[{"user_id":"37888","doi":"10.1007/978-3-658-34067-4_2","language":[{"iso":"ger"}],"_id":"56202","publisher":"Springer Fachmedien Wiesbaden","publication_status":"published","date_updated":"2024-11-26T11:48:53Z","publication_identifier":{"isbn":["9783658340667","9783658340674"],"issn":["2197-8751","2197-876X"]},"author":[{"full_name":"Sjuts, Johann","last_name":"Sjuts","first_name":"Johann"}],"status":"public","title":"Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen","year":"2022","department":[{"_id":"643"}],"type":"book_chapter","date_created":"2024-09-23T08:53:28Z","place":"Wiesbaden","citation":{"apa":"Sjuts, J. (2022). Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen. In <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Springer Fachmedien Wiesbaden. <a href=\"https://doi.org/10.1007/978-3-658-34067-4_2\">https://doi.org/10.1007/978-3-658-34067-4_2</a>","ieee":"J. Sjuts, “Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen,” in <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, Wiesbaden: Springer Fachmedien Wiesbaden, 2022.","short":"J. Sjuts, in: Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, Springer Fachmedien Wiesbaden, Wiesbaden, 2022.","chicago":"Sjuts, Johann. “Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen.” In <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. <a href=\"https://doi.org/10.1007/978-3-658-34067-4_2\">https://doi.org/10.1007/978-3-658-34067-4_2</a>.","mla":"Sjuts, Johann. “Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen.” <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, Springer Fachmedien Wiesbaden, 2022, doi:<a href=\"https://doi.org/10.1007/978-3-658-34067-4_2\">10.1007/978-3-658-34067-4_2</a>.","ama":"Sjuts J. Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen. In: <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Springer Fachmedien Wiesbaden; 2022. doi:<a href=\"https://doi.org/10.1007/978-3-658-34067-4_2\">10.1007/978-3-658-34067-4_2</a>","bibtex":"@inbook{Sjuts_2022, place={Wiesbaden}, title={Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen}, DOI={<a href=\"https://doi.org/10.1007/978-3-658-34067-4_2\">10.1007/978-3-658-34067-4_2</a>}, booktitle={Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Fachmedien Wiesbaden}, author={Sjuts, Johann}, year={2022} }"},"publication":"Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik"},{"department":[{"_id":"91"}],"type":"journal_article","date_created":"2024-02-19T06:36:17Z","citation":{"ama":"Hilgert J, Weich T, Bux K-U. Poisson transforms for trees of bounded degree. <i>J of Spectral Theory</i>. 2022;12:659-681.","bibtex":"@article{Hilgert_Weich_Bux_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, journal={J. of Spectral Theory}, author={Hilgert, Joachim and Weich, Tobias and Bux, K.-U.}, year={2022}, pages={659–681} }","mla":"Hilgert, Joachim, et al. “Poisson Transforms for Trees of Bounded Degree.” <i>J. of Spectral Theory</i>, vol. 12, 2022, pp. 659–81.","chicago":"Hilgert, Joachim, Tobias Weich, and K.-U. Bux. “Poisson Transforms for Trees of Bounded Degree.” <i>J. of Spectral Theory</i> 12 (2022): 659–81.","short":"J. Hilgert, T. Weich, K.-U. Bux, J. of Spectral Theory 12 (2022) 659–681.","apa":"Hilgert, J., Weich, T., &#38; Bux, K.-U. (2022). Poisson transforms for trees of bounded degree. <i>J. of Spectral Theory</i>, <i>12</i>, 659–681.","ieee":"J. Hilgert, T. Weich, and K.-U. Bux, “Poisson transforms for trees of bounded degree,” <i>J. of Spectral Theory</i>, vol. 12, pp. 659–681, 2022."},"publication":"J. of Spectral Theory","volume":12,"user_id":"220","_id":"51385","language":[{"iso":"eng"}],"page":"659-681","intvolume":"        12","publication_status":"published","date_updated":"2026-03-31T08:25:35Z","author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","first_name":"Tobias","orcid":"0000-0002-9648-6919"},{"full_name":"Bux, K.-U.","first_name":"K.-U.","last_name":"Bux"}],"title":"Poisson transforms for trees of bounded degree","status":"public","year":"2022"},{"citation":{"bibtex":"@article{Burban_Alfes-Neumann_Raum_2022, title={A classification of polyharmonic Maaß forms via quiver representations}, author={Burban, Igor and Alfes-Neumann, C. and Raum, M.}, year={2022} }","ama":"Burban I, Alfes-Neumann C, Raum M. A classification of polyharmonic Maaß forms via quiver representations. Published online 2022.","mla":"Burban, Igor, et al. <i>A Classification of Polyharmonic Maaß Forms via Quiver Representations</i>. 2022.","chicago":"Burban, Igor, C. Alfes-Neumann, and M. Raum. “A Classification of Polyharmonic Maaß Forms via Quiver Representations,” 2022.","short":"I. Burban, C. Alfes-Neumann, M. Raum, (2022).","ieee":"I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic Maaß forms via quiver representations.” 2022.","apa":"Burban, I., Alfes-Neumann, C., &#38; Raum, M. (2022). <i>A classification of polyharmonic Maaß forms via quiver representations</i>."},"type":"preprint","department":[{"_id":"602"}],"date_created":"2023-05-07T00:54:50Z","date_updated":"2026-07-07T06:20:58Z","publication_status":"published","year":"2022","status":"public","title":"A classification of polyharmonic Maaß forms via quiver representations","author":[{"full_name":"Burban, Igor","last_name":"Burban","first_name":"Igor","id":"72064"},{"full_name":"Alfes-Neumann, C.","first_name":"C.","last_name":"Alfes-Neumann"},{"full_name":"Raum, M.","first_name":"M.","last_name":"Raum"}],"user_id":"72064","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2207.02278"}],"_id":"44537","language":[{"iso":"eng"}]},{"user_id":"81513","doi":"10.1016/j.physd.2021.133018","article_number":"133018","_id":"24169","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-01-06T06:56:08Z","year":"2021","title":"Tensor-based computation of metastable and coherent sets","status":"public","publication_identifier":{"issn":["0167-2789"]},"author":[{"id":"81513","full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889"},{"full_name":"Gelß, Patrick","last_name":"Gelß","first_name":"Patrick"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"last_name":"Clementi","first_name":"Cecilia","full_name":"Clementi, Cecilia"}],"type":"journal_article","department":[{"_id":"101"}],"date_created":"2021-09-12T08:51:24Z","publication":"Physica D: Nonlinear Phenomena","citation":{"mla":"Nüske, Feliks, et al. “Tensor-Based Computation of Metastable and Coherent Sets.” <i>Physica D: Nonlinear Phenomena</i>, 133018, 2021, doi:<a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>.","bibtex":"@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation of metastable and coherent sets}, DOI={<a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>}, number={133018}, journal={Physica D: Nonlinear Phenomena}, author={Nüske, Feliks and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}, year={2021} }","ama":"Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable and coherent sets. <i>Physica D: Nonlinear Phenomena</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>","ieee":"F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of metastable and coherent sets,” <i>Physica D: Nonlinear Phenomena</i>, Art. no. 133018, 2021, doi: <a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>.","apa":"Nüske, F., Gelß, P., Klus, S., &#38; Clementi, C. (2021). Tensor-based computation of metastable and coherent sets. <i>Physica D: Nonlinear Phenomena</i>, Article 133018. <a href=\"https://doi.org/10.1016/j.physd.2021.133018\">https://doi.org/10.1016/j.physd.2021.133018</a>","short":"F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena (2021).","chicago":"Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based Computation of Metastable and Coherent Sets.” <i>Physica D: Nonlinear Phenomena</i>, 2021. <a href=\"https://doi.org/10.1016/j.physd.2021.133018\">https://doi.org/10.1016/j.physd.2021.133018</a>."}},{"type":"journal_article","department":[{"_id":"101"}],"date_created":"2021-09-12T08:52:57Z","publication":"Machine Learning: Science and Technology","citation":{"bibtex":"@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry}, DOI={<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>}, number={045016}, journal={Machine Learning: Science and Technology}, author={Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }","ama":"Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. <i>Machine Learning: Science and Technology</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>","mla":"Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” <i>Machine Learning: Science and Technology</i>, 045016, 2021, doi:<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>.","short":"S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology (2021).","chicago":"Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” <i>Machine Learning: Science and Technology</i>, 2021. <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">https://doi.org/10.1088/2632-2153/ac14ad</a>.","ieee":"S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry,” <i>Machine Learning: Science and Technology</i>, Art. no. 045016, 2021, doi: <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>.","apa":"Klus, S., Gelß, P., Nüske, F., &#38; Noé, F. (2021). Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. <i>Machine Learning: Science and Technology</i>, Article 045016. <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">https://doi.org/10.1088/2632-2153/ac14ad</a>"},"user_id":"81513","doi":"10.1088/2632-2153/ac14ad","article_number":"045016","language":[{"iso":"eng"}],"_id":"24170","publication_status":"published","date_updated":"2022-01-06T06:56:08Z","year":"2021","title":"Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry","status":"public","author":[{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"full_name":"Gelß, Patrick","first_name":"Patrick","last_name":"Gelß"},{"id":"81513","full_name":"Nüske, Feliks","first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske"},{"full_name":"Noé, Frank","first_name":"Frank","last_name":"Noé"}],"publication_identifier":{"issn":["2632-2153"]}},{"department":[{"_id":"101"}],"type":"journal_article","date_created":"2021-02-08T13:16:07Z","citation":{"short":"C. Goelz, K. Mora, J.K. Stroehlein, F.K. Haase, M. Dellnitz, C. Reinsberger, S. Vieluf, Cognitive Neurodynamics (2021).","chicago":"Goelz, Christian, Karin Mora, Julia Kristin Stroehlein, Franziska Katharina Haase, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” <i>Cognitive Neurodynamics</i>, 2021. <a href=\"https://doi.org/10.1007/s11571-020-09656-9\">https://doi.org/10.1007/s11571-020-09656-9</a>.","apa":"Goelz, C., Mora, K., Stroehlein, J. K., Haase, F. K., Dellnitz, M., Reinsberger, C., &#38; Vieluf, S. (2021). Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. <i>Cognitive Neurodynamics</i>. <a href=\"https://doi.org/10.1007/s11571-020-09656-9\">https://doi.org/10.1007/s11571-020-09656-9</a>","ieee":"C. Goelz <i>et al.</i>, “Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults,” <i>Cognitive Neurodynamics</i>, 2021.","ama":"Goelz C, Mora K, Stroehlein JK, et al. Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. <i>Cognitive Neurodynamics</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s11571-020-09656-9\">10.1007/s11571-020-09656-9</a>","bibtex":"@article{Goelz_Mora_Stroehlein_Haase_Dellnitz_Reinsberger_Vieluf_2021, title={Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults}, DOI={<a href=\"https://doi.org/10.1007/s11571-020-09656-9\">10.1007/s11571-020-09656-9</a>}, journal={Cognitive Neurodynamics}, author={Goelz, Christian and Mora, Karin and Stroehlein, Julia Kristin and Haase, Franziska Katharina and Dellnitz, Michael and Reinsberger, Claus and Vieluf, Solveig}, year={2021} }","mla":"Goelz, Christian, et al. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” <i>Cognitive Neurodynamics</i>, 2021, doi:<a href=\"https://doi.org/10.1007/s11571-020-09656-9\">10.1007/s11571-020-09656-9</a>."},"publication":"Cognitive Neurodynamics","user_id":"32643","doi":"10.1007/s11571-020-09656-9","language":[{"iso":"eng"}],"_id":"21195","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s11571-020-09656-9.pdf"}],"date_updated":"2022-01-06T06:54:49Z","author":[{"first_name":"Christian","last_name":"Goelz","full_name":"Goelz, Christian"},{"last_name":"Mora","first_name":"Karin","full_name":"Mora, Karin"},{"last_name":"Stroehlein","first_name":"Julia Kristin","full_name":"Stroehlein, Julia Kristin"},{"last_name":"Haase","first_name":"Franziska Katharina","full_name":"Haase, Franziska Katharina"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"full_name":"Reinsberger, Claus","last_name":"Reinsberger","first_name":"Claus"},{"last_name":"Vieluf","first_name":"Solveig","full_name":"Vieluf, Solveig"}],"status":"public","year":"2021","title":"Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults"},{"citation":{"bibtex":"@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models}, volume={26}, DOI={<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>}, number={231}, journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2021} }","ama":"Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational Applications</i>. 2021;26(2). doi:<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical and Computational Applications</i>, vol. 26, no. 2, 31, 2021, doi:<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>.","short":"M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26 (2021).","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical and Computational Applications</i> 26, no. 2 (2021). <a href=\"https://doi.org/10.3390/mca26020031\">https://doi.org/10.3390/mca26020031</a>.","ieee":"M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models,” <i>Mathematical and Computational Applications</i>, vol. 26, no. 2, 2021.","apa":"Berkemeier, M. B., &#38; Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational Applications</i>, <i>26</i>(2). <a href=\"https://doi.org/10.3390/mca26020031\">https://doi.org/10.3390/mca26020031</a>"},"oa":"1","status":"public","volume":26,"user_id":"47427","_id":"21337","abstract":[{"lang":"eng","text":"We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous and expensive problems, i.e., problems that have at least one\r\nobjective function that is computationally expensive. The method is\r\nderivative-free in the sense that neither need derivative information be\r\navailable for the expensive objectives nor are gradients approximated using\r\nrepeated function evaluations as is the case in finite-difference methods.\r\nInstead, a multiobjective trust region approach is used that works similarly to\r\nits well-known scalar pendants. Local surrogate models constructed from\r\nevaluation data of the true objective functions are employed to compute\r\npossible descent directions. In contrast to existing multiobjective trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed radial basis function networks. This has the important advantage\r\nthat the number of data points scales linearly with the parameter space\r\ndimension. The local models qualify as fully linear and the corresponding\r\ngeneral scalar framework is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical points is proven and numerical examples\r\nillustrate our findings."}],"publication":"Mathematical and Computational Applications","issue":"2","department":[{"_id":"101"},{"_id":"655"}],"type":"journal_article","date_created":"2021-03-01T10:46:48Z","intvolume":"        26","publication_status":"published","date_updated":"2022-01-06T06:54:55Z","author":[{"id":"51701","full_name":"Berkemeier, Manuel Bastian","first_name":"Manuel Bastian","last_name":"Berkemeier"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian","orcid":"0000-0002-3389-793X","id":"47427"}],"publication_identifier":{"eissn":["2297-8747"]},"title":"Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models","year":"2021","doi":"10.3390/mca26020031","language":[{"iso":"eng"}],"article_number":"31","main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/2297-8747/26/2/31/pdf"}]},{"publication_status":"published","date_updated":"2022-01-06T06:55:16Z","publication_identifier":{"issn":["1099-4300"]},"author":[{"full_name":"Nüske, Feliks","first_name":"Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889","id":"81513"},{"full_name":"Koltai, Péter","first_name":"Péter","last_name":"Koltai"},{"first_name":"Lorenzo","last_name":"Boninsegna","full_name":"Boninsegna, Lorenzo"},{"full_name":"Clementi, Cecilia","last_name":"Clementi","first_name":"Cecilia"}],"title":"Spectral Properties of Effective Dynamics from Conditional Expectations","year":"2021","status":"public","user_id":"81513","doi":"10.3390/e23020134","_id":"21820","language":[{"iso":"eng"}],"article_number":"134","main_file_link":[{"url":"https://www.mdpi.com/1099-4300/23/2/134","open_access":"1"}],"abstract":[{"text":"<jats:p>The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.</jats:p>","lang":"eng"}],"citation":{"short":"F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).","chicago":"Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi. “Spectral Properties of Effective Dynamics from Conditional Expectations.” <i>Entropy</i>, 2021. <a href=\"https://doi.org/10.3390/e23020134\">https://doi.org/10.3390/e23020134</a>.","ieee":"F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties of Effective Dynamics from Conditional Expectations,” <i>Entropy</i>, 2021.","apa":"Nüske, F., Koltai, P., Boninsegna, L., &#38; Clementi, C. (2021). Spectral Properties of Effective Dynamics from Conditional Expectations. <i>Entropy</i>. <a href=\"https://doi.org/10.3390/e23020134\">https://doi.org/10.3390/e23020134</a>","bibtex":"@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties of Effective Dynamics from Conditional Expectations}, DOI={<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>}, number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2021} }","ama":"Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective Dynamics from Conditional Expectations. <i>Entropy</i>. 2021. doi:<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>","mla":"Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional Expectations.” <i>Entropy</i>, 134, 2021, doi:<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>."},"publication":"Entropy","department":[{"_id":"101"}],"oa":"1","type":"journal_article","date_created":"2021-04-28T18:07:56Z"},{"author":[{"last_name":"Gebken","first_name":"Bennet","full_name":"Gebken, Bennet","id":"32643"},{"full_name":"Peitz, Sebastian","first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427"}],"year":"2021","title":"An efficient descent method for locally Lipschitz multiobjective optimization problems","intvolume":"       188","date_updated":"2022-01-06T06:52:57Z","publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf","open_access":"1"}],"doi":"10.1007/s10957-020-01803-w","publication":"Journal of Optimization Theory and Applications","abstract":[{"lang":"eng","text":"In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous multiobjective optimization problems (MOPs). The method is realized\r\nby combining a theoretical result regarding the computation of descent\r\ndirections for nonsmooth MOPs with a practical method to approximate the\r\nsubdifferentials of the objective functions. We show convergence to points\r\nwhich satisfy a necessary condition for Pareto optimality. Using a set of test\r\nproblems, we compare our method to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results indicate that our method is competitive while being\r\neasier to implement. While the number of objective function evaluations is\r\nlarger, the overall number of subgradient evaluations is lower. Finally, we\r\nshow that our method can be combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth MOPs."}],"date_created":"2020-04-27T09:11:22Z","department":[{"_id":"101"}],"type":"journal_article","status":"public","_id":"16867","page":"696-723","volume":188,"user_id":"47427","citation":{"mla":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” <i>Journal of Optimization Theory and Applications</i>, vol. 188, 2021, pp. 696–723, doi:<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>.","ama":"Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. <i>Journal of Optimization Theory and Applications</i>. 2021;188:696-723. doi:<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>","bibtex":"@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, volume={188}, DOI={<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={696–723} }","apa":"Gebken, B., &#38; Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. <i>Journal of Optimization Theory and Applications</i>, <i>188</i>, 696–723. <a href=\"https://doi.org/10.1007/s10957-020-01803-w\">https://doi.org/10.1007/s10957-020-01803-w</a>","ieee":"B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” <i>Journal of Optimization Theory and Applications</i>, vol. 188, pp. 696–723, 2021.","short":"B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188 (2021) 696–723.","chicago":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” <i>Journal of Optimization Theory and Applications</i> 188 (2021): 696–723. <a href=\"https://doi.org/10.1007/s10957-020-01803-w\">https://doi.org/10.1007/s10957-020-01803-w</a>."},"oa":"1"},{"status":"public","_id":"16295","publisher":"Springer","page":"3-29","volume":80,"user_id":"47427","citation":{"apa":"Gebken, B., &#38; Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. <i>Journal of Global Optimization</i>, <i>80</i>, 3–29. <a href=\"https://doi.org/10.1007/s10898-020-00983-z\">https://doi.org/10.1007/s10898-020-00983-z</a>","ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” <i>Journal of Global Optimization</i>, vol. 80, pp. 3–29, 2021.","short":"B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.","chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>Journal of Global Optimization</i> 80 (2021): 3–29. <a href=\"https://doi.org/10.1007/s10898-020-00983-z\">https://doi.org/10.1007/s10898-020-00983-z</a>.","mla":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>Journal of Global Optimization</i>, vol. 80, Springer, 2021, pp. 3–29, doi:<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>.","ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. <i>Journal of Global Optimization</i>. 2021;80:3-29. doi:<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>","bibtex":"@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization: Inferring decision criteria from data}, volume={80}, DOI={<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>}, journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }"},"oa":"1","author":[{"full_name":"Gebken, Bennet","first_name":"Bennet","last_name":"Gebken","id":"32643"},{"last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427"}],"year":"2021","title":"Inverse multiobjective optimization: Inferring decision criteria from data","intvolume":"        80","date_updated":"2022-01-06T06:52:48Z","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf"}],"doi":"10.1007/s10898-020-00983-z","publication":"Journal of Global Optimization","abstract":[{"lang":"eng","text":"It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs."}],"date_created":"2020-03-13T12:45:05Z","department":[{"_id":"101"}],"type":"journal_article"},{"date_updated":"2022-06-20T13:40:30Z","year":"2021","status":"public","title":"The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems","author":[{"id":"32655","full_name":"Gerlach, Raphael","first_name":"Raphael","last_name":"Gerlach"}],"doi":"10.17619/UNIPB/1-1278","user_id":"32643","main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6214949"}],"language":[{"iso":"eng"}],"_id":"32057","abstract":[{"text":"Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung.","lang":"ger"},{"lang":"eng","text":"One central aspect in the study of dynamical systems is the analysis of its invariant sets such as the global attractor and (un)stable manifolds. In particular, when the underlying system depends on a parameter it is crucial to efficiently track those set with respect to this parameter. For the computation of invariant sets we rely on numerical algorithms for their approximation but typically those tools can only be applied to finite-dimensional dynamical systems. Thus, in thesis we present a numerical framework for the global dynamical analysis of infinite-dimensional systems. We will use embedding techniques for the definition of the core dynamical system (CDS) which is a dynamically equivalent finite-dimensional system. The CDS is then used for the approximation of related embedded invariant sets, i.e, one-to-one images, by set-oriented numerical methods. For the construction of the CDS it is crucial to choose an appropriate observation map and to design its corresponding inverse. Therefore, we will present suitable numerical realizations of the CDS for DDEs and PDEs. For a subsequent geometric analysis of the embedded invariant set we will consider a manifold learning technique called diffusion maps which reveals its intrinsic geometry and estimates its dimension. Finally, we apply our develop numerical tools on some well-known infinite-dimensional dynamical systems such as the Mackey-Glass equation, the Kuramoto-Sivashinsky equation and the Navier-Stokes equation."}],"supervisor":[{"full_name":"Dellnitz , Michael","first_name":"Michael","last_name":"Dellnitz "},{"full_name":"Koltai, Péter","first_name":"Péter","last_name":"Koltai"}],"citation":{"short":"R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems, 2021.","chicago":"Gerlach, Raphael. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>, 2021. <a href=\"https://doi.org/10.17619/UNIPB/1-1278\">https://doi.org/10.17619/UNIPB/1-1278</a>.","ieee":"R. Gerlach, <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. 2021.","apa":"Gerlach, R. (2021). <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1278\">https://doi.org/10.17619/UNIPB/1-1278</a>","bibtex":"@book{Gerlach_2021, title={The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>}, author={Gerlach, Raphael}, year={2021} }","ama":"Gerlach R. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>.; 2021. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>","mla":"Gerlach, Raphael. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. 2021, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>."},"type":"dissertation","oa":"1","department":[{"_id":"101"}],"date_created":"2022-06-20T09:54:24Z"},{"type":"journal_article","department":[{"_id":"548"}],"date_created":"2022-06-20T08:46:56Z","publication":"Journal of Symplectic Geometry","issue":"6","doi":"10.4310/JSG.2021.v19.n6.a1","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-06-21T11:54:50Z","article_type":"original","intvolume":"        19","title":"Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions","year":"2021","author":[{"id":"70575","last_name":"Delarue","first_name":"Benjamin","full_name":"Delarue, Benjamin"},{"first_name":"Pablo","last_name":"Ramacher","full_name":"Ramacher, Pablo"}],"publication_identifier":{"unknown":["1540-2347","1527-5256"]},"citation":{"mla":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” <i>Journal of Symplectic Geometry</i>, vol. 19, no. 6, 2021, pp. 1281–337, doi:<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>.","ama":"Delarue B, Ramacher P. Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. <i>Journal of Symplectic Geometry</i>. 2021;19(6):1281-1337. doi:<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>","bibtex":"@article{Delarue_Ramacher_2021, title={Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}, volume={19}, DOI={<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>}, number={6}, journal={Journal of Symplectic Geometry}, author={Delarue, Benjamin and Ramacher, Pablo}, year={2021}, pages={1281–1337} }","apa":"Delarue, B., &#38; Ramacher, P. (2021). Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. <i>Journal of Symplectic Geometry</i>, <i>19</i>(6), 1281–1337. <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">https://doi.org/10.4310/JSG.2021.v19.n6.a1</a>","ieee":"B. Delarue and P. Ramacher, “Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions,” <i>Journal of Symplectic Geometry</i>, vol. 19, no. 6, pp. 1281–1337, 2021, doi: <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>.","short":"B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.","chicago":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” <i>Journal of Symplectic Geometry</i> 19, no. 6 (2021): 1281–1337. <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">https://doi.org/10.4310/JSG.2021.v19.n6.a1</a>."},"user_id":"70575","volume":19,"page":"1281 - 1337","_id":"32016","status":"public"},{"citation":{"bibtex":"@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in toroidal graphs}, volume={153}, DOI={<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>}, journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }","short":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial Theory, Series B 153 (2021) 61–80.","ama":"Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>. 2021;153:61-80. doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>","chicago":"Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i> 153 (2021): 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>.","ieee":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows in toroidal graphs,” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, pp. 61–80, 2021, doi: <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>.","mla":"Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>.","apa":"Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., &#38; Zhang, C.-Q. (2021). Nowhere-zero 3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>, <i>153</i>, 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>"},"_id":"34042","publisher":"Elsevier BV","page":"61-80","volume":153,"user_id":"15540","status":"public","date_created":"2022-11-09T08:43:55Z","department":[{"_id":"542"}],"keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"type":"journal_article","publication":"Journal of Combinatorial Theory, Series B","language":[{"iso":"eng"}],"doi":"10.1016/j.jctb.2021.11.001","author":[{"last_name":"Li","first_name":"Jiaao","full_name":"Li, Jiaao"},{"full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai","id":"92748"},{"full_name":"Miao, Zhengke","last_name":"Miao","first_name":"Zhengke"},{"full_name":"Shi, Yongtang","last_name":"Shi","first_name":"Yongtang"},{"full_name":"Wang, Weifan","last_name":"Wang","first_name":"Weifan"},{"last_name":"Zhang","first_name":"Cun-Quan","full_name":"Zhang, Cun-Quan"}],"publication_identifier":{"issn":["0095-8956"]},"title":"Nowhere-zero 3-flows in toroidal graphs","year":"2021","intvolume":"       153","publication_status":"published","date_updated":"2022-11-09T08:44:37Z"},{"status":"public","_id":"34786","page":"164-214","volume":570,"user_id":"178","citation":{"short":"H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214.","chicago":"Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction Groups, Series and Extensions.” <i>Journal of Algebra</i> 570 (2021): 164–214. <a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.","apa":"Glöckner, H., &#38; Willis, G. A. (2021). Decompositions of locally compact contraction groups, series and extensions. <i>Journal of Algebra</i>, <i>570</i>, 164–214. <a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>","ieee":"H. Glöckner and G. A. Willis, “Decompositions of locally compact contraction groups, series and extensions,” <i>Journal of Algebra</i>, vol. 570, pp. 164–214, 2021, doi: <a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.","ama":"Glöckner H, Willis GA. Decompositions of locally compact contraction groups, series and extensions. <i>Journal of Algebra</i>. 2021;570:164-214. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>","bibtex":"@article{Glöckner_Willis_2021, title={Decompositions of locally compact contraction groups, series and extensions}, volume={570}, DOI={<a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>}, journal={Journal of Algebra}, author={Glöckner, Helge and Willis, George A.}, year={2021}, pages={164–214} }","mla":"Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction Groups, Series and Extensions.” <i>Journal of Algebra</i>, vol. 570, 2021, pp. 164–214, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>."},"quality_controlled":"1","author":[{"full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge","id":"178"},{"full_name":"Willis, George A.","last_name":"Willis","first_name":"George A."}],"publication_identifier":{"issn":["0021-8693"]},"year":"2021","title":"Decompositions of locally compact contraction groups, series and extensions","article_type":"original","intvolume":"       570","date_updated":"2022-12-21T18:58:44Z","language":[{"iso":"eng"}],"doi":"https://doi.org/10.1016/j.jalgebra.2020.11.007","publication":"Journal of Algebra","abstract":[{"lang":"eng","text":"A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups."}],"date_created":"2022-12-21T18:43:08Z","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"keyword":["Contraction group","Torsion group","Extension","Cocycle","Section","Equivariant cohomology","Abelian group","Nilpotent group","Isomorphism types"],"type":"journal_article"},{"language":[{"iso":"eng"}],"doi":"10.1002/mana.201900073","publication_identifier":{"issn":["0025-584X"]},"author":[{"id":"178","first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge"}],"title":"Direct limits of regular Lie groups","year":"2021","intvolume":"       294","article_type":"original","date_updated":"2022-12-21T20:00:29Z","date_created":"2022-12-21T19:57:32Z","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_article","publication":"Mathematische Nachrichten","issue":"1","_id":"34795","page":"74–81","volume":294,"user_id":"178","status":"public","citation":{"mla":"Glöckner, Helge. “Direct Limits of Regular Lie Groups.” <i>Mathematische Nachrichten</i>, vol. 294, no. 1, 2021, pp. 74–81, doi:<a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>.","ama":"Glöckner H. Direct limits of regular Lie groups. <i>Mathematische Nachrichten</i>. 2021;294(1):74–81. doi:<a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>","bibtex":"@article{Glöckner_2021, title={Direct limits of regular Lie groups}, volume={294}, DOI={<a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>}, number={1}, journal={Mathematische Nachrichten}, author={Glöckner, Helge}, year={2021}, pages={74–81} }","apa":"Glöckner, H. (2021). Direct limits of regular Lie groups. <i>Mathematische Nachrichten</i>, <i>294</i>(1), 74–81. <a href=\"https://doi.org/10.1002/mana.201900073\">https://doi.org/10.1002/mana.201900073</a>","ieee":"H. Glöckner, “Direct limits of regular Lie groups,” <i>Mathematische Nachrichten</i>, vol. 294, no. 1, pp. 74–81, 2021, doi: <a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>.","chicago":"Glöckner, Helge. “Direct Limits of Regular Lie Groups.” <i>Mathematische Nachrichten</i> 294, no. 1 (2021): 74–81. <a href=\"https://doi.org/10.1002/mana.201900073\">https://doi.org/10.1002/mana.201900073</a>.","short":"H. Glöckner, Mathematische Nachrichten 294 (2021) 74–81."},"quality_controlled":"1"},{"user_id":"178","language":[{"iso":"eng"}],"_id":"34806","date_updated":"2022-12-22T07:48:29Z","title":"Contraction groups and the big cell for endomorphisms of Lie groups over  local fields","year":"2021","status":"public","author":[{"id":"178","first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge"}],"type":"preprint","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2101.02981"]},"date_created":"2022-12-22T07:47:35Z","abstract":[{"text":"Let $G$ be a Lie group over a totally disconnected local field and $\\alpha$\r\nbe an analytic endomorphism of $G$. The contraction group of $\\alpha$ ist the\r\nset of all $x\\in G$ such that $\\alpha^n(x)\\to e$ as $n\\to\\infty$. Call sequence\r\n$(x_{-n})_{n\\geq 0}$ in $G$ an $\\alpha$-regressive trajectory for $x\\in G$ if\r\n$\\alpha(x_{-n})=x_{-n+1}$ for all $n\\geq 1$ and $x_0=x$. The anti-contraction\r\ngroup of $\\alpha$ is the set of all $x\\in G$ admitting an $\\alpha$-regressive\r\ntrajectory $(x_{-n})_{n\\geq 0}$ such that $x_{-n}\\to e$ as $n\\to\\infty$. The\r\nLevi subgroup is the set of all $x\\in G$ whose $\\alpha$-orbit is relatively\r\ncompact, and such that $x$ admits an $\\alpha$-regressive trajectory\r\n$(x_{-n})_{n\\geq 0}$ such that $\\{x_{-n}\\colon n\\geq 0\\}$ is relatively\r\ncompact. The big cell associated to $\\alpha$ is the set $\\Omega$ of all all\r\nproducts $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and\r\n$z$ in the anti-contraction group. Let $\\pi$ be the mapping from the cartesian\r\nproduct of the contraction group, Levi subgroup and anti-contraction group to\r\n$\\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\\Omega$ is open in $G$ and\r\n$\\pi$ is \\'{e}tale for suitable immersed Lie subgroup structures on the three\r\nsubgroups just mentioned. Moreover, we study group-theoretic properties of\r\ncontraction groups and anti-contraction groups.","lang":"eng"}],"publication":"arXiv:2101.02981","citation":{"mla":"Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of Lie Groups over  Local Fields.” <i>ArXiv:2101.02981</i>, 2021.","ama":"Glöckner H. Contraction groups and the big cell for endomorphisms of Lie groups over  local fields. <i>arXiv:210102981</i>. Published online 2021.","bibtex":"@article{Glöckner_2021, title={Contraction groups and the big cell for endomorphisms of Lie groups over  local fields}, journal={arXiv:2101.02981}, author={Glöckner, Helge}, year={2021} }","apa":"Glöckner, H. (2021). Contraction groups and the big cell for endomorphisms of Lie groups over  local fields. In <i>arXiv:2101.02981</i>.","ieee":"H. Glöckner, “Contraction groups and the big cell for endomorphisms of Lie groups over  local fields,” <i>arXiv:2101.02981</i>. 2021.","chicago":"Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of Lie Groups over  Local Fields.” <i>ArXiv:2101.02981</i>, 2021.","short":"H. Glöckner, ArXiv:2101.02981 (2021)."}},{"author":[{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"M.","last_name":"Vermeeren","full_name":"Vermeeren, M."}],"corporate_editor":["IFAC-PapersOnLine"],"status":"public","title":"Superconvergence of galerkin variational integrators","year":"2021","date_updated":"2022-01-21T13:36:53Z","language":[{"iso":"eng"}],"_id":"29421","page":"327-333","volume":"54(19)","user_id":"15694","citation":{"mla":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp. 327–33.","bibtex":"@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum, Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333} }","ama":"Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators. In: IFAC-PapersOnLine, ed. <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>. Vol 54(19). ; 2021:327-333.","ieee":"S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational integrators,” in <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, 2021, vol. 54(19), pp. 327–333.","apa":"Ober-Blöbaum, S., &#38; Vermeeren, M. (2021). Superconvergence of galerkin variational integrators. In IFAC-PapersOnLine (Ed.), <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)</i> (pp. 327–333).","short":"S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.","chicago":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” In <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, 54(19):327–33, 2021."},"publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC","date_created":"2022-01-18T14:27:56Z","department":[{"_id":"636"}],"type":"conference"},{"date_updated":"2022-01-24T13:27:50Z","title":"Explicit multiobjective model predictive control for nonlinear systems  with symmetries","year":"2021","status":"public","author":[{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"}],"doi":"10.1002/rnc.5281","user_id":"15694","volume":"31(2)","main_file_link":[{"url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281","open_access":"1"}],"page":"380-403","language":[{"iso":"eng"}],"_id":"16294","abstract":[{"lang":"eng","text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving."}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"publication":"International Journal of Robust and Nonlinear Control","citation":{"mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), 2021, pp. 380–403, doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>. 2021;31(2):380-403. doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems  with symmetries}, volume={31(2)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","apa":"Ober-Blöbaum, S., &#38; Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>, <i>31(2)</i>, 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>","ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), pp. 380–403, 2021, doi: <a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i> 31(2) (2021): 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>."},"type":"journal_article","oa":"1","department":[{"_id":"101"}],"date_created":"2020-03-13T12:44:36Z"},{"date_created":"2022-01-26T13:13:06Z","department":[{"_id":"636"}],"keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"type":"journal_article","publication":"Automatica","language":[{"iso":"eng"}],"article_number":"109804","doi":"10.1016/j.automatica.2021.109804","author":[{"last_name":"Djema","first_name":"Walid","full_name":"Djema, Walid"},{"last_name":"Giraldi","first_name":"Laetitia","full_name":"Giraldi, Laetitia"},{"full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya","id":"87909"},{"first_name":"Olivier","last_name":"Bernard","full_name":"Bernard, Olivier"}],"publication_identifier":{"issn":["0005-1098"]},"year":"2021","title":"Turnpike features in optimal selection of species represented by quota models","intvolume":"       132","publication_status":"published","date_updated":"2022-01-26T13:15:33Z","citation":{"chicago":"Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i> 132 (2021). <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>.","short":"W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).","ama":"Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>. 2021;132. doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>","bibtex":"@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features in optimal selection of species represented by quota models}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>}, number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021} }","mla":"Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i>, vol. 132, 109804, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","apa":"Djema, W., Giraldi, L., Maslovskaya, S., &#38; Bernard, O. (2021). Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>, <i>132</i>, Article 109804. <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>","ieee":"W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features in optimal selection of species represented by quota models,” <i>Automatica</i>, vol. 132, Art. no. 109804, 2021, doi: <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>."},"_id":"29543","publisher":"Elsevier BV","volume":132,"user_id":"87909","status":"public"},{"user_id":"50168","language":[{"iso":"eng"}],"_id":"31058","date_updated":"2022-05-17T12:05:52Z","author":[{"full_name":"Schütte, Philipp","first_name":"Philipp","last_name":"Schütte","id":"50168"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"full_name":"Delarue, Benjamin","last_name":"Delarue","first_name":"Benjamin"}],"title":"Resonances and weighted zeta functions for obstacle scattering via smooth models","status":"public","year":"2021","department":[{"_id":"10"},{"_id":"548"}],"type":"preprint","date_created":"2022-05-04T12:25:58Z","external_id":{"arxiv":["2109.05907"]},"abstract":[{"text":"We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.","lang":"eng"}],"citation":{"chicago":"Schütte, Philipp, Tobias Weich, and Benjamin Delarue. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” 2021.","short":"P. Schütte, T. Weich, B. Delarue, (2021).","ieee":"P. Schütte, T. Weich, and B. Delarue, “Resonances and weighted zeta functions for obstacle scattering via smooth models.” 2021.","apa":"Schütte, P., Weich, T., &#38; Delarue, B. (2021). <i>Resonances and weighted zeta functions for obstacle scattering via smooth models</i>.","bibtex":"@article{Schütte_Weich_Delarue_2021, title={Resonances and weighted zeta functions for obstacle scattering via smooth models}, author={Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}, year={2021} }","ama":"Schütte P, Weich T, Delarue B. Resonances and weighted zeta functions for obstacle scattering via smooth models. Published online 2021.","mla":"Schütte, Philipp, et al. <i>Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models</i>. 2021."}}]