[{"year":"2023","citation":{"short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023.","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1.","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (Eds.). (2023). Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023. doi:10.1007/978-3-031-14175-1","mla":"Biehler, Rolf, et al., editors. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing, 2023, doi:10.1007/978-3-031-14175-1.","bibtex":"@book{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education}, DOI={10.1007/978-3-031-14175-1}, publisher={Springer International Publishing}, year={2023} }"},"type":"book_editor","_id":"37469","date_updated":"2023-01-18T22:47:41Z","doi":"10.1007/978-3-031-14175-1","publisher":"Springer International Publishing","department":[{"_id":"10"}],"status":"public","date_created":"2023-01-18T22:17:58Z","editor":[{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"},{"last_name":"Liebendörfer","first_name":"Michael","full_name":"Liebendörfer, Michael"},{"last_name":"Gueudet","first_name":"Ghislaine","full_name":"Gueudet, Ghislaine"},{"last_name":"Rasmussen","full_name":"Rasmussen, Chris","first_name":"Chris"},{"last_name":"Winsløw","full_name":"Winsløw, Carl","first_name":"Carl"}],"publication_identifier":{"isbn":["9783031141744","9783031141751"],"issn":["1869-4918","1869-4926"]},"publication_status":"published","place":"Cham","user_id":"30933","title":"Practice-Oriented Research in Tertiary Mathematics Education"},{"language":[{"iso":"eng"}],"type":"journal_article","year":"2023","citation":{"ama":"Brennecken D, Rösler M. The Dunkl-Laplace transform and Macdonald’s hypergeometric series. Transaction of the American Mathematical Society. doi:10.1090/tran/8860","apa":"Brennecken, D., & Rösler, M. (n.d.). The Dunkl-Laplace transform and Macdonald’s hypergeometric series. Transaction of the American Mathematical Society. https://doi.org/10.1090/tran/8860","chicago":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” Transaction of the American Mathematical Society, n.d. https://doi.org/10.1090/tran/8860.","bibtex":"@article{Brennecken_Rösler, title={The Dunkl-Laplace transform and Macdonald’s hypergeometric series}, DOI={10.1090/tran/8860}, journal={Transaction of the American Mathematical Society}, publisher={ American Mathematical Society}, author={Brennecken, Dominik and Rösler, Margit} }","mla":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” Transaction of the American Mathematical Society, American Mathematical Society, doi:10.1090/tran/8860.","short":"D. Brennecken, M. Rösler, Transaction of the American Mathematical Society (n.d.).","ieee":"D. Brennecken and M. Rösler, “The Dunkl-Laplace transform and Macdonald’s hypergeometric series,” Transaction of the American Mathematical Society, doi: 10.1090/tran/8860."},"_id":"36294","date_updated":"2023-01-24T22:14:22Z","doi":"10.1090/tran/8860","department":[{"_id":"555"}],"publication":"Transaction of the American Mathematical Society","author":[{"first_name":"Dominik","full_name":"Brennecken, Dominik","last_name":"Brennecken","id":"55911"},{"full_name":"Rösler, Margit","first_name":"Margit","id":"37390","last_name":"Rösler"}],"publisher":" American Mathematical Society","date_created":"2023-01-12T08:32:44Z","status":"public","publication_status":"inpress","user_id":"37390","title":"The Dunkl-Laplace transform and Macdonald’s hypergeometric series"},{"user_id":"30905","article_type":"original","date_created":"2022-12-22T09:16:48Z","status":"public","volume":75,"keyword":["extension of differentiable maps"],"publication":"Canadian Journal of Mathematics","publisher":"Canadian Mathematical Society","author":[{"id":"30905","last_name":"Hanusch","full_name":"Hanusch, Maximilian","first_name":"Maximilian"}],"issue":"1","intvolume":" 75","_id":"34814","page":"170-201","citation":{"ieee":"M. Hanusch, “A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus,” Canadian Journal of Mathematics, vol. 75, no. 1, pp. 170–201, 2023, doi: 10.4153/s0008414x21000596.","short":"M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.","mla":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” Canadian Journal of Mathematics, vol. 75, no. 1, Canadian Mathematical Society, 2023, pp. 170–201, doi:10.4153/s0008414x21000596.","bibtex":"@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}, volume={75}, DOI={10.4153/s0008414x21000596}, number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }","apa":"Hanusch, M. (2023). A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. Canadian Journal of Mathematics, 75(1), 170–201. https://doi.org/10.4153/s0008414x21000596","ama":"Hanusch M. A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. Canadian Journal of Mathematics. 2023;75(1):170-201. doi:10.4153/s0008414x21000596","chicago":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” Canadian Journal of Mathematics 75, no. 1 (2023): 170–201. https://doi.org/10.4153/s0008414x21000596."},"type":"journal_article","year":"2023","title":"A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus","project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"publication_identifier":{"issn":["0008-414X","1496-4279"]},"publication_status":"published","department":[{"_id":"93"}],"doi":"10.4153/s0008414x21000596","date_updated":"2023-02-22T11:38:32Z","language":[{"iso":"eng"}]},{"department":[{"_id":"101"},{"_id":"655"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms","language":[{"iso":"eng"}],"date_updated":"2023-03-11T17:16:33Z","oa":"1","doi":"10.1007/s10898-022-01223-2","publication":"Journal of Global Optimization","author":[{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"last_name":"Bieker","id":"32829","first_name":"Katharina","full_name":"Bieker, Katharina"},{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"}],"date_created":"2021-11-15T09:24:59Z","status":"public","volume":85,"abstract":[{"lang":"eng","text":"Regularization is used in many different areas of optimization when solutions\r\nare sought which not only minimize a given function, but also possess a certain\r\ndegree of regularity. Popular applications are image denoising, sparse\r\nregression and machine learning. Since the choice of the regularization\r\nparameter is crucial but often difficult, path-following methods are used to\r\napproximate the entire regularization path, i.e., the set of all possible\r\nsolutions for all regularization parameters. Due to their nature, the\r\ndevelopment of these methods requires structural results about the\r\nregularization path. The goal of this article is to derive these results for\r\nthe case of a smooth objective function which is penalized by a piecewise\r\ndifferentiable regularization term. We do this by treating regularization as a\r\nmultiobjective optimization problem. Our results suggest that even in this\r\ngeneral case, the regularization path is piecewise smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features that occur in between\r\nsmooth parts. This is demonstrated in two applications, namely support-vector\r\nmachines and exact penalty methods."}],"user_id":"47427","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf"}],"page":"709-741","citation":{"short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.","apa":"Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }"},"year":"2023","type":"journal_article","_id":"27426","intvolume":" 85","issue":"3"},{"title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","place":"Hannover","publication_status":"published","editor":[{"last_name":"Trigueros","full_name":"Trigueros, Marı́a","first_name":"Marı́a"},{"last_name":"Barquero","first_name":"Berta","full_name":"Barquero, Berta"},{"full_name":"Hochmuth, Reinhard","first_name":"Reinhard","last_name":"Hochmuth"},{"last_name":"Peters","full_name":"Peters, Jana","first_name":"Jana"}],"department":[{"_id":"97"}],"oa":"1","date_updated":"2023-03-25T10:11:35Z","language":[{"iso":"eng"}],"ddc":["370","510"],"user_id":"32202","date_created":"2022-06-12T11:07:34Z","status":"public","has_accepted_license":"1","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file_date_updated":"2023-03-25T10:01:03Z","keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"author":[{"first_name":"Max","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max","last_name":"Hoffmann","id":"32202"},{"full_name":"Biehler, Rolf","first_name":"Rolf","id":"16274","last_name":"Biehler"}],"publisher":"University of Hannover and INDRUM.","quality_controlled":"1","file":[{"file_size":201942,"creator":"maxh","file_id":"43096","date_updated":"2023-03-25T10:01:03Z","content_type":"application/pdf","relation":"main_file","success":1,"file_name":"HoffmannBiehler2022_indrum_congruence.pdf","date_created":"2023-03-25T10:01:03Z","access_level":"closed"}],"_id":"31849","type":"conference","year":"2023","citation":{"apa":"Hoffmann, M., & Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). University of Hannover and INDRUM.","ama":"Hoffmann M, Biehler R. Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). University of Hannover and INDRUM.; 2023.","chicago":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023.","bibtex":"@inproceedings{Hoffmann_Biehler_2023, place={Hannover}, title={Student Teachers ’ Knowledge of Congruence before a University Course on Geometry}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, publisher={University of Hannover and INDRUM.}, author={Hoffmann, Max and Biehler, Rolf}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","mla":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., University of Hannover and INDRUM., 2023.","short":"M. Hoffmann, R. Biehler, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), University of Hannover and INDRUM., Hannover, 2023.","ieee":"M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry,” in Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023."},"main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}]},{"_id":"43097","type":"conference","citation":{"short":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, R. Martínez-Planell, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), Hannover, 2023.","ieee":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, and R. Martínez-Planell, “Innovations in university teaching based on mathematic education research,” in Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023.","chicago":"Florensa, Ignasio, Max Hoffmann, Avenilde Romo Vázquez, Michelle Zandieh, and Rafael Martínez-Planell. “Innovations in University Teaching Based on Mathematic Education Research.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover, 2023.","apa":"Florensa, I., Hoffmann, M., Romo Vázquez, A., Zandieh, M., & Martínez-Planell, R. (2023). Innovations in university teaching based on mathematic education research. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022).","ama":"Florensa I, Hoffmann M, Romo Vázquez A, Zandieh M, Martínez-Planell R. Innovations in university teaching based on mathematic education research. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). ; 2023.","mla":"Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic Education Research.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., 2023.","bibtex":"@inproceedings{Florensa_Hoffmann_Romo Vázquez_Zandieh_Martínez-Planell_2023, place={Hannover}, title={Innovations in university teaching based on mathematic education research}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, author={Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde and Zandieh, Michelle and Martínez-Planell, Rafael}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }"},"year":"2023","main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}],"user_id":"32202","ddc":["370","510"],"date_created":"2023-03-25T10:09:06Z","has_accepted_license":"1","status":"public","file":[{"file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","date_created":"2023-03-25T10:07:54Z","access_level":"closed","file_size":642388,"file_id":"43098","creator":"maxh","content_type":"application/pdf","date_updated":"2023-03-25T10:07:54Z","success":1,"relation":"main_file"}],"publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file_date_updated":"2023-03-25T10:07:54Z","quality_controlled":"1","author":[{"last_name":"Florensa","full_name":"Florensa, Ignasio","first_name":"Ignasio"},{"last_name":"Hoffmann","id":"32202","first_name":"Max","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max"},{"full_name":"Romo Vázquez, Avenilde","first_name":"Avenilde","last_name":"Romo Vázquez"},{"full_name":"Zandieh, Michelle","first_name":"Michelle","last_name":"Zandieh"},{"full_name":"Martínez-Planell, Rafael","first_name":"Rafael","last_name":"Martínez-Planell"}],"oa":"1","date_updated":"2023-03-25T10:10:58Z","language":[{"iso":"eng"}],"title":"Innovations in university teaching based on mathematic education research","place":"Hannover","editor":[{"last_name":"Trigueros","first_name":"Marı́a","full_name":"Trigueros, Marı́a"},{"last_name":"Barquero","full_name":"Barquero, Berta","first_name":"Berta"},{"full_name":"Hochmuth, Reinhard","first_name":"Reinhard","last_name":"Hochmuth"},{"last_name":"Peters","full_name":"Peters, Jana","first_name":"Jana"}],"department":[{"_id":"97"}]},{"type":"journal_article","citation":{"short":"R. Biehler, M. Liebendörfer, A. Schmitz, Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023) 8–12.","ieee":"R. Biehler, M. Liebendörfer, and A. Schmitz, “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos,” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, pp. 8–12, 2023.","ama":"Biehler R, Liebendörfer M, Schmitz A. Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik. 2023;114:8-12.","apa":"Biehler, R., Liebendörfer, M., & Schmitz, A. (2023). Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik, 114, 8–12.","chicago":"Biehler, Rolf, Michael Liebendörfer, and A. Schmitz. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023): 8–12.","bibtex":"@article{Biehler_Liebendörfer_Schmitz_2023, title={Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos}, volume={114}, journal={Mitteilungen der Gesellschaft für Didaktik der Mathematik}, author={Biehler, Rolf and Liebendörfer, Michael and Schmitz, A.}, year={2023}, pages={8–12} }","mla":"Biehler, Rolf, et al. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, 2023, pp. 8–12."},"year":"2023","page":"8-12","language":[{"iso":"ger"}],"date_updated":"2023-04-14T09:25:27Z","_id":"43504","intvolume":" 114","volume":114,"status":"public","date_created":"2023-04-14T09:25:18Z","author":[{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"id":"30933","last_name":"Liebendörfer","full_name":"Liebendörfer, Michael","orcid":"0000-0001-9887-2074","first_name":"Michael"},{"first_name":"A.","full_name":"Schmitz, A.","last_name":"Schmitz"}],"publication":"Mitteilungen der Gesellschaft für Didaktik der Mathematik","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"title":"Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos","user_id":"37888"},{"publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","language":[{"iso":"eng"}],"doi":"10.1016/j.nonrwa.2023.103868","date_updated":"2023-03-27T07:27:03Z","status":"public","date_created":"2023-03-27T07:25:58Z","volume":73,"publisher":"Elsevier BV","author":[{"id":"23686","last_name":"Black","orcid":"0000-0001-9963-0800","full_name":"Black, Tobias","first_name":"Tobias"},{"last_name":"Fuest","first_name":"Mario","full_name":"Fuest, Mario"},{"full_name":"Lankeit, Johannes","first_name":"Johannes","last_name":"Lankeit"},{"last_name":"Mizukami","first_name":"Masaaki","full_name":"Mizukami, Masaaki"}],"publication":"Nonlinear Analysis: Real World Applications","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"user_id":"23686","citation":{"short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” Nonlinear Analysis: Real World Applications, vol. 73, Art. no. 103868, 2023, doi: 10.1016/j.nonrwa.2023.103868.","apa":"Black, T., Fuest, M., Lankeit, J., & Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real World Applications, 73, Article 103868. https://doi.org/10.1016/j.nonrwa.2023.103868","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real World Applications. 2023;73. doi:10.1016/j.nonrwa.2023.103868","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications 73 (2023). https://doi.org/10.1016/j.nonrwa.2023.103868.","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={10.1016/j.nonrwa.2023.103868}, number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}, year={2023} }","mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications, vol. 73, 103868, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2023.103868."},"year":"2023","type":"journal_article","article_number":"103868","_id":"43105","intvolume":" 73"},{"date_updated":"2023-03-30T10:06:53Z","_id":"43227","doi":"https://doi.org/10.18716/ojs/md/2023.1671","citation":{"ieee":"V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46, 2023.","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.","mla":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1671.","bibtex":"@inbook{Vitt_Häsel-Weide_2023, title={Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}, DOI={https://doi.org/10.18716/ojs/md/2023.1671}, booktitle={Mathematica Didactica, 46}, author={Vitt, Vivian and Häsel-Weide, Uta}, year={2023} }","apa":"Vitt, V., & Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1671","ama":"Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1671","chicago":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1671."},"type":"book_chapter","year":"2023","language":[{"iso":"eng"}],"title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","user_id":"44184","author":[{"last_name":"Vitt","full_name":"Vitt, Vivian","first_name":"Vivian"},{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"}],"department":[{"_id":"543"}],"publication":"Mathematica Didactica, 46","status":"public","date_created":"2023-03-30T10:06:24Z"},{"user_id":"44184","title":"Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.","publication":"Mathematica Didactica, 46","department":[{"_id":"543"}],"author":[{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"},{"first_name":"M.","full_name":"Nührenbörger, M.","last_name":"Nührenbörger"}],"date_created":"2023-03-30T10:04:31Z","status":"public","_id":"43226","date_updated":"2023-03-30T10:06:49Z","doi":"https://doi.org/10.18716/ojs/md/2023.1670","language":[{"iso":"eng"}],"type":"book_chapter","citation":{"ieee":"U. Häsel-Weide and M. Nührenbörger, “Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.,” in Mathematica Didactica, 46, 2023.","short":"U. Häsel-Weide, M. Nührenbörger, in: Mathematica Didactica, 46, 2023.","bibtex":"@inbook{Häsel-Weide_Nührenbörger_2023, title={Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.}, DOI={https://doi.org/10.18716/ojs/md/2023.1670}, booktitle={Mathematica Didactica, 46}, author={Häsel-Weide, Uta and Nührenbörger, M.}, year={2023} }","mla":"Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter Förderung Im Mathematikunterricht.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1670.","chicago":"Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter Förderung Im Mathematikunterricht.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1670.","apa":"Häsel-Weide, U., & Nührenbörger, M. (2023). Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1670","ama":"Häsel-Weide U, Nührenbörger M. Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1670"},"year":"2023"},{"intvolume":" 63","_id":"34832","date_updated":"2023-04-05T18:18:24Z","issue":"21","doi":"10.1007/s10455-023-09888-y","language":[{"iso":"eng"}],"citation":{"ieee":"M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups,” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023, doi: 10.1007/s10455-023-09888-y.","short":"M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).","bibtex":"@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}, volume={63}, DOI={10.1007/s10455-023-09888-y}, number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch, Maximilian}, year={2023} }","mla":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023, doi:10.1007/s10455-023-09888-y.","ama":"Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. Annals of Global Analysis and Geometry. 2023;63(21). doi:10.1007/s10455-023-09888-y","apa":"Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. Annals of Global Analysis and Geometry, 63(21). https://doi.org/10.1007/s10455-023-09888-y","chicago":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” Annals of Global Analysis and Geometry 63, no. 21 (2023). https://doi.org/10.1007/s10455-023-09888-y."},"type":"journal_article","year":"2023","user_id":"30905","title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups","keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"department":[{"_id":"93"}],"publication":"Annals of Global Analysis and Geometry","author":[{"last_name":"Hanusch","id":"30905","first_name":"Maximilian","full_name":"Hanusch, Maximilian"}],"project":[{"_id":"161","name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)"}],"date_created":"2022-12-22T09:45:34Z","status":"public","publication_status":"published","volume":63},{"date_updated":"2023-05-05T06:53:47Z","_id":"44501","type":"preprint","citation":{"bibtex":"@article{Cappello_Naserasr_Steffen_Wang_2023, title={Critically 3-frustrated signed graphs}, journal={arXiv:2304.10243}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2023} }","mla":"Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. arXiv:230410243. Published online 2023.","apa":"Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically 3-frustrated signed graphs. In arXiv:2304.10243.","chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” arXiv:2304.10243. 2023.","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023)."},"year":"2023","language":[{"iso":"eng"}],"title":"Critically 3-frustrated signed graphs","user_id":"15540","abstract":[{"lang":"eng","text":"Extending the notion of maxcut, the study of the frustration index of signed graphs is one of the basic questions in the theory of signed graphs. Recently two of the authors initiated the study of critically frustrated signed graphs. That is a signed graph whose frustration index decreases with the removal of any edge. The main focus of this study is on critical signed graphs which are not edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable signed graphs) and which are not built from other critically frustrated signed graphs by subdivision. We conjecture that for any given k there are only finitely many critically k-frustrated signed graphs of this kind.\r\nProviding support for this conjecture we show that there are only two of such critically 3-frustrated signed graphs where there is no pair of edge-disjoint negative cycles. Similarly, we show that there are exactly ten critically 3-frustrated signed planar graphs that are neither decomposable nor subdivisions of other critically frustrated signed graphs. We present a method for building non-decomposable critically frustrated signed graphs based on two given such signed graphs. We also show that the condition of being non-decomposable is necessary for our conjecture. "}],"external_id":{"arxiv":["2304.10243"]},"status":"public","date_created":"2023-05-05T06:52:39Z","author":[{"last_name":"Cappello","id":"72874","first_name":"Chiara","full_name":"Cappello, Chiara"},{"last_name":"Naserasr","full_name":"Naserasr, Reza","first_name":"Reza"},{"orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"first_name":"Zhouningxin","full_name":"Wang, Zhouningxin","last_name":"Wang"}],"publication":"arXiv:2304.10243","department":[{"_id":"542"}]},{"date_updated":"2023-05-16T08:49:30Z","doi":"10.1051/ro/2023052","language":[{"iso":"eng"}],"title":"Algorithms for the genome median under a restricted measure of rearrangement","department":[{"_id":"542"}],"publication_status":"published","publication_identifier":{"issn":["0399-0559","2804-7303"]},"intvolume":" 57","_id":"44857","issue":"3","citation":{"mla":"Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3, EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052.","bibtex":"@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms for the genome median under a restricted measure of rearrangement}, volume={57}, DOI={10.1051/ro/2023052}, number={3}, journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }","apa":"Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052","ama":"Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052","chicago":"Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023): 1045–58. https://doi.org/10.1051/ro/2023052.","ieee":"H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V. Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,” RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi: 10.1051/ro/2023052.","short":"H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058."},"year":"2023","type":"journal_article","page":"1045-1058","abstract":[{"text":"Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives.","lang":"eng"}],"user_id":"15540","author":[{"first_name":"Helmuth O.M.","full_name":"Silva, Helmuth O.M.","last_name":"Silva"},{"full_name":"Rubert, Diego P.","first_name":"Diego P.","last_name":"Rubert"},{"last_name":"Araujo","first_name":"Eloi","full_name":"Araujo, Eloi"},{"id":"15548","last_name":"Steffen","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","first_name":"Eckhard"},{"last_name":"Doerr","full_name":"Doerr, Daniel","first_name":"Daniel"},{"first_name":"Fábio V.","full_name":"Martinez, Fábio V.","last_name":"Martinez"}],"publisher":"EDP Sciences","publication":"RAIRO - Operations Research","keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"status":"public","date_created":"2023-05-16T08:48:22Z","volume":57},{"_id":"44859","date_updated":"2023-05-16T11:17:26Z","year":"2023","citation":{"ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” arXiv:2305.08619. 2023.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In arXiv:2305.08619.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs. arXiv:230508619. Published online 2023.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023."},"type":"preprint","language":[{"iso":"eng"}],"title":"Sets of r-graphs that color all r-graphs","user_id":"15540","external_id":{"arxiv":["2305.08619"]},"date_created":"2023-05-16T10:07:47Z","status":"public","publication":"arXiv:2305.08619","department":[{"_id":"542"}],"author":[{"last_name":"Ma","id":"92748","first_name":"Yulai","full_name":"Ma, Yulai"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","last_name":"Steffen","id":"15548"},{"full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","id":"88145","last_name":"Wolf"}]},{"language":[{"iso":"eng"}],"citation":{"chicago":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes Mathematicae. 34, no. 4 (2023): 752–811. https://doi.org/10.1016/j.indag.2023.02.003.","ama":"Hanusch M. Decompositions of Analytic 1-Manifolds. Indagationes Mathematicae. 2023;34(4):752-811. doi:10.1016/j.indag.2023.02.003","apa":"Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. Indagationes Mathematicae., 34(4), 752–811. https://doi.org/10.1016/j.indag.2023.02.003","mla":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes Mathematicae., vol. 34, no. 4, 2023, pp. 752–811, doi:10.1016/j.indag.2023.02.003.","bibtex":"@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds}, volume={34}, DOI={10.1016/j.indag.2023.02.003}, number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian}, year={2023}, pages={752–811} }","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.","ieee":"M. Hanusch, “Decompositions of Analytic 1-Manifolds,” Indagationes Mathematicae., vol. 34, no. 4, pp. 752–811, 2023, doi: 10.1016/j.indag.2023.02.003."},"year":"2023","type":"journal_article","page":"752-811","date_updated":"2023-05-25T07:32:38Z","_id":"34833","intvolume":" 34","issue":"4","doi":"10.1016/j.indag.2023.02.003","author":[{"first_name":"Maximilian","full_name":"Hanusch, Maximilian","last_name":"Hanusch","id":"30905"}],"department":[{"_id":"93"}],"publication":"Indagationes Mathematicae.","keyword":["Lie group actions and analytic 1-submanifolds"],"status":"public","date_created":"2022-12-22T09:46:36Z","volume":34,"publication_status":"published","user_id":"30905","title":"Decompositions of Analytic 1-Manifolds"},{"_id":"45498","date_updated":"2023-06-07T07:59:06Z","language":[{"iso":"eng"}],"type":"preprint","citation":{"bibtex":"@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }","mla":"von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.","ama":"von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order phase reduction in coupled oscillator networks. arXiv:230603320.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320, n.d.","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320. .","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.)."},"year":"2023","page":"29","main_file_link":[{"url":"https://arxiv.org/pdf/2306.03320"}],"user_id":"97359","title":"A parametrisation method for high-order phase reduction in coupled oscillator networks","abstract":[{"text":"We present a novel method for high-order phase reduction in networks of\r\nweakly coupled oscillators and, more generally, perturbations of reducible\r\nnormally hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic expansion for an embedding of the perturbed invariant torus, as well\r\nas for the reduced phase dynamics in local coordinates. Both can be determined\r\nto arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly be obtained in normal form. We apply the method to predict remote\r\nsynchronisation in a chain of coupled Stuart-Landau oscillators.","lang":"eng"}],"external_id":{"arxiv":["2306.03320"]},"status":"public","date_created":"2023-06-07T07:57:28Z","publication_status":"submitted","author":[{"last_name":"von der Gracht","id":"97359","first_name":"Sören","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058"},{"last_name":"Nijholt","first_name":"Eddie","full_name":"Nijholt, Eddie"},{"first_name":"Bob","full_name":"Rink, Bob","last_name":"Rink"}],"department":[{"_id":"101"}],"publication":"arXiv:2306.03320"},{"language":[{"iso":"ger"}],"page":"6-11","type":"journal_article","year":"2023","citation":{"mla":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift, no. 339, Friedrich Verlag, 2023, pp. 6–11.","bibtex":"@article{Häsel-Weide_2023, title={ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen}, number={339}, journal={Die Grundschulzeitschrift}, publisher={Friedrich Verlag}, author={Häsel-Weide, Uta}, year={2023}, pages={6–11} }","chicago":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift, no. 339 (2023): 6–11.","ama":"Häsel-Weide U. Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift. 2023;(339):6-11.","apa":"Häsel-Weide, U. (2023). Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift, 339, 6–11.","ieee":"U. Häsel-Weide, “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen,” Die Grundschulzeitschrift, no. 339, pp. 6–11, 2023.","short":"U. Häsel-Weide, Die Grundschulzeitschrift (2023) 6–11."},"issue":"339","_id":"45712","date_updated":"2023-06-22T09:34:13Z","date_created":"2023-06-22T09:28:22Z","status":"public","department":[{"_id":"543"}],"publication":"Die Grundschulzeitschrift","author":[{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"}],"publisher":"Friedrich Verlag","related_material":{"link":[{"url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991","relation":"other"}]},"user_id":"44184","title":" Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen"},{"date_created":"2023-06-22T09:33:59Z","status":"public","publication":"Die Grundschulzeitschrift","department":[{"_id":"543"}],"author":[{"full_name":"Graf, Lara Marie","first_name":"Lara Marie","id":"89837","last_name":"Graf"},{"first_name":"Inga","full_name":"Wienhues, Inga","last_name":"Wienhues","id":"61635"},{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"}],"publisher":"Friedrich Verlag","user_id":"44184","related_material":{"link":[{"url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991","relation":"other"}]},"title":"Addition und Subtraktion verstehen","language":[{"iso":"ger"}],"page":"20-23","citation":{"ieee":"L. M. Graf, I. Wienhues, and U. Häsel-Weide, “Addition und Subtraktion verstehen,” Die Grundschulzeitschrift, no. 339, pp. 20–23, 2023.","short":"L.M. Graf, I. Wienhues, U. Häsel-Weide, Die Grundschulzeitschrift (2023) 20–23.","bibtex":"@article{Graf_Wienhues_Häsel-Weide_2023, title={Addition und Subtraktion verstehen}, number={339}, journal={Die Grundschulzeitschrift}, publisher={Friedrich Verlag}, author={Graf, Lara Marie and Wienhues, Inga and Häsel-Weide, Uta}, year={2023}, pages={20–23} }","mla":"Graf, Lara Marie, et al. “Addition und Subtraktion verstehen.” Die Grundschulzeitschrift, no. 339, Friedrich Verlag, 2023, pp. 20–23.","apa":"Graf, L. M., Wienhues, I., & Häsel-Weide, U. (2023). Addition und Subtraktion verstehen. Die Grundschulzeitschrift, 339, 20–23.","ama":"Graf LM, Wienhues I, Häsel-Weide U. Addition und Subtraktion verstehen. Die Grundschulzeitschrift. 2023;(339):20-23.","chicago":"Graf, Lara Marie, Inga Wienhues, and Uta Häsel-Weide. “Addition und Subtraktion verstehen.” Die Grundschulzeitschrift, no. 339 (2023): 20–23."},"year":"2023","type":"journal_article","issue":"339","_id":"45713","date_updated":"2023-06-22T09:34:18Z"},{"language":[{"iso":"eng"}],"date_updated":"2023-07-13T09:41:20Z","oa":"1","doi":"10.1007/s11858-023-01505-3","department":[{"_id":"97"},{"_id":"643"}],"publication_status":"published","publication_identifier":{"issn":["1863-9690","1863-9704"]},"title":"Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s11858-023-01505-3","open_access":"1"}],"year":"2023","citation":{"short":"M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2023).","ieee":"M. Hoffmann and R. Biehler, “Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01505-3.","apa":"Hoffmann, M., & Biehler, R. (2023). Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-023-01505-3","ama":"Hoffmann M, Biehler R. Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. 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The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers."}],"user_id":"32202","ddc":["510","370"]},{"doi":"10.1016/j.jmaa.2023.127558","date_updated":"2023-07-20T05:11:12Z","language":[{"iso":"eng"}],"title":"Super-Gaussian decay of exponentials: A sufficient condition","external_id":{"arxiv":["2205.09189"]},"publication_status":"published","publication_identifier":{"issn":["0022-247X"]},"department":[{"_id":"799"}],"issue":"1","article_number":"127558","_id":"46100","intvolume":" 528","citation":{"chicago":"Hinrichs, Benjamin, Daan W. 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We show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$.","lang":"eng"}],"user_id":"45027","title":"Temperedness of locally symmetric spaces: The product case","publication":"arXiv:2304.09573","department":[{"_id":"10"}],"author":[{"first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"last_name":"Wolf","full_name":"Wolf, Lasse L.","first_name":"Lasse L."}],"date_created":"2023-07-24T07:52:23Z","status":"public","_id":"46117","date_updated":"2023-07-24T07:53:29Z","language":[{"iso":"eng"}],"year":"2023","type":"preprint","citation":{"ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” arXiv:2304.09573. 2023.","short":"T. Weich, L.L. 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Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” ArXiv:2304.09573, 2023."}},{"publication":"Teaching and Teacher Education","keyword":["Education"],"author":[{"last_name":"Bruns","full_name":"Bruns, Julia","first_name":"Julia"},{"last_name":"Hagena","first_name":"Maike","full_name":"Hagena, Maike"},{"last_name":"Gasteiger","full_name":"Gasteiger, Hedwig","first_name":"Hedwig"}],"publisher":"Elsevier BV","volume":132,"date_created":"2023-07-26T08:55:26Z","status":"public","user_id":"72183","citation":{"short":"J. Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023).","ieee":"J. Bruns, M. Hagena, and H. Gasteiger, “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?,” Teaching and Teacher Education, vol. 132, Art. no. 104270, 2023, doi: 10.1016/j.tate.2023.104270.","chicago":"Bruns, Julia, Maike Hagena, and Hedwig Gasteiger. “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?” Teaching and Teacher Education 132 (2023). https://doi.org/10.1016/j.tate.2023.104270.","ama":"Bruns J, Hagena M, Gasteiger H. Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects? Teaching and Teacher Education. 2023;132. doi:10.1016/j.tate.2023.104270","apa":"Bruns, J., Hagena, M., & Gasteiger, H. (2023). Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects? 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Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023.","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1.","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023. doi:10.1007/978-3-031-14175-1","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (Eds.). (2023). 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Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. 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Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE."}],"volume":14071,"status":"public","has_accepted_license":"1","date_created":"2023-02-16T11:32:48Z","publisher":"Springer, Cham.","author":[{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","id":"85279","last_name":"Offen"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"quality_controlled":"1","publication":"Geometric Science of Information","file_date_updated":"2023-08-02T12:04:17Z","keyword":["System identification","discrete Lagrangians","travelling waves"],"file":[{"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","creator":"coffen","file_id":"46273","file_size":1938962,"relation":"main_file","description":"The article shows how to learn models of dynamical systems\nfrom data which are governed by an unknown variational PDE. Rather\nthan employing reduction techniques, we learn a discrete field theory\ngoverned by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is\nnecessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of\nthe discrete Euler–Lagrange equations. Secondly, we develop a method to\nfind solutions to machine learned discrete field theories which constitute\ntravelling waves of the underlying continuous PDE.","content_type":"application/pdf","date_updated":"2023-08-02T12:04:17Z","file_name":"LDensityLearning.pdf","date_created":"2023-08-02T12:04:17Z","access_level":"open_access"}],"intvolume":" 14071","_id":"42163","conference":{"end_date":"2023-09-01","name":" GSI'23 6th International Conference on Geometric Science of Information","start_date":"2023-08-30","location":"Saint-Malo, Palais du Grand Large, France"},"year":"2023","citation":{"short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in Geometric Science of Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.","ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. Geometric Science of Information. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:10.1007/978-3-031-38271-0_57","apa":"Offen, C., & Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen & F. Barbaresco (Eds.), Geometric Science of Information (Vol. 14071, pp. 569–579). Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_57","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In Geometric Science of Information, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. https://doi.org/10.1007/978-3-031-38271-0_57.","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57.","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }"},"type":"conference","page":"569-579","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianDensityML","description":"GitHub","relation":"software"}]},"external_id":{"arxiv":["2302.08232 "]},"editor":[{"last_name":"Nielsen","full_name":"Nielsen, F","first_name":"F"},{"last_name":"Barbaresco","full_name":"Barbaresco, F","first_name":"F"}],"publication_status":"published","publication_identifier":{"eisbn":["978-3-031-38271-0"]},"department":[{"_id":"636"}],"doi":"10.1007/978-3-031-38271-0_57","oa":"1","date_updated":"2023-08-10T08:34:04Z","language":[{"iso":"eng"}],"series_title":"Lecture Notes in Computer Science (LNCS)"},{"has_accepted_license":"1","status":"public","date_created":"2022-01-11T13:24:00Z","volume":421,"file":[{"access_level":"open_access","date_created":"2022-06-28T15:25:50Z","file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","title":"Variational Learning of Euler–Lagrange Dynamics from Data","file_size":3640770,"description":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions\nconnecting two points in a phase space, the system will exhibit those motions which extremise an action functional.\nMany qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-\ntions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms\nfor dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features\nwith the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-\ntions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position\ndata of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no\nprior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward\nerror analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the\nlearned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of\nvariational backward error analysis. (3) Finally, we introduce a method to perform system identification from position\nobservations only, based on variational backward error analysis.","relation":"main_file","content_type":"application/pdf","date_updated":"2022-06-28T15:25:50Z","creator":"coffen","file_id":"32274"}],"quality_controlled":"1","publisher":"Elsevier","author":[{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Christian","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279"}],"file_date_updated":"2022-06-28T15:25:50Z","publication":"Journal of Computational and Applied Mathematics","keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"user_id":"85279","ddc":["510"],"article_type":"original","abstract":[{"text":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\r\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.","lang":"eng"}],"year":"2023","citation":{"chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics 421 (2023): 114780. https://doi.org/10.1016/j.cam.2022.114780.","apa":"Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics, 421, 114780. https://doi.org/10.1016/j.cam.2022.114780","ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics. 2023;421:114780. doi:10.1016/j.cam.2022.114780","bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics, vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780.","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” Journal of Computational and Applied Mathematics, vol. 421, p. 114780, 2023, doi: 10.1016/j.cam.2022.114780."},"type":"journal_article","page":"114780","intvolume":" 421","_id":"29240","publication_status":"epub_ahead","publication_identifier":{"issn":["0377-0427"]},"department":[{"_id":"636"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/LagrangianShadowIntegration"}]},"title":"Variational Learning of Euler–Lagrange Dynamics from Data","external_id":{"arxiv":["2112.12619"]},"language":[{"iso":"eng"}],"oa":"1","doi":"10.1016/j.cam.2022.114780","date_updated":"2023-08-10T08:42:39Z"},{"issue":"1","_id":"29236","intvolume":" 15","page":"98-115","type":"journal_article","year":"2023","citation":{"ieee":"R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” Journal of Geometric Mechanics, vol. 15, no. 1, pp. 98–115, 2023, doi: 10.3934/jgm.2023005.","short":"R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.","bibtex":"@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={10.3934/jgm.2023005}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }","mla":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:10.3934/jgm.2023005.","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005","apa":"McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115. https://doi.org/10.3934/jgm.2023005","chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115. https://doi.org/10.3934/jgm.2023005."},"ddc":["510"],"user_id":"85279","abstract":[{"text":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","lang":"eng"}],"article_type":"original","volume":15,"date_created":"2022-01-11T12:48:39Z","has_accepted_license":"1","status":"public","file_date_updated":"2022-08-12T16:48:59Z","publication":"Journal of Geometric Mechanics","keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"quality_controlled":"1","author":[{"last_name":"McLachlan","first_name":"Robert","full_name":"McLachlan, Robert"},{"id":"85279","last_name":"Offen","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian"}],"publisher":"AIMS Press","file":[{"file_size":827030,"title":"Backward error analysis for conjugate symplectic methods","file_name":"BEA_MultiStep_Matrix.pdf","date_created":"2022-08-12T16:48:59Z","access_level":"open_access","file_id":"32801","creator":"coffen","date_updated":"2022-08-12T16:48:59Z","content_type":"application/pdf","description":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","relation":"main_file"}],"doi":"10.3934/jgm.2023005","oa":"1","date_updated":"2023-08-10T08:40:30Z","language":[{"iso":"eng"}],"title":"Backward error analysis for conjugate symplectic methods","related_material":{"link":[{"url":"https://github.com/Christian-Offen/BEAConjugateSymplectic","relation":"software"}]},"external_id":{"arxiv":["2201.03911"]},"publication_status":"published","department":[{"_id":"636"}]},{"language":[{"iso":"eng"}],"date_updated":"2023-08-10T08:37:01Z","oa":"1","doi":"10.1063/5.0142969","department":[{"_id":"636"}],"publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","external_id":{"arxiv":["2301.07928"]},"related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","year":"2023","type":"journal_article","citation":{"bibtex":"@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }","mla":"Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.","chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos 33, no. 6 (2023). https://doi.org/10.1063/5.0142969.","apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos, 33(6), Article 063115. https://doi.org/10.1063/5.0142969","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969","ieee":"E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art. no. 063115, 2023, doi: 10.1063/5.0142969.","short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023)."},"_id":"37654","intvolume":" 33","issue":"6","article_number":"063115","file":[{"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","file_size":5200111,"access_level":"open_access","date_created":"2023-04-26T16:20:56Z","file_name":"JournalPaper_main.pdf","relation":"main_file","description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously.","date_updated":"2023-04-26T16:20:56Z","content_type":"application/pdf","creator":"coffen","file_id":"44205"}],"file_date_updated":"2023-04-26T16:20:56Z","publication":"Chaos","publisher":"AIP Publishing","author":[{"last_name":"Dierkes","first_name":"Eva","full_name":"Dierkes, Eva"},{"id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian"},{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"}],"date_created":"2023-01-20T09:10:06Z","status":"public","has_accepted_license":"1","volume":33,"abstract":[{"text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered.","lang":"eng"}],"article_type":"original","user_id":"85279","ddc":["510"]},{"abstract":[{"text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.","lang":"eng"}],"user_id":"47427","author":[{"full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","first_name":"Feliks","id":"81513","last_name":"Nüske"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"last_name":"Schaller","first_name":"Manuel","full_name":"Schaller, Manuel"},{"full_name":"Worthmann, Karl","first_name":"Karl","last_name":"Worthmann"}],"publication":"Journal of Nonlinear Science","volume":33,"status":"public","date_created":"2021-08-17T12:25:09Z","intvolume":" 33","_id":"23428","article_number":"14","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"type":"journal_article","year":"2023","citation":{"short":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023).","ieee":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” Journal of Nonlinear Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.","chicago":"Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.","apa":"Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1","ama":"Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-022-09862-1","bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1."},"title":"Finite-data error bounds for Koopman-based prediction and control","department":[{"_id":"101"},{"_id":"655"}],"publication_status":"published","date_updated":"2023-08-24T07:50:12Z","doi":"10.1007/s00332-022-09862-1","oa":"1","language":[{"iso":"eng"}]},{"issue":"2","intvolume":" 45","_id":"21600","page":"A579-A595","year":"2023","citation":{"chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing. 2023;45(2):A579-A595. doi:10.1137/21M1412682","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing, 45(2), A579–A595. https://doi.org/10.1137/21M1412682","mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol. 45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement learning}, volume={45}, DOI={10.1137/21M1412682}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.","ieee":"M. Dellnitz et al., “Efficient time stepping for numerical integration using reinforcement learning,” SIAM Journal on Scientific Computing, vol. 45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682."},"type":"journal_article","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"user_id":"47427","ddc":["510"],"abstract":[{"text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.","lang":"eng"}],"date_created":"2021-04-09T07:59:19Z","status":"public","has_accepted_license":"1","volume":45,"publication":"SIAM Journal on Scientific Computing","author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"first_name":"Eyke","full_name":"Hüllermeier, Eyke","last_name":"Hüllermeier","id":"48129"},{"last_name":"Lücke","full_name":"Lücke, Marvin","first_name":"Marvin"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","last_name":"Offen","id":"85279"},{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"last_name":"Pfannschmidt","id":"13472","first_name":"Karlson","full_name":"Pfannschmidt, Karlson","orcid":"0000-0001-9407-7903"}],"doi":"10.1137/21M1412682","date_updated":"2023-08-25T09:24:50Z","language":[{"iso":"eng"}],"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/lueckem/quadrature-ML"}]},"title":"Efficient time stepping for numerical integration using reinforcement learning","external_id":{"arxiv":["arXiv:2104.03562"]},"publication_status":"published","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}]},{"publication":"International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education","department":[{"_id":"543"}],"publisher":"Charles University","author":[{"first_name":"Imke","full_name":"Schwerin, Imke","last_name":"Schwerin","id":"48912"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"date_created":"2023-08-30T09:40:23Z","status":"public","editor":[{"last_name":"Novotna","full_name":"Novotna, J.","first_name":"J."},{"last_name":"Moraova","first_name":"H.","full_name":"Moraova, H."}],"user_id":"44184","title":"Second grader´s understanding of doubling and halfing in various representations","language":[{"iso":"eng"}],"page":"297-305","type":"conference","citation":{"ieee":"I. Schwerin and U. Häsel-Weide, “Second grader´s understanding of doubling and halfing in various representations,” in International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, Prag, 2023, pp. 297–305.","short":"I. Schwerin, U. Häsel-Weide, in: J. Novotna, H. Moraova (Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, Charles University, 2023, pp. 297–305.","bibtex":"@inproceedings{Schwerin_Häsel-Weide_2023, title={Second grader´s understanding of doubling and halfing in various representations}, booktitle={International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}, publisher={Charles University}, author={Schwerin, Imke and Häsel-Weide, Uta}, editor={Novotna, J. and Moraova, H.}, year={2023}, pages={297–305} }","mla":"Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of Doubling and Halfing in Various Representations.” International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, edited by J. Novotna and H. Moraova, Charles University, 2023, pp. 297–305.","apa":"Schwerin, I., & Häsel-Weide, U. (2023). Second grader´s understanding of doubling and halfing in various representations. In J. Novotna & H. Moraova (Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education (pp. 297–305). Charles University.","ama":"Schwerin I, Häsel-Weide U. Second grader´s understanding of doubling and halfing in various representations. In: Novotna J, Moraova H, eds. International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education. Charles University; 2023:297-305.","chicago":"Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of Doubling and Halfing in Various Representations.” In International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, edited by J. Novotna and H. Moraova, 297–305. Charles University, 2023."},"year":"2023","conference":{"name":"International Symposium in Elementary Mathematics Teaching","location":"Prag"},"date_updated":"2023-08-30T09:55:41Z","_id":"46757"},{"title":"Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern","user_id":"44184","editor":[{"full_name":"Vöing, N.","first_name":"N.","last_name":"Vöing"},{"full_name":"Schmidt, R.","first_name":"R.","last_name":"Schmidt"},{"full_name":"Neiske, I.","first_name":"I.","last_name":"Neiske"}],"date_created":"2023-08-30T09:54:47Z","status":"public","department":[{"_id":"543"}],"publication":"Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre","author":[{"last_name":"Schmidt","id":"58565","first_name":"Rebekka","full_name":"Schmidt, Rebekka"},{"first_name":"Claudia","full_name":"Tenberge, Claudia","last_name":"Tenberge","id":"67302"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"publisher":"Visual Ink Publishing","_id":"46758","date_updated":"2023-08-30T09:55:46Z","page":"297-318","type":"book_chapter","year":"2023","citation":{"ieee":"R. Schmidt, C. Tenberge, and U. Häsel-Weide, “Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern,” in Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, N. Vöing, R. Schmidt, and I. Neiske, Eds. Visual Ink Publishing, 2023, pp. 297–318.","short":"R. Schmidt, C. Tenberge, U. Häsel-Weide, in: N. Vöing, R. Schmidt, I. Neiske (Eds.), Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, Visual Ink Publishing, 2023, pp. 297–318.","mla":"Schmidt, Rebekka, et al. “Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern.” Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, edited by N. Vöing et al., Visual Ink Publishing, 2023, pp. 297–318.","bibtex":"@inbook{Schmidt_Tenberge_Häsel-Weide_2023, title={Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern}, booktitle={Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre}, publisher={Visual Ink Publishing}, author={Schmidt, Rebekka and Tenberge, Claudia and Häsel-Weide, Uta}, editor={Vöing, N. and Schmidt, R. and Neiske, I.}, year={2023}, pages={297–318} }","chicago":"Schmidt, Rebekka, Claudia Tenberge, and Uta Häsel-Weide. “Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern.” In Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, edited by N. Vöing, R. Schmidt, and I. Neiske, 297–318. Visual Ink Publishing, 2023.","apa":"Schmidt, R., Tenberge, C., & Häsel-Weide, U. (2023). Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern. In N. Vöing, R. Schmidt, & I. Neiske (Eds.), Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre (pp. 297–318). Visual Ink Publishing.","ama":"Schmidt R, Tenberge C, Häsel-Weide U. Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern. In: Vöing N, Schmidt R, Neiske I, eds. Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre. Visual Ink Publishing; 2023:297-318."},"language":[{"iso":"ger"}]},{"language":[{"iso":"eng"}],"type":"book_chapter","citation":{"mla":"Biehler, Rolf, et al. “Stochastik: Leitidee Daten Und Zufall.” Handbuch Der Mathematikdidaktik, edited by Regina Bruder et al., Springer, 2023, doi:10.1007/978-3-662-66604-3_8.","bibtex":"@inbook{Biehler_Engel_Frischemeier_2023, place={Berlin, Heidelberg}, title={Stochastik: Leitidee Daten und Zufall}, DOI={10.1007/978-3-662-66604-3_8}, booktitle={Handbuch der Mathematikdidaktik}, publisher={Springer}, author={Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel}, editor={Bruder, Regina and Büchter, A. and Gasteiger, H. and Schmidt-Thieme, B. and Weigand, HG.}, year={2023} }","chicago":"Biehler, Rolf, Joachim Engel, and Daniel Frischemeier. “Stochastik: Leitidee Daten Und Zufall.” In Handbuch Der Mathematikdidaktik, edited by Regina Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, and HG. Weigand. Berlin, Heidelberg: Springer, 2023. https://doi.org/10.1007/978-3-662-66604-3_8.","apa":"Biehler, R., Engel, J., & Frischemeier, D. (2023). Stochastik: Leitidee Daten und Zufall. In R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, & HG. Weigand (Eds.), Handbuch der Mathematikdidaktik. Springer. https://doi.org/10.1007/978-3-662-66604-3_8","ama":"Biehler R, Engel J, Frischemeier D. Stochastik: Leitidee Daten und Zufall. In: Bruder R, Büchter A, Gasteiger H, Schmidt-Thieme B, Weigand HG, eds. Handbuch Der Mathematikdidaktik. Springer; 2023. doi:10.1007/978-3-662-66604-3_8","ieee":"R. Biehler, J. Engel, and D. Frischemeier, “Stochastik: Leitidee Daten und Zufall,” in Handbuch der Mathematikdidaktik, R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, and HG. Weigand, Eds. Berlin, Heidelberg: Springer, 2023.","short":"R. Biehler, J. Engel, D. Frischemeier, in: R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, HG. Weigand (Eds.), Handbuch Der Mathematikdidaktik, Springer, Berlin, Heidelberg, 2023."},"year":"2023","doi":"10.1007/978-3-662-66604-3_8","date_updated":"2023-09-25T11:18:19Z","_id":"47416","status":"public","date_created":"2023-09-25T11:15:18Z","editor":[{"last_name":"Bruder","full_name":"Bruder, Regina","first_name":"Regina"},{"full_name":"Büchter, A.","first_name":"A.","last_name":"Büchter"},{"last_name":"Gasteiger","first_name":"H.","full_name":"Gasteiger, H."},{"last_name":"Schmidt-Thieme","first_name":"B.","full_name":"Schmidt-Thieme, B."},{"last_name":"Weigand","full_name":"Weigand, HG.","first_name":"HG."}],"publication_identifier":{"isbn":["9783662666036","9783662666043"]},"publication_status":"published","author":[{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler","id":"16274"},{"last_name":"Engel","full_name":"Engel, Joachim","first_name":"Joachim"},{"first_name":"Daniel","full_name":"Frischemeier, Daniel","last_name":"Frischemeier"}],"publisher":"Springer","publication":"Handbuch der Mathematikdidaktik","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"user_id":"37888","title":"Stochastik: Leitidee Daten und Zufall","place":"Berlin, Heidelberg"},{"department":[{"_id":"799"},{"_id":"623"}],"publication":"arXiv:2309.09005","author":[{"id":"99427","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","first_name":"Benjamin"},{"full_name":"Matte, Oliver","first_name":"Oliver","last_name":"Matte"}],"date_created":"2023-10-02T06:21:37Z","project":[{"name":"PhoQC: PhoQC: Photonisches Quantencomputing","_id":"266"}],"status":"public","external_id":{"arxiv":["2309.09005"]},"abstract":[{"lang":"eng","text":"In this proceeding we consider a translation invariant Nelson type model in\r\ntwo spatial dimensions modeling a scalar relativistic particle in interaction\r\nwith a massive radiation field. As is well-known, the corresponding Hamiltonian\r\ncan be defined with the help of an energy renormalization. First, we review a\r\nFeynman-Kac formula for the semigroup generated by this Hamiltonian proven by\r\nthe authors in a recent preprint (where several matter particles and exterior\r\npotentials are treated as well). After that, we employ a few technical key\r\nrelations and estimates obtained in our preprint to present an otherwise\r\nself-contained derivation of new Feynman-Kac formulas for the fiber\r\nHamiltonians attached to fixed total momenta of the translation invariant\r\nsystem. We conclude by inferring an alternative derivation of the Feynman-Kac\r\nformula for the full translation invariant Hamiltonian."}],"user_id":"99427","title":"Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Hinrichs_Matte_2023, title={Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions}, journal={arXiv:2309.09005}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023} }","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson Model in Two Spatial Dimensions.” ArXiv:2309.09005, 2023.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson Model in Two Spatial Dimensions.” ArXiv:2309.09005, 2023.","apa":"Hinrichs, B., & Matte, O. (2023). Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions. In arXiv:2309.09005.","ama":"Hinrichs B, Matte O. Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions. arXiv:230909005. Published online 2023.","ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions,” arXiv:2309.09005. 2023.","short":"B. Hinrichs, O. Matte, ArXiv:2309.09005 (2023)."},"year":"2023","type":"preprint","_id":"47534","date_updated":"2023-10-02T06:22:55Z"},{"date_updated":"2023-10-12T11:31:47Z","_id":"48042","language":[{"iso":"eng"}],"type":"book_chapter","citation":{"chicago":"Biehler, Rolf, Daniel Frischemeier, Ronald Gould, and Maxine Pfannkuch. “Impacts of Digitalization on Content and Goals of Statistics Education.” In Handbook of Digital Resources in Mathematics Education, edited by Birgit Pepin, Ghislaine Gueudet, and Jeffrey Choppin. Cham: Springer International Publishing, 2023.","ama":"Biehler R, Frischemeier D, Gould R, Pfannkuch M. Impacts of Digitalization on Content and Goals of Statistics Education. In: Pepin B, Gueudet G, Choppin J, eds. Handbook of Digital Resources in Mathematics Education. Springer International Publishing; 2023.","apa":"Biehler, R., Frischemeier, D., Gould, R., & Pfannkuch, M. (2023). Impacts of Digitalization on Content and Goals of Statistics Education. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of Digital Resources in Mathematics Education. Springer International Publishing.","bibtex":"@inbook{Biehler_Frischemeier_Gould_Pfannkuch_2023, place={Cham}, title={Impacts of Digitalization on Content and Goals of Statistics Education}, booktitle={Handbook of Digital Resources in Mathematics Education}, publisher={Springer International Publishing}, author={Biehler, Rolf and Frischemeier, Daniel and Gould, Ronald and Pfannkuch, Maxine}, editor={Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeffrey}, year={2023} }","mla":"Biehler, Rolf, et al. “Impacts of Digitalization on Content and Goals of Statistics Education.” Handbook of Digital Resources in Mathematics Education, edited by Birgit Pepin et al., Springer International Publishing, 2023.","short":"R. Biehler, D. Frischemeier, R. Gould, M. Pfannkuch, in: B. Pepin, G. Gueudet, J. Choppin (Eds.), Handbook of Digital Resources in Mathematics Education, Springer International Publishing, Cham, 2023.","ieee":"R. Biehler, D. Frischemeier, R. Gould, and M. Pfannkuch, “Impacts of Digitalization on Content and Goals of Statistics Education,” in Handbook of Digital Resources in Mathematics Education, B. Pepin, G. Gueudet, and J. Choppin, Eds. Cham: Springer International Publishing, 2023."},"year":"2023","user_id":"37888","title":"Impacts of Digitalization on Content and Goals of Statistics Education","place":"Cham","status":"public","date_created":"2023-10-12T11:31:22Z","editor":[{"last_name":"Pepin","first_name":"Birgit","full_name":"Pepin, Birgit"},{"first_name":"Ghislaine","full_name":"Gueudet, Ghislaine","last_name":"Gueudet"},{"first_name":"Jeffrey","full_name":"Choppin, Jeffrey","last_name":"Choppin"}],"author":[{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler","id":"16274"},{"last_name":"Frischemeier","first_name":"Daniel","full_name":"Frischemeier, Daniel"},{"last_name":"Gould","full_name":"Gould, Ronald","first_name":"Ronald"},{"last_name":"Pfannkuch","first_name":"Maxine","full_name":"Pfannkuch, Maxine"}],"publisher":"Springer International Publishing","publication":"Handbook of Digital Resources in Mathematics Education","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}]},{"date_created":"2023-10-19T09:12:45Z","status":"public","publication_status":"published","publication_identifier":{"isbn":["9783662666036","9783662666043"]},"publication":"Handbuch der Mathematikdidaktik","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"publisher":"Springer Berlin Heidelberg","author":[{"first_name":"Dominik","full_name":"Leiss, Dominik","last_name":"Leiss"},{"first_name":"Kerstin","full_name":"Gerlach, Kerstin","last_name":"Gerlach"},{"id":"85190","last_name":"Wessel","full_name":"Wessel, Lena","first_name":"Lena"},{"full_name":"Schmidt-Thieme, Barbara","first_name":"Barbara","last_name":"Schmidt-Thieme"}],"user_id":"37888","title":"Sprache und Mathematiklernen","place":"Berlin, Heidelberg","language":[{"iso":"ger"}],"page":"561-595","citation":{"bibtex":"@inbook{Leiss_Gerlach_Wessel_Schmidt-Thieme_2023, place={Berlin, Heidelberg}, title={Sprache und Mathematiklernen}, DOI={10.1007/978-3-662-66604-3_18}, booktitle={Handbuch der Mathematikdidaktik}, publisher={Springer Berlin Heidelberg}, author={Leiss, Dominik and Gerlach, Kerstin and Wessel, Lena and Schmidt-Thieme, Barbara}, year={2023}, pages={561–595} }","mla":"Leiss, Dominik, et al. “Sprache und Mathematiklernen.” Handbuch der Mathematikdidaktik, Springer Berlin Heidelberg, 2023, pp. 561–95, doi:10.1007/978-3-662-66604-3_18.","apa":"Leiss, D., Gerlach, K., Wessel, L., & Schmidt-Thieme, B. 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Schmidt-Thieme, in: Handbuch der Mathematikdidaktik, Springer Berlin Heidelberg, Berlin, Heidelberg, 2023, pp. 561–595."},"type":"book_chapter","year":"2023","doi":"10.1007/978-3-662-66604-3_18","date_updated":"2023-10-19T09:33:54Z","_id":"48319"},{"file":[{"date_updated":"2023-10-26T07:00:55Z","content_type":"application/pdf","relation":"main_file","success":1,"file_size":1389445,"file_id":"48481","creator":"krueter","access_level":"closed","file_name":"Kortemeyer Biehler aus CalcConf2023_Proceedings.pdf","date_created":"2023-10-26T07:00:55Z"}],"publication":"The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference","file_date_updated":"2023-10-26T07:00:55Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publisher":"MatRIC","author":[{"last_name":"Kortmeyer","first_name":"Jörg","full_name":"Kortmeyer, Jörg"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"}],"date_created":"2023-10-26T07:01:34Z","status":"public","has_accepted_license":"1","editor":[{"full_name":"Dreyfus, T.","first_name":"T.","last_name":"Dreyfus"},{"last_name":"Gonzalez-Martin","full_name":"Gonzalez-Martin, A. S.","first_name":"A. S."},{"last_name":"Nardi","first_name":"E.","full_name":"Nardi, E."},{"first_name":"J.","full_name":"Monaghan, J.","last_name":"Monaghan"},{"last_name":"Thompson","first_name":"P. W.","full_name":"Thompson, P. W."}],"user_id":"37888","ddc":["510"],"title":"The use of integrals for accumulation and mean values in basic electrical engineering courses","language":[{"iso":"eng"}],"page":"121-124","year":"2023","type":"book_chapter","citation":{"ieee":"J. Kortmeyer and R. Biehler, “The use of integrals for accumulation and mean values in basic electrical engineering courses,” in The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference, T. Dreyfus, A. S. Gonzalez-Martin, E. Nardi, J. Monaghan, and P. W. Thompson, Eds. MatRIC, 2023, pp. 121–124.","short":"J. Kortmeyer, R. Biehler, in: T. Dreyfus, A.S. Gonzalez-Martin, E. Nardi, J. Monaghan, P.W. Thompson (Eds.), The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference, MatRIC, 2023, pp. 121–124.","mla":"Kortmeyer, Jörg, and Rolf Biehler. “The Use of Integrals for Accumulation and Mean Values in Basic Electrical Engineering Courses.” The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference, edited by T. Dreyfus et al., MatRIC, 2023, pp. 121–24.","bibtex":"@inbook{Kortmeyer_Biehler_2023, title={The use of integrals for accumulation and mean values in basic electrical engineering courses}, booktitle={The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference}, publisher={MatRIC}, author={Kortmeyer, Jörg and Biehler, Rolf}, editor={Dreyfus, T. and Gonzalez-Martin, A. S. and Nardi, E. and Monaghan, J. and Thompson, P. W.}, year={2023}, pages={121–124} }","chicago":"Kortmeyer, Jörg, and Rolf Biehler. “The Use of Integrals for Accumulation and Mean Values in Basic Electrical Engineering Courses.” In The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference, edited by T. Dreyfus, A. S. Gonzalez-Martin, E. Nardi, J. Monaghan, and P. W. Thompson, 121–24. MatRIC, 2023.","ama":"Kortmeyer J, Biehler R. The use of integrals for accumulation and mean values in basic electrical engineering courses. In: Dreyfus T, Gonzalez-Martin AS, Nardi E, Monaghan J, Thompson PW, eds. The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference. MatRIC; 2023:121-124.","apa":"Kortmeyer, J., & Biehler, R. (2023). The use of integrals for accumulation and mean values in basic electrical engineering courses. In T. Dreyfus, A. S. Gonzalez-Martin, E. Nardi, J. Monaghan, & P. W. Thompson (Eds.), The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference (pp. 121–124). MatRIC."},"date_updated":"2023-10-26T07:01:40Z","_id":"48480"},{"_id":"49049","date_updated":"2023-11-20T08:23:56Z","issue":"115","page":"57-65","type":"journal_article","citation":{"ieee":"R. Biehler and K. Krüger, “Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel,” GDM-Mitteilungen, no. 115, pp. 57–65, 2023.","short":"R. Biehler, K. Krüger, GDM-Mitteilungen (2023) 57–65.","mla":"Biehler, Rolf, and Katja Krüger. “Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel.” GDM-Mitteilungen, no. 115, 2023, pp. 57–65.","bibtex":"@article{Biehler_Krüger_2023, title={Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel}, number={115}, journal={GDM-Mitteilungen}, author={Biehler, Rolf and Krüger, Katja}, year={2023}, pages={57–65} }","ama":"Biehler R, Krüger K. Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel. GDM-Mitteilungen. 2023;(115):57-65.","apa":"Biehler, R., & Krüger, K. (2023). Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel. GDM-Mitteilungen, 115, 57–65.","chicago":"Biehler, Rolf, and Katja Krüger. “Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel.” GDM-Mitteilungen, no. 115 (2023): 57–65."},"year":"2023","language":[{"iso":"ger"}],"title":"Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel","ddc":["510"],"user_id":"37888","file_date_updated":"2023-11-20T08:23:14Z","publication":"GDM-Mitteilungen","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"author":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"first_name":"Katja","full_name":"Krüger, Katja","last_name":"Krüger"}],"file":[{"creator":"krueter","file_id":"49050","file_size":316979,"relation":"main_file","success":1,"date_updated":"2023-11-20T08:23:14Z","content_type":"application/pdf","date_created":"2023-11-20T08:23:14Z","file_name":"Biehler_2023_NachrufEngel_MGM115.pdf","access_level":"closed"}],"date_created":"2023-11-20T08:23:51Z","has_accepted_license":"1","status":"public"},{"page":"346-354","year":"2023","type":"conference","citation":{"mla":"Wallner, Melina, and Uta Häsel-Weide. “Conceptual Understanding of Third Grades for Axial Symmetry.” International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, edited by J. Novotna and H. Moraova, Charles University, 2023, pp. 346–54.","bibtex":"@inproceedings{Wallner_Häsel-Weide_2023, title={Conceptual understanding of third grades for axial symmetry}, booktitle={International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}, publisher={Charles University}, author={Wallner, Melina and Häsel-Weide, Uta}, editor={Novotna, J. and Moraova, H.}, year={2023}, pages={346–354} }","apa":"Wallner, M., & Häsel-Weide, U. (2023). Conceptual understanding of third grades for axial symmetry. In J. Novotna & H. Moraova (Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education (pp. 346–354). Charles University.","ama":"Wallner M, Häsel-Weide U. Conceptual understanding of third grades for axial symmetry. In: Novotna J, Moraova H, eds. International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education. Charles University; 2023:346-354.","chicago":"Wallner, Melina, and Uta Häsel-Weide. “Conceptual Understanding of Third Grades for Axial Symmetry.” In International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, edited by J. Novotna and H. Moraova, 346–54. Charles University, 2023.","ieee":"M. Wallner and U. Häsel-Weide, “Conceptual understanding of third grades for axial symmetry,” in International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, Prag, 2023, pp. 346–354.","short":"M. Wallner, U. Häsel-Weide, in: J. Novotna, H. Moraova (Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, Charles University, 2023, pp. 346–354."},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://semt.cz/proceedings/semt-23.pdf"}],"conference":{"name":"International Symposium in Elementary Mathematics Teaching","location":"Prag"},"date_updated":"2023-11-24T16:33:37Z","_id":"46756","editor":[{"first_name":"J.","full_name":"Novotna, J.","last_name":"Novotna"},{"last_name":"Moraova","first_name":"H.","full_name":"Moraova, H."}],"date_created":"2023-08-30T09:24:29Z","status":"public","department":[{"_id":"543"}],"publication":"International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education","publisher":"Charles University","author":[{"last_name":"Wallner","id":"45445","first_name":"Melina","full_name":"Wallner, Melina"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"title":"Conceptual understanding of third grades for axial symmetry","user_id":"45445"},{"department":[{"_id":"101"}],"publication_status":"published","publication_identifier":{"issn":["0036-1399","1095-712X"]},"external_id":{"arxiv":["2302.08974"]},"title":"Hypernetworks: Cluster Synchronization Is a Higher-Order Effect","language":[{"iso":"eng"}],"date_updated":"2023-11-29T10:52:23Z","doi":"10.1137/23m1561075","publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","last_name":"von der Gracht","id":"97359"},{"last_name":"Nijholt","first_name":"Eddie","full_name":"Nijholt, Eddie"},{"first_name":"Bob","full_name":"Rink, Bob","last_name":"Rink"}],"keyword":["Applied Mathematics"],"publication":"SIAM Journal on Applied Mathematics","volume":83,"status":"public","date_created":"2023-11-29T10:50:05Z","abstract":[{"text":"Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.","lang":"eng"}],"user_id":"97359","citation":{"ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect,” SIAM Journal on Applied Mathematics, vol. 83, no. 6, pp. 2329–2353, 2023, doi: 10.1137/23m1561075.","short":"S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics 83 (2023) 2329–2353.","mla":"von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics, vol. 83, no. 6, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2329–53, doi:10.1137/23m1561075.","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}, volume={83}, DOI={10.1137/23m1561075}, number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }","ama":"von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics. 2023;83(6):2329-2353. doi:10.1137/23m1561075","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (2023). Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics, 83(6), 2329–2353. https://doi.org/10.1137/23m1561075","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics 83, no. 6 (2023): 2329–53. https://doi.org/10.1137/23m1561075."},"type":"journal_article","year":"2023","page":"2329-2353","_id":"49326","intvolume":" 83","issue":"6"},{"type":"preprint","year":"2023","citation":{"chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” ArXiv:2311.17186, 2023.","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (2023). Higher order interactions lead to “reluctant” synchrony breaking. In arXiv:2311.17186.","ama":"von der Gracht S, Nijholt E, Rink B. Higher order interactions lead to “reluctant” synchrony breaking. arXiv:231117186. Published online 2023.","mla":"von der Gracht, Sören, et al. “Higher Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” ArXiv:2311.17186, 2023.","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Higher order interactions lead to “reluctant” synchrony breaking}, journal={arXiv:2311.17186}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023} }","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2311.17186 (2023).","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Higher order interactions lead to ‘reluctant’ synchrony breaking,” arXiv:2311.17186. 2023."},"language":[{"iso":"eng"}],"_id":"49371","date_updated":"2023-12-01T06:38:44Z","author":[{"id":"97359","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","first_name":"Sören"},{"first_name":"Eddie","full_name":"Nijholt, Eddie","last_name":"Nijholt"},{"last_name":"Rink","first_name":"Bob","full_name":"Rink, Bob"}],"publication":"arXiv:2311.17186","department":[{"_id":"101"}],"status":"public","date_created":"2023-12-01T06:35:29Z","external_id":{"arxiv":["2311.17186"]},"abstract":[{"text":"To model dynamical systems on networks with higher order (non-pairwise)\r\ninteractions, we recently introduced a new class of ODEs on hypernetworks. Here\r\nwe consider one-parameter synchrony breaking bifurcations in such ODEs. We call\r\na synchrony breaking steady state branch \"reluctant\" if it is tangent to a\r\nsynchrony space, but does not lie inside it. We prove that reluctant synchrony\r\nbreaking is ubiquitous in hypernetwork systems, by constructing a large class\r\nof examples that support it. We also give an explicit formula for the order of\r\ntangency to the synchrony space of a reluctant steady state branch.","lang":"eng"}],"title":"Higher order interactions lead to \"reluctant\" synchrony breaking","user_id":"97359"},{"doi":"10.1007/s44007-023-00067-w","_id":"49372","date_updated":"2023-12-06T09:50:43Z","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg Extensions}, DOI={10.1007/s44007-023-00067-w}, journal={La Matematica}, publisher={Springer Science and Business Media LLC}, author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }","mla":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” La Matematica, Springer Science and Business Media LLC, 2023, doi:10.1007/s44007-023-00067-w.","chicago":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” La Matematica, 2023. https://doi.org/10.1007/s44007-023-00067-w.","ama":"Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. La Matematica. Published online 2023. doi:10.1007/s44007-023-00067-w","apa":"Klüners, J., & Wang, J. (2023). Idélic Approach in Enumerating Heisenberg Extensions. La Matematica. https://doi.org/10.1007/s44007-023-00067-w","ieee":"J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,” La Matematica, 2023, doi: 10.1007/s44007-023-00067-w.","short":"J. Klüners, J. Wang, La Matematica (2023)."},"year":"2023","type":"journal_article","user_id":"21202","title":"Idélic Approach in Enumerating Heisenberg Extensions","date_created":"2023-12-01T09:23:59Z","status":"public","publication_identifier":{"issn":["2730-9657"]},"publication_status":"published","publication":"La Matematica","department":[{"_id":"102"}],"author":[{"last_name":"Klüners","id":"21202","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"full_name":"Wang, Jiuya","first_name":"Jiuya","last_name":"Wang"}],"publisher":"Springer Science and Business Media LLC"},{"date_updated":"2023-12-13T12:51:03Z","_id":"49425","doi":"https://doi.org/10.1080/13540602.2023.2284876 ","page":"1-16","year":"2023","type":"journal_article","citation":{"bibtex":"@article{Seitz_Häsel-Weide_Wilke_Wallner_2023, title={Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research}, DOI={https://doi.org/10.1080/13540602.2023.2284876 }, journal={Teachers and Teaching}, author={Seitz, Simone and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}, year={2023}, pages={1–16} }","mla":"Seitz, Simone, et al. “Expertise and Professionalism for Inclusive (Mathematics) Teaching and Learning: Reflections on Findings from Interdisciplinary Professionalisation Research.” Teachers and Teaching, 2023, pp. 1–16, doi:https://doi.org/10.1080/13540602.2023.2284876 .","ama":"Seitz S, Häsel-Weide U, Wilke Y, Wallner M. Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research. Teachers and Teaching. Published online 2023:1-16. doi:https://doi.org/10.1080/13540602.2023.2284876 ","apa":"Seitz, S., Häsel-Weide, U., Wilke, Y., & Wallner, M. (2023). Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research. Teachers and Teaching, 1–16. https://doi.org/10.1080/13540602.2023.2284876 ","chicago":"Seitz, Simone, Uta Häsel-Weide, Yannik Wilke, and Melina Wallner. “Expertise and Professionalism for Inclusive (Mathematics) Teaching and Learning: Reflections on Findings from Interdisciplinary Professionalisation Research.” Teachers and Teaching, 2023, 1–16. https://doi.org/10.1080/13540602.2023.2284876 .","ieee":"S. Seitz, U. Häsel-Weide, Y. Wilke, and M. Wallner, “Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research,” Teachers and Teaching, pp. 1–16, 2023, doi: https://doi.org/10.1080/13540602.2023.2284876 .","short":"S. Seitz, U. Häsel-Weide, Y. Wilke, M. Wallner, Teachers and Teaching (2023) 1–16."},"language":[{"iso":"eng"}],"title":"Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research","user_id":"45445","publication":"Teachers and Teaching","department":[{"_id":"543"}],"author":[{"last_name":"Seitz","full_name":"Seitz, Simone","first_name":"Simone"},{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"},{"full_name":"Wilke, Yannik","first_name":"Yannik","last_name":"Wilke"},{"full_name":"Wallner, Melina","first_name":"Melina","id":"45445","last_name":"Wallner"}],"date_created":"2023-12-04T09:45:04Z","status":"public"},{"conference":{"end_date":"2023-07-14","location":" Yokohama, Japan","name":"The 22nd World Congress of the International Federation of Automatic Control","start_date":"2023-07-09"},"intvolume":" 56","_id":"34135","issue":"2","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"page":"3203-3210","type":"conference","year":"2023","citation":{"ieee":"Y. Lishkova et al., “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery,” in IFAC-PapersOnLine, Yokohama, Japan, 2023, vol. 56, no. 2, pp. 3203–3210, doi: 10.1016/j.ifacol.2023.10.1457.","short":"Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum, C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210.","bibtex":"@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023, title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}, volume={56}, DOI={10.1016/j.ifacol.2023.10.1457}, number={2}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier}, author={Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={3203–3210} }","mla":"Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” IFAC-PapersOnLine, vol. 56, no. 2, Elsevier, 2023, pp. 3203–10, doi:10.1016/j.ifacol.2023.10.1457.","chicago":"Lishkova, Yana, Paul Scherer, Steffen Ridderbusch, Mateja Jamnik, Pietro Liò, Sina Ober-Blöbaum, and Christian Offen. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” In IFAC-PapersOnLine, 56:3203–10. Elsevier, 2023. https://doi.org/10.1016/j.ifacol.2023.10.1457.","ama":"Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. In: IFAC-PapersOnLine. Vol 56. Elsevier; 2023:3203-3210. doi:10.1016/j.ifacol.2023.10.1457","apa":"Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum, S., & Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. IFAC-PapersOnLine, 56(2), 3203–3210. https://doi.org/10.1016/j.ifacol.2023.10.1457"},"abstract":[{"lang":"eng","text":"By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise."}],"ddc":["510"],"user_id":"85279","file_date_updated":"2023-04-17T08:05:55Z","publication":"IFAC-PapersOnLine","author":[{"last_name":"Lishkova","full_name":"Lishkova, Yana","first_name":"Yana"},{"full_name":"Scherer, Paul","first_name":"Paul","last_name":"Scherer"},{"last_name":"Ridderbusch","first_name":"Steffen","full_name":"Ridderbusch, Steffen"},{"first_name":"Mateja","full_name":"Jamnik, Mateja","last_name":"Jamnik"},{"first_name":"Pietro","full_name":"Liò, Pietro","last_name":"Liò"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","id":"85279","last_name":"Offen"}],"quality_controlled":"1","publisher":"Elsevier","file":[{"date_created":"2023-04-17T08:05:55Z","file_name":"LNN_project.pdf","access_level":"open_access","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","file_size":576115,"file_id":"44037","creator":"coffen","relation":"main_file","description":"By one of the most fundamental principles in physics, a dynamical system will\nexhibit those motions which extremise an action functional. This leads to the formation of\nthe Euler-Lagrange equations, which serve as a model of how the system will behave in time.\nIf the dynamics exhibit additional symmetries, then the motion fulfils additional conservation\nlaws, such as conservation of energy (time invariance), momentum (translation invariance), or\nangular momentum (rotational invariance). To learn a system representation, one could learn\nthe discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function\nLd which defines them. Based on ideas from Lie group theory, we introduce a framework to learn\na discrete Lagrangian along with its symmetry group from discrete observations of motions and,\ntherefore, identify conserved quantities. The learning process does not restrict the form of the\nLagrangian, does not require velocity or momentum observations or predictions and incorporates\na cost term which safeguards against unwanted solutions and against potential numerical issues\nin forward simulations. The learnt discrete quantities are related to their continuous analogues\nusing variational backward error analysis and numerical results demonstrate the improvement\nsuch models can have both qualitatively and quantitatively even in the presence of noise.","content_type":"application/pdf","date_updated":"2023-04-17T08:05:55Z"}],"volume":56,"date_created":"2022-11-23T08:17:10Z","status":"public","has_accepted_license":"1","date_updated":"2023-12-29T14:26:00Z","doi":"10.1016/j.ifacol.2023.10.1457","oa":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2211.10830"]},"title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","related_material":{"link":[{"url":"https://github.com/yanalish/SymDLNN","description":"GitHub","relation":"software"}]},"department":[{"_id":"636"}],"publication_status":"published"},{"_id":"44840","main_file_link":[{"url":"https://arxiv.org/abs/2305.06632"}],"page":"38","year":"2023","type":"preprint","citation":{"mla":"Gerlach, Raphael, et al. “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies.” ArXiv:2305.06632.","bibtex":"@article{Gerlach_von der Gracht_Dellnitz, title={On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies}, journal={arXiv:2305.06632}, author={Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael} }","chicago":"Gerlach, Raphael, Sören von der Gracht, and Michael Dellnitz. “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies.” ArXiv:2305.06632, n.d.","apa":"Gerlach, R., von der Gracht, S., & Dellnitz, M. (n.d.). On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. In arXiv:2305.06632.","ama":"Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. arXiv:230506632.","ieee":"R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies,” arXiv:2305.06632. .","short":"R. Gerlach, S. von der Gracht, M. Dellnitz, ArXiv:2305.06632 (n.d.)."},"abstract":[{"text":"In this article we investigate the convergence behavior of gathering protocols with fixed circulant topologies using tools form dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we model a gathering protocol as a system of ordinary differential equations whose equilibria are exactly all possible gathering points. Then, we find necessary and sufficient conditions for the structure of the underlying interaction graph such that the protocol is stable and converging, i.e., gathering, in the distributive computing sense by using tools from dynamical systems. Moreover, these tools allow for a more fine grained analysis in terms of speed of convergence in the dynamical systems sense. In fact, we derive a decomposition\r\nof the state space into stable invariant subspaces with different convergence\r\nrates. In particular, this decomposition is identical for every (linear)\r\ncirculant gathering protocol, whereas only the convergence rates depend on the\r\nweights in interaction graph itself.","lang":"eng"}],"user_id":"32655","publication":"arXiv:2305.06632","keyword":["Dynamical Systems","Coupled Systems","Distributed Computing","Robot Swarms","Autonomous Mobile Robots","Gathering"],"author":[{"first_name":"Raphael","full_name":"Gerlach, Raphael","last_name":"Gerlach","id":"32655"},{"full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","id":"97359","last_name":"von der Gracht"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2023-05-12T10:16:06Z","status":"public","date_updated":"2024-01-03T17:00:48Z","language":[{"iso":"eng"}],"external_id":{"arxiv":["2305.06632"]},"related_material":{"link":[{"url":"https://math.uni-paderborn.de/en/ag/chair-of-applied-mathematics/research/research-projects/swarmdynamics","relation":"supplementary_material"}]},"title":"On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies","department":[{"_id":"101"}],"project":[{"_id":"106","grant_number":"453112019","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"publication_status":"submitted"},{"title":"Packings and Steiner systems in polar spaces","user_id":"70420","abstract":[{"lang":"eng","text":"A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces."}],"volume":3,"publication_status":"published","date_created":"2024-01-08T14:33:54Z","status":"public","department":[{"_id":"100"}],"publication":"Combinatorial Theory","author":[{"full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe","last_name":"Schmidt"},{"last_name":"Weiß","id":"70420","first_name":"Charlene","full_name":"Weiß, Charlene"}],"doi":"10.5070/c63160424","issue":"1","_id":"50298","intvolume":" 3","date_updated":"2024-01-08T14:39:20Z","citation":{"short":"K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).","ieee":"K.-U. Schmidt and C. Weiß, “Packings and Steiner systems in polar spaces,” Combinatorial Theory, vol. 3, no. 1, 2023, doi: 10.5070/c63160424.","chicago":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” Combinatorial Theory 3, no. 1 (2023). https://doi.org/10.5070/c63160424.","apa":"Schmidt, K.-U., & Weiß, C. (2023). Packings and Steiner systems in polar spaces. Combinatorial Theory, 3(1). https://doi.org/10.5070/c63160424","ama":"Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. Combinatorial Theory. 2023;3(1). doi:10.5070/c63160424","mla":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” Combinatorial Theory, vol. 3, no. 1, 2023, doi:10.5070/c63160424.","bibtex":"@article{Schmidt_Weiß_2023, title={Packings and Steiner systems in polar spaces}, volume={3}, DOI={10.5070/c63160424}, number={1}, journal={Combinatorial Theory}, author={Schmidt, Kai-Uwe and Weiß, Charlene}, year={2023} }"},"year":"2023","type":"journal_article","language":[{"iso":"eng"}]},{"title":"Existence of small ordered orthogonal arrays","department":[{"_id":"100"}],"publication_status":"published","date_updated":"2024-01-08T14:38:53Z","doi":"10.1002/jcd.21903","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled."}],"user_id":"70420","publication":"Journal of Combinatorial Designs","author":[{"last_name":"Schmidt","full_name":"Schmidt, Kai‐Uwe","first_name":"Kai‐Uwe"},{"full_name":"Weiß, Charlene","first_name":"Charlene","id":"70420","last_name":"Weiß"}],"publisher":"Wiley","volume":31,"date_created":"2024-01-08T14:25:28Z","status":"public","_id":"50297","intvolume":" 31","issue":"9","page":"422-431","type":"journal_article","citation":{"short":"K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431.","ieee":"K. Schmidt and C. Weiß, “Existence of small ordered orthogonal arrays,” Journal of Combinatorial Designs, vol. 31, no. 9, pp. 422–431, 2023, doi: 10.1002/jcd.21903.","chicago":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” Journal of Combinatorial Designs 31, no. 9 (2023): 422–31. https://doi.org/10.1002/jcd.21903.","ama":"Schmidt K, Weiß C. Existence of small ordered orthogonal arrays. Journal of Combinatorial Designs. 2023;31(9):422-431. doi:10.1002/jcd.21903","apa":"Schmidt, K., & Weiß, C. (2023). Existence of small ordered orthogonal arrays. Journal of Combinatorial Designs, 31(9), 422–431. https://doi.org/10.1002/jcd.21903","mla":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” Journal of Combinatorial Designs, vol. 31, no. 9, Wiley, 2023, pp. 422–31, doi:10.1002/jcd.21903.","bibtex":"@article{Schmidt_Weiß_2023, title={Existence of small ordered orthogonal arrays}, volume={31}, DOI={10.1002/jcd.21903}, number={9}, journal={Journal of Combinatorial Designs}, publisher={Wiley}, author={Schmidt, Kai‐Uwe and Weiß, Charlene}, year={2023}, pages={422–431} }"},"year":"2023"},{"author":[{"last_name":"Weiß","id":"70420","first_name":"Charlene","full_name":"Weiß, Charlene"}],"department":[{"_id":"100"}],"status":"public","date_created":"2024-01-08T14:42:12Z","abstract":[{"text":"Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases.","lang":"eng"}],"title":"Linear programming bounds in classical association schemes","user_id":"70420","year":"2023","type":"dissertation","citation":{"mla":"Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes. 2023, doi:10.17619/UNIPB/1-1672.","bibtex":"@book{Weiß_2023, title={Linear programming bounds in classical association schemes}, DOI={10.17619/UNIPB/1-1672}, author={Weiß, Charlene}, year={2023} }","chicago":"Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes, 2023. https://doi.org/10.17619/UNIPB/1-1672.","ama":"Weiß C. Linear Programming Bounds in Classical Association Schemes.; 2023. doi:10.17619/UNIPB/1-1672","apa":"Weiß, C. (2023). Linear programming bounds in classical association schemes. https://doi.org/10.17619/UNIPB/1-1672","ieee":"C. Weiß, Linear programming bounds in classical association schemes. 2023.","short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023."},"language":[{"iso":"eng"}],"date_updated":"2024-01-08T14:46:14Z","_id":"50300","doi":"10.17619/UNIPB/1-1672"},{"language":[{"iso":"eng"}],"citation":{"ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” arXiv:2311.08288. .","short":"C. Weiß, ArXiv:2311.08288 (n.d.).","bibtex":"@article{Weiß, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, journal={arXiv:2311.08288}, author={Weiß, Charlene} }","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” ArXiv:2311.08288.","apa":"Weiß, C. (n.d.). Nontrivial $t$-designs in polar spaces exist for all $t$. In arXiv:2311.08288.","ama":"Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. arXiv:231108288.","chicago":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” ArXiv:2311.08288, n.d."},"type":"preprint","year":"2023","_id":"50299","date_updated":"2024-01-08T14:41:18Z","status":"public","date_created":"2024-01-08T14:39:54Z","publication_status":"submitted","author":[{"id":"70420","last_name":"Weiß","full_name":"Weiß, Charlene","first_name":"Charlene"}],"publication":"arXiv:2311.08288","department":[{"_id":"100"}],"user_id":"70420","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","abstract":[{"lang":"eng","text":"A finite classical polar space of rank $n$ consists of the totally isotropic\r\nsubspaces of a finite vector space over $\\mathbb{F}_p$ equipped with a\r\nnondegenerate form such that $n$ is the maximal dimension of such a subspace. A\r\n$t$-$(n,k,\\lambda)$ design in a finite classical polar space of rank $n$ is a\r\ncollection $Y$ of totally isotropic $k$-spaces such that each totally isotropic\r\n$t$-space is contained in exactly $\\lambda$ members of $Y$. Nontrivial examples\r\nare currently only known for $t\\leq 2$. We show that $t$-$(n,k,\\lambda)$\r\ndesigns in polar spaces exist for all $t$ and $p$ provided that\r\n$k>\\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a\r\nprobabilistic method by Kuperberg, Lovett, and Peled, and it is thus\r\nnonconstructive."}],"external_id":{"arxiv":["2311.08288"]}},{"issue":"1","_id":"48596","intvolume":" 5","date_updated":"2024-01-11T13:32:19Z","year":"2023","type":"journal_article","citation":{"ama":"Häsel-Weide U, Schmidt R, Büker P. „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung. Zeitschrift für Schul- Und Professionsentwicklung (PFLB). 2023;5(1):215-229.","apa":"Häsel-Weide, U., Schmidt, R., & Büker, P. (2023). „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung. Zeitschrift Für Schul- Und Professionsentwicklung. (PFLB), 5(1), 215–229.","chicago":"Häsel-Weide, Uta, R. Schmidt, and Petra Büker. “„FInDig“: Fach – Inklusion – Digitalisierung Vernetzen. Ein Planungs- Und Reflexionsmodell Für Die Lehrkräftebildung.” Zeitschrift Für Schul- Und Professionsentwicklung. (PFLB) 5, no. 1 (2023): 215–29.","bibtex":"@article{Häsel-Weide_Schmidt_Büker_2023, title={„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung}, volume={5}, number={1}, journal={Zeitschrift für Schul- Und Professionsentwicklung. (PFLB)}, author={Häsel-Weide, Uta and Schmidt, R. and Büker, Petra}, year={2023}, pages={215–229} }","mla":"Häsel-Weide, Uta, et al. “„FInDig“: Fach – Inklusion – Digitalisierung Vernetzen. Ein Planungs- Und Reflexionsmodell Für Die Lehrkräftebildung.” Zeitschrift Für Schul- Und Professionsentwicklung. (PFLB), vol. 5, no. 1, 2023, pp. 215–29.","short":"U. Häsel-Weide, R. Schmidt, P. Büker, Zeitschrift Für Schul- Und Professionsentwicklung. (PFLB) 5 (2023) 215–229.","ieee":"U. Häsel-Weide, R. Schmidt, and P. Büker, “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung,” Zeitschrift für Schul- Und Professionsentwicklung. (PFLB), vol. 5, no. 1, pp. 215–229, 2023."},"page":"215-229","language":[{"iso":"eng"}],"title":"„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung","related_material":{"link":[{"relation":"original","url":"https://doi.org/10.11576/pflb-6763 "}]},"user_id":"14931","volume":5,"status":"public","date_created":"2023-11-02T11:22:34Z","author":[{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"},{"first_name":"R.","full_name":"Schmidt, R.","last_name":"Schmidt"},{"id":"21978","last_name":"Büker","full_name":"Büker, Petra","first_name":"Petra"}],"publication":"Zeitschrift für Schul- Und Professionsentwicklung. (PFLB)","department":[{"_id":"543"},{"_id":"458"}]},{"author":[{"id":"89837","last_name":"Graf","full_name":"Graf, Lara Marie","first_name":"Lara Marie"},{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"},{"last_name":"Höveler","full_name":"Höveler, K.","first_name":"K."},{"last_name":"Nührenbörger","first_name":"M.","full_name":"Nührenbörger, M."}],"department":[{"_id":"543"}],"publication":"Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)","editor":[{"full_name":"Drijvers, P.","first_name":"P.","last_name":"Drijvers"},{"last_name":"Csapodi","full_name":"Csapodi, C.","first_name":"C."},{"first_name":"H.","full_name":"Palmér, H.","last_name":"Palmér"},{"full_name":"Gosztonyi, K.","first_name":"K.","last_name":"Gosztonyi"},{"last_name":"Kónya","full_name":"Kónya, E.","first_name":"E."}],"status":"public","date_created":"2024-02-05T08:47:35Z","title":"Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics","user_id":"14931","year":"2023","type":"conference","citation":{"short":"L.M. Graf, U. Häsel-Weide, K. Höveler, M. Nührenbörger, in: P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, Alfréd Rényi Institute of Mathematics and ERME (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), 2023, pp. 3203–3210.","ieee":"L. M. Graf, U. Häsel-Weide, K. Höveler, and M. Nührenbörger, “Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics,” in Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), 2023, pp. 3203–3210.","apa":"Graf, L. M., Häsel-Weide, U., Höveler, K., & Nührenbörger, M. (2023). Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, & Alfréd Rényi Institute of Mathematics and ERME (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 3203–3210).","ama":"Graf LM, Häsel-Weide U, Höveler K, Nührenbörger M. Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics. In: Drijvers P, Csapodi C, Palmér H, Gosztonyi K, Kónya E, Alfréd Rényi Institute of Mathematics and ERME, eds. Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). ; 2023:3203-3210.","chicago":"Graf, Lara Marie, Uta Häsel-Weide, K. Höveler, and M. Nührenbörger. “Insights into Out-of-Field Teachers’ Self-Reports: Fostering the Understanding of Addition and Subtraction as a Basis for Children to Overcome Difficulties in Mathematics.” In Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), edited by P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, and Alfréd Rényi Institute of Mathematics and ERME, 3203–10, 2023.","mla":"Graf, Lara Marie, et al. “Insights into Out-of-Field Teachers’ Self-Reports: Fostering the Understanding of Addition and Subtraction as a Basis for Children to Overcome Difficulties in Mathematics.” Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), edited by P. Drijvers et al., 2023, pp. 3203–10.","bibtex":"@inproceedings{Graf_Häsel-Weide_Höveler_Nührenbörger_2023, title={Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics}, booktitle={Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)}, author={Graf, Lara Marie and Häsel-Weide, Uta and Höveler, K. and Nührenbörger, M.}, editor={Drijvers, P. and Csapodi, C. and Palmér, H. and Gosztonyi, K. and Kónya, E. and Alfréd Rényi Institute of Mathematics and ERME}, year={2023}, pages={3203–3210} }"},"page":"3203-3210","language":[{"iso":"eng"}],"date_updated":"2024-02-05T08:55:43Z","_id":"51131","corporate_editor":["Alfréd Rényi Institute of Mathematics and ERME"]},{"type":"journal_article","year":"2023","citation":{"chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric Spaces.” Communications in Mathematical Physics 403 (2023). https://doi.org/10.1007/s00220-023-04819-1.","apa":"Weich, T., & Wolf, L. L. (2023). Absence of principal eigenvalues for higher rank locally symmetric spaces. Communications in Mathematical Physics, 403. https://doi.org/10.1007/s00220-023-04819-1","ama":"Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric spaces. Communications in Mathematical Physics. 2023;403. doi:https://doi.org/10.1007/s00220-023-04819-1","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric Spaces.” Communications in Mathematical Physics, vol. 403, 2023, doi:https://doi.org/10.1007/s00220-023-04819-1.","bibtex":"@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher rank locally symmetric spaces}, volume={403}, DOI={https://doi.org/10.1007/s00220-023-04819-1}, journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2023} }","short":"T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).","ieee":"T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric spaces,” Communications in Mathematical Physics, vol. 403, 2023, doi: https://doi.org/10.1007/s00220-023-04819-1."},"language":[{"iso":"eng"}],"doi":"https://doi.org/10.1007/s00220-023-04819-1","intvolume":" 403","_id":"31189","date_updated":"2024-02-06T20:52:40Z","volume":403,"publication_identifier":{"unknown":["1275-1295"]},"date_created":"2022-05-11T10:38:11Z","status":"public","publication":"Communications in Mathematical Physics","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"author":[{"id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","first_name":"Tobias"},{"last_name":"Wolf","id":"45027","first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart"}],"title":"Absence of principal eigenvalues for higher rank locally symmetric spaces","user_id":"49178","external_id":{"arxiv":["2205.03167"]},"abstract":[{"text":"Given a geometrically finite hyperbolic surface of infinite volume it is a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding principal eigenvalues. A large class of examples fulfilling these\r\nassumptions are the non-compact quotients by Anosov subgroups.","lang":"eng"}]},{"intvolume":" 398","_id":"31059","date_updated":"2024-02-11T19:56:15Z","doi":"ttps://doi.org/10.1007/s00220-022-04538-z","page":"655-678","year":"2023","type":"journal_article","citation":{"short":"P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678.","ieee":"P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems,” Communications in Mathematical Physics, vol. 398, pp. 655–678, 2023, doi: ttps://doi.org/10.1007/s00220-022-04538-z.","apa":"Schütte, P., Weich, T., & Barkhofen, S. (2023). Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. Communications in Mathematical Physics, 398, 655–678. https://doi.org/ttps://doi.org/10.1007/s00220-022-04538-z","ama":"Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. Communications in Mathematical Physics. 2023;398:655-678. doi:ttps://doi.org/10.1007/s00220-022-04538-z","chicago":"Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” Communications in Mathematical Physics 398 (2023): 655–78. https://doi.org/ttps://doi.org/10.1007/s00220-022-04538-z.","bibtex":"@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={ttps://doi.org/10.1007/s00220-022-04538-z}, journal={Communications in Mathematical Physics}, author={Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }","mla":"Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” Communications in Mathematical Physics, vol. 398, 2023, pp. 655–78, doi:ttps://doi.org/10.1007/s00220-022-04538-z."},"language":[{"iso":"eng"}],"abstract":[{"text":"In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.","lang":"eng"}],"external_id":{"arxiv":["2112.05791"]},"title":"Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems","user_id":"49178","publication":"Communications in Mathematical Physics","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"author":[{"id":"50168","last_name":"Schütte","full_name":"Schütte, Philipp","first_name":"Philipp"},{"id":"49178","last_name":"Weich","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"full_name":"Barkhofen, Sonja","first_name":"Sonja","id":"48188","last_name":"Barkhofen"}],"volume":398,"date_created":"2022-05-04T12:27:46Z","status":"public"},{"_id":"51206","date_updated":"2024-02-11T19:56:01Z","language":[{"iso":"eng"}],"citation":{"short":"P. Schütte, T. Weich, ArXiv:2308.13463 (2023).","ieee":"P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions,” arXiv:2308.13463. 2023.","ama":"Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions. arXiv:230813463. Published online 2023.","apa":"Schütte, P., & Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions. In arXiv:2308.13463.","chicago":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions.” ArXiv:2308.13463, 2023.","mla":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions.” ArXiv:2308.13463, 2023.","bibtex":"@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463}, author={Schütte, Philipp and Weich, Tobias}, year={2023} }"},"year":"2023","type":"preprint","user_id":"49178","title":"Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions","external_id":{"arxiv":["2308.13463"]},"abstract":[{"lang":"eng","text":"We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the connection between invariant Ruelle distributions and residues\r\nof meromorphically continued weighted zeta functions established by the authors\r\ntogether with Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer operator has to include a contracting direction which\r\nwe account for with techniques developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed for our algorithm in the case of surfaces with\r\nadditional symmetries by proving and applying a symmetry reduction of weighted\r\nzeta functions."}],"date_created":"2024-02-06T20:58:35Z","status":"public","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"publication":"arXiv:2308.13463","author":[{"id":"50168","last_name":"Schütte","full_name":"Schütte, Philipp","first_name":"Philipp"},{"id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","first_name":"Tobias"}]},{"year":"2023","citation":{"bibtex":"@article{Weich_Wolf_2023, title={Temperedness of locally symmetric spaces: The product case}, journal={arXiv:2304.09573}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2023} }","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” ArXiv:2304.09573, 2023.","ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. arXiv:230409573. Published online 2023.","apa":"Weich, T., & Wolf, L. L. (2023). Temperedness of locally symmetric spaces: The product case. In arXiv:2304.09573.","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” ArXiv:2304.09573, 2023.","ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” arXiv:2304.09573. 2023.","short":"T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023)."},"type":"preprint","language":[{"iso":"eng"}],"date_updated":"2024-02-11T19:55:58Z","_id":"51207","status":"public","date_created":"2024-02-06T21:00:55Z","author":[{"first_name":"Tobias","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178"},{"id":"45027","last_name":"Wolf","full_name":"Wolf, Lasse Lennart","first_name":"Lasse Lennart"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"publication":"arXiv:2304.09573","title":"Temperedness of locally symmetric spaces: The product case","user_id":"49178","external_id":{"arxiv":["2304.09573"]},"abstract":[{"lang":"eng","text":"Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."}]},{"user_id":"15540","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"publication":"Discrete Applied Mathematics","author":[{"id":"15548","last_name":"Steffen","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","first_name":"Eckhard"},{"id":"88145","last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus"}],"publisher":"Elsevier BV","volume":337,"date_created":"2024-02-14T17:33:29Z","status":"public","_id":"51351","intvolume":" 337","page":"185-189","citation":{"chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” Discrete Applied Mathematics 337 (2023): 185–89. https://doi.org/10.1016/j.dam.2023.05.008.","ama":"Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. Discrete Applied Mathematics. 2023;337:185-189. doi:10.1016/j.dam.2023.05.008","apa":"Steffen, E., & Wolf, I. H. (2023). Bounds for the chromatic index of signed multigraphs. Discrete Applied Mathematics, 337, 185–189. https://doi.org/10.1016/j.dam.2023.05.008","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” Discrete Applied Mathematics, vol. 337, Elsevier BV, 2023, pp. 185–89, doi:10.1016/j.dam.2023.05.008.","bibtex":"@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed multigraphs}, volume={337}, DOI={10.1016/j.dam.2023.05.008}, journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }","short":"E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.","ieee":"E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,” Discrete Applied Mathematics, vol. 337, pp. 185–189, 2023, doi: 10.1016/j.dam.2023.05.008."},"type":"journal_article","year":"2023","title":"Bounds for the chromatic index of signed multigraphs","department":[{"_id":"542"}],"publication_status":"published","publication_identifier":{"issn":["0166-218X"]},"date_updated":"2024-02-14T17:33:59Z","doi":"10.1016/j.dam.2023.05.008","language":[{"iso":"eng"}]},{"page":"93--110","citation":{"ieee":"C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks,” in The Digital Twin of Humans, Cham: Springer International Publishing, 2023, pp. 93--110.","short":"C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International Publishing, Cham, 2023, pp. 93--110.","mla":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” The Digital Twin of Humans, Springer International Publishing, 2023, pp. 93--110, doi:10.1007/978-3-031-26104-6_5.","bibtex":"@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks}, DOI={10.1007/978-3-031-26104-6_5}, booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing}, author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }","ama":"Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In: The Digital Twin of Humans. Springer International Publishing; 2023:93--110. doi:10.1007/978-3-031-26104-6_5","apa":"Cappello, C., & Steffen, E. (2023). Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In The Digital Twin of Humans (pp. 93--110). Springer International Publishing. https://doi.org/10.1007/978-3-031-26104-6_5","chicago":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” In The Digital Twin of Humans, 93--110. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-26104-6_5."},"year":"2023","type":"book_chapter","language":[{"iso":"eng"}],"doi":"10.1007/978-3-031-26104-6_5","_id":"45190","date_updated":"2024-02-16T07:42:38Z","publication_identifier":{"isbn":["9783031261039","9783031261046"]},"publication_status":"published","date_created":"2023-05-22T10:22:21Z","status":"public","department":[{"_id":"542"}],"publication":"The Digital Twin of Humans","publisher":"Springer International Publishing","author":[{"last_name":"Cappello","id":"72874","first_name":"Chiara","full_name":"Cappello, Chiara"},{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","last_name":"Steffen","id":"15548"}],"title":"Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks","user_id":"15540","place":"Cham"},{"keyword":["Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"publication":"Discrete Mathematics","department":[{"_id":"542"}],"author":[{"first_name":"Eckhard","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548"},{"id":"88145","last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus"}],"publisher":"Elsevier BV","publication_identifier":{"issn":["0012-365X"]},"publication_status":"published","date_created":"2024-02-16T08:44:50Z","status":"public","title":"Rotation r-graphs","user_id":"15540","type":"journal_article","year":"2023","citation":{"chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete Mathematics, 2023. https://doi.org/10.1016/j.disc.2023.113457.","apa":"Steffen, E., & Wolf, I. H. (2023). Rotation r-graphs. Discrete Mathematics, Article 113457. https://doi.org/10.1016/j.disc.2023.113457","ama":"Steffen E, Wolf IH. Rotation r-graphs. Discrete Mathematics. Published online 2023. doi:10.1016/j.disc.2023.113457","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete Mathematics, 113457, Elsevier BV, 2023, doi:10.1016/j.disc.2023.113457.","bibtex":"@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={10.1016/j.disc.2023.113457}, number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","short":"E. Steffen, I.H. Wolf, Discrete Mathematics (2023).","ieee":"E. Steffen and I. H. Wolf, “Rotation r-graphs,” Discrete Mathematics, Art. no. 113457, 2023, doi: 10.1016/j.disc.2023.113457."},"language":[{"iso":"eng"}],"date_updated":"2024-02-16T08:45:10Z","_id":"51357","doi":"10.1016/j.disc.2023.113457","article_number":"113457"},{"publication":"arXiv:2310.17736","department":[{"_id":"799"}],"author":[{"first_name":"Benjamin","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","id":"99427"},{"first_name":"Marius","full_name":"Lemm, Marius","last_name":"Lemm"},{"first_name":"Oliver","full_name":"Siebert, Oliver","last_name":"Siebert"}],"date_created":"2024-02-18T12:33:21Z","project":[{"grant_number":"PROFILNRW-2020-067","name":"PhoQC: PhoQC: Photonisches Quantencomputing","_id":"266"}],"status":"public","abstract":[{"lang":"eng","text":"We consider the quantum dynamics of a many-fermion system in $\\mathbb R^d$\r\nwith an ultraviolet regularized pair interaction as previously studied in [M.\r\nGebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\\'e 21.11\r\n(2020)]. We provide a Lieb-Robinson bound under substantially relaxed\r\nassumptions on the potentials. We also improve the associated one-body\r\nLieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an\r\nalmost linear light cone) under the same relaxed assumptions. Applications\r\ninclude the existence of the infinite-volume dynamics and clustering of ground\r\nstates in the presence of a spectral gap. We also develop a fermionic continuum\r\nnotion of conditional expectation and use it to approximate time-evolved\r\nfermionic observables by local ones, which opens the door to other applications\r\nof the Lieb-Robinson bounds."}],"external_id":{"arxiv":["2310.17736"]},"title":"On Lieb-Robinson bounds for a class of continuum fermions","user_id":"99427","citation":{"short":"B. Hinrichs, M. Lemm, O. Siebert, ArXiv:2310.17736 (2023).","ieee":"B. Hinrichs, M. Lemm, and O. Siebert, “On Lieb-Robinson bounds for a class of continuum fermions,” arXiv:2310.17736. 2023.","chicago":"Hinrichs, Benjamin, Marius Lemm, and Oliver Siebert. “On Lieb-Robinson Bounds for a Class of Continuum Fermions.” ArXiv:2310.17736, 2023.","ama":"Hinrichs B, Lemm M, Siebert O. On Lieb-Robinson bounds for a class of continuum fermions. arXiv:231017736. Published online 2023.","apa":"Hinrichs, B., Lemm, M., & Siebert, O. (2023). On Lieb-Robinson bounds for a class of continuum fermions. In arXiv:2310.17736.","mla":"Hinrichs, Benjamin, et al. “On Lieb-Robinson Bounds for a Class of Continuum Fermions.” ArXiv:2310.17736, 2023.","bibtex":"@article{Hinrichs_Lemm_Siebert_2023, title={On Lieb-Robinson bounds for a class of continuum fermions}, journal={arXiv:2310.17736}, author={Hinrichs, Benjamin and Lemm, Marius and Siebert, Oliver}, year={2023} }"},"type":"preprint","year":"2023","language":[{"iso":"eng"}],"_id":"51375","date_updated":"2024-02-18T12:34:43Z"},{"author":[{"id":"99427","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","first_name":"Benjamin"},{"first_name":"Jonas","full_name":"Lampart, Jonas","last_name":"Lampart"}],"publication":"arXiv:2311.05361","department":[{"_id":"799"}],"status":"public","date_created":"2024-02-18T12:33:48Z","project":[{"_id":"266","grant_number":"PROFILNRW-2020-067","name":"PhoQC: PhoQC: Photonisches Quantencomputing"}],"abstract":[{"text":"In the Bogoliubov-Fr\\\"ohlich model, we prove that an impurity immersed in a\r\nBose-Einstein condensate forms a stable quasi-particle when the total momentum\r\nis less than its mass times the speed of sound. The system thus exhibits\r\nsuperfluid behavior, as this quasi-particle does not experience friction. We do\r\nnot assume any infrared or ultraviolet regularization of the model, which\r\ncontains massless excitations and point-like interactions.","lang":"eng"}],"external_id":{"arxiv":["2311.05361"]},"title":"A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate","user_id":"99427","type":"preprint","citation":{"short":"B. Hinrichs, J. Lampart, ArXiv:2311.05361 (2023).","ieee":"B. Hinrichs and J. Lampart, “A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate,” arXiv:2311.05361. 2023.","chicago":"Hinrichs, Benjamin, and Jonas Lampart. “A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate.” ArXiv:2311.05361, 2023.","apa":"Hinrichs, B., & Lampart, J. (2023). A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate. In arXiv:2311.05361.","ama":"Hinrichs B, Lampart J. A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate. arXiv:231105361. Published online 2023.","mla":"Hinrichs, Benjamin, and Jonas Lampart. “A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate.” ArXiv:2311.05361, 2023.","bibtex":"@article{Hinrichs_Lampart_2023, title={A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate}, journal={arXiv:2311.05361}, author={Hinrichs, Benjamin and Lampart, Jonas}, year={2023} }"},"year":"2023","language":[{"iso":"eng"}],"_id":"51376","date_updated":"2024-02-18T12:34:22Z"},{"page":"2241–2265","citation":{"short":"J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.","ieee":"J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” Analysis & PDE, vol. 16, no. 10, pp. 2241–2265, 2023.","chicago":"Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” Analysis & PDE 16, no. 10 (2023): 2241–2265.","apa":"Hilgert, J., Weich, T., & Wolf, L. L. (2023). Higher rank quantum-classical correspondence. Analysis & PDE, 16(10), 2241–2265.","ama":"Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. Analysis & PDE. 2023;16(10):2241–2265.","mla":"Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” Analysis & PDE, vol. 16, no. 10, MSP, 2023, pp. 2241–2265.","bibtex":"@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical correspondence}, volume={16}, number={10}, journal={Analysis & PDE}, publisher={MSP}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }"},"type":"journal_article","year":"2023","language":[{"iso":"eng"}],"issue":"10","date_updated":"2024-02-19T06:29:52Z","_id":"31190","intvolume":" 16","volume":16,"date_created":"2022-05-11T10:41:35Z","status":"public","publication":"Analysis & PDE","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"publisher":"MSP","author":[{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","first_name":"Tobias","id":"49178","last_name":"Weich"},{"last_name":"Wolf","id":"45027","first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart"}],"title":"Higher rank quantum-classical correspondence","user_id":"49063","abstract":[{"text":"For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$ of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions of the algebra of invariant differential\r\noperators on $G/K$.","lang":"eng"}],"external_id":{"arxiv":["2103.05667"]}},{"citation":{"apa":"Bux, K.-U., Hilgert, J., & Weich, T. (2023). Spectral correspondences for finite graphs without dead ends. In arXiv:2307.10876.","ama":"Bux K-U, Hilgert J, Weich T. Spectral correspondences for finite graphs without dead ends. arXiv:230710876. Published online 2023.","chicago":"Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Spectral Correspondences for Finite Graphs without Dead Ends.” ArXiv:2307.10876, 2023.","mla":"Bux, Kai-Uwe, et al. “Spectral Correspondences for Finite Graphs without Dead Ends.” ArXiv:2307.10876, 2023.","bibtex":"@article{Bux_Hilgert_Weich_2023, title={Spectral correspondences for finite graphs without dead ends}, journal={arXiv:2307.10876}, author={Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}, year={2023} }","short":"K.-U. Bux, J. Hilgert, T. Weich, ArXiv:2307.10876 (2023).","ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Spectral correspondences for finite graphs without dead ends,” arXiv:2307.10876. 2023."},"type":"preprint","year":"2023","language":[{"iso":"eng"}],"date_updated":"2024-02-19T06:29:24Z","_id":"51205","publication":"arXiv:2307.10876","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"author":[{"last_name":"Bux","first_name":"Kai-Uwe","full_name":"Bux, Kai-Uwe"},{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","first_name":"Tobias","id":"49178","last_name":"Weich"}],"date_created":"2024-02-06T20:54:28Z","status":"public","external_id":{"arxiv":["2307.10876"]},"abstract":[{"text":"We compare the spectral properties of two kinds of linear operators\r\ncharacterizing the (classical) geodesic flow and its quantization on connected\r\nlocally finite graphs without dead ends. The first kind are transfer operators\r\nacting on vector spaces associated with the set of non backtracking paths in\r\nthe graphs. The second kind of operators are averaging operators acting on\r\nvector spaces associated with the space of vertices of the graph. The choice of\r\nvector spaces reflects regularity properties. Our main results are\r\ncorrespondences between classical and quantum spectral objects as well as some\r\nautomatic regularity properties for eigenfunctions of transfer operators.","lang":"eng"}],"title":"Spectral correspondences for finite graphs without dead ends","user_id":"49063"},{"user_id":"49063","abstract":[{"lang":"eng","text":"In this paper we complete the program of relating the Laplace spectrum for\r\nrank one compact locally symmetric spaces with the first band Ruelle-Pollicott\r\nresonances of the geodesic flow on its sphere bundle. This program was started\r\nby Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and\r\nGuillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for\r\ngeneral rank one spaces. Except for the case of hyperbolic surfaces a countable\r\nset of exceptional spectral parameters always left untreated since the\r\ncorresponding Poisson transforms are neither injective nor surjective. We use\r\nvector valued Poisson transforms to treat also the exceptional spectral\r\nparameters. For surfaces the exceptional spectral parameters lead to discrete\r\nseries representations of $\\mathrm{SL}(2,\\mathbb R)$. In higher dimensions the\r\nsituation is more complicated, but can be described completely."}],"volume":10,"status":"public","date_created":"2022-05-11T12:27:00Z","author":[{"first_name":"Christian","full_name":"Arends, Christian","last_name":"Arends","id":"43994"},{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"}],"keyword":["Ruelle resonances","Poisson transforms","locally symmetric spaces","principal series representations"],"publication":"Journal de l’École polytechnique — Mathématiques","_id":"31210","intvolume":" 10","citation":{"apa":"Arends, C., & Hilgert, J. (2023). Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. Journal de l’École Polytechnique — Mathématiques, 10, 335–403. https://doi.org/10.5802/jep.220","ama":"Arends C, Hilgert J. Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. Journal de l’École polytechnique — Mathématiques. 2023;10:335-403. doi:10.5802/jep.220","chicago":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” Journal de l’École Polytechnique — Mathématiques 10 (2023): 335–403. https://doi.org/10.5802/jep.220.","bibtex":"@article{Arends_Hilgert_2023, title={Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}, volume={10}, DOI={10.5802/jep.220}, journal={Journal de l’École polytechnique — Mathématiques}, author={Arends, Christian and Hilgert, Joachim}, year={2023}, pages={335–403} }","mla":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” Journal de l’École Polytechnique — Mathématiques, vol. 10, 2023, pp. 335–403, doi:10.5802/jep.220.","short":"C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","ieee":"C. Arends and J. Hilgert, “Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters,” Journal de l’École polytechnique — Mathématiques, vol. 10, pp. 335–403, 2023, doi: 10.5802/jep.220."},"year":"2023","type":"journal_article","page":"335-403","title":"Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters","external_id":{"arxiv":["2112.11073"]},"publication_status":"published","publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"doi":"10.5802/jep.220","date_updated":"2024-02-19T06:30:26Z","language":[{"iso":"eng"}]},{"user_id":"49063","title":"Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters","status":"public","date_created":"2024-02-19T06:34:11Z","publication_status":"published","volume":10,"author":[{"id":"220","last_name":"Hilgert","full_name":"Hilgert, Joachim","first_name":"Joachim"},{"last_name":"Arends","full_name":"Arends, C.","first_name":"C."}],"department":[{"_id":"91"}],"publication":"J. de l'École polytechnique — Mathématiques","date_updated":"2024-02-19T06:34:16Z","_id":"51383","intvolume":" 10","language":[{"iso":"eng"}],"type":"journal_article","citation":{"ieee":"J. Hilgert and C. Arends, “Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters,” J. de l’École polytechnique — Mathématiques, vol. 10, pp. 335–403, 2023.","short":"J. Hilgert, C. Arends, J. de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","bibtex":"@article{Hilgert_Arends_2023, title={Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}, volume={10}, journal={J. de l’École polytechnique — Mathématiques}, author={Hilgert, Joachim and Arends, C.}, year={2023}, pages={335–403} }","mla":"Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally Symmetric Spaces - The Case of Exceptional Parameters.” J. de l’École Polytechnique — Mathématiques, vol. 10, 2023, pp. 335–403.","chicago":"Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally Symmetric Spaces - The Case of Exceptional Parameters.” J. de l’École Polytechnique — Mathématiques 10 (2023): 335–403.","apa":"Hilgert, J., & Arends, C. (2023). Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters. J. de l’École Polytechnique — Mathématiques, 10, 335–403.","ama":"Hilgert J, Arends C. Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters. J de l’École polytechnique — Mathématiques. 2023;10:335-403."},"year":"2023","page":"335-403"},{"date_created":"2024-02-19T06:35:08Z","status":"public","volume":343,"publication_status":"published","department":[{"_id":"91"}],"publication":"J. Diff. Equations","author":[{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"full_name":"Glöckner, H.","first_name":"H.","last_name":"Glöckner"}],"user_id":"49063","title":"Aspects of control theory on infinite-dimensional Lie groups and G-manifolds","language":[{"iso":"eng"}],"page":"186-232","type":"journal_article","year":"2023","citation":{"ieee":"J. Hilgert and H. Glöckner, “Aspects of control theory on infinite-dimensional Lie groups and G-manifolds,” J. Diff. Equations, vol. 343, pp. 186–232, 2023.","short":"J. Hilgert, H. Glöckner, J. Diff. Equations 343 (2023) 186–232.","bibtex":"@article{Hilgert_Glöckner_2023, title={Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}, volume={343}, journal={J. Diff. Equations}, author={Hilgert, Joachim and Glöckner, H.}, year={2023}, pages={186–232} }","mla":"Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” J. Diff. Equations, vol. 343, 2023, pp. 186–232.","ama":"Hilgert J, Glöckner H. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. J Diff Equations. 2023;343:186-232.","apa":"Hilgert, J., & Glöckner, H. (2023). Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. J. Diff. Equations, 343, 186–232.","chicago":"Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” J. Diff. Equations 343 (2023): 186–232."},"date_updated":"2024-02-19T06:35:13Z","_id":"51384","intvolume":" 343"},{"oa":"1","date_updated":"2024-02-19T10:31:18Z","_id":"51499","citation":{"mla":"Hilgert, Joachim, et al. A Pairing Formula for Resonant States on Finite Regular Graphs. 2023.","bibtex":"@article{Hilgert_Arends_Frahm_2023, title={A pairing formula for resonant states on finite regular graphs}, author={Hilgert, Joachim and Arends, C. and Frahm, J.}, year={2023} }","ama":"Hilgert J, Arends C, Frahm J. A pairing formula for resonant states on finite regular graphs. Published online 2023.","apa":"Hilgert, J., Arends, C., & Frahm, J. (2023). A pairing formula for resonant states on finite regular graphs.","chicago":"Hilgert, Joachim, C. Arends, and J. Frahm. “A Pairing Formula for Resonant States on Finite Regular Graphs,” 2023.","ieee":"J. Hilgert, C. Arends, and J. Frahm, “A pairing formula for resonant states on finite regular graphs.” 2023.","short":"J. Hilgert, C. Arends, J. Frahm, (2023)."},"year":"2023","type":"preprint","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2312.10509.pdf"}],"title":"A pairing formula for resonant states on finite regular graphs","user_id":"49063","publication_status":"published","date_created":"2024-02-19T10:30:18Z","status":"public","department":[{"_id":"91"}],"author":[{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"last_name":"Arends","full_name":"Arends, C.","first_name":"C."},{"last_name":"Frahm","first_name":"J.","full_name":"Frahm, J."}]},{"main_file_link":[{"url":"https://arxiv.org/pdf/2312.09101.pdf","open_access":"1"}],"citation":{"chicago":"Hilgert, Joachim, C. Arends, and J. Frahm. “Edge Laplacians and Vector Valued Poisson Transforms for Graphs,” 2023.","ama":"Hilgert J, Arends C, Frahm J. Edge Laplacians and vector valued Poisson transforms for graphs. Published online 2023.","apa":"Hilgert, J., Arends, C., & Frahm, J. (2023). Edge Laplacians and vector valued Poisson transforms for graphs.","bibtex":"@article{Hilgert_Arends_Frahm_2023, title={Edge Laplacians and vector valued Poisson transforms for graphs}, author={Hilgert, Joachim and Arends, C. and Frahm, J.}, year={2023} }","mla":"Hilgert, Joachim, et al. Edge Laplacians and Vector Valued Poisson Transforms for Graphs. 2023.","short":"J. Hilgert, C. Arends, J. Frahm, (2023).","ieee":"J. Hilgert, C. Arends, and J. Frahm, “Edge Laplacians and vector valued Poisson transforms for graphs.” 2023."},"type":"preprint","year":"2023","language":[{"iso":"eng"}],"_id":"51500","date_updated":"2024-02-19T10:31:18Z","oa":"1","department":[{"_id":"91"}],"author":[{"full_name":"Hilgert, Joachim","first_name":"Joachim","id":"220","last_name":"Hilgert"},{"last_name":"Arends","full_name":"Arends, C.","first_name":"C."},{"last_name":"Frahm","full_name":"Frahm, J.","first_name":"J."}],"publication_status":"published","date_created":"2024-02-19T10:31:14Z","status":"public","title":"Edge Laplacians and vector valued Poisson transforms for graphs","user_id":"49063"},{"publication_status":"published","date_created":"2024-02-19T10:33:16Z","status":"public","department":[{"_id":"91"}],"author":[{"full_name":"Hilgert, Joachim","first_name":"Joachim","id":"220","last_name":"Hilgert"},{"first_name":"T.","full_name":"Baier, T.","last_name":"Baier"},{"last_name":"Kaya","full_name":"Kaya, O.","first_name":"O."},{"full_name":"Mourao, J.","first_name":"J.","last_name":"Mourao"},{"first_name":"J.","full_name":"Nunes, J.","last_name":"Nunes"}],"title":"Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem","user_id":"49063","citation":{"apa":"Hilgert, J., Baier, T., Kaya, O., Mourao, J., & Nunes, J. (2023). Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem.","ama":"Hilgert J, Baier T, Kaya O, Mourao J, Nunes J. Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem. Published online 2023.","chicago":"Hilgert, Joachim, T. Baier, O. Kaya, J. Mourao, and J. Nunes. “Quantization in Fibering Polarizations, Mabuchi Rays and Geometric Peter--Weyl Theorem,” 2023.","bibtex":"@article{Hilgert_Baier_Kaya_Mourao_Nunes_2023, title={Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem}, author={Hilgert, Joachim and Baier, T. and Kaya, O. and Mourao, J. and Nunes, J.}, year={2023} }","mla":"Hilgert, Joachim, et al. Quantization in Fibering Polarizations, Mabuchi Rays and Geometric Peter--Weyl Theorem. 2023.","short":"J. Hilgert, T. Baier, O. Kaya, J. Mourao, J. Nunes, (2023).","ieee":"J. Hilgert, T. Baier, O. Kaya, J. Mourao, and J. Nunes, “Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem.” 2023."},"year":"2023","type":"preprint","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2301.10853.pdf","open_access":"1"}],"oa":"1","_id":"51502","date_updated":"2024-02-19T10:33:20Z"},{"date_created":"2024-02-20T08:20:13Z","status":"public","publication_status":"published","department":[{"_id":"91"}],"author":[{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"first_name":"Y.","full_name":"Guedes Bonthonneau, Y.","last_name":"Guedes Bonthonneau"},{"last_name":"Guillarmou","first_name":"C.","full_name":"Guillarmou, C."},{"last_name":"Weich","id":"49178","first_name":"Tobias","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919"}],"user_id":"49063","title":"Ruelle-Taylor resonances of Anosov actions","language":[{"iso":"eng"}],"year":"2023","type":"preprint","citation":{"bibtex":"@article{Hilgert_Guedes Bonthonneau_Guillarmou_Weich_2023, title={Ruelle-Taylor resonances of Anosov actions}, author={Hilgert, Joachim and Guedes Bonthonneau, Y. and Guillarmou, C. and Weich, Tobias}, year={2023} }","mla":"Hilgert, Joachim, et al. Ruelle-Taylor Resonances of Anosov Actions. 2023.","apa":"Hilgert, J., Guedes Bonthonneau, Y., Guillarmou, C., & Weich, T. (2023). Ruelle-Taylor resonances of Anosov actions.","ama":"Hilgert J, Guedes Bonthonneau Y, Guillarmou C, Weich T. Ruelle-Taylor resonances of Anosov actions. Published online 2023.","chicago":"Hilgert, Joachim, Y. Guedes Bonthonneau, C. Guillarmou, and Tobias Weich. “Ruelle-Taylor Resonances of Anosov Actions,” 2023.","ieee":"J. Hilgert, Y. Guedes Bonthonneau, C. Guillarmou, and T. Weich, “Ruelle-Taylor resonances of Anosov actions.” 2023.","short":"J. Hilgert, Y. Guedes Bonthonneau, C. Guillarmou, T. Weich, (2023)."},"main_file_link":[{"url":"https://arxiv.org/pdf/2007.14275.pdf","open_access":"1"}],"oa":"1","date_updated":"2024-02-20T08:20:16Z","_id":"51521"},{"oa":"1","_id":"32447","date_updated":"2024-02-21T10:15:33Z","language":[{"iso":"eng"}],"year":"2023","citation":{"ieee":"K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping,” arXiv:2307.00975. 2023.","short":"K. Sonntag, S. Peitz, ArXiv:2307.00975 (2023).","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975, 2023.","bibtex":"@article{Sonntag_Peitz_2023, title={Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping}, journal={arXiv:2307.00975}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2023} }","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975, 2023.","apa":"Sonntag, K., & Peitz, S. (2023). Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping. In arXiv:2307.00975.","ama":"Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping. arXiv:230700975. Published online 2023."},"type":"preprint","main_file_link":[{"url":"https://arxiv.org/pdf/2307.00975.pdf","open_access":"1"}],"user_id":"56399","title":"Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping","abstract":[{"text":"We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order O(t−2) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.","lang":"eng"}],"external_id":{"arxiv":["2307.00975"]},"date_created":"2022-07-28T11:53:02Z","status":"public","department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2307.00975","author":[{"id":"56399","last_name":"Sonntag","full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"},{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"}]},{"language":[{"iso":"eng"}],"type":"preprint","year":"2023","citation":{"ieee":"M. Bernreuther et al., “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems,” arXiv:2308.01113. 2023.","short":"M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag, S. Volkwein, ArXiv:2308.01113 (2023).","mla":"Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.","bibtex":"@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023, title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113}, author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023} }","chicago":"Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.","apa":"Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag, K., & Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. In arXiv:2308.01113.","ama":"Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. arXiv:230801113. Published online 2023."},"main_file_link":[{"url":"https://arxiv.org/pdf/2308.01113","open_access":"1"}],"oa":"1","date_updated":"2024-02-21T12:22:20Z","_id":"46578","date_created":"2023-08-21T05:50:12Z","status":"public","department":[{"_id":"655"},{"_id":"101"}],"publication":"arXiv:2308.01113","author":[{"last_name":"Bernreuther","full_name":"Bernreuther, Marco","first_name":"Marco"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"last_name":"Müller","first_name":"Georg","full_name":"Müller, Georg"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X"},{"id":"56399","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","first_name":"Konstantin"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"user_id":"47427","title":"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems","external_id":{"arxiv":["2308.01113"]},"abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 \"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction\" of the DFG Priority Programm 1962 \"Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization\"."}]},{"user_id":"178","title":"Deep neural networks on diffeomorphism groups for optimal shape reparametrization","external_id":{"arxiv":["2207.11141"]},"status":"public","date_created":"2022-12-22T07:37:20Z","volume":63,"publisher":"Springer","author":[{"first_name":"Elena","full_name":"Celledoni, Elena","last_name":"Celledoni"},{"id":"178","last_name":"Glöckner","full_name":"Glöckner, Helge","first_name":"Helge"},{"full_name":"Riseth, Jørgen","first_name":"Jørgen","last_name":"Riseth"},{"last_name":"Schmeding","full_name":"Schmeding, Alexander","first_name":"Alexander"}],"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"publication":"BIT Numerical Mathematics","article_number":"50","doi":"10.1007/s10543-023-00989-05","intvolume":" 63","_id":"34803","date_updated":"2024-03-22T15:53:58Z","language":[{"iso":"eng"}],"type":"journal_article","citation":{"chicago":"Celledoni, Elena, Helge Glöckner, Jørgen Riseth, and Alexander Schmeding. “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.” BIT Numerical Mathematics 63 (2023). https://doi.org/10.1007/s10543-023-00989-05.","apa":"Celledoni, E., Glöckner, H., Riseth, J., & Schmeding, A. (2023). Deep neural networks on diffeomorphism groups for optimal shape reparametrization. BIT Numerical Mathematics, 63, Article 50. https://doi.org/10.1007/s10543-023-00989-05","ama":"Celledoni E, Glöckner H, Riseth J, Schmeding A. Deep neural networks on diffeomorphism groups for optimal shape reparametrization. BIT Numerical Mathematics. 2023;63. doi:10.1007/s10543-023-00989-05","bibtex":"@article{Celledoni_Glöckner_Riseth_Schmeding_2023, title={Deep neural networks on diffeomorphism groups for optimal shape reparametrization}, volume={63}, DOI={10.1007/s10543-023-00989-05}, number={50}, journal={BIT Numerical Mathematics}, publisher={Springer}, author={Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}, year={2023} }","mla":"Celledoni, Elena, et al. “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.” BIT Numerical Mathematics, vol. 63, 50, Springer, 2023, doi:10.1007/s10543-023-00989-05.","short":"E. Celledoni, H. Glöckner, J. Riseth, A. Schmeding, BIT Numerical Mathematics 63 (2023).","ieee":"E. Celledoni, H. Glöckner, J. Riseth, and A. Schmeding, “Deep neural networks on diffeomorphism groups for optimal shape reparametrization,” BIT Numerical Mathematics, vol. 63, Art. no. 50, 2023, doi: 10.1007/s10543-023-00989-05."},"year":"2023"},{"_id":"34793","intvolume":" 343","page":"186–232","citation":{"ieee":"H. Glöckner and J. Hilgert, “Aspects of control theory on infinite-dimensional Lie groups and G-manifolds,” Journal of Differential Equations, vol. 343, pp. 186–232, 2023, doi: 10.1016/j.jde.2022.10.001.","short":"H. Glöckner, J. Hilgert, Journal of Differential Equations 343 (2023) 186–232.","bibtex":"@article{Glöckner_Hilgert_2023, title={Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}, volume={343}, DOI={10.1016/j.jde.2022.10.001}, journal={Journal of Differential Equations}, author={Glöckner, Helge and Hilgert, Joachim}, year={2023}, pages={186–232} }","mla":"Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” Journal of Differential Equations, vol. 343, 2023, pp. 186–232, doi:10.1016/j.jde.2022.10.001.","chicago":"Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” Journal of Differential Equations 343 (2023): 186–232. https://doi.org/10.1016/j.jde.2022.10.001.","ama":"Glöckner H, Hilgert J. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. Journal of Differential Equations. 2023;343:186–232. doi:10.1016/j.jde.2022.10.001","apa":"Glöckner, H., & Hilgert, J. (2023). Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. Journal of Differential Equations, 343, 186–232. https://doi.org/10.1016/j.jde.2022.10.001"},"year":"2023","type":"journal_article","user_id":"178","article_type":"original","volume":343,"date_created":"2022-12-21T19:31:13Z","status":"public","keyword":["22E65","28B05","34A12","34H05","46E30","46E40"],"publication":"Journal of Differential Equations","quality_controlled":"1","author":[{"last_name":"Glöckner","id":"178","first_name":"Helge","full_name":"Glöckner, Helge"},{"id":"220","last_name":"Hilgert","full_name":"Hilgert, Joachim","first_name":"Joachim"}],"doi":"10.1016/j.jde.2022.10.001","date_updated":"2024-03-22T16:02:32Z","language":[{"iso":"eng"}],"title":"Aspects of control theory on infinite-dimensional Lie groups and G-manifolds","external_id":{"arxiv":["2007.11277"]},"publication_identifier":{"issn":["0022-0396"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"},{"_id":"91"}]},{"page":"343-358","type":"journal_article","year":"2023","citation":{"ieee":"H. Glöckner, “Diffeomorphism groups of convex polytopes,” Journal of Convex Analysis, vol. 30, no. 1, pp. 343–358, 2023.","short":"H. Glöckner, Journal of Convex Analysis 30 (2023) 343–358.","mla":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” Journal of Convex Analysis, vol. 30, no. 1, Heldermann, 2023, pp. 343–58.","bibtex":"@article{Glöckner_2023, title={Diffeomorphism groups of convex polytopes}, volume={30}, number={1}, journal={Journal of Convex Analysis}, publisher={Heldermann}, author={Glöckner, Helge}, year={2023}, pages={343–358} }","apa":"Glöckner, H. (2023). Diffeomorphism groups of convex polytopes. Journal of Convex Analysis, 30(1), 343–358.","ama":"Glöckner H. Diffeomorphism groups of convex polytopes. Journal of Convex Analysis. 2023;30(1):343-358.","chicago":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” Journal of Convex Analysis 30, no. 1 (2023): 343–58."},"language":[{"iso":"eng"}],"issue":"1","date_updated":"2024-03-22T16:07:00Z","_id":"34805","intvolume":" 30","volume":30,"date_created":"2022-12-22T07:45:13Z","status":"public","publication":"Journal of Convex Analysis","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"publisher":"Heldermann","author":[{"id":"178","last_name":"Glöckner","full_name":"Glöckner, Helge","first_name":"Helge"}],"title":"Diffeomorphism groups of convex polytopes","user_id":"178","external_id":{"arxiv":["2203.09285"]},"abstract":[{"lang":"eng","text":"Let $E$ be a finite-dimensional real vector space and $M\\subseteq E$ be a\r\nconvex polytope with non-empty interior. We turn the group of all\r\n$C^\\infty$-diffeomorphisms of $M$ into a regular Lie group."}]},{"external_id":{"arxiv":["2210.01246"]},"title":"Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ","user_id":"178","publisher":"Heldermann","author":[{"first_name":"Helge","full_name":"Glöckner, Helge","last_name":"Glöckner","id":"178"},{"last_name":"Tárrega","first_name":"Luis","full_name":"Tárrega, Luis"}],"publication":"Journal of Lie Theory","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"volume":33,"status":"public","date_created":"2022-12-22T07:23:57Z","_id":"34801","intvolume":" 33","date_updated":"2024-03-22T16:07:34Z","issue":"1","type":"journal_article","citation":{"ieee":"H. Glöckner and L. Tárrega, “Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ,” Journal of Lie Theory, vol. 33, no. 1, pp. 271–296, 2023.","short":"H. Glöckner, L. Tárrega, Journal of Lie Theory 33 (2023) 271–296.","bibtex":"@article{Glöckner_Tárrega_2023, title={Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }, volume={33}, number={1}, journal={Journal of Lie Theory}, publisher={Heldermann}, author={Glöckner, Helge and Tárrega, Luis}, year={2023}, pages={271–296} }","mla":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” Journal of Lie Theory, vol. 33, no. 1, Heldermann, 2023, pp. 271–96.","apa":"Glöckner, H., & Tárrega, L. (2023). Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . Journal of Lie Theory, 33(1), 271–296.","ama":"Glöckner H, Tárrega L. Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . Journal of Lie Theory. 2023;33(1):271-296.","chicago":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” Journal of Lie Theory 33, no. 1 (2023): 271–96."},"year":"2023","page":"271-296","language":[{"iso":"eng"}]},{"_id":"45191","date_updated":"2024-03-25T09:07:55Z","doi":"10.1007/978-3-031-26104-6","language":[{"iso":"eng"}],"type":"book_editor","year":"2023","citation":{"short":"I. Gräßler, G.W. Maier, E. Steffen, D. Roesmann, eds., The Digital Twin of Humans, Springer International Publishing, Cham, 2023.","ieee":"I. Gräßler, G. W. Maier, E. Steffen, and D. Roesmann, Eds., The Digital Twin of Humans. Cham: Springer International Publishing, 2023.","ama":"Gräßler I, Maier GW, Steffen E, Roesmann D, eds. The Digital Twin of Humans. Springer International Publishing; 2023. doi:10.1007/978-3-031-26104-6","apa":"Gräßler, I., Maier, G. W., Steffen, E., & Roesmann, D. (Eds.). (2023). The Digital Twin of Humans. Springer International Publishing. https://doi.org/10.1007/978-3-031-26104-6","chicago":"Gräßler, Iris, Günter W. Maier, Eckhard Steffen, and Daniel Roesmann, eds. The Digital Twin of Humans. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-26104-6.","mla":"Gräßler, Iris, et al., editors. The Digital Twin of Humans. 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Jahrestagung der Gesellschaft für Didaktik der Mathematik}, publisher={WTM}, author={Krämer, Sandra and Liebendörfer, Michael}, editor={Goethe-Universität Frankfur, IDMI-Primar}, year={2023}, pages={949–952} }","mla":"Krämer, Sandra, and Michael Liebendörfer. “Förderung Prozeduraler Flexibilität Durch Lernvideos Mit Interaktiven Aufgaben.” Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfur, vol. 2, WTM, 2023, pp. 949–952, doi:10.37626/GA9783959872089.0.","short":"S. Krämer, M. Liebendörfer, in: I.-P. Goethe-Universität Frankfur (Ed.), Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, WTM, Münster, 2023, pp. 949–952.","ieee":"S. Krämer and M. Liebendörfer, “Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben,” in Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, vol. 2, I.-P. Goethe-Universität Frankfur, Ed. Münster: WTM, 2023, pp. 949–952."},"user_id":"30933","title":"Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben","place":"Münster","date_created":"2024-03-25T10:06:16Z","status":"public","volume":2,"publication_identifier":{"isbn":["978-3-95987-208-9"]},"editor":[{"first_name":"IDMI-Primar","full_name":"Goethe-Universität Frankfur, IDMI-Primar","last_name":"Goethe-Universität Frankfur"}],"publication":"Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","department":[{"_id":"10"},{"_id":"625"},{"_id":"34"},{"_id":"97"},{"_id":"98"}],"author":[{"last_name":"Krämer","full_name":"Krämer, Sandra","first_name":"Sandra"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"}],"publisher":"WTM"},{"date_created":"2024-03-25T10:02:25Z","status":"public","department":[{"_id":"10"},{"_id":"625"},{"_id":"34"},{"_id":"97"},{"_id":"98"}],"user_id":"30933","title":"Preservice teachers’ mathematics-related values and expectancy in the transition from school to university","abstract":[{"lang":"eng","text":"Many preservice mathematics teachers lose their motivation during their first year at university. This phenomenon has been repeatedly described in recent years but is not yet fully understood. Since motivation may relate to different objects such as mathematics or teaching, we aim to qualitatively reconstruct different facets of the central motivational constructs of Situated-Expectancy-Value theory (intrinsic value, attainment value, utility value, cost, and expectancy of success) for preservice mathematics teachers. The analysis of longitudinal group interviews of 14 preservice higher-secondary mathematic teachers from a German university revealed different objects of motivation (e.g., teaching mathematics, scientific mathematics, procedural mathematics, or proof-based mathematics) in preservice teachers' values and expectancy of success. Furthermore, relations between those values and expectancy of success were identified that played a significant role in preservice teachers’ motivational development over their first semester (e.g., relations of attainment value for scientific mathematics and psychological cost). Theoretical and practical implications towards a teaching-specific conceptualization of expectancy of success and values and value interventions are being discussed."}],"language":[{"iso":"en"}],"type":"journal_article","citation":{"chicago":"“Preservice Teachers’ Mathematics-Related Values and Expectancy in the Transition from School to University,” 2023. https://doi.org/10.48489/QUADRANTE.31191.","ama":"Preservice teachers’ mathematics-related values and expectancy in the transition from school to university. Published online 2023. doi:10.48489/QUADRANTE.31191","apa":"Preservice teachers’ mathematics-related values and expectancy in the transition from school to university. (2023). https://doi.org/10.48489/QUADRANTE.31191","bibtex":"@article{Preservice teachers’ mathematics-related values and expectancy in the transition from school to university_2023, DOI={10.48489/QUADRANTE.31191}, year={2023} }","mla":"Preservice Teachers’ Mathematics-Related Values and Expectancy in the Transition from School to University. 2023, doi:10.48489/QUADRANTE.31191.","short":"(2023).","ieee":"“Preservice teachers’ mathematics-related values and expectancy in the transition from school to university,” 2023, doi: 10.48489/QUADRANTE.31191."},"year":"2023","doi":"10.48489/QUADRANTE.31191","date_updated":"2024-03-25T10:10:11Z","_id":"52807"},{"title":"ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation","place":"Cham","editor":[{"first_name":"Hintermüller","full_name":"Michael, Hintermüller","last_name":"Michael"},{"last_name":"Roland","full_name":"Roland, Herzog","first_name":"Herzog"},{"last_name":"Christian","full_name":"Christian, Kanzow","first_name":"Kanzow"},{"first_name":"Ulbrich","full_name":"Michael, Ulbrich","last_name":"Michael"},{"last_name":"Stefan","first_name":"Ulbrich","full_name":"Stefan, Ulbrich"}],"publication_identifier":{"isbn":["978-3-030-79392-0"]},"department":[{"_id":"101"},{"_id":"655"}],"oa":"1","doi":"10.1007/978-3-030-79393-7_3","date_updated":"2022-03-14T13:04:51Z","language":[{"iso":"eng"}],"user_id":"47427","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"}],"status":"public","date_created":"2020-03-13T12:45:31Z","publisher":"Springer","author":[{"last_name":"Banholzer","first_name":"Stefan","full_name":"Banholzer, Stefan"},{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"publication":"Non-Smooth and Complementarity-Based Distributed Parameter Systems","_id":"16296","citation":{"ieee":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in Non-Smooth and Complementarity-Based Distributed Parameter Systems, H. Michael, H. Roland, K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.","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.","bibtex":"@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={10.1007/978-3-030-79393-7_3}, 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} }","mla":"Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” Non-Smooth and Complementarity-Based Distributed Parameter Systems, edited by Hintermüller Michael et al., Springer, 2022, pp. 43–76, doi:10.1007/978-3-030-79393-7_3.","chicago":"Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” In Non-Smooth and Complementarity-Based Distributed Parameter Systems, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian, Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. https://doi.org/10.1007/978-3-030-79393-7_3.","apa":"Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., & Volkwein, S. (2022). ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In H. Michael, H. Roland, K. Christian, U. Michael, & U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems (pp. 43–76). Springer. https://doi.org/10.1007/978-3-030-79393-7_3","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. Non-Smooth and Complementarity-Based Distributed Parameter Systems. Springer; 2022:43-76. doi:10.1007/978-3-030-79393-7_3"},"year":"2022","type":"book_chapter","page":"43-76","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1906.09075.pdf"}]},{"citation":{"apa":"Peitz, S., Dellnitz, M., & Bannenberg, S. (2022). Efficient Virtual Design and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, & V. Schulz (Eds.), German Success Stories in Industrial Mathematics (Vol. 35). Springer International Publishing. https://doi.org/10.1007/978-3-030-81455-7_23","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. German Success Stories in Industrial Mathematics. Vol 35. Mathematics in Industry. Springer International Publishing; 2022. doi:10.1007/978-3-030-81455-7_23","chicago":"Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient Virtual Design and Testing of Autonomous Vehicles.” In German Success Stories in Industrial Mathematics, 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. https://doi.org/10.1007/978-3-030-81455-7_23.","bibtex":"@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles}, volume={35}, DOI={10.1007/978-3-030-81455-7_23}, 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.” German Success Stories in Industrial Mathematics, edited by H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:10.1007/978-3-030-81455-7_23.","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.","ieee":"S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing of Autonomous Vehicles,” in German Success Stories in Industrial Mathematics, vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham: Springer International Publishing, 2022."},"type":"book_chapter","year":"2022","intvolume":" 35","_id":"30294","volume":35,"date_created":"2022-03-14T07:32:41Z","status":"public","publication":"German Success Stories in Industrial Mathematics","author":[{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Bannenberg","first_name":"Sebastian","full_name":"Bannenberg, Sebastian"}],"publisher":"Springer International Publishing","user_id":"47427","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"series_title":"Mathematics in Industry","doi":"10.1007/978-3-030-81455-7_23","date_updated":"2022-03-14T07:42:01Z","publication_identifier":{"issn":["1612-3956","2198-3283"],"isbn":["9783030814540","9783030814557"]},"publication_status":"published","editor":[{"first_name":"H. G.","full_name":"Bock, H. G.","last_name":"Bock"},{"last_name":"Küfer","full_name":"Küfer, K.-H.","first_name":"K.-H."},{"last_name":"Maas","full_name":"Maas, P.","first_name":"P."},{"full_name":"Milde, A.","first_name":"A.","last_name":"Milde"},{"last_name":"Schulz","full_name":"Schulz, V.","first_name":"V."}],"department":[{"_id":"101"},{"_id":"655"}],"title":"Efficient Virtual Design and Testing of Autonomous Vehicles","place":"Cham"},{"date_created":"2022-03-24T12:26:10Z","status":"public","volume":"14(1)","department":[{"_id":"636"}],"publication":"AIMS","author":[{"full_name":"Cresson, Jacky","first_name":"Jacky","last_name":"Cresson"},{"full_name":"Jiménez, Fernando","first_name":"Fernando","last_name":"Jiménez"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"user_id":"15694","title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","language":[{"iso":"eng"}],"page":"57-89","citation":{"ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations,” AIMS, vol. 14(1), pp. 57–89, 2022.","mla":"Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” AIMS, 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. AIMS. 2022;14(1):57-89.","apa":"Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2022). Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. AIMS, 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.” AIMS 14(1) (2022): 57–89."},"type":"journal_article","year":"2022","date_updated":"2022-03-24T12:26:32Z","_id":"30490"},{"title":"Turnpike Property in Optimal Microbial Metabolite Production","user_id":"87909","abstract":[{"lang":"eng","text":"AbstractWe 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 Fuller 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 turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies."}],"publication_status":"published","publication_identifier":{"issn":["0022-3239","1573-2878"]},"date_created":"2022-04-08T17:23:13Z","status":"public","publication":"Journal of Optimization Theory and Applications","department":[{"_id":"636"}],"keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"author":[{"last_name":"Caillau","first_name":"Jean-Baptiste","full_name":"Caillau, Jean-Baptiste"},{"last_name":"Djema","full_name":"Djema, Walid","first_name":"Walid"},{"first_name":"Jean-Luc","full_name":"Gouzé, Jean-Luc","last_name":"Gouzé"},{"last_name":"Maslovskaya","id":"87909","first_name":"Sofya","full_name":"Maslovskaya, Sofya"},{"first_name":"Jean-Baptiste","full_name":"Pomet, Jean-Baptiste","last_name":"Pomet"}],"publisher":"Springer Science and Business Media LLC","doi":"10.1007/s10957-022-02023-0","_id":"30861","date_updated":"2022-04-08T18:23:02Z","year":"2022","type":"journal_article","citation":{"mla":"Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite Production.” Journal of Optimization Theory and Applications, Springer Science and Business Media LLC, 2022, doi:10.1007/s10957-022-02023-0.","bibtex":"@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property in Optimal Microbial Metabolite Production}, DOI={10.1007/s10957-022-02023-0}, 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} }","chicago":"Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.” Journal of Optimization Theory and Applications, 2022. https://doi.org/10.1007/s10957-022-02023-0.","ama":"Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property in Optimal Microbial Metabolite Production. Journal of Optimization Theory and Applications. Published online 2022. doi:10.1007/s10957-022-02023-0","apa":"Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., & Pomet, J.-B. (2022). Turnpike Property in Optimal Microbial Metabolite Production. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-022-02023-0","ieee":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike Property in Optimal Microbial Metabolite Production,” Journal of Optimization Theory and Applications, 2022, doi: 10.1007/s10957-022-02023-0.","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022)."},"language":[{"iso":"eng"}]},{"date_created":"2022-06-20T08:24:17Z","status":"public","volume":229,"keyword":["General Mathematics"],"publication":"Inventiones mathematicae","author":[{"last_name":"Cekić","first_name":"Mihajlo","full_name":"Cekić, Mihajlo"},{"first_name":"Benjamin","full_name":"Delarue, Benjamin","last_name":"Delarue","id":"70575"},{"first_name":"Semyon","full_name":"Dyatlov, Semyon","last_name":"Dyatlov"},{"first_name":"Gabriel P.","full_name":"Paternain, Gabriel P.","last_name":"Paternain"}],"publisher":"Springer Science and Business Media LLC","user_id":"70575","abstract":[{"text":"AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $$\\Sigma $$\r\n Σ\r\n with Betti number $$b_1$$\r\n \r\n b\r\n 1\r\n \r\n , the order of vanishing of the Ruelle zeta function at zero equals $$4-b_1$$\r\n \r\n 4\r\n -\r\n \r\n b\r\n 1\r\n \r\n \r\n , while in the hyperbolic case it is equal to $$4-2b_1$$\r\n \r\n 4\r\n -\r\n 2\r\n \r\n b\r\n 1\r\n \r\n \r\n . 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 $$S\\Sigma $$\r\n \r\n S\r\n Σ\r\n \r\n with harmonic 1-forms on $$\\Sigma $$\r\n Σ\r\n .","lang":"eng"}],"page":"303-394","citation":{"ieee":"M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” Inventiones mathematicae, vol. 229, no. 1, pp. 303–394, 2022, doi: 10.1007/s00222-022-01108-x.","short":"M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.","mla":"Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” Inventiones Mathematicae, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:10.1007/s00222-022-01108-x.","bibtex":"@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={10.1007/s00222-022-01108-x}, 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., & Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. Inventiones Mathematicae, 229(1), 303–394. https://doi.org/10.1007/s00222-022-01108-x","ama":"Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. Inventiones mathematicae. 2022;229(1):303-394. doi:10.1007/s00222-022-01108-x","chicago":"Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” Inventiones Mathematicae 229, no. 1 (2022): 303–94. https://doi.org/10.1007/s00222-022-01108-x."},"type":"journal_article","year":"2022","issue":"1","_id":"31982","intvolume":" 229","publication_identifier":{"issn":["0020-9910","1432-1297"]},"publication_status":"published","department":[{"_id":"548"}],"title":"The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds","language":[{"iso":"eng"}],"doi":"10.1007/s00222-022-01108-x","date_updated":"2022-06-21T11:55:15Z"},{"year":"2022","type":"book_chapter","citation":{"ieee":"U. Häsel-Weide, M. Wallner, and M. Hattermann, “Symmetrieverständnis von Anfang an,” in Anfangsunterricht für alle Kinder - Willkommen in der Schule!, M. Gutzmann, U. Carle, and Grundschulverband e. V., Eds. Frankfurt a. M., 2022, pp. 200–215.","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} }","mla":"Häsel-Weide, Uta, et al. “Symmetrieverständnis von Anfang an.” Anfangsunterricht für alle Kinder - Willkommen in der Schule!, edited by M. Gutzmann et al., 2022, pp. 200–15.","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.","apa":"Häsel-Weide, U., Wallner, M., & Hattermann, M. (2022). Symmetrieverständnis von Anfang an. In M. Gutzmann, U. Carle, & Grundschulverband e. V. (Eds.), Anfangsunterricht für alle Kinder - Willkommen in der Schule! (pp. 200–215).","ama":"Häsel-Weide U, Wallner M, Hattermann M. Symmetrieverständnis von Anfang an. In: Gutzmann M, Carle U, Grundschulverband e. V., eds. Anfangsunterricht für alle Kinder - Willkommen in der Schule!. ; 2022:200-215.","chicago":"Häsel-Weide, Uta, Melina Wallner, and M. Hattermann. “Symmetrieverständnis von Anfang an.” In Anfangsunterricht für alle Kinder - Willkommen in der Schule!, edited by M. Gutzmann, U. Carle, and Grundschulverband e. V., 200–215. Frankfurt a. M., 2022."},"page":"200-215","language":[{"iso":"ger"}],"corporate_editor":["Grundschulverband e. V."],"date_updated":"2022-07-05T06:48:40Z","_id":"32233","editor":[{"full_name":"Gutzmann, M.","first_name":"M.","last_name":"Gutzmann"},{"first_name":"U.","full_name":"Carle, U.","last_name":"Carle"}],"publication_status":"published","status":"public","date_created":"2022-06-28T06:30:12Z","author":[{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"},{"first_name":"Melina","full_name":"Wallner, Melina","last_name":"Wallner","id":"45445"},{"last_name":"Hattermann","full_name":"Hattermann, M.","first_name":"M."}],"department":[{"_id":"98"},{"_id":"543"}],"publication":"Anfangsunterricht für alle Kinder - Willkommen in der Schule!","title":"Symmetrieverständnis von Anfang an","user_id":"45445","place":"Frankfurt a. M."},{"_id":"32339","date_updated":"2022-07-11T05:31:46Z","language":[{"iso":"ger"}],"citation":{"apa":"Häsel-Weide, U., Seitz, S., Wallner, M., & 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, & M. Urban (Eds.), Qualifizierung für Inklusion. Sekundarstufe (pp. 83–100). Waxmann.","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. Qualifizierung für Inklusion. Sekundarstufe. Waxmann; 2022:83-100.","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.","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 Qualifizierung für Inklusion. Sekundarstufe, edited by D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, 83–100. Münster: Waxmann, 2022.","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 Qualifizierung für Inklusion. Sekundarstufe, D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, Eds. Münster: Waxmann, 2022, pp. 83–100.","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} }","mla":"Häsel-Weide, Uta, et al. “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe.” Qualifizierung für Inklusion. Sekundarstufe, edited by D. Lutz et al., Waxmann, 2022, pp. 83–100."},"type":"book_chapter","year":"2022","page":"83-100","place":"Münster","user_id":"85821","title":"Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe","author":[{"id":"60267","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","first_name":"Uta"},{"full_name":"Seitz, S.","first_name":"S.","last_name":"Seitz"},{"full_name":"Wallner, Melina","first_name":"Melina","id":"45445","last_name":"Wallner"},{"first_name":"Y.","full_name":"Wilke, Y.","last_name":"Wilke"}],"publisher":"Waxmann","publication":"Qualifizierung für Inklusion. Sekundarstufe","department":[{"_id":"98"},{"_id":"543"}],"status":"public","date_created":"2022-07-11T05:31:28Z","editor":[{"last_name":"Lutz","first_name":"D.","full_name":"Lutz, D."},{"first_name":"J.","full_name":"Becker, J.","last_name":"Becker"},{"full_name":"Buchhaupt, F.","first_name":"F.","last_name":"Buchhaupt"},{"full_name":"Katzenbach, D.","first_name":"D.","last_name":"Katzenbach"},{"last_name":"Strecker","first_name":"A.","full_name":"Strecker, A."},{"last_name":"Urban","first_name":"M.","full_name":"Urban, M."}],"publication_status":"published"},{"publication_status":"published","volume":3,"date_created":"2022-07-11T05:13:52Z","status":"public","department":[{"_id":"98"},{"_id":"543"}],"publication":"QfI - Qualifizierung für Inklusion","author":[{"last_name":"Hähn","first_name":"K.","full_name":"Hähn, K."},{"id":"60267","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","first_name":"Uta"},{"full_name":"Scherer, P.","first_name":"P.","last_name":"Scherer"}],"title":"Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.","user_id":"85821","related_material":{"link":[{"url":"https://doi.org/10.21248/qfi.72","relation":"contains"}]},"type":"journal_article","citation":{"ieee":"K. Hähn, U. Häsel-Weide, and P. Scherer, “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.,” QfI - Qualifizierung für Inklusion, vol. 3, no. 2, 2022.","short":"K. Hähn, U. Häsel-Weide, P. Scherer, QfI - Qualifizierung für Inklusion 3 (2022).","mla":"Hähn, K., et al. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” QfI - Qualifizierung für Inklusion, 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} }","chicago":"Hähn, K., Uta Häsel-Weide, and P. Scherer. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” QfI - Qualifizierung für Inklusion 3, no. 2 (2022).","ama":"Hähn K, Häsel-Weide U, Scherer P. Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. QfI - Qualifizierung für Inklusion. 2022;3(2).","apa":"Hähn, K., Häsel-Weide, U., & Scherer, P. (2022). Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. QfI - Qualifizierung für Inklusion, 3(2)."},"year":"2022","language":[{"iso":"ger"}],"issue":"2","intvolume":" 3","_id":"32338","date_updated":"2022-07-11T05:31:41Z"},{"status":"public","date_created":"2022-01-31T09:49:40Z","volume":55,"publisher":"IOP Publishing Ltd.","author":[{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"},{"orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","first_name":"Feliks","id":"81513","last_name":"Nüske"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"}],"publication":"Journal of Physics A: Mathematical and Theoretical","user_id":"47427","abstract":[{"lang":"eng","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."}],"citation":{"ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 31, p. 314002, 2022, doi: 10.1088/1751-8121/ac7d22.","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.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:10.1088/1751-8121/ac7d22.","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={10.1088/1751-8121/ac7d22}, 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} }","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” Journal of Physics A: Mathematical and Theoretical 55, no. 31 (2022): 314002. https://doi.org/10.1088/1751-8121/ac7d22.","apa":"Klus, S., Nüske, F., & Peitz, S. (2022). Koopman analysis of quantum systems. Journal of Physics A: Mathematical and Theoretical, 55(31), 314002. https://doi.org/10.1088/1751-8121/ac7d22","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. Journal of Physics A: Mathematical and Theoretical. 2022;55(31):314002. doi:10.1088/1751-8121/ac7d22"},"year":"2022","type":"journal_article","page":"314002","main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf","open_access":"1"}],"issue":"31","_id":"29673","intvolume":" 55","publication_status":"published","department":[{"_id":"655"},{"_id":"101"}],"title":"Koopman analysis of quantum systems","external_id":{"arxiv":["2201.12062"]},"language":[{"iso":"eng"}],"oa":"1","doi":"10.1088/1751-8121/ac7d22","date_updated":"2022-07-18T14:26:41Z"},{"main_file_link":[{"url":"https://arxiv.org/pdf/2210.04579","open_access":"1"}],"language":[{"iso":"eng"}],"citation":{"ieee":"B. Gebken, “Using second-order information in gradient sampling methods for nonsmooth optimization,” arXiv:2210.04579. 2022.","short":"B. Gebken, ArXiv:2210.04579 (2022).","mla":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for Nonsmooth Optimization.” ArXiv:2210.04579, 2022.","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. arXiv:221004579. Published online 2022.","apa":"Gebken, B. (2022). Using second-order information in gradient sampling methods for nonsmooth optimization. In arXiv:2210.04579.","chicago":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for Nonsmooth Optimization.” ArXiv:2210.04579, 2022."},"year":"2022","type":"preprint","date_updated":"2022-12-20T15:28:54Z","_id":"34618","oa":"1","publication":"arXiv:2210.04579","department":[{"_id":"101"}],"author":[{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"}],"date_created":"2022-12-20T15:25:17Z","status":"public","external_id":{"arxiv":["2210.04579"]},"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"}],"user_id":"32643","title":"Using second-order information in gradient sampling methods for nonsmooth optimization"},{"volume":14,"status":"public","date_created":"2022-12-21T19:27:51Z","author":[{"id":"178","last_name":"Glöckner","full_name":"Glöckner, Helge","first_name":"Helge"}],"quality_controlled":"1","publication":"p-Adic Numbers, Ultrametric Analysis, and Applications","keyword":["20Exx","22Exx","32Cxx"],"user_id":"178","article_type":"original","type":"journal_article","citation":{"apa":"Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive characteristic. P-Adic Numbers, Ultrametric Analysis, and Applications, 14(2), 138–144. https://doi.org/10.1134/S2070046622020042","ama":"Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic. p-Adic Numbers, Ultrametric Analysis, and Applications. 2022;14(2):138–144. doi:10.1134/S2070046622020042","chicago":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” P-Adic Numbers, Ultrametric Analysis, and Applications 14, no. 2 (2022): 138–144. https://doi.org/10.1134/S2070046622020042.","mla":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” P-Adic Numbers, Ultrametric Analysis, and Applications, vol. 14, no. 2, 2022, pp. 138–144, doi:10.1134/S2070046622020042.","bibtex":"@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local fields of positive characteristic}, volume={14}, DOI={10.1134/S2070046622020042}, number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications}, author={Glöckner, Helge}, year={2022}, pages={138–144} }","short":"H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022) 138–144.","ieee":"H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive characteristic,” p-Adic Numbers, Ultrametric Analysis, and Applications, vol. 14, no. 2, pp. 138–144, 2022, doi: 10.1134/S2070046622020042."},"year":"2022","page":"138–144","issue":"2","_id":"34792","intvolume":" 14","publication_identifier":{"issn":["2070-0466"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"title":"Non-Lie subgroups in Lie groups over local fields of positive characteristic","language":[{"iso":"eng"}],"doi":"10.1134/S2070046622020042","date_updated":"2022-12-21T19:30:25Z"},{"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"publication_identifier":{"issn":["0232-704X"]},"title":"Manifolds of mappings on Cartesian products","language":[{"iso":"eng"}],"date_updated":"2022-12-21T19:27:09Z","doi":"10.1007/s10455-021-09816-y","publication":"Annals of Global Analysis and Geometry","keyword":["58D15","22E65","26E15","26E20","46E40","46T20","58A05"],"author":[{"full_name":"Glöckner, Helge","first_name":"Helge","id":"178","last_name":"Glöckner"},{"full_name":"Schmeding, Alexander","first_name":"Alexander","last_name":"Schmeding"}],"quality_controlled":"1","volume":61,"date_created":"2022-12-21T19:24:48Z","status":"public","article_type":"original","user_id":"178","page":"359–398","year":"2022","citation":{"ieee":"H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,” Annals of Global Analysis and Geometry, vol. 61, no. 2, pp. 359–398, 2022, doi: 10.1007/s10455-021-09816-y.","short":"H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022) 359–398.","mla":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” Annals of Global Analysis and Geometry, vol. 61, no. 2, 2022, pp. 359–398, doi:10.1007/s10455-021-09816-y.","bibtex":"@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian products}, volume={61}, DOI={10.1007/s10455-021-09816-y}, number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner, Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }","ama":"Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. Annals of Global Analysis and Geometry. 2022;61(2):359–398. doi:10.1007/s10455-021-09816-y","apa":"Glöckner, H., & Schmeding, A. (2022). Manifolds of mappings on Cartesian products. Annals of Global Analysis and Geometry, 61(2), 359–398. https://doi.org/10.1007/s10455-021-09816-y","chicago":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” Annals of Global Analysis and Geometry 61, no. 2 (2022): 359–398. https://doi.org/10.1007/s10455-021-09816-y."},"type":"journal_article","_id":"34791","intvolume":" 61","issue":"2"},{"author":[{"last_name":"Glöckner","id":"178","first_name":"Helge","full_name":"Glöckner, Helge"}],"quality_controlled":"1","publication":"Axioms","volume":11,"status":"public","date_created":"2022-12-21T20:02:29Z","article_type":"original","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×E is a kR-space."}],"user_id":"178","year":"2022","citation":{"ieee":"H. Glöckner, “Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces,” Axioms, vol. 11, no. 5, 2022, doi: 10.3390/axioms11050221.","short":"H. Glöckner, Axioms 11 (2022).","mla":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” Axioms, vol. 11, no. 5, 2022, doi:10.3390/axioms11050221.","bibtex":"@article{Glöckner_2022, title={Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11}, DOI={10.3390/axioms11050221}, number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }","chicago":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” Axioms 11, no. 5 (2022). https://doi.org/10.3390/axioms11050221.","apa":"Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. Axioms, 11(5). https://doi.org/10.3390/axioms11050221","ama":"Glöckner H. Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. Axioms. 2022;11(5). doi:10.3390/axioms11050221"},"type":"journal_article","_id":"34796","intvolume":" 11","issue":"5","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"publication_identifier":{"issn":["2075-1680"]},"title":"Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces","language":[{"iso":"eng"}],"date_updated":"2022-12-22T07:31:55Z","doi":"10.3390/axioms11050221"},{"language":[{"iso":"eng"}],"type":"preprint","year":"2022","citation":{"apa":"Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient algebras. In arXiv:2206.11711.","ama":"Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras. arXiv:220611711. Published online 2022.","chicago":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” ArXiv:2206.11711, 2022.","mla":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” ArXiv:2206.11711, 2022.","bibtex":"@article{Glöckner_2022, title={Birkhoff decompositions for loop groups with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge}, year={2022} }","short":"H. Glöckner, ArXiv:2206.11711 (2022).","ieee":"H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,” arXiv:2206.11711. 2022."},"date_updated":"2022-12-22T07:44:08Z","_id":"34804","date_created":"2022-12-22T07:42:07Z","status":"public","publication":"arXiv:2206.11711","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"author":[{"last_name":"Glöckner","id":"178","first_name":"Helge","full_name":"Glöckner, Helge"}],"user_id":"178","title":"Birkhoff decompositions for loop groups with coefficient algebras","external_id":{"arxiv":["2206.11711"]},"abstract":[{"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.","lang":"eng"}]},{"doi":"10.17619/UNIPB/1-1327","oa":"1","date_updated":"2022-06-01T07:13:09Z","_id":"31556","type":"dissertation","year":"2022","citation":{"ieee":"B. Gebken, Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization. 2022.","short":"B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization, 2022.","mla":"Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization. 2022, doi:10.17619/UNIPB/1-1327.","bibtex":"@book{Gebken_2022, title={Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization}, DOI={10.17619/UNIPB/1-1327}, author={Gebken, Bennet}, year={2022} }","chicago":"Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization, 2022. https://doi.org/10.17619/UNIPB/1-1327.","apa":"Gebken, B. (2022). Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization. https://doi.org/10.17619/UNIPB/1-1327","ama":"Gebken B. Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization.; 2022. doi:10.17619/UNIPB/1-1327"},"supervisor":[{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779","open_access":"1"}],"title":"Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization","user_id":"32643","abstract":[{"lang":"ger","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."},{"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"}],"date_created":"2022-06-01T06:48:08Z","status":"public","department":[{"_id":"101"}],"author":[{"first_name":"Bennet","full_name":"Gebken, Bennet","last_name":"Gebken","id":"32643"}]},{"author":[{"last_name":"Berkemeier","id":"51701","first_name":"Manuel Bastian","full_name":"Berkemeier, Manuel Bastian"},{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2208.12094","status":"public","date_created":"2022-08-26T06:08:06Z","external_id":{"arxiv":["2208.12094"]},"abstract":[{"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.","lang":"eng"}],"title":"Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients","user_id":"47427","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2208.12094"}],"citation":{"ieee":"M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients,” arXiv:2208.12094. 2022.","short":"M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (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} }","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094, 2022.","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094, 2022.","ama":"Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. arXiv:220812094. Published online 2022.","apa":"Berkemeier, M. B., & Peitz, S. (2022). Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. In arXiv:2208.12094."},"type":"preprint","year":"2022","language":[{"iso":"eng"}],"date_updated":"2022-08-26T06:12:10Z","_id":"33150","oa":"1"},{"ddc":["510"],"user_id":"47427","article_type":"original","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"}],"volume":44,"status":"public","has_accepted_license":"1","date_created":"2020-12-15T07:46:36Z","author":[{"full_name":"Bieker, Katharina","first_name":"Katharina","id":"32829","last_name":"Bieker"},{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"},{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"}],"publisher":"IEEE","file_date_updated":"2021-09-25T11:59:15Z","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","file":[{"file_size":7990831,"creator":"speitz","file_id":"25040","content_type":"application/pdf","date_updated":"2021-09-25T11:59:15Z","success":1,"relation":"main_file","file_name":"On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf","date_created":"2021-09-25T11:59:15Z","access_level":"closed"}],"issue":"11","_id":"20731","intvolume":" 44","year":"2022","citation":{"mla":"Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, IEEE, 2022, pp. 7797–808, doi:10.1109/TPAMI.2021.3114962.","bibtex":"@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44}, DOI={10.1109/TPAMI.2021.3114962}, 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} }","chicago":"Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 44, no. 11 (2022): 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962.","apa":"Bieker, K., Gebken, B., & Peitz, S. (2022). On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(11), 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962","ama":"Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2022;44(11):7797-7808. doi:10.1109/TPAMI.2021.3114962","ieee":"K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 7797–7808, 2022, doi: 10.1109/TPAMI.2021.3114962.","short":"K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (2022) 7797–7808."},"type":"journal_article","page":"7797-7808","main_file_link":[{"open_access":"1","url":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772"}],"title":"On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation","publication_status":"epub_ahead","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"doi":"10.1109/TPAMI.2021.3114962","oa":"1","date_updated":"2022-10-21T12:27:16Z","language":[{"iso":"eng"}]}]