[{"date_created":"2024-04-17T13:16:39Z","keyword":["Applied Mathematics","Numerical Analysis","Analysis"],"type":"journal_article","department":[{"_id":"555"}],"publication":"Journal of Elliptic and Parabolic Equations","citation":{"ieee":"E. Papageorgiou, “Asymptotics for the infinite Brownian loop on noncompact symmetric spaces,” <i>Journal of Elliptic and Parabolic Equations</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>.","apa":"Papageorgiou, E. (2023). Asymptotics for the infinite Brownian loop on noncompact symmetric spaces. <i>Journal of Elliptic and Parabolic Equations</i>. <a href=\"https://doi.org/10.1007/s41808-023-00250-8\">https://doi.org/10.1007/s41808-023-00250-8</a>","chicago":"Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on Noncompact Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>, 2023. <a href=\"https://doi.org/10.1007/s41808-023-00250-8\">https://doi.org/10.1007/s41808-023-00250-8</a>.","short":"E. Papageorgiou, Journal of Elliptic and Parabolic Equations (2023).","mla":"Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on Noncompact Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>.","bibtex":"@article{Papageorgiou_2023, title={Asymptotics for the infinite Brownian loop on noncompact symmetric spaces}, DOI={<a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2023} }","ama":"Papageorgiou E. Asymptotics for the infinite Brownian loop on noncompact symmetric spaces. <i>Journal of Elliptic and Parabolic Equations</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>"},"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length <jats:italic>T</jats:italic> around a fixed origin when <jats:inline-formula><jats:alternatives><jats:tex-math>$$T \\rightarrow +\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>T</mml:mi>\r\n                  <mml:mo>→</mml:mo>\r\n                  <mml:mo>+</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>. The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact type and of general rank. This amounts to the behavior of solutions to the heat equation subject to the Doob transform induced by the ground spherical function. Unlike the standard Brownian motion, we observe in this case phenomena which are similar to the Euclidean setting, namely <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n                </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without requiring bi-<jats:italic>K</jats:italic>-invariance for initial data, and strong <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\infty }$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mi>∞</mml:mi>\r\n                </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula> convergence.</jats:p>","lang":"eng"}],"_id":"53539","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","user_id":"100325","doi":"10.1007/s41808-023-00250-8","year":"2023","title":"Asymptotics for the infinite Brownian loop on noncompact symmetric spaces","status":"public","author":[{"id":"100325","first_name":"Efthymia","last_name":"Papageorgiou","full_name":"Papageorgiou, Efthymia"}],"publication_identifier":{"issn":["2296-9020","2296-9039"]},"publication_status":"published","date_updated":"2026-07-03T12:36:17Z"},{"oa":"1","place":"Cham","citation":{"mla":"Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>, edited by Hintermüller Michael et al., Springer, 2022, pp. 43–76, doi:<a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">10.1007/978-3-030-79393-7_3</a>.","bibtex":"@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">10.1007/978-3-030-79393-7_3</a>}, booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems}, publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}, year={2022}, pages={43–76} }","ama":"Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland H, Christian K, Michael U, Stefan U, eds. <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>. Springer; 2022:43-76. doi:<a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">10.1007/978-3-030-79393-7_3</a>","ieee":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>, H. Michael, H. Roland, K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.","apa":"Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2022). ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In H. Michael, H. Roland, K. Christian, U. Michael, &#38; U. Stefan (Eds.), <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i> (pp. 43–76). Springer. <a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">https://doi.org/10.1007/978-3-030-79393-7_3</a>","short":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael, H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76.","chicago":"Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” In <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian, Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. <a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">https://doi.org/10.1007/978-3-030-79393-7_3</a>."},"editor":[{"last_name":"Michael","first_name":"Hintermüller","full_name":"Michael, Hintermüller"},{"first_name":"Herzog","last_name":"Roland","full_name":"Roland, Herzog"},{"last_name":"Christian","first_name":"Kanzow","full_name":"Christian, Kanzow"},{"full_name":"Michael, Ulbrich","first_name":"Ulbrich","last_name":"Michael"},{"full_name":"Stefan, Ulbrich","first_name":"Ulbrich","last_name":"Stefan"}],"user_id":"47427","publisher":"Springer","_id":"16296","page":"43-76","status":"public","department":[{"_id":"101"},{"_id":"655"}],"type":"book_chapter","date_created":"2020-03-13T12:45:31Z","abstract":[{"text":"Multiobjective optimization plays an increasingly important role in modern\r\napplications, where several objectives are often of equal importance. The task\r\nin multiobjective optimization and multiobjective optimal control is therefore\r\nto compute the set of optimal compromises (the Pareto set) between the\r\nconflicting objectives. Since the Pareto set generally consists of an infinite\r\nnumber of solutions, the computational effort can quickly become challenging\r\nwhich is particularly problematic when the objectives are costly to evaluate as\r\nis the case for models governed by partial differential equations (PDEs). To\r\ndecrease the numerical effort to an affordable amount, surrogate models can be\r\nused to replace the expensive PDE evaluations. Existing multiobjective\r\noptimization methods using model reduction are limited either to low parameter\r\ndimensions or to few (ideally two) objectives. In this article, we present a\r\ncombination of the reduced basis model reduction method with a continuation\r\napproach using inexact gradients. The resulting approach can handle an\r\narbitrary number of objectives while yielding a significant reduction in\r\ncomputing time.","lang":"eng"}],"publication":"Non-Smooth and Complementarity-Based Distributed Parameter Systems","doi":"10.1007/978-3-030-79393-7_3","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/1906.09075.pdf","open_access":"1"}],"date_updated":"2022-03-14T13:04:51Z","publication_identifier":{"isbn":["978-3-030-79392-0"]},"author":[{"last_name":"Banholzer","first_name":"Stefan","full_name":"Banholzer, Stefan"},{"full_name":"Gebken, Bennet","first_name":"Bennet","last_name":"Gebken","id":"32643"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427"},{"full_name":"Volkwein, Stefan","last_name":"Volkwein","first_name":"Stefan"}],"year":"2022","title":"ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation"},{"publication":"German Success Stories in Industrial Mathematics","abstract":[{"lang":"eng","text":"With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios."}],"date_created":"2022-03-14T07:32:41Z","department":[{"_id":"101"},{"_id":"655"}],"type":"book_chapter","publication_identifier":{"isbn":["9783030814540","9783030814557"],"issn":["1612-3956","2198-3283"]},"author":[{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian","full_name":"Peitz, Sebastian"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Bannenberg","first_name":"Sebastian","full_name":"Bannenberg, Sebastian"}],"year":"2022","title":"Efficient Virtual Design and Testing of Autonomous Vehicles","intvolume":"        35","date_updated":"2022-03-14T07:42:01Z","publication_status":"published","series_title":"Mathematics in Industry","language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-81455-7_23","citation":{"chicago":"Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient Virtual Design and Testing of Autonomous Vehicles.” In <i>German Success Stories in Industrial Mathematics</i>, edited by H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International Publishing, 2022. <a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">https://doi.org/10.1007/978-3-030-81455-7_23</a>.","short":"S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas, A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics, Springer International Publishing, Cham, 2022.","apa":"Peitz, S., Dellnitz, M., &#38; Bannenberg, S. (2022). Efficient Virtual Design and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, &#38; V. Schulz (Eds.), <i>German Success Stories in Industrial Mathematics</i> (Vol. 35). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">https://doi.org/10.1007/978-3-030-81455-7_23</a>","ieee":"S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing of Autonomous Vehicles,” in <i>German Success Stories in Industrial Mathematics</i>, vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham: Springer International Publishing, 2022.","ama":"Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. <i>German Success Stories in Industrial Mathematics</i>. Vol 35. Mathematics in Industry. Springer International Publishing; 2022. doi:<a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">10.1007/978-3-030-81455-7_23</a>","bibtex":"@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles}, volume={35}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">10.1007/978-3-030-81455-7_23</a>}, booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }","mla":"Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous Vehicles.” <i>German Success Stories in Industrial Mathematics</i>, edited by H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:<a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">10.1007/978-3-030-81455-7_23</a>."},"place":"Cham","status":"public","_id":"30294","publisher":"Springer International Publishing","editor":[{"first_name":"H. G.","last_name":"Bock","full_name":"Bock, H. G."},{"full_name":"Küfer, K.-H.","first_name":"K.-H.","last_name":"Küfer"},{"full_name":"Maas, P.","last_name":"Maas","first_name":"P."},{"first_name":"A.","last_name":"Milde","full_name":"Milde, A."},{"full_name":"Schulz, V.","last_name":"Schulz","first_name":"V."}],"volume":35,"user_id":"47427"},{"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-03-24T12:26:10Z","publication":"AIMS","citation":{"ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations,” <i>AIMS</i>, vol. 14(1), pp. 57–89, 2022.","apa":"Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2022). Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>, <i>14(1)</i>, 57–89.","mla":"Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i>, vol. 14(1), 2022, pp. 57–89.","bibtex":"@article{Cresson_Jiménez_Ober-Blöbaum_2022, title={Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations}, volume={14(1)}, journal={AIMS}, author={Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}, year={2022}, pages={57–89} }","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.","ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>. 2022;14(1):57-89.","chicago":"Cresson, Jacky, Fernando Jiménez, and Sina Ober-Blöbaum. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i> 14(1) (2022): 57–89."},"user_id":"15694","volume":"14(1)","page":"57-89","_id":"30490","language":[{"iso":"eng"}],"date_updated":"2022-03-24T12:26:32Z","status":"public","title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","year":"2022","author":[{"first_name":"Jacky","last_name":"Cresson","full_name":"Cresson, Jacky"},{"full_name":"Jiménez, Fernando","first_name":"Fernando","last_name":"Jiménez"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"}]},{"publication":"Journal of Optimization Theory and Applications","citation":{"ama":"Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>","bibtex":"@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property in Optimal Microbial Metabolite Production}, DOI={<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022} }","mla":"Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","chicago":"Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, 2022. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>.","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022).","apa":"Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., &#38; Pomet, J.-B. (2022). Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>","ieee":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike Property in Optimal Microbial Metabolite Production,” <i>Journal of Optimization Theory and Applications</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>."},"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic> phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property is further used in order to design simple and realistic suboptimal control strategies.</jats:p>"}],"date_created":"2022-04-08T17:23:13Z","type":"journal_article","keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"department":[{"_id":"636"}],"status":"public","title":"Turnpike Property in Optimal Microbial Metabolite Production","year":"2022","author":[{"full_name":"Caillau, Jean-Baptiste","last_name":"Caillau","first_name":"Jean-Baptiste"},{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"full_name":"Gouzé, Jean-Luc","first_name":"Jean-Luc","last_name":"Gouzé"},{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"first_name":"Jean-Baptiste","last_name":"Pomet","full_name":"Pomet, Jean-Baptiste"}],"publication_identifier":{"issn":["0022-3239","1573-2878"]},"date_updated":"2022-04-08T18:23:02Z","publication_status":"published","_id":"30861","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","doi":"10.1007/s10957-022-02023-0","user_id":"87909"},{"_id":"31982","publisher":"Springer Science and Business Media LLC","page":"303-394","volume":229,"user_id":"70575","status":"public","citation":{"mla":"Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i>, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>.","ama":"Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones mathematicae</i>. 2022;229(1):303-394. doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>","bibtex":"@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>}, number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }","apa":"Cekić, M., Delarue, B., Dyatlov, S., &#38; Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones Mathematicae</i>, <i>229</i>(1), 303–394. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>","ieee":"M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” <i>Inventiones mathematicae</i>, vol. 229, no. 1, pp. 303–394, 2022, doi: <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>.","chicago":"Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i> 229, no. 1 (2022): 303–94. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>.","short":"M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394."},"language":[{"iso":"eng"}],"doi":"10.1007/s00222-022-01108-x","publication_identifier":{"issn":["0020-9910","1432-1297"]},"author":[{"first_name":"Mihajlo","last_name":"Cekić","full_name":"Cekić, Mihajlo"},{"full_name":"Delarue, Benjamin","last_name":"Delarue","first_name":"Benjamin","id":"70575"},{"full_name":"Dyatlov, Semyon","first_name":"Semyon","last_name":"Dyatlov"},{"first_name":"Gabriel P.","last_name":"Paternain","full_name":"Paternain, Gabriel P."}],"year":"2022","title":"The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds","intvolume":"       229","date_updated":"2022-06-21T11:55:15Z","publication_status":"published","date_created":"2022-06-20T08:24:17Z","department":[{"_id":"548"}],"keyword":["General Mathematics"],"type":"journal_article","issue":"1","publication":"Inventiones mathematicae","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with Betti number <jats:inline-formula><jats:alternatives><jats:tex-math>$$b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mi>b</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, the order of vanishing of the Ruelle zeta function at zero equals <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, while in the hyperbolic case it is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-2b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>Σ</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with harmonic 1-forms on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>","lang":"eng"}]},{"publication":"Anfangsunterricht für alle Kinder - Willkommen in der Schule!","citation":{"apa":"Häsel-Weide, U., Wallner, M., &#38; Hattermann, M. (2022). Symmetrieverständnis von Anfang an. In M. Gutzmann, U. Carle, &#38; Grundschulverband e. V. (Eds.), <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i> (pp. 200–215).","mla":"Häsel-Weide, Uta, et al. “Symmetrieverständnis von Anfang an.” <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>, edited by M. Gutzmann et al., 2022, pp. 200–15.","ieee":"U. Häsel-Weide, M. Wallner, and M. Hattermann, “Symmetrieverständnis von Anfang an,” in <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>, M. Gutzmann, U. Carle, and Grundschulverband e. V., Eds. Frankfurt a. M., 2022, pp. 200–215.","short":"U. Häsel-Weide, M. Wallner, M. Hattermann, in: M. Gutzmann, U. Carle, Grundschulverband e. V. (Eds.), Anfangsunterricht für alle Kinder - Willkommen in der Schule!, Frankfurt a. M., 2022, pp. 200–215.","ama":"Häsel-Weide U, Wallner M, Hattermann M. Symmetrieverständnis von Anfang an. In: Gutzmann M, Carle U, Grundschulverband e. V., eds. <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>. ; 2022:200-215.","chicago":"Häsel-Weide, Uta, Melina Wallner, and M. Hattermann. “Symmetrieverständnis von Anfang an.” In <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>, edited by M. Gutzmann, U. Carle, and Grundschulverband e. V., 200–215. Frankfurt a. M., 2022.","bibtex":"@inbook{Häsel-Weide_Wallner_Hattermann_2022, place={Frankfurt a. M.}, title={Symmetrieverständnis von Anfang an}, booktitle={Anfangsunterricht für alle Kinder - Willkommen in der Schule!}, author={Häsel-Weide, Uta and Wallner, Melina and Hattermann, M.}, editor={Gutzmann, M. and Carle, U. and Grundschulverband e. V.}, year={2022}, pages={200–215} }"},"type":"book_chapter","department":[{"_id":"98"},{"_id":"543"}],"date_created":"2022-06-28T06:30:12Z","place":"Frankfurt a. M.","publication_status":"published","date_updated":"2022-07-05T06:48:40Z","title":"Symmetrieverständnis von Anfang an","year":"2022","status":"public","author":[{"full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta","id":"60267"},{"id":"45445","last_name":"Wallner","first_name":"Melina","full_name":"Wallner, Melina"},{"last_name":"Hattermann","first_name":"M.","full_name":"Hattermann, M."}],"corporate_editor":["Grundschulverband e. V."],"user_id":"45445","editor":[{"full_name":"Gutzmann, M.","last_name":"Gutzmann","first_name":"M."},{"full_name":"Carle, U.","last_name":"Carle","first_name":"U."}],"page":"200-215","language":[{"iso":"ger"}],"_id":"32233"},{"publication":"Qualifizierung für Inklusion. Sekundarstufe","citation":{"bibtex":"@inbook{Häsel-Weide_Seitz_Wallner_Wilke_2022, place={Münster}, title={Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe}, booktitle={Qualifizierung für Inklusion. Sekundarstufe}, publisher={Waxmann}, author={Häsel-Weide, Uta and Seitz, S. and Wallner, Melina and Wilke, Y.}, editor={Lutz, D. and Becker, J. and Buchhaupt, F. and Katzenbach, D. and Strecker, A. and Urban, M.}, year={2022}, pages={83–100} }","chicago":"Häsel-Weide, Uta, S. Seitz, Melina Wallner, and Y. Wilke. “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe.” In <i>Qualifizierung für Inklusion. Sekundarstufe</i>, edited by D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, 83–100. Münster: Waxmann, 2022.","short":"U. Häsel-Weide, S. Seitz, M. Wallner, Y. Wilke, in: D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, M. Urban (Eds.), Qualifizierung für Inklusion. Sekundarstufe, Waxmann, Münster, 2022, pp. 83–100.","ama":"Häsel-Weide U, Seitz S, Wallner M, Wilke Y. Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe. In: Lutz D, Becker J, Buchhaupt F, Katzenbach D, Strecker A, Urban M, eds. <i>Qualifizierung für Inklusion. Sekundarstufe</i>. Waxmann; 2022:83-100.","ieee":"U. Häsel-Weide, S. Seitz, M. Wallner, and Y. Wilke, “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe,” in <i>Qualifizierung für Inklusion. Sekundarstufe</i>, D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, Eds. Münster: Waxmann, 2022, pp. 83–100.","mla":"Häsel-Weide, Uta, et al. “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe.” <i>Qualifizierung für Inklusion. Sekundarstufe</i>, edited by D. Lutz et al., Waxmann, 2022, pp. 83–100.","apa":"Häsel-Weide, U., Seitz, S., Wallner, M., &#38; Wilke, Y. (2022). Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe. In D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, &#38; M. Urban (Eds.), <i>Qualifizierung für Inklusion. Sekundarstufe</i> (pp. 83–100). Waxmann."},"type":"book_chapter","department":[{"_id":"98"},{"_id":"543"}],"date_created":"2022-07-11T05:31:28Z","place":"Münster","publication_status":"published","date_updated":"2022-07-11T05:31:46Z","year":"2022","title":"Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe","status":"public","author":[{"id":"60267","full_name":"Häsel-Weide, Uta","first_name":"Uta","last_name":"Häsel-Weide"},{"first_name":"S.","last_name":"Seitz","full_name":"Seitz, S."},{"id":"45445","first_name":"Melina","last_name":"Wallner","full_name":"Wallner, Melina"},{"full_name":"Wilke, Y.","last_name":"Wilke","first_name":"Y."}],"user_id":"85821","editor":[{"last_name":"Lutz","first_name":"D.","full_name":"Lutz, D."},{"first_name":"J.","last_name":"Becker","full_name":"Becker, J."},{"full_name":"Buchhaupt, F.","first_name":"F.","last_name":"Buchhaupt"},{"full_name":"Katzenbach, D.","first_name":"D.","last_name":"Katzenbach"},{"full_name":"Strecker, A.","first_name":"A.","last_name":"Strecker"},{"first_name":"M.","last_name":"Urban","full_name":"Urban, M."}],"page":"83-100","publisher":"Waxmann","_id":"32339","language":[{"iso":"ger"}]},{"citation":{"mla":"Hähn, K., et al. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2, 2022.","bibtex":"@article{Hähn_Häsel-Weide_Scherer_2022, title={Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.}, volume={3}, number={2}, journal={QfI - Qualifizierung für Inklusion}, author={Hähn, K. and Häsel-Weide, Uta and Scherer, P.}, year={2022} }","ama":"Hähn K, Häsel-Weide U, Scherer P. Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>. 2022;3(2).","ieee":"K. Hähn, U. Häsel-Weide, and P. Scherer, “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.,” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2, 2022.","apa":"Hähn, K., Häsel-Weide, U., &#38; Scherer, P. (2022). Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>, <i>3</i>(2).","short":"K. Hähn, U. Häsel-Weide, P. Scherer, QfI - Qualifizierung für Inklusion 3 (2022).","chicago":"Hähn, K., Uta Häsel-Weide, and P. Scherer. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i> 3, no. 2 (2022)."},"publication":"QfI - Qualifizierung für Inklusion","issue":"2","related_material":{"link":[{"relation":"contains","url":"https://doi.org/10.21248/qfi.72"}]},"date_created":"2022-07-11T05:13:52Z","department":[{"_id":"98"},{"_id":"543"}],"type":"journal_article","author":[{"full_name":"Hähn, K.","last_name":"Hähn","first_name":"K."},{"first_name":"Uta","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","id":"60267"},{"full_name":"Scherer, P.","last_name":"Scherer","first_name":"P."}],"title":"Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.","year":"2022","status":"public","intvolume":"         3","publication_status":"published","date_updated":"2022-07-11T05:31:41Z","_id":"32338","language":[{"iso":"ger"}],"volume":3,"user_id":"85821"},{"doi":"10.1088/1751-8121/ac7d22","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf","open_access":"1"}],"intvolume":"        55","date_updated":"2022-07-18T14:26:41Z","publication_status":"published","author":[{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"},{"full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889","id":"81513"},{"id":"47427","first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"}],"title":"Koopman analysis of quantum systems","year":"2022","department":[{"_id":"655"},{"_id":"101"}],"type":"journal_article","date_created":"2022-01-31T09:49:40Z","abstract":[{"text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science.","lang":"eng"}],"issue":"31","publication":"Journal of Physics A: Mathematical and Theoretical","volume":55,"user_id":"47427","publisher":"IOP Publishing Ltd.","_id":"29673","page":"314002","status":"public","oa":"1","external_id":{"arxiv":["2201.12062"]},"citation":{"apa":"Klus, S., Nüske, F., &#38; Peitz, S. (2022). Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(31), 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>","ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, p. 314002, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 31 (2022): 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>.","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002.","mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(31):314002. doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }"}},{"date_updated":"2022-12-20T15:28:54Z","author":[{"first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643"}],"year":"2022","status":"public","title":"Using second-order information in gradient sampling methods for  nonsmooth optimization","user_id":"32643","language":[{"iso":"eng"}],"_id":"34618","main_file_link":[{"url":"https://arxiv.org/pdf/2210.04579","open_access":"1"}],"abstract":[{"text":"In this article, we show how second-order derivative information can be\r\nincorporated into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order information we consider is essentially the set of coefficients of\r\nall second-order Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based on this concept, we define a model of the objective as the\r\nmaximum of these Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed ball) results in a simple descent method, for which\r\nwe prove convergence to minimal points in case the objective is convex. To\r\nobtain an implementable method, we construct an approximation scheme for the\r\nsecond-order information based on sampling objective values, gradients and\r\nHessian matrices at finitely many points. Using a set of test problems, we\r\ncompare the resulting method to five other available solvers. Considering the\r\nnumber of function evaluations, the results suggest that the method we propose\r\nis superior to the standard gradient sampling method, and competitive compared\r\nto other methods.","lang":"eng"}],"citation":{"bibtex":"@article{Gebken_2022, title={Using second-order information in gradient sampling methods for  nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken, Bennet}, year={2022} }","ama":"Gebken B. Using second-order information in gradient sampling methods for  nonsmooth optimization. <i>arXiv:221004579</i>. Published online 2022.","mla":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.","chicago":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.","short":"B. Gebken, ArXiv:2210.04579 (2022).","ieee":"B. Gebken, “Using second-order information in gradient sampling methods for  nonsmooth optimization,” <i>arXiv:2210.04579</i>. 2022.","apa":"Gebken, B. (2022). Using second-order information in gradient sampling methods for  nonsmooth optimization. In <i>arXiv:2210.04579</i>."},"publication":"arXiv:2210.04579","department":[{"_id":"101"}],"oa":"1","type":"preprint","date_created":"2022-12-20T15:25:17Z","external_id":{"arxiv":["2210.04579"]}},{"publication":"p-Adic Numbers, Ultrametric Analysis, and Applications","issue":"2","date_created":"2022-12-21T19:27:51Z","keyword":["20Exx","22Exx","32Cxx"],"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"title":"Non-Lie subgroups in Lie groups over local fields of positive characteristic","year":"2022","publication_identifier":{"issn":["2070-0466"]},"author":[{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"}],"date_updated":"2022-12-21T19:30:25Z","intvolume":"        14","article_type":"original","language":[{"iso":"eng"}],"doi":"10.1134/S2070046622020042","citation":{"ieee":"H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive characteristic,” <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>, vol. 14, no. 2, pp. 138–144, 2022, doi: <a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>.","apa":"Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive characteristic. <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>, <i>14</i>(2), 138–144. <a href=\"https://doi.org/10.1134/S2070046622020042\">https://doi.org/10.1134/S2070046622020042</a>","chicago":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i> 14, no. 2 (2022): 138–144. <a href=\"https://doi.org/10.1134/S2070046622020042\">https://doi.org/10.1134/S2070046622020042</a>.","short":"H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022) 138–144.","mla":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>, vol. 14, no. 2, 2022, pp. 138–144, doi:<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>.","bibtex":"@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local fields of positive characteristic}, volume={14}, DOI={<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>}, number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications}, author={Glöckner, Helge}, year={2022}, pages={138–144} }","ama":"Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic. <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>. 2022;14(2):138–144. doi:<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>"},"quality_controlled":"1","status":"public","page":"138–144","_id":"34792","user_id":"178","volume":14},{"date_created":"2022-12-21T19:24:48Z","keyword":["58D15","22E65","26E15","26E20","46E40","46T20","58A05"],"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"issue":"2","publication":"Annals of Global Analysis and Geometry","language":[{"iso":"eng"}],"doi":"10.1007/s10455-021-09816-y","title":"Manifolds of mappings on Cartesian products","year":"2022","publication_identifier":{"issn":["0232-704X"]},"author":[{"full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge","id":"178"},{"full_name":"Schmeding, Alexander","last_name":"Schmeding","first_name":"Alexander"}],"date_updated":"2022-12-21T19:27:09Z","intvolume":"        61","article_type":"original","citation":{"short":"H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022) 359–398.","chicago":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” <i>Annals of Global Analysis and Geometry</i> 61, no. 2 (2022): 359–398. <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">https://doi.org/10.1007/s10455-021-09816-y</a>.","apa":"Glöckner, H., &#38; Schmeding, A. (2022). Manifolds of mappings on Cartesian products. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(2), 359–398. <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">https://doi.org/10.1007/s10455-021-09816-y</a>","ieee":"H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, pp. 359–398, 2022, doi: <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>.","ama":"Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. <i>Annals of Global Analysis and Geometry</i>. 2022;61(2):359–398. doi:<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>","bibtex":"@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian products}, volume={61}, DOI={<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>}, number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner, Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }","mla":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, 2022, pp. 359–398, doi:<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>."},"quality_controlled":"1","page":"359–398","_id":"34791","user_id":"178","volume":61,"status":"public"},{"publication":"Axioms","issue":"5","abstract":[{"lang":"eng","text":"We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E&times;E is a kR-space."}],"date_created":"2022-12-21T20:02:29Z","type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"title":"Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces","year":"2022","publication_identifier":{"issn":["2075-1680"]},"author":[{"full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge","id":"178"}],"date_updated":"2022-12-22T07:31:55Z","intvolume":"        11","article_type":"original","language":[{"iso":"eng"}],"doi":"10.3390/axioms11050221","citation":{"apa":"Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href=\"https://doi.org/10.3390/axioms11050221\">https://doi.org/10.3390/axioms11050221</a>","ieee":"H. Glöckner, “Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022, doi: <a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>.","short":"H. Glöckner, Axioms 11 (2022).","chicago":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i> 11, no. 5 (2022). <a href=\"https://doi.org/10.3390/axioms11050221\">https://doi.org/10.3390/axioms11050221</a>.","mla":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022, doi:<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>.","ama":"Glöckner H. Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. <i>Axioms</i>. 2022;11(5). doi:<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>","bibtex":"@article{Glöckner_2022, title={Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11}, DOI={<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>}, number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }"},"quality_controlled":"1","status":"public","_id":"34796","user_id":"178","volume":11},{"date_updated":"2022-12-22T07:44:08Z","author":[{"full_name":"Glöckner, Helge","first_name":"Helge","last_name":"Glöckner","id":"178"}],"year":"2022","status":"public","title":"Birkhoff decompositions for loop groups with coefficient algebras","user_id":"178","language":[{"iso":"eng"}],"_id":"34804","abstract":[{"lang":"eng","text":"Starting with a finite-dimensional complex Lie algebra, we extend scalars\r\nusing suitable commutative topological algebras. We study Birkhoff\r\ndecompositions for the corresponding loop groups. Some results remain valid for\r\nloop groups with valued in complex Banach-Lie groups."}],"citation":{"bibtex":"@article{Glöckner_2022, title={Birkhoff decompositions for loop groups with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge}, year={2022} }","ama":"Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras. <i>arXiv:220611711</i>. Published online 2022.","mla":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” <i>ArXiv:2206.11711</i>, 2022.","short":"H. Glöckner, ArXiv:2206.11711 (2022).","chicago":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” <i>ArXiv:2206.11711</i>, 2022.","ieee":"H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,” <i>arXiv:2206.11711</i>. 2022.","apa":"Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient algebras. In <i>arXiv:2206.11711</i>."},"publication":"arXiv:2206.11711","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"preprint","date_created":"2022-12-22T07:42:07Z","external_id":{"arxiv":["2206.11711"]}},{"main_file_link":[{"url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779","open_access":"1"}],"_id":"31556","language":[{"iso":"eng"}],"doi":"10.17619/UNIPB/1-1327","user_id":"32643","status":"public","title":"Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization","year":"2022","author":[{"id":"32643","last_name":"Gebken","first_name":"Bennet","full_name":"Gebken, Bennet"}],"date_updated":"2022-06-01T07:13:09Z","date_created":"2022-06-01T06:48:08Z","type":"dissertation","oa":"1","department":[{"_id":"101"}],"supervisor":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"citation":{"chicago":"Gebken, Bennet. <i>Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization</i>, 2022. <a href=\"https://doi.org/10.17619/UNIPB/1-1327\">https://doi.org/10.17619/UNIPB/1-1327</a>.","short":"B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization, 2022.","apa":"Gebken, B. (2022). <i>Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1327\">https://doi.org/10.17619/UNIPB/1-1327</a>","ieee":"B. Gebken, <i>Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization</i>. 2022.","ama":"Gebken B. <i>Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization</i>.; 2022. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1327\">10.17619/UNIPB/1-1327</a>","bibtex":"@book{Gebken_2022, title={Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1327\">10.17619/UNIPB/1-1327</a>}, author={Gebken, Bennet}, year={2022} }","mla":"Gebken, Bennet. <i>Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization</i>. 2022, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1327\">10.17619/UNIPB/1-1327</a>."},"abstract":[{"text":"Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten. Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor gefunden werden soll, für den die Datenpunkte kritisch sind.","lang":"ger"},{"text":"Multiobjective optimization is concerned with the simultaneous optimization of multiple scalar-valued functions. In this case, a point is optimal if there is no other point that is at least as good in all objectives and better in at least one objective. A necessary condition for optimality can be derived based on first-order information of the objectives. The set of points that satisfy this necessary condition is called the Pareto critical set. This thesis presents new results about Pareto critical sets for smooth and nonsmooth multiobjective optimization problems, both in terms of their efficient computation and structural properties. In the smooth case they are computed via a continuation method and in the nonsmooth case via a descent method. Afterwards, the structure of the boundary of the Pareto critical set is analyzed, which consists of Pareto critical sets of smaller subproblems. Finally, inverse problems are considered, where a data set is given and an objective vector is sought for which the data points are critical.","lang":"eng"}]},{"external_id":{"arxiv":["2208.12094"]},"date_created":"2022-08-26T06:08:06Z","type":"preprint","department":[{"_id":"101"},{"_id":"655"}],"oa":"1","publication":"arXiv:2208.12094","citation":{"mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>, 2022.","ama":"Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. <i>arXiv:220812094</i>. Published online 2022.","bibtex":"@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }","apa":"Berkemeier, M. B., &#38; Peitz, S. (2022). Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. In <i>arXiv:2208.12094</i>.","ieee":"M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients,” <i>arXiv:2208.12094</i>. 2022.","short":"M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>, 2022."},"abstract":[{"lang":"eng","text":"In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem."}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2208.12094"}],"language":[{"iso":"eng"}],"_id":"33150","user_id":"47427","status":"public","title":"Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients","year":"2022","author":[{"id":"51701","full_name":"Berkemeier, Manuel Bastian","last_name":"Berkemeier","first_name":"Manuel Bastian"},{"id":"47427","last_name":"Peitz","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"}],"date_updated":"2022-08-26T06:12:10Z"},{"citation":{"bibtex":"@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44}, DOI={<a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>}, number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian}, year={2022}, pages={7797–7808} }","ama":"Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 2022;44(11):7797-7808. doi:<a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>","mla":"Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 44, no. 11, IEEE, 2022, pp. 7797–808, doi:<a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>.","short":"K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (2022) 7797–7808.","chicago":"Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i> 44, no. 11 (2022): 7797–7808. <a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">https://doi.org/10.1109/TPAMI.2021.3114962</a>.","ieee":"K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 44, no. 11, pp. 7797–7808, 2022, doi: <a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>.","apa":"Bieker, K., Gebken, B., &#38; Peitz, S. (2022). On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, <i>44</i>(11), 7797–7808. <a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">https://doi.org/10.1109/TPAMI.2021.3114962</a>"},"file_date_updated":"2021-09-25T11:59:15Z","oa":"1","status":"public","has_accepted_license":"1","publisher":"IEEE","_id":"20731","page":"7797-7808","volume":44,"ddc":["510"],"user_id":"47427","issue":"11","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","abstract":[{"text":"We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach.","lang":"eng"}],"date_created":"2020-12-15T07:46:36Z","file":[{"date_updated":"2021-09-25T11:59:15Z","relation":"main_file","file_size":7990831,"access_level":"closed","file_name":"On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf","success":1,"content_type":"application/pdf","file_id":"25040","creator":"speitz","date_created":"2021-09-25T11:59:15Z"}],"department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"type":"journal_article","author":[{"id":"32829","full_name":"Bieker, Katharina","first_name":"Katharina","last_name":"Bieker"},{"full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet","id":"32643"},{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian","full_name":"Peitz, Sebastian"}],"year":"2022","title":"On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation","intvolume":"        44","article_type":"original","date_updated":"2022-10-21T12:27:16Z","publication_status":"epub_ahead","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772","open_access":"1"}],"doi":"10.1109/TPAMI.2021.3114962"},{"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","keyword":["Applied Mathematics","General Mathematics"],"date_created":"2023-01-05T16:23:34Z","publication":"Journal of the European Mathematical Society","issue":"3","doi":"10.4171/jems/1103","language":[{"iso":"eng"}],"intvolume":"        24","publication_status":"published","date_updated":"2023-01-06T08:47:35Z","publication_identifier":{"issn":["1435-9855"]},"author":[{"first_name":"Yannick","last_name":"Guedes Bonthonneau","full_name":"Guedes Bonthonneau, Yannick"},{"full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178"}],"year":"2022","title":"Ruelle–Pollicott resonances for manifolds with hyperbolic cusps","citation":{"ama":"Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>. 2022;24(3):851-923. doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>","bibtex":"@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}, volume={24}, DOI={<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>}, number={3}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau, Yannick and Weich, Tobias}, year={2022}, pages={851–923} }","mla":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 851–923, doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","chicago":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i> 24, no. 3 (2022): 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>.","short":"Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.","apa":"Guedes Bonthonneau, Y., &#38; Weich, T. (2022). Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>, <i>24</i>(3), 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>","ieee":"Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds with hyperbolic cusps,” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, pp. 851–923, 2022, doi: <a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>."},"volume":24,"user_id":"49178","_id":"35306","publisher":"European Mathematical Society - EMS - Publishing House GmbH","page":"851-923","status":"public"},{"date_created":"2022-12-20T17:37:16Z","keyword":["Applied Mathematics","Computational Mathematics"],"type":"journal_article","department":[{"_id":"10"}],"publication":"Journal of Computational and Applied Mathematics","article_number":"114118","language":[{"iso":"eng"}],"doi":"10.1016/j.cam.2022.114118","year":"2022","title":"L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data","publication_identifier":{"issn":["0377-0427"]},"author":[{"id":"42608","last_name":"Hesse","orcid":"0000-0003-4125-1941","first_name":"Kerstin","full_name":"Hesse, Kerstin"},{"full_name":"Le Gia, Quoc Thong","first_name":"Quoc Thong","last_name":"Le Gia"}],"publication_status":"published","date_updated":"2023-01-09T08:23:56Z","intvolume":"       408","citation":{"ama":"Hesse K, Le Gia QT. L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. <i>Journal of Computational and Applied Mathematics</i>. 2022;408. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>","bibtex":"@article{Hesse_Le Gia_2022, title={L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}, volume={408}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>}, number={114118}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier BV}, author={Hesse, Kerstin and Le Gia, Quoc Thong}, year={2022} }","mla":"Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 408, 114118, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>.","short":"K. Hesse, Q.T. Le Gia, Journal of Computational and Applied Mathematics 408 (2022).","chicago":"Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.” <i>Journal of Computational and Applied Mathematics</i> 408 (2022). <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">https://doi.org/10.1016/j.cam.2022.114118</a>.","apa":"Hesse, K., &#38; Le Gia, Q. T. (2022). L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. <i>Journal of Computational and Applied Mathematics</i>, <i>408</i>, Article 114118. <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">https://doi.org/10.1016/j.cam.2022.114118</a>","ieee":"K. Hesse and Q. T. Le Gia, “L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 408, Art. no. 114118, 2022, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>."},"_id":"34633","publisher":"Elsevier BV","user_id":"14931","volume":408,"status":"public"}]