[{"status":"public","external_id":{"isi":["000920370700001"],"pmid":["36638318"]},"citation":{"ama":"Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. <i>Journal of Chemical Information and Modeling</i>. 2023;63(3):973-985. doi:<a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">10.1021/acs.jcim.2c01346</a>","apa":"Koehl, P., Akopyan, A., &#38; Edelsbrunner, H. (2023). Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. <i>Journal of Chemical Information and Modeling</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">https://doi.org/10.1021/acs.jcim.2c01346</a>","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.” <i>Journal of Chemical Information and Modeling</i>, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85, doi:<a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">10.1021/acs.jcim.2c01346</a>.","chicago":"Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” <i>Journal of Chemical Information and Modeling</i>. American Chemical Society, 2023. <a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">https://doi.org/10.1021/acs.jcim.2c01346</a>.","ieee":"P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives,” <i>Journal of Chemical Information and Modeling</i>, vol. 63, no. 3. American Chemical Society, pp. 973–985, 2023.","short":"P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985."},"intvolume":"        63","has_accepted_license":"1","publication_status":"published","oa":1,"date_published":"2023-02-13T00:00:00Z","ddc":["510","540"],"year":"2023","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).","_id":"12544","month":"02","oa_version":"Published Version","type":"journal_article","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."}],"date_updated":"2023-08-16T12:22:07Z","page":"973-985","file_date_updated":"2023-08-16T12:21:13Z","date_created":"2023-02-12T23:00:59Z","volume":63,"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"issue":"3","language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"eissn":["1549-960X"],"issn":["1549-9596"]},"quality_controlled":"1","doi":"10.1021/acs.jcim.2c01346","department":[{"_id":"HeEd"}],"pmid":1,"publisher":"American Chemical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"scopus_import":"1","ec_funded":1,"article_processing_charge":"No","publication":"Journal of Chemical Information and Modeling","day":"13","file":[{"content_type":"application/pdf","relation":"main_file","file_size":8069223,"creator":"dernst","success":1,"file_name":"2023_JCIM_Koehl.pdf","date_created":"2023-08-16T12:21:13Z","access_level":"open_access","date_updated":"2023-08-16T12:21:13Z","file_id":"14070","checksum":"7d20562269edff1e31b9d6019d4983b0"}],"author":[{"last_name":"Koehl","first_name":"Patrice","full_name":"Koehl, Patrice"},{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"title":"Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives"},{"status":"public","external_id":{"arxiv":["1912.12685"]},"citation":{"ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. 2022;8(4):1309-1312. doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>","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?” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>.","apa":"Akopyan, A., &#38; Karasev, R. (2022). When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” <i>European Journal of Mathematics</i>, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022.","chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312."},"intvolume":"         8","has_accepted_license":"1","oa":1,"publication_status":"published","ddc":["510"],"date_published":"2022-12-01T00:00:00Z","year":"2022","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.","_id":"7791","oa_version":"Published Version","type":"journal_article","month":"12","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."}],"date_updated":"2024-02-22T15:58:42Z","page":"1309 - 1312","file_date_updated":"2020-07-14T12:48:03Z","date_created":"2020-05-03T22:00:48Z","volume":8,"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"issue":"4","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"quality_controlled":"1","doi":"10.1007/s40879-020-00405-0","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","ec_funded":1,"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","publication":"European Journal of Mathematics","file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":263926,"file_name":"2020_EuropMathematics_Akopyan.pdf","access_level":"open_access","date_created":"2020-05-04T10:33:42Z","checksum":"f53e71fd03744075adcd0b8fc1b8423d","date_updated":"2020-07-14T12:48:03Z","file_id":"7796"}],"day":"01","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"title":"When different norms lead to same billiard trajectories?","arxiv":1},{"volume":66,"date_created":"2020-09-06T22:01:13Z","page":"938-976","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."}],"date_updated":"2024-03-07T14:51:11Z","month":"10","type":"journal_article","oa_version":"Preprint","_id":"8338","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).","year":"2021","date_published":"2021-10-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1908.00856","open_access":"1"}],"oa":1,"publication_status":"published","intvolume":"        66","citation":{"apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., &#38; Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00240-w\">https://doi.org/10.1007/s00454-020-00240-w</a>","mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” <i>Discrete and Computational Geometry</i>, vol. 66, Springer Nature, 2021, pp. 938–76, doi:<a href=\"https://doi.org/10.1007/s00454-020-00240-w\">10.1007/s00454-020-00240-w</a>.","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.","ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. <i>Discrete and Computational Geometry</i>. 2021;66:938-976. doi:<a href=\"https://doi.org/10.1007/s00454-020-00240-w\">10.1007/s00454-020-00240-w</a>","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00240-w\">https://doi.org/10.1007/s00454-020-00240-w</a>.","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” <i>Discrete and Computational Geometry</i>, vol. 66. Springer Nature, pp. 938–976, 2021."},"status":"public","external_id":{"arxiv":["1908.00856"],"isi":["000564488500002"]},"arxiv":1,"title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","author":[{"first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"last_name":"Bobenko","first_name":"Alexander I.","full_name":"Bobenko, Alexander I."},{"full_name":"Schief, Wolfgang K.","last_name":"Schief","first_name":"Wolfgang K."},{"full_name":"Techter, Jan","last_name":"Techter","first_name":"Jan"}],"day":"01","publication":"Discrete and Computational Geometry","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","article_type":"original","publisher":"Springer Nature","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"doi":"10.1007/s00454-020-00240-w","quality_controlled":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}]},{"title":"The beauty of random polytopes inscribed in the 2-sphere","arxiv":1,"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy"},{"first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko"}],"file":[{"date_created":"2023-08-14T11:55:10Z","access_level":"open_access","file_id":"14053","date_updated":"2023-08-14T11:55:10Z","checksum":"3514382e3a1eb87fa6c61ad622874415","file_size":1966019,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_name":"2023_ExperimentalMath_Akopyan.pdf","success":1}],"day":"25","publication":"Experimental Mathematics","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Taylor and Francis","department":[{"_id":"HeEd"}],"doi":"10.1080/10586458.2021.1980459","quality_controlled":"1","publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"file_date_updated":"2023-08-14T11:55:10Z","date_created":"2021-11-07T23:01:25Z","page":"1-15","month":"10","type":"journal_article","oa_version":"Published Version","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."}],"date_updated":"2023-08-14T11:57:07Z","_id":"10222","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.","year":"2021","ddc":["510"],"date_published":"2021-10-25T00:00:00Z","publication_status":"published","oa":1,"has_accepted_license":"1","citation":{"apa":"Akopyan, A., Edelsbrunner, H., &#38; Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. <i>Experimental Mathematics</i>. Taylor and Francis. <a href=\"https://doi.org/10.1080/10586458.2021.1980459\">https://doi.org/10.1080/10586458.2021.1980459</a>","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.” <i>Experimental Mathematics</i>, Taylor and Francis, 2021, pp. 1–15, doi:<a href=\"https://doi.org/10.1080/10586458.2021.1980459\">10.1080/10586458.2021.1980459</a>.","ama":"Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. <i>Experimental Mathematics</i>. 2021:1-15. doi:<a href=\"https://doi.org/10.1080/10586458.2021.1980459\">10.1080/10586458.2021.1980459</a>","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.","chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” <i>Experimental Mathematics</i>. Taylor and Francis, 2021. <a href=\"https://doi.org/10.1080/10586458.2021.1980459\">https://doi.org/10.1080/10586458.2021.1980459</a>.","ieee":"A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” <i>Experimental Mathematics</i>. Taylor and Francis, pp. 1–15, 2021."},"external_id":{"arxiv":["2007.07783"],"isi":["000710893500001"]},"status":"public"},{"date_published":"2020-02-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.07513"}],"publication_status":"published","oa":1,"intvolume":"      2020","citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>.","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","apa":"Akopyan, A., &#38; Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. 2020;2020(3):669-697. doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2020. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>."},"status":"public","external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"volume":2020,"date_created":"2022-03-18T11:39:30Z","page":"669-697","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."}],"date_updated":"2023-08-24T14:19:55Z","month":"02","type":"journal_article","oa_version":"Preprint","_id":"10867","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","year":"2020","doi":"10.1093/imrn/rny037","quality_controlled":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"isi":1,"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"issue":"3","arxiv":1,"title":"Waist of balls in hyperbolic and spherical spaces","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"day":"01","publication":"International Mathematics Research Notices","article_processing_charge":"No","scopus_import":"1","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Oxford University Press","department":[{"_id":"HeEd"}]},{"oa":1,"publication_status":"published","date_published":"2020-09-09T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.02934"}],"external_id":{"arxiv":["2001.02934"]},"status":"public","citation":{"chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>.","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” <i>European Journal of Mathematics</i>. Springer Nature, 2020.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020).","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. 2020. doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>","apa":"Akopyan, A., Schwartz, R., &#38; Tabachnikov, S. (2020). Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>","mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>, Springer Nature, 2020, doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>.","ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics."},"date_updated":"2021-12-02T15:10:17Z","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","month":"09","date_created":"2020-09-20T22:01:38Z","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.","year":"2020","_id":"8538","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"doi":"10.1007/s40879-020-00426-9","quality_controlled":"1","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"}],"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Schwartz, Richard","first_name":"Richard","last_name":"Schwartz"},{"first_name":"Serge","last_name":"Tabachnikov","full_name":"Tabachnikov, Serge"}],"day":"09","arxiv":1,"title":"Billiards in ellipses revisited","publisher":"Springer Nature","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"publication":"European Journal of Mathematics","article_processing_charge":"No","ec_funded":1,"scopus_import":"1","article_type":"original"},{"publication_status":"published","oa":1,"date_published":"2020-06-21T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"editor":[{"first_name":"Bo'az","last_name":"Klartag","full_name":"Klartag, Bo'az"},{"full_name":"Milman, Emanuel","last_name":"Milman","first_name":"Emanuel"}],"external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"status":"public","intvolume":"      2256","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. <i>Geometric Aspects of Functional Analysis</i>. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>","apa":"Akopyan, A., &#38; Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag &#38; E. Milman (Eds.), <i>Geometric Aspects of Functional Analysis</i> (Vol. 2256, pp. 1–27). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>.","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.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>.","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in <i>Geometric Aspects of Functional Analysis</i>, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27."},"page":"1-27","abstract":[{"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.","lang":"eng"}],"date_updated":"2023-08-17T13:48:31Z","oa_version":"Preprint","month":"06","type":"book_chapter","volume":2256,"date_created":"2018-12-11T11:44:29Z","year":"2020","_id":"74","publication_identifier":{"issn":["00758434"],"eisbn":["9783030360207"],"isbn":["9783030360191"],"eissn":["16179692"]},"doi":"10.1007/978-3-030-36020-7_1","quality_controlled":"1","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"isi":1,"series_title":"LNM","language":[{"iso":"eng"}],"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"day":"21","arxiv":1,"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publication":"Geometric Aspects of Functional Analysis","ec_funded":1,"article_processing_charge":"No","scopus_import":"1"},{"_id":"9156","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).","year":"2020","volume":8,"date_created":"2021-02-17T15:12:44Z","file_date_updated":"2021-02-19T13:33:19Z","page":"74-88","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."}],"date_updated":"2023-10-17T12:35:10Z","month":"07","oa_version":"Published Version","type":"journal_article","intvolume":"         8","citation":{"ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):74-88. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>"},"external_id":{"arxiv":["1908.06777"]},"status":"public","date_published":"2020-07-21T00:00:00Z","ddc":["510"],"publication_status":"published","oa":1,"has_accepted_license":"1","publication":"Computational and Mathematical Biophysics","ec_funded":1,"article_processing_charge":"No","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"De Gruyter","department":[{"_id":"HeEd"}],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","arxiv":1,"author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"file":[{"checksum":"ca43a7440834eab6bbea29c59b56ef3a","date_updated":"2021-02-19T13:33:19Z","file_id":"9170","access_level":"open_access","date_created":"2021-02-19T13:33:19Z","success":1,"file_name":"2020_CompMathBiophysics_Akopyan.pdf","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":707452}],"day":"21","language":[{"iso":"eng"}],"issue":"1","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"doi":"10.1515/cmb-2020-0101","quality_controlled":"1","publication_identifier":{"issn":["2544-7297"]}},{"article_processing_charge":"No","ec_funded":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication":"Computational and Mathematical Biophysics","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"De Gruyter","title":"The weighted mean curvature derivative of a space-filling diagram","day":"20","file":[{"creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":562359,"success":1,"file_name":"2020_CompMathBiophysics_Akopyan2.pdf","access_level":"open_access","date_created":"2021-02-19T13:56:24Z","checksum":"cea41de9937d07a3b927d71ee8b4e432","date_updated":"2021-02-19T13:56:24Z","file_id":"9171"}],"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"language":[{"iso":"eng"}],"issue":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.1515/cmb-2020-0100","publication_identifier":{"issn":["2544-7297"]},"_id":"9157","year":"2020","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).","date_created":"2021-02-17T15:13:01Z","file_date_updated":"2021-02-19T13:56:24Z","volume":8,"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."}],"date_updated":"2023-10-17T12:34:51Z","oa_version":"Published Version","month":"06","type":"journal_article","page":"51-67","citation":{"ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):51-67. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>"},"intvolume":"         8","status":"public","ddc":["510"],"date_published":"2020-06-20T00:00:00Z","has_accepted_license":"1","oa":1,"publication_status":"published"},{"publication_status":"published","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"date_published":"2019-06-01T00:00:00Z","status":"public","external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"citation":{"ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism, 2019. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. 2019;53(2):457-490. doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>","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.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>.","apa":"Akopyan, A., Hubard, A., &#38; Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>"},"intvolume":"        53","date_updated":"2023-08-29T06:32:48Z","abstract":[{"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.","lang":"eng"}],"month":"06","oa_version":"Preprint","type":"journal_article","page":"457-490","date_created":"2019-07-14T21:59:19Z","volume":53,"year":"2019","_id":"6634","quality_controlled":"1","doi":"10.12775/TMNA.2019.008","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"language":[{"iso":"eng"}],"issue":"2","isi":1,"day":"01","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Hubard, Alfredo","last_name":"Hubard","first_name":"Alfredo"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"title":"Lower and upper bounds for the waists of different spaces","arxiv":1,"department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Akademicka Platforma Czasopism","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","publication":"Topological Methods in Nonlinear Analysis"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"date_published":"2019-10-01T00:00:00Z","publication_status":"published","oa":1,"citation":{"chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2019. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>.","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. 2019;51(5):765-775. doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>","apa":"Akopyan, A., &#38; Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>.","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."},"intvolume":"        51","external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"status":"public","date_created":"2019-08-11T21:59:23Z","volume":51,"abstract":[{"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.","lang":"eng"}],"date_updated":"2023-08-29T07:08:34Z","type":"journal_article","oa_version":"Preprint","month":"10","page":"765-775","_id":"6793","year":"2019","quality_controlled":"1","doi":"10.1112/blms.12276","publication_identifier":{"issn":["00246093"],"eissn":["14692120"]},"language":[{"iso":"eng"}],"issue":"5","isi":1,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"}],"title":"The Regge symmetry, confocal conics, and the Schläfli formula","arxiv":1,"day":"01","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Izmestiev, Ivan","last_name":"Izmestiev","first_name":"Ivan"}],"scopus_import":"1","ec_funded":1,"article_processing_charge":"No","article_type":"original","publication":"Bulletin of the London Mathematical Society","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"London Mathematical Society"},{"oa":1,"publication_status":"published","date_published":"2019-01-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"status":"public","intvolume":"       147","citation":{"ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. 2019;147:91-102. doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, AMS, 2019, pp. 91–102, doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>.","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","apa":"Akopyan, A., &#38; Fedorov, R. (2019). Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. AMS. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” <i>Proceedings of the American Mathematical Society</i>, vol. 147. AMS, pp. 91–102, 2019.","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>. AMS, 2019. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102."},"page":"91-102","month":"01","oa_version":"Preprint","type":"journal_article","date_updated":"2023-08-24T14:48:59Z","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. "}],"volume":147,"date_created":"2019-02-24T22:59:19Z","year":"2019","_id":"6050","doi":"10.1090/proc/14240","quality_controlled":"1","isi":1,"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Fedorov, Roman","last_name":"Fedorov","first_name":"Roman"}],"day":"01","arxiv":1,"title":"Two circles and only a straightedge","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"AMS","department":[{"_id":"HeEd"}],"publication":"Proceedings of the American Mathematical Society","scopus_import":"1","article_processing_charge":"No"},{"date_created":"2019-05-13T07:58:38Z","file_date_updated":"2020-07-14T12:47:30Z","volume":15,"type":"journal_article","month":"04","oa_version":"Published Version","date_updated":"2023-08-25T10:30:37Z","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."}],"_id":"6419","year":"2019","date_published":"2019-04-10T00:00:00Z","ddc":["570"],"has_accepted_license":"1","publication_status":"published","oa":1,"citation":{"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).","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.” <i>PLoS Genetics</i>. Public Library of Science, 2019. <a href=\"https://doi.org/10.1371/journal.pgen.1008079\">https://doi.org/10.1371/journal.pgen.1008079</a>.","ieee":"V. Pokusaeva <i>et al.</i>, “An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape,” <i>PLoS Genetics</i>, vol. 15, no. 4. Public Library of Science, 2019.","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. <i>PLoS Genetics</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pgen.1008079\">https://doi.org/10.1371/journal.pgen.1008079</a>","mla":"Pokusaeva, Victoria, et al. “An Experimental Assay of the Interactions of Amino Acids from Orthologous Sequences Shaping a Complex Fitness Landscape.” <i>PLoS Genetics</i>, vol. 15, no. 4, e1008079, Public Library of Science, 2019, doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079\">10.1371/journal.pgen.1008079</a>.","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.","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. <i>PLoS Genetics</i>. 2019;15(4). doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079\">10.1371/journal.pgen.1008079</a>"},"related_material":{"record":[{"relation":"research_data","id":"9789","status":"public"},{"status":"public","id":"9790","relation":"research_data"},{"id":"9797","status":"public","relation":"research_data"}]},"intvolume":"        15","external_id":{"isi":["000466866000029"]},"status":"public","article_number":"e1008079","title":"An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape","day":"10","file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":3726017,"file_name":"2019_PLOSGenetics_Pokusaeva.pdf","access_level":"open_access","date_created":"2019-05-14T08:26:08Z","checksum":"cf3889c8a8a16053dacf9c3776cbe217","date_updated":"2020-07-14T12:47:30Z","file_id":"6445"}],"author":[{"orcid":"0000-0001-7660-444X","id":"3184041C-F248-11E8-B48F-1D18A9856A87","full_name":"Pokusaeva, Victoria","last_name":"Pokusaeva","first_name":"Victoria"},{"first_name":"Dinara R.","last_name":"Usmanova","full_name":"Usmanova, Dinara R."},{"last_name":"Putintseva","first_name":"Ekaterina V.","full_name":"Putintseva, Ekaterina V."},{"first_name":"Lorena","last_name":"Espinar","full_name":"Espinar, Lorena"},{"full_name":"Sarkisyan, Karen","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5375-6341","first_name":"Karen","last_name":"Sarkisyan"},{"full_name":"Mishin, Alexander S.","first_name":"Alexander S.","last_name":"Mishin"},{"first_name":"Natalya S.","last_name":"Bogatyreva","full_name":"Bogatyreva, Natalya S."},{"last_name":"Ivankov","first_name":"Dmitry","full_name":"Ivankov, Dmitry","id":"49FF1036-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","first_name":"Sergey"},{"last_name":"Povolotskaya","first_name":"Inna S.","full_name":"Povolotskaya, Inna S."},{"full_name":"Filion, Guillaume J.","last_name":"Filion","first_name":"Guillaume J."},{"full_name":"Carey, Lucas B.","first_name":"Lucas B.","last_name":"Carey"},{"first_name":"Fyodor","last_name":"Kondrashov","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8243-4694","full_name":"Kondrashov, Fyodor"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_processing_charge":"No","ec_funded":1,"scopus_import":"1","publication":"PLoS Genetics","department":[{"_id":"FyKo"}],"publisher":"Public Library of Science","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","doi":"10.1371/journal.pgen.1008079","publication_identifier":{"eissn":["15537404"]},"issue":"4","language":[{"iso":"eng"}],"isi":1,"project":[{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}]},{"doi":"10.1371/journal.pgen.1008079.s010","date_published":"2019-04-10T00:00:00Z","status":"public","citation":{"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. <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s010\">https://doi.org/10.1371/journal.pgen.1008079.s010</a>.","ieee":"V. Pokusaeva <i>et al.</i>, “Multiple alignment of His3 orthologues.” Public Library of Science, 2019.","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).","ama":"Pokusaeva V, Usmanova DR, Putintseva EV, et al. Multiple alignment of His3 orthologues. 2019. doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079.s010\">10.1371/journal.pgen.1008079.s010</a>","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. <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s010\">https://doi.org/10.1371/journal.pgen.1008079.s010</a>","mla":"Pokusaeva, Victoria, et al. <i>Multiple Alignment of His3 Orthologues</i>. Public Library of Science, 2019, doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079.s010\">10.1371/journal.pgen.1008079.s010</a>.","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, <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s010\">10.1371/journal.pgen.1008079.s010</a>."},"related_material":{"record":[{"relation":"used_in_publication","status":"public","id":"6419"}]},"date_updated":"2023-08-25T10:30:36Z","day":"10","month":"04","type":"research_data_reference","oa_version":"Published Version","author":[{"first_name":"Victoria","last_name":"Pokusaeva","full_name":"Pokusaeva, Victoria","orcid":"0000-0001-7660-444X","id":"3184041C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Usmanova, Dinara R.","first_name":"Dinara R.","last_name":"Usmanova"},{"full_name":"Putintseva, Ekaterina V.","first_name":"Ekaterina V.","last_name":"Putintseva"},{"last_name":"Espinar","first_name":"Lorena","full_name":"Espinar, Lorena"},{"orcid":"0000-0002-5375-6341","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87","full_name":"Sarkisyan, Karen","first_name":"Karen","last_name":"Sarkisyan"},{"last_name":"Mishin","first_name":"Alexander S.","full_name":"Mishin, Alexander S."},{"first_name":"Natalya S.","last_name":"Bogatyreva","full_name":"Bogatyreva, Natalya S."},{"last_name":"Ivankov","first_name":"Dmitry","full_name":"Ivankov, Dmitry","id":"49FF1036-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Inna S.","last_name":"Povolotskaya","full_name":"Povolotskaya, Inna S."},{"last_name":"Filion","first_name":"Guillaume J.","full_name":"Filion, Guillaume J."},{"full_name":"Carey, Lucas B.","last_name":"Carey","first_name":"Lucas B."},{"id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8243-4694","full_name":"Kondrashov, Fyodor","first_name":"Fyodor","last_name":"Kondrashov"}],"date_created":"2021-08-06T08:38:50Z","title":"Multiple alignment of His3 orthologues","department":[{"_id":"FyKo"}],"year":"2019","publisher":"Public Library of Science","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","article_processing_charge":"No","_id":"9789"},{"publisher":"Public Library of Science","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","department":[{"_id":"FyKo"}],"year":"2019","_id":"9790","article_processing_charge":"No","author":[{"full_name":"Pokusaeva, Victoria","orcid":"0000-0001-7660-444X","id":"3184041C-F248-11E8-B48F-1D18A9856A87","last_name":"Pokusaeva","first_name":"Victoria"},{"full_name":"Usmanova, Dinara R.","last_name":"Usmanova","first_name":"Dinara R."},{"full_name":"Putintseva, Ekaterina V.","last_name":"Putintseva","first_name":"Ekaterina V."},{"first_name":"Lorena","last_name":"Espinar","full_name":"Espinar, Lorena"},{"last_name":"Sarkisyan","first_name":"Karen","full_name":"Sarkisyan, Karen","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5375-6341"},{"last_name":"Mishin","first_name":"Alexander S.","full_name":"Mishin, Alexander S."},{"first_name":"Natalya S.","last_name":"Bogatyreva","full_name":"Bogatyreva, Natalya S."},{"id":"49FF1036-F248-11E8-B48F-1D18A9856A87","full_name":"Ivankov, Dmitry","first_name":"Dmitry","last_name":"Ivankov"},{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov"},{"first_name":"Inna S.","last_name":"Povolotskaya","full_name":"Povolotskaya, Inna S."},{"full_name":"Filion, Guillaume J.","first_name":"Guillaume J.","last_name":"Filion"},{"last_name":"Carey","first_name":"Lucas B.","full_name":"Carey, Lucas B."},{"last_name":"Kondrashov","first_name":"Fyodor","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8243-4694","full_name":"Kondrashov, Fyodor"}],"date_updated":"2023-08-25T10:30:36Z","day":"10","oa_version":"Published Version","month":"04","type":"research_data_reference","title":"A statistical summary of segment libraries and sequencing results","date_created":"2021-08-06T08:50:15Z","status":"public","related_material":{"record":[{"id":"6419","status":"public","relation":"used_in_publication"}]},"citation":{"mla":"Pokusaeva, Victoria, et al. <i>A Statistical Summary of Segment Libraries and Sequencing Results</i>. Public Library of Science, 2019, doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">10.1371/journal.pgen.1008079.s011</a>.","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, <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">10.1371/journal.pgen.1008079.s011</a>.","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. <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">https://doi.org/10.1371/journal.pgen.1008079.s011</a>","ama":"Pokusaeva V, Usmanova DR, Putintseva EV, et al. A statistical summary of segment libraries and sequencing results. 2019. doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">10.1371/journal.pgen.1008079.s011</a>","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).","ieee":"V. Pokusaeva <i>et al.</i>, “A statistical summary of segment libraries and sequencing results.” Public Library of Science, 2019.","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. <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">https://doi.org/10.1371/journal.pgen.1008079.s011</a>."},"doi":"10.1371/journal.pgen.1008079.s011","date_published":"2019-04-10T00:00:00Z"},{"status":"public","citation":{"ama":"Pokusaeva V, Usmanova DR, Putintseva EV, et al. A statistical summary of segment libraries and sequencing results. 2019. doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">10.1371/journal.pgen.1008079.s011</a>","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. <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">https://doi.org/10.1371/journal.pgen.1008079.s011</a>","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, <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">10.1371/journal.pgen.1008079.s011</a>.","mla":"Pokusaeva, Victoria, et al. <i>A Statistical Summary of Segment Libraries and Sequencing Results</i>. Public Library of Science, 2019, doi:<a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">10.1371/journal.pgen.1008079.s011</a>.","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. <a href=\"https://doi.org/10.1371/journal.pgen.1008079.s011\">https://doi.org/10.1371/journal.pgen.1008079.s011</a>.","ieee":"V. Pokusaeva <i>et al.</i>, “A statistical summary of segment libraries and sequencing results.” Public Library of Science, 2019.","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)."},"related_material":{"record":[{"relation":"used_in_publication","id":"6419","status":"public"}]},"date_published":"2019-04-10T00:00:00Z","doi":"10.1371/journal.pgen.1008079.s011","year":"2019","department":[{"_id":"FyKo"}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","publisher":"Public Library of Science","article_processing_charge":"No","_id":"9797","date_updated":"2023-08-25T10:30:36Z","day":"10","oa_version":"Published Version","month":"04","type":"research_data_reference","author":[{"first_name":"Victoria","last_name":"Pokusaeva","full_name":"Pokusaeva, Victoria","orcid":"0000-0001-7660-444X","id":"3184041C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dinara R.","last_name":"Usmanova","full_name":"Usmanova, Dinara R."},{"first_name":"Ekaterina V.","last_name":"Putintseva","full_name":"Putintseva, Ekaterina V."},{"full_name":"Espinar, Lorena","first_name":"Lorena","last_name":"Espinar"},{"first_name":"Karen","last_name":"Sarkisyan","full_name":"Sarkisyan, Karen","orcid":"0000-0002-5375-6341","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mishin, Alexander S.","first_name":"Alexander S.","last_name":"Mishin"},{"first_name":"Natalya S.","last_name":"Bogatyreva","full_name":"Bogatyreva, Natalya S."},{"first_name":"Dmitry","last_name":"Ivankov","id":"49FF1036-F248-11E8-B48F-1D18A9856A87","full_name":"Ivankov, Dmitry"},{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"first_name":"Inna S.","last_name":"Povolotskaya","full_name":"Povolotskaya, Inna S."},{"full_name":"Filion, Guillaume J.","last_name":"Filion","first_name":"Guillaume J."},{"full_name":"Carey, Lucas B.","last_name":"Carey","first_name":"Lucas B."},{"full_name":"Kondrashov, Fyodor","orcid":"0000-0001-8243-4694","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","last_name":"Kondrashov","first_name":"Fyodor"}],"date_created":"2021-08-06T11:08:20Z","title":"A statistical summary of segment libraries and sequencing results"},{"publist_id":"7014","title":"3-Webs generated by confocal conics and circles","file":[{"checksum":"1febcfc1266486053a069e3425ea3713","file_id":"7222","date_updated":"2020-07-14T12:47:44Z","access_level":"open_access","date_created":"2020-01-03T11:35:08Z","file_name":"2018_Springer_Akopyan.pdf","creator":"kschuh","file_size":1140860,"relation":"main_file","content_type":"application/pdf"}],"day":"01","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan"}],"ec_funded":1,"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publication":"Geometriae Dedicata","department":[{"_id":"HeEd"}],"publisher":"Springer","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","doi":"10.1007/s10711-017-0265-6","language":[{"iso":"eng"}],"issue":"1","isi":1,"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"date_created":"2018-12-11T11:47:57Z","file_date_updated":"2020-07-14T12:47:44Z","volume":194,"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."}],"date_updated":"2023-09-08T11:40:29Z","oa_version":"Published Version","type":"journal_article","month":"06","page":"55 - 64","_id":"692","year":"2018","date_published":"2018-06-01T00:00:00Z","ddc":["510"],"has_accepted_license":"1","oa":1,"publication_status":"published","citation":{"ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” <i>Geometriae Dedicata</i>, vol. 194, no. 1. Springer, pp. 55–64, 2018.","chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” <i>Geometriae Dedicata</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s10711-017-0265-6\">https://doi.org/10.1007/s10711-017-0265-6</a>.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. <i>Geometriae Dedicata</i>. 2018;194(1):55-64. doi:<a href=\"https://doi.org/10.1007/s10711-017-0265-6\">10.1007/s10711-017-0265-6</a>","mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” <i>Geometriae Dedicata</i>, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:<a href=\"https://doi.org/10.1007/s10711-017-0265-6\">10.1007/s10711-017-0265-6</a>.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64.","apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. <i>Geometriae Dedicata</i>. Springer. <a href=\"https://doi.org/10.1007/s10711-017-0265-6\">https://doi.org/10.1007/s10711-017-0265-6</a>"},"intvolume":"       194","external_id":{"isi":["000431418800004"]},"status":"public"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","publication_status":"published","oa":1,"citation":{"short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. <a href=\"https://doi.org/10.48550/arXiv.1804.03057\">https://doi.org/10.48550/arXiv.1804.03057</a>.","mla":"Akopyan, Arseniy, et al. <i>Convex Fair Partitions into Arbitrary Number of Pieces</i>. 1804.03057, arXiv, 2018, doi:<a href=\"https://doi.org/10.48550/arXiv.1804.03057\">10.48550/arXiv.1804.03057</a>.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","apa":"Akopyan, A., Avvakumov, S., &#38; Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. <a href=\"https://doi.org/10.48550/arXiv.1804.03057\">https://doi.org/10.48550/arXiv.1804.03057</a>","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:<a href=\"https://doi.org/10.48550/arXiv.1804.03057\">10.48550/arXiv.1804.03057</a>"},"language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"status":"public","external_id":{"arxiv":["1804.03057"]},"project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"}],"date_created":"2018-12-11T11:44:30Z","article_number":"1804.03057","arxiv":1,"title":"Convex fair partitions into arbitrary number of pieces","month":"09","oa_version":"Preprint","type":"preprint","day":"13","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."}],"date_updated":"2023-12-18T10:51:02Z","author":[{"first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"ec_funded":1,"article_processing_charge":"No","_id":"75","year":"2018","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"arXiv"},{"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]","year":"2018","_id":"458","page":"2825 - 2854","oa_version":"Preprint","month":"04","type":"journal_article","date_updated":"2023-09-11T14:19:12Z","abstract":[{"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.","lang":"eng"}],"volume":370,"date_created":"2018-12-11T11:46:35Z","external_id":{"isi":["000423197800019"]},"status":"public","intvolume":"       370","citation":{"short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2018. <a href=\"https://doi.org/10.1090/tran/7292\">https://doi.org/10.1090/tran/7292</a>.","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” <i>Transactions of the American Mathematical Society</i>, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","apa":"Akopyan, A., &#38; Bobenko, A. (2018). Incircular nets and confocal conics. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7292\">https://doi.org/10.1090/tran/7292</a>","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.” <i>Transactions of the American Mathematical Society</i>, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:<a href=\"https://doi.org/10.1090/tran/7292\">10.1090/tran/7292</a>.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. <i>Transactions of the American Mathematical Society</i>. 2018;370(4):2825-2854. doi:<a href=\"https://doi.org/10.1090/tran/7292\">10.1090/tran/7292</a>"},"publication_status":"published","oa":1,"date_published":"2018-04-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1602.04637","open_access":"1"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"American Mathematical Society","department":[{"_id":"HeEd"}],"publication":"Transactions of the American Mathematical Society","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","author":[{"first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bobenko","first_name":"Alexander","full_name":"Bobenko, Alexander"}],"day":"01","title":"Incircular nets and confocal conics","publist_id":"7363","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"isi":1,"issue":"4","language":[{"iso":"eng"}],"doi":"10.1090/tran/7292","quality_controlled":"1"},{"intvolume":"        32","citation":{"ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics , 2018. <a href=\"https://doi.org/10.1137/16M110407X\">https://doi.org/10.1137/16M110407X</a>.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. 2018;32(3):2242-2257. doi:<a href=\"https://doi.org/10.1137/16M110407X\">10.1137/16M110407X</a>","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:<a href=\"https://doi.org/10.1137/16M110407X\">10.1137/16M110407X</a>.","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","apa":"Akopyan, A., &#38; Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/16M110407X\">https://doi.org/10.1137/16M110407X</a>"},"status":"public","external_id":{"isi":["000450810500036"],"arxiv":["1604.00960"]},"date_published":"2018-09-06T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"publication_status":"published","oa":1,"_id":"58","year":"2018","volume":32,"date_created":"2018-12-11T11:44:24Z","page":"2242 - 2257","date_updated":"2023-09-11T12:48:39Z","abstract":[{"text":"Inside a two-dimensional region (``cake&quot;&quot;), there are m nonoverlapping tiles of a certain kind (``toppings&quot;&quot;). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,&quot;&quot; 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.","lang":"eng"}],"oa_version":"Preprint","type":"journal_article","month":"09","isi":1,"language":[{"iso":"eng"}],"issue":"3","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"doi":"10.1137/16M110407X","quality_controlled":"1","publication":"SIAM Journal on Discrete Mathematics","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","publisher":"Society for Industrial and Applied Mathematics ","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"HeEd"}],"title":"Counting blanks in polygonal arrangements","arxiv":1,"publist_id":"7996","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Segal Halevi, Erel","first_name":"Erel","last_name":"Segal Halevi"}],"day":"06"}]