--- _id: '181' 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. acknowledgement: The work of the second author was also partially supported by the Hausdorff Center of Mathematics. article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: David T full_name: Renfrew, David T id: 4845BF6A-F248-11E8-B48F-1D18A9856A87 last_name: Renfrew orcid: 0000-0003-3493-121X citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:45:03Z date_published: 2018-01-01T00:00:00Z date_updated: 2023-09-15T12:05:52Z day: '01' department: - _id: LaEr doi: 10.1137/17M1143125 ec_funded: 1 external_id: arxiv: - '1708.01546' isi: - '000437018500032' intvolume: ' 50' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.01546 month: '01' oa: 1 oa_version: Published Version page: 3271 - 3290 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 258F40A4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02080 name: Structured Non-Hermitian Random Matrices publication: SIAM Journal on Mathematical Analysis publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '7740' quality_controlled: '1' scopus_import: '1' status: public title: Power law decay for systems of randomly coupled differential equations type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 50 year: '2018' ... --- _id: '322' abstract: - lang: eng 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. 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" article_processing_charge: No author: - first_name: Iordan V full_name: Ganev, Iordan V id: 447491B8-F248-11E8-B48F-1D18A9856A87 last_name: Ganev citation: 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 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 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. 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. ista: Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128. 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_created: 2018-12-11T11:45:49Z date_published: 2018-07-15T00:00:00Z date_updated: 2023-09-15T12:08:38Z day: '15' department: - _id: TaHa doi: 10.1016/j.jalgebra.2018.03.015 ec_funded: 1 external_id: arxiv: - '1412.7211' isi: - '000433270600005' intvolume: ' 506' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1412.7211 month: '07' oa: 1 oa_version: Preprint page: 92 - 128 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Journal of Algebra publication_status: published publisher: World Scientific Publishing publist_id: '7543' quality_controlled: '1' scopus_import: '1' status: public title: Quantizations of multiplicative hypertoric varieties at a root of unity type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 506 year: '2018' ... --- _id: '9831' abstract: - lang: eng 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.' article_processing_charge: No author: - first_name: Katarína full_name: Bod’Ová, Katarína last_name: Bod’Ová - first_name: Gabriel full_name: Mitchell, Gabriel id: 315BCD80-F248-11E8-B48F-1D18A9856A87 last_name: Mitchell - first_name: Roy full_name: Harpaz, Roy last_name: Harpaz - first_name: Elad full_name: Schneidman, Elad last_name: Schneidman - first_name: Gašper full_name: Tkačik, Gašper id: 3D494DCA-F248-11E8-B48F-1D18A9856A87 last_name: Tkačik orcid: 0000-0002-6699-1455 citation: 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 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 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. 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. 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. 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). date_created: 2021-08-09T07:01:24Z date_published: 2018-03-07T00:00:00Z date_updated: 2023-09-15T12:06:18Z day: '07' department: - _id: GaTk doi: 10.1371/journal.pone.0193049.s001 month: '03' oa_version: Published Version publisher: Public Library of Science related_material: record: - id: '406' relation: used_in_publication status: public status: public title: Implementation of the inference method in Matlab type: research_data_reference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf year: '2018' ... --- _id: '142' abstract: - lang: eng 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. acknowledgement: 'Austrian Science Fund FWF: S11402-N23, S11405-N23, Z211-N32' alternative_title: - LNCS article_processing_charge: No author: - first_name: Hui full_name: Kong, Hui id: 3BDE25AA-F248-11E8-B48F-1D18A9856A87 last_name: Kong orcid: 0000-0002-3066-6941 - first_name: Ezio full_name: Bartocci, Ezio last_name: Bartocci - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 citation: 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' 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' 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. 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.' 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.' 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. conference: end_date: 2018-07-17 location: Oxford, United Kingdom name: 'CAV: Computer Aided Verification' start_date: 2018-07-14 date_created: 2018-12-11T11:44:51Z date_published: 2018-07-18T00:00:00Z date_updated: 2023-09-15T12:12:08Z day: '18' ddc: - '000' department: - _id: ToHe doi: 10.1007/978-3-319-96145-3_24 external_id: isi: - '000491481600024' file: - access_level: open_access checksum: fd95e8026deacef3dc752a733bb9355f content_type: application/pdf creator: dernst date_created: 2018-12-17T15:57:06Z date_updated: 2020-07-14T12:44:53Z file_id: '5718' file_name: 2018_LNCS_Kong.pdf file_size: 5591566 relation: main_file file_date_updated: 2020-07-14T12:44:53Z has_accepted_license: '1' intvolume: ' 10981' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '07' oa: 1 oa_version: Published Version page: 449 - 467 project: - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 25F42A32-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z211 name: The Wittgenstein Prize publication_status: published publisher: Springer publist_id: '7781' quality_controlled: '1' scopus_import: '1' status: public title: Reachable set over-approximation for nonlinear systems using piecewise barrier tubes tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 10981 year: '2018' ... --- _id: '427' 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. 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" article_number: '022510' article_processing_charge: No article_type: original author: - first_name: Pedro full_name: Amaro, Pedro last_name: Amaro - first_name: Ulisses full_name: Loureiro, Ulisses last_name: Loureiro - first_name: Laleh full_name: Safari, Laleh id: 3C325E5E-F248-11E8-B48F-1D18A9856A87 last_name: Safari - first_name: Filippo full_name: Fratini, Filippo last_name: Fratini - first_name: Paul full_name: Indelicato, Paul last_name: Indelicato - first_name: Thomas full_name: Stöhlker, Thomas last_name: Stöhlker - first_name: José full_name: Santos, José last_name: Santos citation: 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 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 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. 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. 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. 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. 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). date_created: 2018-12-11T11:46:25Z date_published: 2018-02-21T00:00:00Z date_updated: 2023-09-15T12:09:35Z day: '21' department: - _id: MiLe doi: 10.1103/PhysRevA.97.022510 ec_funded: 1 external_id: arxiv: - '1802.07920' isi: - '000425601000004' intvolume: ' 97' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1802.07920 month: '02' oa: 1 oa_version: Preprint project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: ' Physical Review A - Atomic, Molecular, and Optical Physics' publication_status: published publisher: American Physical Society publist_id: '7396' quality_controlled: '1' scopus_import: '1' status: public title: Quantum interference in laser spectroscopy of highly charged lithiumlike ions type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 97 year: '2018' ...