago: Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena
Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “An
Experimental Assay of the Interactions of Amino Acids from Orthologous Sequences
Shaping a Complex Fitness Landscape.” PLoS Genetics. Public Library of
Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.
ieee: V. Pokusaeva et al., “An experimental assay of the interactions of
amino acids from orthologous sequences shaping a complex fitness landscape,” PLoS
Genetics, vol. 15, no. 4. Public Library of Science, 2019.
ista: Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS,
Bogatyreva NS, Ivankov D, Akopyan A, Avvakumov S, Povolotskaya IS, Filion GJ,
Carey LB, Kondrashov F. 2019. An experimental assay of the interactions of amino
acids from orthologous sequences shaping a complex fitness landscape. PLoS Genetics.
15(4), e1008079.
mla: Pokusaeva, Victoria, et al. “An Experimental Assay of the Interactions of Amino
Acids from Orthologous Sequences Shaping a Complex Fitness Landscape.” PLoS
Genetics, vol. 15, no. 4, e1008079, Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079.
short: V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S.
Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, S. Avvakumov, I.S. Povolotskaya,
G.J. Filion, L.B. Carey, F. Kondrashov, PLoS Genetics 15 (2019).
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title: An experimental assay of the interactions of amino acids from orthologous sequences
shaping a complex fitness landscape
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)
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orcid: 0000-0001-7660-444X
- first_name: Dinara R.
full_name: Usmanova, Dinara R.
last_name: Usmanova
- first_name: Ekaterina V.
full_name: Putintseva, Ekaterina V.
last_name: Putintseva
- first_name: Lorena
full_name: Espinar, Lorena
last_name: Espinar
- first_name: Karen
full_name: Sarkisyan, Karen
id: 39A7BF80-F248-11E8-B48F-1D18A9856A87
last_name: Sarkisyan
orcid: 0000-0002-5375-6341
- first_name: Alexander S.
full_name: Mishin, Alexander S.
last_name: Mishin
- first_name: Natalya S.
full_name: Bogatyreva, Natalya S.
last_name: Bogatyreva
- first_name: Dmitry
full_name: Ivankov, Dmitry
id: 49FF1036-F248-11E8-B48F-1D18A9856A87
last_name: Ivankov
- 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: Inna S.
full_name: Povolotskaya, Inna S.
last_name: Povolotskaya
- first_name: Guillaume J.
full_name: Filion, Guillaume J.
last_name: Filion
- first_name: Lucas B.
full_name: Carey, Lucas B.
last_name: Carey
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
citation:
ama: Pokusaeva V, Usmanova DR, Putintseva EV, et al. A statistical summary of segment
libraries and sequencing results. 2019. doi:10.1371/journal.pgen.1008079.s011
apa: Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan,
K., Mishin, A. S., … Kondrashov, F. (2019). A statistical summary of segment libraries
and sequencing results. Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079.s011
chicago: Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena
Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “A
Statistical Summary of Segment Libraries and Sequencing Results.” Public Library
of Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.s011.
ieee: V. Pokusaeva et al., “A statistical summary of segment libraries and
sequencing results.” Public Library of Science, 2019.
ista: Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS,
Bogatyreva NS, Ivankov D, Akopyan A, Avvakumov S, Povolotskaya IS, Filion GJ,
Carey LB, Kondrashov F. 2019. A statistical summary of segment libraries and sequencing
results, Public Library of Science, 10.1371/journal.pgen.1008079.s011.
mla: Pokusaeva, Victoria, et al. A Statistical Summary of Segment Libraries and
Sequencing Results. Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079.s011.
short: V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S.
Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, S. Avvakumov, I.S. Povolotskaya,
G.J. Filion, L.B. Carey, F. Kondrashov, (2019).
date_created: 2021-08-06T08:50:15Z
date_published: 2019-04-10T00:00:00Z
date_updated: 2023-08-25T10:30:36Z
day: '10'
department:
- _id: FyKo
doi: 10.1371/journal.pgen.1008079.s011
month: '04'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '6419'
relation: used_in_publication
status: public
status: public
title: A statistical summary of segment libraries and sequencing results
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2019'
...
---
_id: '9797'
article_processing_charge: No
author:
- first_name: Victoria
full_name: Pokusaeva, Victoria
id: 3184041C-F248-11E8-B48F-1D18A9856A87
last_name: Pokusaeva
orcid: 0000-0001-7660-444X
- first_name: Dinara R.
full_name: Usmanova, Dinara R.
last_name: Usmanova
- first_name: Ekaterina V.
full_name: Putintseva, Ekaterina V.
last_name: Putintseva
- first_name: Lorena
full_name: Espinar, Lorena
last_name: Espinar
- first_name: Karen
full_name: Sarkisyan, Karen
id: 39A7BF80-F248-11E8-B48F-1D18A9856A87
last_name: Sarkisyan
orcid: 0000-0002-5375-6341
- first_name: Alexander S.
full_name: Mishin, Alexander S.
last_name: Mishin
- first_name: Natalya S.
full_name: Bogatyreva, Natalya S.
last_name: Bogatyreva
- first_name: Dmitry
full_name: Ivankov, Dmitry
id: 49FF1036-F248-11E8-B48F-1D18A9856A87
last_name: Ivankov
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Inna S.
full_name: Povolotskaya, Inna S.
last_name: Povolotskaya
- first_name: Guillaume J.
full_name: Filion, Guillaume J.
last_name: Filion
- first_name: Lucas B.
full_name: Carey, Lucas B.
last_name: Carey
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
citation:
ama: Pokusaeva V, Usmanova DR, Putintseva EV, et al. A statistical summary of segment
libraries and sequencing results. 2019. doi:10.1371/journal.pgen.1008079.s011
apa: Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan,
K., Mishin, A. S., … Kondrashov, F. (2019). A statistical summary of segment libraries
and sequencing results. Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079.s011
chicago: Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena
Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “A
Statistical Summary of Segment Libraries and Sequencing Results.” Public Library
of Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.s011.
ieee: V. Pokusaeva et al., “A statistical summary of segment libraries and
sequencing results.” Public Library of Science, 2019.
ista: Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS,
Bogatyreva NS, Ivankov D, Akopyan A, Povolotskaya IS, Filion GJ, Carey LB, Kondrashov
F. 2019. A statistical summary of segment libraries and sequencing results, Public
Library of Science, 10.1371/journal.pgen.1008079.s011.
mla: Pokusaeva, Victoria, et al. A Statistical Summary of Segment Libraries and
Sequencing Results. Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079.s011.
short: V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S.
Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, I.S. Povolotskaya, G.J. Filion,
L.B. Carey, F. Kondrashov, (2019).
date_created: 2021-08-06T11:08:20Z
date_published: 2019-04-10T00:00:00Z
date_updated: 2023-08-25T10:30:36Z
day: '10'
department:
- _id: FyKo
doi: 10.1371/journal.pgen.1008079.s011
month: '04'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '6419'
relation: used_in_publication
status: public
status: public
title: A statistical summary of segment libraries and sequencing results
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2019'
...
---
_id: '9789'
article_processing_charge: No
author:
- first_name: Victoria
full_name: Pokusaeva, Victoria
id: 3184041C-F248-11E8-B48F-1D18A9856A87
last_name: Pokusaeva
orcid: 0000-0001-7660-444X
- first_name: Dinara R.
full_name: Usmanova, Dinara R.
last_name: Usmanova
- first_name: Ekaterina V.
full_name: Putintseva, Ekaterina V.
last_name: Putintseva
- first_name: Lorena
full_name: Espinar, Lorena
last_name: Espinar
- first_name: Karen
full_name: Sarkisyan, Karen
id: 39A7BF80-F248-11E8-B48F-1D18A9856A87
last_name: Sarkisyan
orcid: 0000-0002-5375-6341
- first_name: Alexander S.
full_name: Mishin, Alexander S.
last_name: Mishin
- first_name: Natalya S.
full_name: Bogatyreva, Natalya S.
last_name: Bogatyreva
- first_name: Dmitry
full_name: Ivankov, Dmitry
id: 49FF1036-F248-11E8-B48F-1D18A9856A87
last_name: Ivankov
- 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: Inna S.
full_name: Povolotskaya, Inna S.
last_name: Povolotskaya
- first_name: Guillaume J.
full_name: Filion, Guillaume J.
last_name: Filion
- first_name: Lucas B.
full_name: Carey, Lucas B.
last_name: Carey
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
citation:
ama: Pokusaeva V, Usmanova DR, Putintseva EV, et al. Multiple alignment of His3
orthologues. 2019. doi:10.1371/journal.pgen.1008079.s010
apa: Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan,
K., Mishin, A. S., … Kondrashov, F. (2019). Multiple alignment of His3 orthologues.
Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079.s010
chicago: Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena
Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “Multiple
Alignment of His3 Orthologues.” Public Library of Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.s010.
ieee: V. Pokusaeva et al., “Multiple alignment of His3 orthologues.” Public
Library of Science, 2019.
ista: Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS,
Bogatyreva NS, Ivankov D, Akopyan A, Avvakumov S, Povolotskaya IS, Filion GJ,
Carey LB, Kondrashov F. 2019. Multiple alignment of His3 orthologues, Public Library
of Science, 10.1371/journal.pgen.1008079.s010.
mla: Pokusaeva, Victoria, et al. Multiple Alignment of His3 Orthologues.
Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079.s010.
short: V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S.
Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, S. Avvakumov, I.S. Povolotskaya,
G.J. Filion, L.B. Carey, F. Kondrashov, (2019).
date_created: 2021-08-06T08:38:50Z
date_published: 2019-04-10T00:00:00Z
date_updated: 2023-08-25T10:30:36Z
day: '10'
department:
- _id: FyKo
doi: 10.1371/journal.pgen.1008079.s010
month: '04'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '6419'
relation: used_in_publication
status: public
status: public
title: Multiple alignment of His3 orthologues
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2019'
...
---
_id: '6634'
abstract:
- lang: eng
text: In this paper we prove several new results around Gromov's waist theorem.
We give a simple proof of Vaaler's theorem on sections of the unit cube using
the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective
spaces, flat tori, convex bodies in Euclidean space; and establish waist-type
results in terms of the Hausdorff measure.
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: Alfredo
full_name: Hubard, Alfredo
last_name: Hubard
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different
spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490.
doi:10.12775/TMNA.2019.008
apa: Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for
the waists of different spaces. Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008
chicago: Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds
for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.
ieee: A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists
of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53,
no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.
ista: Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists
of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.
mla: Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different
Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka
Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.
short: A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis
53 (2019) 457–490.
date_created: 2019-07-14T21:59:19Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-08-29T06:32:48Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2019.008
ec_funded: 1
external_id:
arxiv:
- '1612.06926'
isi:
- '000472541600004'
intvolume: ' 53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.06926
month: '06'
oa: 1
oa_version: Preprint
page: 457-490
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Akademicka Platforma Czasopism
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower and upper bounds for the waists of different spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2019'
...
---
_id: '6793'
abstract:
- lang: eng
text: The Regge symmetry is a set of remarkable relations between two tetrahedra
whose edge lengths are related in a simple fashion. It was first discovered as
a consequence of an asymptotic formula in mathematical physics. Here, we give
a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic
geometry.
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
- first_name: Ivan
full_name: Izmestiev, Ivan
last_name: Izmestiev
citation:
ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli
formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775.
doi:10.1112/blms.12276
apa: Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics,
and the Schläfli formula. Bulletin of the London Mathematical Society.
London Mathematical Society. https://doi.org/10.1112/blms.12276
chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society.
London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.
ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the
Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51,
no. 5. London Mathematical Society, pp. 765–775, 2019.
ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the
Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.
mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society,
vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.
short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51
(2019) 765–775.
date_created: 2019-08-11T21:59:23Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-29T07:08:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12276
ec_funded: 1
external_id:
arxiv:
- '1903.04929'
isi:
- '000478560200001'
intvolume: ' 51'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.04929
month: '10'
oa: 1
oa_version: Preprint
page: 765-775
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- '14692120'
issn:
- '00246093'
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Regge symmetry, confocal conics, and the Schläfli formula
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 51
year: '2019'
...
---
_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'
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- '000431418800004'
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call_identifier: FP7
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publication: Geometriae Dedicata
publication_status: published
publisher: Springer
publist_id: '7014'
quality_controlled: '1'
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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: '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
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: '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: '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: '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'
...
---
_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
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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intvolume: ' 6'
isi: 1
language:
- iso: eng
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:
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- 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: '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)
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type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 59
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
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: '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: '1180'
abstract:
- lang: eng
text: In this article we define an algebraic vertex of a generalized polyhedron
and show that the set of algebraic vertices is the smallest set of points needed
to define the polyhedron. We prove that the indicator function of a generalized
polytope P is a linear combination of indicator functions of simplices whose vertices
are algebraic vertices of P. We also show that the indicator function of any generalized
polyhedron is a linear combination, with integer coefficients, of indicator functions
of cones with apices at algebraic vertices and line-cones. The concept of an algebraic
vertex is closely related to the Fourier–Laplace transform. We show that a point
v is an algebraic vertex of a generalized polyhedron P if and only if the tangent
cone of P, at v, has non-zero Fourier–Laplace transform.
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Imre
full_name: Bárány, Imre
last_name: Bárány
- first_name: Sinai
full_name: Robins, Sinai
last_name: Robins
citation:
ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026
apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex
polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026
chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of
Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.
ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,”
Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.
ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 308, 627–644.
mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances
in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.
short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.
date_created: 2018-12-11T11:50:34Z
date_published: 2017-02-21T00:00:00Z
date_updated: 2023-09-20T11:21:27Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
isi:
- '000409292900015'
intvolume: ' 308'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07594
month: '02'
oa: 1
oa_version: Submitted Version
page: 627 - 644
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Advances in Mathematics
publication_identifier:
issn:
- '00018708'
publication_status: published
publisher: Academic Press
publist_id: '6173'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Algebraic vertices of non-convex polyhedra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 308
year: '2017'
...
---
_id: '909'
abstract:
- lang: eng
text: We study the lengths of curves passing through a fixed number of points on
the boundary of a convex shape in the plane. We show that, for any convex shape
K, there exist four points on the boundary of K such that the length of any curve
passing through these points is at least half of the perimeter of K. It is also
shown that the same statement does not remain valid with the additional constraint
that the points are extreme points of K. Moreover, the factor ½ cannot
be achieved with any fixed number of extreme points. We conclude the paper with
a few other inequalities related to the perimeter of a convex shape.
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Vladislav
full_name: Vysotsky, Vladislav
last_name: Vysotsky
citation:
ama: Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points
of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596.
doi:10.4169/amer.math.monthly.124.7.588
apa: Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through
boundary points of a planar convex shape. The American Mathematical Monthly.
Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588
chicago: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.
ieee: A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary
points of a planar convex shape,” The American Mathematical Monthly, vol.
124, no. 7. Mathematical Association of America, pp. 588–596, 2017.
ista: Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary
points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.
mla: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96,
doi:10.4169/amer.math.monthly.124.7.588.
short: A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.
date_created: 2018-12-11T11:49:09Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-10-17T11:24:57Z
day: '01'
department:
- _id: HeEd
doi: 10.4169/amer.math.monthly.124.7.588
ec_funded: 1
external_id:
arxiv:
- '1605.07997'
isi:
- '000413947300002'
intvolume: ' 124'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.07997
month: '01'
oa: 1
oa_version: Submitted Version
page: 588 - 596
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: The American Mathematical Monthly
publication_identifier:
issn:
- '00029890'
publication_status: published
publisher: Mathematical Association of America
publist_id: '6534'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the lengths of curves passing through boundary points of a planar convex
shape
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 124
year: '2017'
...
---
_id: '1330'
abstract:
- lang: eng
text: In this paper we investigate the existence of closed billiard trajectories
in not necessarily smooth convex bodies. In particular, we show that if a body
K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K
is acute (in a certain sense), then there is a closed billiard trajectory in K.
acknowledgement: Supported by People Programme (Marie Curie Actions) of the European
Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734].
Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a
ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part
by the Moebius Contest Foundation for Young Scientists, and in part by the Simons
Foundation.
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
citation:
ama: Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel
Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z
apa: Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute
angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z
chicago: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with
Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.
ieee: A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,”
Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845,
2016.
ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles.
Israel Journal of Mathematics. 216(2), 833–845.
mla: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute
Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016,
pp. 833–45, doi:10.1007/s11856-016-1429-z.
short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.
date_created: 2018-12-11T11:51:24Z
date_published: 2016-10-15T00:00:00Z
date_updated: 2021-01-12T06:49:56Z
day: '15'
department:
- _id: HeEd
doi: 10.1007/s11856-016-1429-z
ec_funded: 1
intvolume: ' 216'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1506.06014
month: '10'
oa: 1
oa_version: Preprint
page: 833 - 845
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Israel Journal of Mathematics
publication_status: published
publisher: Springer
publist_id: '5938'
quality_controlled: '1'
scopus_import: 1
status: public
title: Billiards in convex bodies with acute angles
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 216
year: '2016'
...
---
_id: '1360'
abstract:
- lang: eng
text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard
trajectories in convex bodies, when the length is measured with a (possibly asymmetric)
norm. We prove a lower bound for the length of the shortest closed billiard trajectory,
related to the non-symmetric Mahler problem. With this technique we are able to
give short and elementary proofs to some known results. '
acknowledgement: The first and third authors were supported by the Dynasty Foundation.
The first, second and third authors were supported by the Russian Foundation for
Basic Re- search grant 15-31-20403 (mol a ved).
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
- first_name: Anastasia
full_name: Sharipova, Anastasia
last_name: Sharipova
citation:
ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed
billiard trajectories in asymmetric normed spaces. Proceedings of the American
Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062
apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary
approach to closed billiard trajectories in asymmetric normed spaces. Proceedings
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062
chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova.
“Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2016. https://doi.org/10.1090/proc/13062.
ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach
to closed billiard trajectories in asymmetric normed spaces,” Proceedings of
the American Mathematical Society, vol. 144, no. 10. American Mathematical
Society, pp. 4501–4513, 2016.
ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach
to closed billiard trajectories in asymmetric normed spaces. Proceedings of the
American Mathematical Society. 144(10), 4501–4513.
mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories
in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society,
vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.
short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American
Mathematical Society 144 (2016) 4501–4513.
date_created: 2018-12-11T11:51:34Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:50:09Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
intvolume: ' 144'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.0442
month: '10'
oa: 1
oa_version: Preprint
page: 4501 - 4513
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5885'
quality_controlled: '1'
scopus_import: 1
status: public
title: Elementary approach to closed billiard trajectories in asymmetric normed spaces
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1710'
abstract:
- lang: eng
text: 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by
a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles
incident on the hollow. It is assumed that u satisfies the so-called single impact
condition (SIC): each incident particle is elastically reflected by graph(u) and
goes away without hitting the graph of u anymore. We solve the problem: find the
function u minimizing the force of resistance created by the flow. We show that
the graph of the minimizer is formed by two arcs of parabolas symmetric to each
other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals
1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This
result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014),
pp. 2730-2742] stating in particular that the minimal resistance of a hollow in
higher dimensions equals 0.5. We additionally consider a similar problem of minimal
resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1
is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x =
(x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow
is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides
with 0.6435 when d = 1) and converges to 0.5 as d → ∞.'
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: Plakhov, Alexander
last_name: Plakhov
citation:
ama: Akopyan A, Plakhov A. Minimal resistance of curves under the single impact
assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769.
doi:10.1137/140993843
apa: Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the
single impact assumption. Society for Industrial and Applied Mathematics.
SIAM. https://doi.org/10.1137/140993843
chicago: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves
under the Single Impact Assumption.” Society for Industrial and Applied Mathematics.
SIAM, 2015. https://doi.org/10.1137/140993843.
ieee: A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single
impact assumption,” Society for Industrial and Applied Mathematics, vol.
47, no. 4. SIAM, pp. 2754–2769, 2015.
ista: Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single
impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.
mla: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under
the Single Impact Assumption.” Society for Industrial and Applied Mathematics,
vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843.
short: A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47
(2015) 2754–2769.
date_created: 2018-12-11T11:53:36Z
date_published: 2015-07-14T00:00:00Z
date_updated: 2021-01-12T06:52:41Z
day: '14'
department:
- _id: HeEd
doi: 10.1137/140993843
ec_funded: 1
intvolume: ' 47'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1410.3736
month: '07'
oa: 1
oa_version: Preprint
page: 2754 - 2769
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Society for Industrial and Applied Mathematics
publication_status: published
publisher: SIAM
publist_id: '5423'
quality_controlled: '1'
scopus_import: 1
status: public
title: Minimal resistance of curves under the single impact assumption
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
year: '2015'
...
---
_id: '1828'
abstract:
- lang: eng
text: We construct a non-linear Markov process connected with a biological model
of a bacterial genome recombination. The description of invariant measures of
this process gives us the solution of one problem in elementary probability theory.
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: Sergey
full_name: Pirogov, Sergey
last_name: Pirogov
- first_name: Aleksandr
full_name: Rybko, Aleksandr
last_name: Rybko
citation:
ama: Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination
process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5
apa: Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic
recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5
chicago: Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures
of Genetic Recombination Process.” Journal of Statistical Physics. Springer,
2015. https://doi.org/10.1007/s10955-015-1238-5.
ieee: A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination
process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp.
163–167, 2015.
ista: Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination
process. Journal of Statistical Physics. 160(1), 163–167.
mla: Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.”
Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67,
doi:10.1007/s10955-015-1238-5.
short: A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015)
163–167.
date_created: 2018-12-11T11:54:14Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2021-01-12T06:53:28Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10955-015-1238-5
ec_funded: 1
intvolume: ' 160'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: arxiv.org/abs/1406.5313
month: '07'
oa: 1
oa_version: Preprint
page: 163 - 167
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '5276'
quality_controlled: '1'
scopus_import: 1
status: public
title: Invariant measures of genetic recombination process
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 160
year: '2015'
...