[{"article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2018-01-01T00:00:00Z","citation":{"chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.","apa":"Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125"},"publication":"SIAM Journal on Mathematical Analysis","page":"3271 - 3290","issue":"3","abstract":[{"lang":"eng","text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2."}],"type":"journal_article","oa_version":"Published Version","_id":"181","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 50","title":"Power law decay for systems of randomly coupled differential equations","status":"public","month":"01","doi":"10.1137/17M1143125","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"external_id":{"arxiv":["1708.01546"],"isi":["000437018500032"]},"oa":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"Structured Non-Hermitian Random Matrices","call_identifier":"FWF","_id":"258F40A4-B435-11E9-9278-68D0E5697425","grant_number":"M02080"}],"quality_controlled":"1","isi":1,"publist_id":"7740","ec_funded":1,"author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger","full_name":"Krüger, Torben H"},{"full_name":"Renfrew, David T","first_name":"David T","last_name":"Renfrew","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3493-121X"}],"volume":50,"date_updated":"2023-09-15T12:05:52Z","date_created":"2018-12-11T11:45:03Z","year":"2018","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"LaEr"}],"publication_status":"published"},{"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces","grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["1412.7211"],"isi":["000433270600005"]},"main_file_link":[{"url":"https://arxiv.org/abs/1412.7211","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2018.03.015","month":"07","publication_status":"published","department":[{"_id":"TaHa"}],"publisher":"World Scientific Publishing","acknowledgement":"National Science Foundation: Graduate Research Fellowship and grant No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project and providing guidance throughout, particularly for the formulation of Frobenius quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and constant encouragement, and for suggesting the term ‘hypertoric quantum group.’ Many results appearing in the current paper were proven independently by Nicholas Cooney; the author is grateful to Nicholas for sharing his insight on various topics, including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating the definition of multiplicative hypertoric varieties, as well as the content of Remark 2.14. The author also benefited immensely from the close reading and detailed comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n","year":"2018","date_updated":"2023-09-15T12:08:38Z","date_created":"2018-12-11T11:45:49Z","volume":506,"author":[{"id":"447491B8-F248-11E8-B48F-1D18A9856A87","last_name":"Ganev","first_name":"Iordan V","full_name":"Ganev, Iordan V"}],"publist_id":"7543","ec_funded":1,"page":"92 - 128","publication":"Journal of Algebra","citation":{"ista":"Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128.","apa":"Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. World Scientific Publishing. https://doi.org/10.1016/j.jalgebra.2018.03.015","ieee":"I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root of unity,” Journal of Algebra, vol. 506. World Scientific Publishing, pp. 92–128, 2018.","ama":"Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 2018;506:92-128. doi:10.1016/j.jalgebra.2018.03.015","chicago":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” Journal of Algebra. World Scientific Publishing, 2018. https://doi.org/10.1016/j.jalgebra.2018.03.015.","mla":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” Journal of Algebra, vol. 506, World Scientific Publishing, 2018, pp. 92–128, doi:10.1016/j.jalgebra.2018.03.015.","short":"I.V. Ganev, Journal of Algebra 506 (2018) 92–128."},"date_published":"2018-07-15T00:00:00Z","scopus_import":"1","day":"15","article_processing_charge":"No","status":"public","title":"Quantizations of multiplicative hypertoric varieties at a root of unity","intvolume":" 506","_id":"322","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"We construct quantizations of multiplicative hypertoric varieties using an algebra of q-difference operators on affine space, where q is a root of unity in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety and admits an explicit finite étale splitting. The global sections of this Azumaya algebra is a hypertoric quantum group, and we prove a localization theorem. We introduce a general framework of Frobenius quantum moment maps and their Hamiltonian reductions; our results shed light on an instance of this framework.","lang":"eng"}]},{"abstract":[{"text":"Implementation of the inference method in Matlab, including three applications of the method: The first one for the model of ant motion, the second one for bacterial chemotaxis, and the third one for the motion of fish.","lang":"eng"}],"type":"research_data_reference","date_created":"2021-08-09T07:01:24Z","date_updated":"2023-09-15T12:06:18Z","oa_version":"Published Version","author":[{"full_name":"Bod’Ová, Katarína","last_name":"Bod’Ová","first_name":"Katarína"},{"full_name":"Mitchell, Gabriel","id":"315BCD80-F248-11E8-B48F-1D18A9856A87","last_name":"Mitchell","first_name":"Gabriel"},{"full_name":"Harpaz, Roy","first_name":"Roy","last_name":"Harpaz"},{"last_name":"Schneidman","first_name":"Elad","full_name":"Schneidman, Elad"},{"full_name":"Tkačik, Gašper","orcid":"0000-0002-6699-1455","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","last_name":"Tkačik","first_name":"Gašper"}],"related_material":{"record":[{"status":"public","relation":"used_in_publication","id":"406"}]},"status":"public","title":"Implementation of the inference method in Matlab","department":[{"_id":"GaTk"}],"publisher":"Public Library of Science","year":"2018","_id":"9831","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","day":"07","month":"03","article_processing_charge":"No","doi":"10.1371/journal.pone.0193049.s001","date_published":"2018-03-07T00:00:00Z","citation":{"ista":"Bod’Ová K, Mitchell G, Harpaz R, Schneidman E, Tkačik G. 2018. Implementation of the inference method in Matlab, Public Library of Science, 10.1371/journal.pone.0193049.s001.","ieee":"K. Bod’Ová, G. Mitchell, R. Harpaz, E. Schneidman, and G. Tkačik, “Implementation of the inference method in Matlab.” Public Library of Science, 2018.","apa":"Bod’Ová, K., Mitchell, G., Harpaz, R., Schneidman, E., & Tkačik, G. (2018). Implementation of the inference method in Matlab. Public Library of Science. https://doi.org/10.1371/journal.pone.0193049.s001","ama":"Bod’Ová K, Mitchell G, Harpaz R, Schneidman E, Tkačik G. Implementation of the inference method in Matlab. 2018. doi:10.1371/journal.pone.0193049.s001","chicago":"Bod’Ová, Katarína, Gabriel Mitchell, Roy Harpaz, Elad Schneidman, and Gašper Tkačik. “Implementation of the Inference Method in Matlab.” Public Library of Science, 2018. https://doi.org/10.1371/journal.pone.0193049.s001.","mla":"Bod’Ová, Katarína, et al. Implementation of the Inference Method in Matlab. Public Library of Science, 2018, doi:10.1371/journal.pone.0193049.s001.","short":"K. Bod’Ová, G. Mitchell, R. Harpaz, E. Schneidman, G. Tkačik, (2018)."}},{"article_processing_charge":"No","has_accepted_license":"1","day":"18","scopus_import":"1","date_published":"2018-07-18T00:00:00Z","page":"449 - 467","citation":{"chicago":"Kong, Hui, Ezio Bartocci, and Thomas A Henzinger. “Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes,” 10981:449–67. Springer, 2018. https://doi.org/10.1007/978-3-319-96145-3_24.","mla":"Kong, Hui, et al. Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes. Vol. 10981, Springer, 2018, pp. 449–67, doi:10.1007/978-3-319-96145-3_24.","short":"H. Kong, E. Bartocci, T.A. Henzinger, in:, Springer, 2018, pp. 449–467.","ista":"Kong H, Bartocci E, Henzinger TA. 2018. Reachable set over-approximation for nonlinear systems using piecewise barrier tubes. CAV: Computer Aided Verification, LNCS, vol. 10981, 449–467.","apa":"Kong, H., Bartocci, E., & Henzinger, T. A. (2018). Reachable set over-approximation for nonlinear systems using piecewise barrier tubes (Vol. 10981, pp. 449–467). Presented at the CAV: Computer Aided Verification, Oxford, United Kingdom: Springer. https://doi.org/10.1007/978-3-319-96145-3_24","ieee":"H. Kong, E. Bartocci, and T. A. Henzinger, “Reachable set over-approximation for nonlinear systems using piecewise barrier tubes,” presented at the CAV: Computer Aided Verification, Oxford, United Kingdom, 2018, vol. 10981, pp. 449–467.","ama":"Kong H, Bartocci E, Henzinger TA. Reachable set over-approximation for nonlinear systems using piecewise barrier tubes. In: Vol 10981. Springer; 2018:449-467. doi:10.1007/978-3-319-96145-3_24"},"abstract":[{"text":"We address the problem of analyzing the reachable set of a polynomial nonlinear continuous system by over-approximating the flowpipe of its dynamics. The common approach to tackle this problem is to perform a numerical integration over a given time horizon based on Taylor expansion and interval arithmetic. However, this method results to be very conservative when there is a large difference in speed between trajectories as time progresses. In this paper, we propose to use combinations of barrier functions, which we call piecewise barrier tube (PBT), to over-approximate flowpipe. The basic idea of PBT is that for each segment of a flowpipe, a coarse box which is big enough to contain the segment is constructed using sampled simulation and then in the box we compute by linear programming a set of barrier functions (called barrier tube or BT for short) which work together to form a tube surrounding the flowpipe. The benefit of using PBT is that (1) BT is independent of time and hence can avoid being stretched and deformed by time; and (2) a small number of BTs can form a tight over-approximation for the flowpipe, which means that the computation required to decide whether the BTs intersect the unsafe set can be reduced significantly. We implemented a prototype called PBTS in C++. Experiments on some benchmark systems show that our approach is effective.","lang":"eng"}],"alternative_title":["LNCS"],"type":"conference","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"5718","date_created":"2018-12-17T15:57:06Z","date_updated":"2020-07-14T12:44:53Z","checksum":"fd95e8026deacef3dc752a733bb9355f","file_name":"2018_LNCS_Kong.pdf","access_level":"open_access","content_type":"application/pdf","file_size":5591566,"creator":"dernst"}],"intvolume":" 10981","status":"public","ddc":["000"],"title":"Reachable set over-approximation for nonlinear systems using piecewise barrier tubes","_id":"142","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"07","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-96145-3_24","conference":{"name":"CAV: Computer Aided Verification","start_date":"2018-07-14","location":"Oxford, United Kingdom","end_date":"2018-07-17"},"project":[{"grant_number":"S 11407_N23","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering"},{"_id":"25F42A32-B435-11E9-9278-68D0E5697425","grant_number":"Z211","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"isi":1,"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000491481600024"]},"oa":1,"license":"https://creativecommons.org/licenses/by/4.0/","publist_id":"7781","file_date_updated":"2020-07-14T12:44:53Z","volume":10981,"date_updated":"2023-09-15T12:12:08Z","date_created":"2018-12-11T11:44:51Z","author":[{"last_name":"Kong","first_name":"Hui","orcid":"0000-0002-3066-6941","id":"3BDE25AA-F248-11E8-B48F-1D18A9856A87","full_name":"Kong, Hui"},{"full_name":"Bartocci, Ezio","last_name":"Bartocci","first_name":"Ezio"},{"orcid":"0000−0002−2985−7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A","full_name":"Henzinger, Thomas A"}],"publisher":"Springer","department":[{"_id":"ToHe"}],"publication_status":"published","acknowledgement":"Austrian Science Fund FWF: S11402-N23, S11405-N23, Z211-N32","year":"2018"},{"abstract":[{"lang":"eng","text":"We investigate the quantum interference induced shifts between energetically close states in highly charged ions, with the energy structure being observed by laser spectroscopy. In this work, we focus on hyperfine states of lithiumlike heavy-Z isotopes and quantify how much quantum interference changes the observed transition frequencies. The process of photon excitation and subsequent photon decay for the transition 2s→2p→2s is implemented with fully relativistic and full-multipole frameworks, which are relevant for such relativistic atomic systems. We consider the isotopes Pb79+207 and Bi80+209 due to experimental interest, as well as other examples of isotopes with lower Z, namely Pr56+141 and Ho64+165. We conclude that quantum interference can induce shifts up to 11% of the linewidth in the measurable resonances of the considered isotopes, if interference between resonances is neglected. The inclusion of relativity decreases the cross section by 35%, mainly due to the complete retardation form of the electric dipole multipole. However, the contribution of the next higher multipoles (e.g., magnetic quadrupole) to the cross section is negligible. This makes the contribution of relativity and higher-order multipoles to the quantum interference induced shifts a minor effect, even for heavy-Z elements."}],"issue":"2","type":"journal_article","oa_version":"Preprint","status":"public","title":"Quantum interference in laser spectroscopy of highly charged lithiumlike ions","intvolume":" 97","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"427","day":"21","article_processing_charge":"No","scopus_import":"1","date_published":"2018-02-21T00:00:00Z","article_type":"original","publication":" Physical Review A - Atomic, Molecular, and Optical Physics","citation":{"short":"P. Amaro, U. Loureiro, L. Safari, F. Fratini, P. Indelicato, T. Stöhlker, J. Santos, Physical Review A - Atomic, Molecular, and Optical Physics 97 (2018).","mla":"Amaro, Pedro, et al. “Quantum Interference in Laser Spectroscopy of Highly Charged Lithiumlike Ions.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 97, no. 2, 022510, American Physical Society, 2018, doi:10.1103/PhysRevA.97.022510.","chicago":"Amaro, Pedro, Ulisses Loureiro, Laleh Safari, Filippo Fratini, Paul Indelicato, Thomas Stöhlker, and José Santos. “Quantum Interference in Laser Spectroscopy of Highly Charged Lithiumlike Ions.” Physical Review A - Atomic, Molecular, and Optical Physics. American Physical Society, 2018. https://doi.org/10.1103/PhysRevA.97.022510.","ama":"Amaro P, Loureiro U, Safari L, et al. Quantum interference in laser spectroscopy of highly charged lithiumlike ions. Physical Review A - Atomic, Molecular, and Optical Physics. 2018;97(2). doi:10.1103/PhysRevA.97.022510","ieee":"P. Amaro et al., “Quantum interference in laser spectroscopy of highly charged lithiumlike ions,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 97, no. 2. American Physical Society, 2018.","apa":"Amaro, P., Loureiro, U., Safari, L., Fratini, F., Indelicato, P., Stöhlker, T., & Santos, J. (2018). Quantum interference in laser spectroscopy of highly charged lithiumlike ions. Physical Review A - Atomic, Molecular, and Optical Physics. American Physical Society. https://doi.org/10.1103/PhysRevA.97.022510","ista":"Amaro P, Loureiro U, Safari L, Fratini F, Indelicato P, Stöhlker T, Santos J. 2018. Quantum interference in laser spectroscopy of highly charged lithiumlike ions. Physical Review A - Atomic, Molecular, and Optical Physics. 97(2), 022510."},"ec_funded":1,"publist_id":"7396","article_number":"022510","date_updated":"2023-09-15T12:09:35Z","date_created":"2018-12-11T11:46:25Z","volume":97,"author":[{"last_name":"Amaro","first_name":"Pedro","full_name":"Amaro, Pedro"},{"first_name":"Ulisses","last_name":"Loureiro","full_name":"Loureiro, Ulisses"},{"full_name":"Safari, Laleh","id":"3C325E5E-F248-11E8-B48F-1D18A9856A87","first_name":"Laleh","last_name":"Safari"},{"first_name":"Filippo","last_name":"Fratini","full_name":"Fratini, Filippo"},{"last_name":"Indelicato","first_name":"Paul","full_name":"Indelicato, Paul"},{"last_name":"Stöhlker","first_name":"Thomas","full_name":"Stöhlker, Thomas"},{"first_name":"José","last_name":"Santos","full_name":"Santos, José"}],"publication_status":"published","department":[{"_id":"MiLe"}],"publisher":"American Physical Society","year":"2018","acknowledgement":"This work was funded by the Portuguese Fundação para a Ciência e a Tecnologia (FCT/MCTES/PIDDAC) under Grant No. UID/FIS/04559/2013 (LIBPhys). P.A. acknowledges the support of the FCT, under Contract No. SFRH/BPD/92329/2013. L.S. acknowledges financial support from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. (291734). Laboratoire Kastler Brossel (LKB) is “Unité Mixte de Recherche de Sorbonne Université, de ENS-PSL Research University, du Collège de France et du CNRS No. 8552.” APPENDIX:\r\n","month":"02","language":[{"iso":"eng"}],"doi":"10.1103/PhysRevA.97.022510","isi":1,"quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.07920"}],"external_id":{"isi":["000425601000004"],"arxiv":["1802.07920"]}}]