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Schaper, “Framing Goals of Mathematics Support Measures,” in Practice-Oriented Research in Tertiary Mathematics Education, Cham: Springer International Publishing, 2023, pp. 91–117.","short":"M. Liebendörfer, C. Büdenbender-Kuklinski, E. Lankeit, M. Schürmann, R. Biehler, N. Schaper, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 91–117."},"year":"2023","type":"book_chapter","page":"91-117","language":[{"iso":"eng"}]},{"user_id":"30933","title":"Practice-Oriented Research in Tertiary Mathematics Education","place":"Cham","status":"public","date_created":"2023-01-18T22:17:58Z","editor":[{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"},{"last_name":"Liebendörfer","first_name":"Michael","full_name":"Liebendörfer, Michael"},{"first_name":"Ghislaine","full_name":"Gueudet, Ghislaine","last_name":"Gueudet"},{"full_name":"Rasmussen, Chris","first_name":"Chris","last_name":"Rasmussen"},{"first_name":"Carl","full_name":"Winsløw, Carl","last_name":"Winsløw"}],"publication_status":"published","publication_identifier":{"isbn":["9783031141744","9783031141751"],"issn":["1869-4918","1869-4926"]},"publisher":"Springer International Publishing","department":[{"_id":"10"}],"doi":"10.1007/978-3-031-14175-1","_id":"37469","date_updated":"2023-01-18T22:47:41Z","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","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} }","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."},"year":"2023","type":"book_editor"},{"_id":"36294","date_updated":"2023-01-24T22:14:22Z","doi":"10.1090/tran/8860","language":[{"iso":"eng"}],"type":"journal_article","citation":{"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.","short":"D. Brennecken, M. Rösler, Transaction of the American Mathematical Society (n.d.).","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.","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."},"year":"2023","user_id":"37390","title":"The Dunkl-Laplace transform and Macdonald’s hypergeometric series","department":[{"_id":"555"}],"publication":"Transaction of the American Mathematical Society","author":[{"last_name":"Brennecken","id":"55911","first_name":"Dominik","full_name":"Brennecken, Dominik"},{"first_name":"Margit","full_name":"Rösler, Margit","last_name":"Rösler","id":"37390"}],"publisher":" American Mathematical Society","date_created":"2023-01-12T08:32:44Z","status":"public","publication_status":"inpress"},{"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":[{"full_name":"Hanusch, Maximilian","first_name":"Maximilian","id":"30905","last_name":"Hanusch"}],"user_id":"30905","article_type":"original","page":"170-201","citation":{"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} }","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.","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.","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","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","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."},"year":"2023","type":"journal_article","issue":"1","intvolume":" 75","_id":"34814","project":[{"_id":"161","name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)"}],"publication_identifier":{"issn":["0008-414X","1496-4279"]},"publication_status":"published","department":[{"_id":"93"}],"title":"A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus","language":[{"iso":"eng"}],"doi":"10.4153/s0008414x21000596","date_updated":"2023-02-22T11:38:32Z"},{"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","publication":"Journal of Global Optimization","author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"},{"first_name":"Katharina","full_name":"Bieker, Katharina","last_name":"Bieker","id":"32829"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"date_created":"2021-11-15T09:24:59Z","status":"public","volume":85,"intvolume":" 85","_id":"27426","issue":"3","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"page":"709-741","year":"2023","type":"journal_article","citation":{"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} }","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."},"title":"On the structure of regularization paths for piecewise differentiable regularization terms","department":[{"_id":"101"},{"_id":"655"}],"date_updated":"2023-03-11T17:16:33Z","oa":"1","doi":"10.1007/s10898-022-01223-2","language":[{"iso":"eng"}]},{"date_updated":"2023-03-25T10:11:35Z","oa":"1","language":[{"iso":"eng"}],"place":"Hannover","title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","department":[{"_id":"97"}],"editor":[{"first_name":"Marı́a","full_name":"Trigueros, Marı́a","last_name":"Trigueros"},{"full_name":"Barquero, Berta","first_name":"Berta","last_name":"Barquero"},{"first_name":"Reinhard","full_name":"Hochmuth, Reinhard","last_name":"Hochmuth"},{"full_name":"Peters, Jana","first_name":"Jana","last_name":"Peters"}],"publication_status":"published","_id":"31849","main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"year":"2023","citation":{"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.","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.","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.","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."},"type":"conference","user_id":"32202","ddc":["370","510"],"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","date_updated":"2023-03-25T10:01:03Z","file_id":"43096","creator":"maxh","file_size":201942,"access_level":"closed","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","date_created":"2023-03-25T10:01:03Z"}],"author":[{"id":"32202","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max","first_name":"Max"},{"full_name":"Biehler, Rolf","first_name":"Rolf","id":"16274","last_name":"Biehler"}],"publisher":"University of Hannover and INDRUM.","quality_controlled":"1","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."],"publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","status":"public","has_accepted_license":"1","date_created":"2022-06-12T11:07:34Z"},{"editor":[{"last_name":"Trigueros","first_name":"Marı́a","full_name":"Trigueros, Marı́a"},{"last_name":"Barquero","first_name":"Berta","full_name":"Barquero, Berta"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"first_name":"Jana","full_name":"Peters, Jana","last_name":"Peters"}],"department":[{"_id":"97"}],"title":"Innovations in university teaching based on mathematic education research","place":"Hannover","language":[{"iso":"eng"}],"oa":"1","date_updated":"2023-03-25T10:10:58Z","status":"public","has_accepted_license":"1","date_created":"2023-03-25T10:09:06Z","quality_controlled":"1","author":[{"full_name":"Florensa, Ignasio","first_name":"Ignasio","last_name":"Florensa"},{"first_name":"Max","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123","last_name":"Hoffmann","id":"32202"},{"full_name":"Romo Vázquez, Avenilde","first_name":"Avenilde","last_name":"Romo Vázquez"},{"last_name":"Zandieh","full_name":"Zandieh, Michelle","first_name":"Michelle"},{"last_name":"Martínez-Planell","full_name":"Martínez-Planell, Rafael","first_name":"Rafael"}],"file_date_updated":"2023-03-25T10:07:54Z","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file":[{"file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","date_created":"2023-03-25T10:07:54Z","access_level":"closed","file_size":642388,"creator":"maxh","file_id":"43098","content_type":"application/pdf","date_updated":"2023-03-25T10:07:54Z","relation":"main_file","success":1}],"ddc":["370","510"],"user_id":"32202","type":"conference","citation":{"short":"I. 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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.","short":"R. Biehler, M. Liebendörfer, A. Schmitz, Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023) 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.","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} }","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.","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.","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."},"page":"8-12","language":[{"iso":"ger"}]},{"date_updated":"2023-03-27T07:27:03Z","doi":"10.1016/j.nonrwa.2023.103868","language":[{"iso":"eng"}],"title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","intvolume":" 73","_id":"43105","article_number":"103868","type":"journal_article","year":"2023","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.","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","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","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."},"user_id":"23686","publication":"Nonlinear Analysis: Real World Applications","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"author":[{"id":"23686","last_name":"Black","full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias"},{"first_name":"Mario","full_name":"Fuest, Mario","last_name":"Fuest"},{"first_name":"Johannes","full_name":"Lankeit, Johannes","last_name":"Lankeit"},{"last_name":"Mizukami","first_name":"Masaaki","full_name":"Mizukami, Masaaki"}],"publisher":"Elsevier BV","date_created":"2023-03-27T07:25:58Z","status":"public","volume":73},{"type":"book_chapter","citation":{"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.","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","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} }","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.","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.","ieee":"V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46, 2023."},"year":"2023","language":[{"iso":"eng"}],"date_updated":"2023-03-30T10:06:53Z","_id":"43227","doi":"https://doi.org/10.18716/ojs/md/2023.1671","author":[{"full_name":"Vitt, Vivian","first_name":"Vivian","last_name":"Vitt"},{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"}],"department":[{"_id":"543"}],"publication":"Mathematica Didactica, 46","status":"public","date_created":"2023-03-30T10:06:24Z","title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","user_id":"44184"},{"author":[{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"},{"last_name":"Nührenbörger","first_name":"M.","full_name":"Nührenbörger, M."}],"publication":"Mathematica Didactica, 46","department":[{"_id":"543"}],"status":"public","date_created":"2023-03-30T10:04:31Z","user_id":"44184","title":"Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.","language":[{"iso":"eng"}],"year":"2023","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"},"type":"book_chapter","date_updated":"2023-03-30T10:06:49Z","_id":"43226","doi":"https://doi.org/10.18716/ojs/md/2023.1670"},{"volume":63,"publication_status":"published","status":"public","date_created":"2022-12-22T09:45:34Z","project":[{"_id":"161","name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)"}],"author":[{"full_name":"Hanusch, Maximilian","first_name":"Maximilian","id":"30905","last_name":"Hanusch"}],"publication":"Annals of Global Analysis and Geometry","department":[{"_id":"93"}],"keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups","user_id":"30905","type":"journal_article","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).","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.","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} }","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","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","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."},"year":"2023","language":[{"iso":"eng"}],"doi":"10.1007/s10455-023-09888-y","issue":"21","_id":"34832","intvolume":" 63","date_updated":"2023-04-05T18:18:24Z"},{"publication":"arXiv:2304.10243","department":[{"_id":"542"}],"author":[{"id":"72874","last_name":"Cappello","full_name":"Cappello, Chiara","first_name":"Chiara"},{"full_name":"Naserasr, Reza","first_name":"Reza","last_name":"Naserasr"},{"last_name":"Steffen","id":"15548","first_name":"Eckhard","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401"},{"full_name":"Wang, Zhouningxin","first_name":"Zhouningxin","last_name":"Wang"}],"date_created":"2023-05-05T06:52:39Z","status":"public","abstract":[{"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. ","lang":"eng"}],"external_id":{"arxiv":["2304.10243"]},"user_id":"15540","title":"Critically 3-frustrated signed graphs","language":[{"iso":"eng"}],"type":"preprint","year":"2023","citation":{"apa":"Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically 3-frustrated signed graphs. In arXiv:2304.10243.","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. arXiv:230410243. Published online 2023.","chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","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.","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023).","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” arXiv:2304.10243. 2023."},"_id":"44501","date_updated":"2023-05-05T06:53:47Z"},{"language":[{"iso":"eng"}],"doi":"10.1051/ro/2023052","date_updated":"2023-05-16T08:49:30Z","publication_identifier":{"issn":["0399-0559","2804-7303"]},"publication_status":"published","department":[{"_id":"542"}],"title":"Algorithms for the genome median under a restricted measure of rearrangement","year":"2023","citation":{"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.","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} }","short":"H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058.","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."},"type":"journal_article","page":"1045-1058","issue":"3","_id":"44857","intvolume":" 57","status":"public","date_created":"2023-05-16T08:48:22Z","volume":57,"author":[{"first_name":"Helmuth O.M.","full_name":"Silva, Helmuth O.M.","last_name":"Silva"},{"first_name":"Diego P.","full_name":"Rubert, Diego P.","last_name":"Rubert"},{"first_name":"Eloi","full_name":"Araujo, Eloi","last_name":"Araujo"},{"full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"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"],"user_id":"15540","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"}]},{"date_updated":"2023-05-16T11:17:26Z","_id":"44859","citation":{"short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” arXiv:2305.08619. 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.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs. arXiv:230508619. Published online 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.","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} }"},"year":"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","department":[{"_id":"542"}],"publication":"arXiv:2305.08619","author":[{"first_name":"Yulai","full_name":"Ma, Yulai","last_name":"Ma","id":"92748"},{"last_name":"Mattiolo","full_name":"Mattiolo, Davide","first_name":"Davide"},{"orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf","id":"88145"}]},{"language":[{"iso":"eng"}],"page":"752-811","year":"2023","type":"journal_article","citation":{"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.","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.","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} }","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.","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"},"issue":"4","doi":"10.1016/j.indag.2023.02.003","_id":"34833","date_updated":"2023-05-25T07:32:38Z","intvolume":" 34","date_created":"2022-12-22T09:46:36Z","status":"public","volume":34,"publication_status":"published","keyword":["Lie group actions and analytic 1-submanifolds"],"department":[{"_id":"93"}],"publication":"Indagationes Mathematicae.","author":[{"id":"30905","last_name":"Hanusch","full_name":"Hanusch, Maximilian","first_name":"Maximilian"}],"user_id":"30905","title":"Decompositions of Analytic 1-Manifolds"},{"main_file_link":[{"url":"https://arxiv.org/pdf/2306.03320"}],"language":[{"iso":"eng"}],"citation":{"short":"S. von der Gracht, E. Nijholt, B. Rink, 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. .","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.","mla":"von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.","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} }"},"type":"preprint","year":"2023","page":"29","_id":"45498","date_updated":"2023-06-07T07:59:06Z","author":[{"orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","first_name":"Sören","id":"97359","last_name":"von der Gracht"},{"last_name":"Nijholt","full_name":"Nijholt, Eddie","first_name":"Eddie"},{"full_name":"Rink, Bob","first_name":"Bob","last_name":"Rink"}],"department":[{"_id":"101"}],"publication":"arXiv:2306.03320","status":"public","date_created":"2023-06-07T07:57:28Z","publication_status":"submitted","external_id":{"arxiv":["2306.03320"]},"abstract":[{"lang":"eng","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."}],"user_id":"97359","title":"A parametrisation method for high-order phase reduction in coupled oscillator networks"},{"related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"user_id":"44184","title":" Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen","author":[{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"}],"publisher":"Friedrich Verlag","publication":"Die Grundschulzeitschrift","department":[{"_id":"543"}],"status":"public","date_created":"2023-06-22T09:28:22Z","date_updated":"2023-06-22T09:34:13Z","_id":"45712","issue":"339","language":[{"iso":"ger"}],"citation":{"short":"U. Häsel-Weide, Die Grundschulzeitschrift (2023) 6–11.","ieee":"U. Häsel-Weide, “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen,” Die Grundschulzeitschrift, no. 339, pp. 6–11, 2023.","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.","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} }"},"type":"journal_article","year":"2023","page":"6-11"},{"language":[{"iso":"ger"}],"type":"journal_article","citation":{"mla":"Graf, Lara Marie, et al. “Addition und Subtraktion verstehen.” Die Grundschulzeitschrift, no. 339, Friedrich Verlag, 2023, pp. 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} }","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.","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."},"year":"2023","page":"20-23","_id":"45713","date_updated":"2023-06-22T09:34:18Z","issue":"339","publisher":"Friedrich Verlag","author":[{"first_name":"Lara Marie","full_name":"Graf, Lara Marie","last_name":"Graf","id":"89837"},{"first_name":"Inga","full_name":"Wienhues, Inga","last_name":"Wienhues","id":"61635"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"department":[{"_id":"543"}],"publication":"Die Grundschulzeitschrift","status":"public","date_created":"2023-06-22T09:33:59Z","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":"eng"}],"doi":"10.1007/s11858-023-01505-3","oa":"1","date_updated":"2023-07-13T09:41:20Z","publication_status":"published","publication_identifier":{"issn":["1863-9690","1863-9704"]},"department":[{"_id":"97"},{"_id":"643"}],"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","type":"journal_article","year":"2023","citation":{"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.","short":"M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2023).","bibtex":"@article{Hoffmann_Biehler_2023, 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}, DOI={10.1007/s11858-023-01505-3}, journal={ZDM – Mathematics Education}, publisher={Springer}, author={Hoffmann, Max and Biehler, Rolf}, year={2023} }","mla":"Hoffmann, Max, and Rolf 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, Springer, 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. Published online 2023. doi:10.1007/s11858-023-01505-3","chicago":"Hoffmann, Max, and Rolf 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. https://doi.org/10.1007/s11858-023-01505-3."},"main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/s11858-023-01505-3"}],"_id":"45786","has_accepted_license":"1","status":"public","date_created":"2023-06-27T11:45:25Z","author":[{"full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123","first_name":"Max","id":"32202","last_name":"Hoffmann"},{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler","id":"16274"}],"quality_controlled":"1","publisher":"Springer","publication":"ZDM – Mathematics Education","keyword":["General Mathematics","Education"],"file_date_updated":"2023-07-13T09:40:02Z","file":[{"access_level":"closed","date_created":"2023-07-13T09:40:02Z","file_name":"s11858-023-01505-3.pdf","relation":"main_file","success":1,"content_type":"application/pdf","date_updated":"2023-07-13T09:40:02Z","creator":"maxh","file_id":"46041","file_size":1460246}],"ddc":["510","370"],"user_id":"32202","article_type":"original","abstract":[{"text":"Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). 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.","lang":"eng"}]},{"volume":528,"date_created":"2023-07-20T05:08:49Z","status":"public","keyword":["Applied Mathematics","Analysis"],"publication":"Journal of Mathematical Analysis and Applications","publisher":"Elsevier BV","author":[{"id":"99427","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","first_name":"Benjamin"},{"full_name":"Janssen, Daan W.","first_name":"Daan W.","last_name":"Janssen"},{"last_name":"Ziebell","first_name":"Jobst","full_name":"Ziebell, Jobst"}],"user_id":"99427","type":"journal_article","citation":{"bibtex":"@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of exponentials: A sufficient condition}, volume={528}, DOI={10.1016/j.jmaa.2023.127558}, number={1127558}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}, year={2023} }","mla":"Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” Journal of Mathematical Analysis and Applications, vol. 528, no. 1, 127558, Elsevier BV, 2023, doi:10.1016/j.jmaa.2023.127558.","chicago":"Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” Journal of Mathematical Analysis and Applications 528, no. 1 (2023). https://doi.org/10.1016/j.jmaa.2023.127558.","apa":"Hinrichs, B., Janssen, D. W., & Ziebell, J. (2023). Super-Gaussian decay of exponentials: A sufficient condition. Journal of Mathematical Analysis and Applications, 528(1), Article 127558. https://doi.org/10.1016/j.jmaa.2023.127558","ama":"Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A sufficient condition. Journal of Mathematical Analysis and Applications. 2023;528(1). doi:10.1016/j.jmaa.2023.127558","ieee":"B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials: A sufficient condition,” Journal of Mathematical Analysis and Applications, vol. 528, no. 1, Art. no. 127558, 2023, doi: 10.1016/j.jmaa.2023.127558.","short":"B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and Applications 528 (2023)."},"year":"2023","article_number":"127558","issue":"1","intvolume":" 528","_id":"46100","publication_status":"published","publication_identifier":{"issn":["0022-247X"]},"department":[{"_id":"799"}],"title":"Super-Gaussian decay of exponentials: A sufficient condition","external_id":{"arxiv":["2205.09189"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.jmaa.2023.127558","date_updated":"2023-07-20T05:11:12Z"},{"title":"Temperedness of locally symmetric spaces: The product case","user_id":"45027","external_id":{"arxiv":["2304.09573"]},"abstract":[{"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$\\Gamma$.","lang":"eng"}],"status":"public","date_created":"2023-07-24T07:52:23Z","author":[{"first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"full_name":"Wolf, Lasse L.","first_name":"Lasse L.","last_name":"Wolf"}],"department":[{"_id":"10"}],"publication":"arXiv:2304.09573","_id":"46117","date_updated":"2023-07-24T07:53:29Z","type":"preprint","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 L.}, year={2023} }","mla":"Weich, Tobias, and Lasse L. 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 L. 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)."},"language":[{"iso":"eng"}]},{"title":"Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?","publication_status":"published","publication_identifier":{"issn":["0742-051X"]},"department":[{"_id":"611"}],"doi":"10.1016/j.tate.2023.104270","date_updated":"2023-07-26T08:57:01Z","language":[{"iso":"eng"}],"user_id":"72183","status":"public","date_created":"2023-07-26T08:55:26Z","volume":132,"publisher":"Elsevier BV","author":[{"first_name":"Julia","full_name":"Bruns, Julia","last_name":"Bruns"},{"first_name":"Maike","full_name":"Hagena, Maike","last_name":"Hagena"},{"last_name":"Gasteiger","full_name":"Gasteiger, Hedwig","first_name":"Hedwig"}],"keyword":["Education"],"publication":"Teaching and Teacher Education","article_number":"104270","_id":"46155","intvolume":" 132","year":"2023","citation":{"bibtex":"@article{Bruns_Hagena_Gasteiger_2023, title={Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?}, volume={132}, DOI={10.1016/j.tate.2023.104270}, number={104270}, journal={Teaching and Teacher Education}, publisher={Elsevier BV}, author={Bruns, Julia and Hagena, Maike and Gasteiger, Hedwig}, year={2023} }","mla":"Bruns, Julia, et al. “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?” Teaching and Teacher Education, vol. 132, 104270, Elsevier BV, 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.","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? Teaching and Teacher Education, 132, Article 104270. 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","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.","short":"J. Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023)."},"type":"journal_article"},{"language":[{"iso":"eng"}],"citation":{"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} }","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. 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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.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. 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","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.","mla":"Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }"},"year":"2023","type":"journal_article","intvolume":" 37","_id":"46256","issue":"3","keyword":["General Mathematics"],"publication":"SIAM Journal on Discrete Mathematics","publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"last_name":"Ma","id":"92748","first_name":"Yulai","full_name":"Ma, Yulai"},{"full_name":"Mattiolo, Davide","first_name":"Davide","last_name":"Mattiolo"},{"id":"15548","last_name":"Steffen","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","first_name":"Eckhard"},{"last_name":"Wolf","id":"88145","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus"}],"date_created":"2023-08-01T10:08:32Z","status":"public","volume":37,"user_id":"15540"},{"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/Christian-Offen/LagrangianDensityML"}]},"external_id":{"arxiv":["2302.08232 "]},"publication_status":"published","publication_identifier":{"eisbn":["978-3-031-38271-0"]},"editor":[{"last_name":"Nielsen","full_name":"Nielsen, F","first_name":"F"},{"last_name":"Barbaresco","full_name":"Barbaresco, F","first_name":"F"}],"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)","ddc":["510"],"user_id":"85279","abstract":[{"lang":"eng","text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. 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,"date_created":"2023-02-16T11:32:48Z","has_accepted_license":"1","status":"public","file_date_updated":"2023-08-02T12:04:17Z","publication":"Geometric Science of Information","keyword":["System identification","discrete Lagrangians","travelling waves"],"quality_controlled":"1","author":[{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"}],"publisher":"Springer, Cham.","file":[{"file_name":"LDensityLearning.pdf","date_created":"2023-08-02T12:04:17Z","access_level":"open_access","file_size":1938962,"creator":"coffen","file_id":"46273","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","content_type":"application/pdf","date_updated":"2023-08-02T12:04:17Z","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."}],"conference":{"end_date":"2023-09-01","location":"Saint-Malo, Palais du Grand Large, France","start_date":"2023-08-30","name":" GSI'23 6th International Conference on Geometric Science of Information"},"_id":"42163","intvolume":" 14071","page":"569-579","year":"2023","citation":{"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)} }","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.","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","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","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.","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.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579."},"type":"conference"},{"article_type":"original","abstract":[{"lang":"eng","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."}],"user_id":"85279","ddc":["510"],"file":[{"relation":"main_file","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.","content_type":"application/pdf","date_updated":"2022-06-28T15:25:50Z","creator":"coffen","file_id":"32274","access_level":"open_access","file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","date_created":"2022-06-28T15:25:50Z","title":"Variational Learning of Euler–Lagrange Dynamics from Data","file_size":3640770}],"author":[{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"}],"publisher":"Elsevier","quality_controlled":"1","keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"file_date_updated":"2022-06-28T15:25:50Z","publication":"Journal of Computational and Applied Mathematics","status":"public","has_accepted_license":"1","date_created":"2022-01-11T13:24:00Z","volume":421,"intvolume":" 421","_id":"29240","type":"journal_article","citation":{"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.","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} }","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.","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","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","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.","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780."},"year":"2023","page":"114780","external_id":{"arxiv":["2112.12619"]},"related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianShadowIntegration","relation":"software"}]},"title":"Variational Learning of Euler–Lagrange Dynamics from Data","department":[{"_id":"636"}],"publication_identifier":{"issn":["0377-0427"]},"publication_status":"epub_ahead","date_updated":"2023-08-10T08:42:39Z","oa":"1","doi":"10.1016/j.cam.2022.114780","language":[{"iso":"eng"}]},{"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","user_id":"85279","ddc":["510"],"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"}],"publication":"Journal of Geometric Mechanics","keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"file_date_updated":"2022-08-12T16:48:59Z","author":[{"last_name":"McLachlan","first_name":"Robert","full_name":"McLachlan, Robert"},{"last_name":"Offen","id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian"}],"publisher":"AIMS Press","quality_controlled":"1","date_created":"2022-01-11T12:48:39Z","has_accepted_license":"1","status":"public","volume":15,"_id":"29236","intvolume":" 15","issue":"1","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.","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.","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","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"},"external_id":{"arxiv":["2201.03911"]},"related_material":{"link":[{"url":"https://github.com/Christian-Offen/BEAConjugateSymplectic","relation":"software"}]},"title":"Backward error analysis for conjugate symplectic methods","department":[{"_id":"636"}],"publication_status":"published","date_updated":"2023-08-10T08:40:30Z","oa":"1","doi":"10.3934/jgm.2023005","language":[{"iso":"eng"}]},{"user_id":"85279","ddc":["510"],"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","date_created":"2023-01-20T09:10:06Z","status":"public","has_accepted_license":"1","volume":33,"file":[{"file_size":5200111,"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","file_name":"JournalPaper_main.pdf","date_created":"2023-04-26T16:20:56Z","access_level":"open_access","file_id":"44205","creator":"coffen","date_updated":"2023-04-26T16:20:56Z","content_type":"application/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."}],"file_date_updated":"2023-04-26T16:20:56Z","publication":"Chaos","author":[{"last_name":"Dierkes","first_name":"Eva","full_name":"Dierkes, Eva"},{"id":"85279","last_name":"Offen","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"full_name":"Flaßkamp, Kathrin","first_name":"Kathrin","last_name":"Flaßkamp"}],"publisher":"AIP Publishing","issue":"6","article_number":"063115","intvolume":" 33","_id":"37654","year":"2023","citation":{"short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","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.","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","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.","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."},"type":"journal_article","related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","external_id":{"arxiv":["2301.07928"]},"publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","department":[{"_id":"636"}],"oa":"1","doi":"10.1063/5.0142969","date_updated":"2023-08-10T08:37:01Z","language":[{"iso":"eng"}]},{"article_number":"14","_id":"23428","intvolume":" 33","year":"2023","type":"journal_article","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","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.","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} }"},"main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"user_id":"47427","abstract":[{"lang":"eng","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."}],"status":"public","date_created":"2021-08-17T12:25:09Z","volume":33,"author":[{"id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","first_name":"Feliks"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"last_name":"Schaller","full_name":"Schaller, Manuel","first_name":"Manuel"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"}],"publication":"Journal of Nonlinear Science","oa":"1","doi":"10.1007/s00332-022-09862-1","date_updated":"2023-08-24T07:50:12Z","language":[{"iso":"eng"}],"title":"Finite-data error bounds for Koopman-based prediction and control","publication_status":"published","department":[{"_id":"101"},{"_id":"655"}]},{"volume":45,"date_created":"2021-04-09T07:59:19Z","has_accepted_license":"1","status":"public","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"},{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"first_name":"Karlson","full_name":"Pfannschmidt, Karlson","orcid":"0000-0001-9407-7903","last_name":"Pfannschmidt","id":"13472"}],"ddc":["510"],"user_id":"47427","abstract":[{"lang":"eng","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."}],"page":"A579-A595","type":"journal_article","citation":{"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","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.","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} }","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.","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."},"year":"2023","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"issue":"2","_id":"21600","intvolume":" 45","publication_status":"published","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"title":"Efficient time stepping for numerical integration using reinforcement learning","related_material":{"link":[{"url":"https://github.com/lueckem/quadrature-ML","relation":"software","description":"GitHub"}]},"external_id":{"arxiv":["arXiv:2104.03562"]},"language":[{"iso":"eng"}],"doi":"10.1137/21M1412682","date_updated":"2023-08-25T09:24:50Z"},{"language":[{"iso":"eng"}],"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. 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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.","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"},"_id":"47416","date_updated":"2023-09-25T11:18:19Z","doi":"10.1007/978-3-662-66604-3_8"},{"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."}],"title":"Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions","user_id":"99427","department":[{"_id":"799"},{"_id":"623"}],"publication":"arXiv:2309.09005","author":[{"last_name":"Hinrichs","id":"99427","first_name":"Benjamin","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin"},{"last_name":"Matte","full_name":"Matte, Oliver","first_name":"Oliver"}],"date_created":"2023-10-02T06:21:37Z","project":[{"_id":"266","name":"PhoQC: PhoQC: Photonisches Quantencomputing"}],"status":"public","date_updated":"2023-10-02T06:22:55Z","_id":"47534","type":"preprint","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.","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.","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.","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","language":[{"iso":"eng"}]},{"place":"Cham","title":"Impacts of Digitalization on Content and Goals of Statistics Education","user_id":"37888","publisher":"Springer International Publishing","author":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"first_name":"Daniel","full_name":"Frischemeier, Daniel","last_name":"Frischemeier"},{"last_name":"Gould","full_name":"Gould, Ronald","first_name":"Ronald"},{"first_name":"Maxine","full_name":"Pfannkuch, Maxine","last_name":"Pfannkuch"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"Handbook of Digital Resources in Mathematics Education","editor":[{"full_name":"Pepin, Birgit","first_name":"Birgit","last_name":"Pepin"},{"last_name":"Gueudet","full_name":"Gueudet, Ghislaine","first_name":"Ghislaine"},{"full_name":"Choppin, Jeffrey","first_name":"Jeffrey","last_name":"Choppin"}],"status":"public","date_created":"2023-10-12T11:31:22Z","_id":"48042","date_updated":"2023-10-12T11:31:47Z","year":"2023","citation":{"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.","short":"R. Biehler, D. Frischemeier, R. Gould, M. Pfannkuch, in: B. Pepin, G. Gueudet, J. 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Choppin (Eds.), Handbook of Digital Resources in Mathematics Education. Springer International Publishing.","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.","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."},"type":"book_chapter","language":[{"iso":"eng"}]},{"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.","chicago":"Leiss, Dominik, Kerstin Gerlach, Lena Wessel, and Barbara Schmidt-Thieme. “Sprache und Mathematiklernen.” In Handbuch der Mathematikdidaktik, 561–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. https://doi.org/10.1007/978-3-662-66604-3_18.","ama":"Leiss D, Gerlach K, Wessel L, Schmidt-Thieme B. 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Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel. GDM-Mitteilungen, 115, 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.","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.","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} }","short":"R. Biehler, K. Krüger, GDM-Mitteilungen (2023) 57–65.","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."},"type":"journal_article","page":"57-65","language":[{"iso":"ger"}],"issue":"115","_id":"49049","date_updated":"2023-11-20T08:23:56Z"},{"_id":"46756","date_updated":"2023-11-24T16:33:37Z","conference":{"location":"Prag","name":"International Symposium in Elementary Mathematics Teaching"},"language":[{"iso":"eng"}],"citation":{"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.","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} }","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.","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.","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."},"type":"conference","year":"2023","page":"346-354","main_file_link":[{"url":"https://semt.cz/proceedings/semt-23.pdf"}],"user_id":"45445","title":"Conceptual understanding of third grades for axial symmetry","status":"public","date_created":"2023-08-30T09:24:29Z","editor":[{"full_name":"Novotna, J.","first_name":"J.","last_name":"Novotna"},{"full_name":"Moraova, H.","first_name":"H.","last_name":"Moraova"}],"publisher":"Charles University","author":[{"first_name":"Melina","full_name":"Wallner, Melina","last_name":"Wallner","id":"45445"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"publication":"International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education","department":[{"_id":"543"}]},{"external_id":{"arxiv":["2302.08974"]},"title":"Hypernetworks: Cluster Synchronization Is a Higher-Order Effect","department":[{"_id":"101"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"publication_status":"published","date_updated":"2023-11-29T10:52:23Z","doi":"10.1137/23m1561075","language":[{"iso":"eng"}],"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","keyword":["Applied Mathematics"],"publication":"SIAM Journal on Applied Mathematics","publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"last_name":"von der Gracht","id":"97359","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"last_name":"Rink","full_name":"Rink, Bob","first_name":"Bob"}],"date_created":"2023-11-29T10:50:05Z","status":"public","volume":83,"intvolume":" 83","_id":"49326","issue":"6","page":"2329-2353","year":"2023","citation":{"short":"S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics 83 (2023) 2329–2353.","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.","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.","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} }"},"type":"journal_article"},{"publication":"arXiv:2311.17186","department":[{"_id":"101"}],"author":[{"first_name":"Sören","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht","id":"97359"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"full_name":"Rink, Bob","first_name":"Bob","last_name":"Rink"}],"date_created":"2023-12-01T06:35:29Z","status":"public","external_id":{"arxiv":["2311.17186"]},"abstract":[{"lang":"eng","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."}],"title":"Higher order interactions lead to \"reluctant\" synchrony breaking","user_id":"97359","type":"preprint","citation":{"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} }","mla":"von der Gracht, Sören, et al. “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.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” 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.","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2311.17186 (2023)."},"year":"2023","language":[{"iso":"eng"}],"_id":"49371","date_updated":"2023-12-01T06:38:44Z"},{"status":"public","date_created":"2023-12-01T09:23:59Z","publication_identifier":{"issn":["2730-9657"]},"publication_status":"published","publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Jürgen","full_name":"Klüners, Jürgen","last_name":"Klüners","id":"21202"},{"full_name":"Wang, Jiuya","first_name":"Jiuya","last_name":"Wang"}],"publication":"La Matematica","department":[{"_id":"102"}],"user_id":"21202","title":"Idélic Approach in Enumerating Heisenberg Extensions","language":[{"iso":"eng"}],"citation":{"short":"J. Klüners, J. Wang, La Matematica (2023).","ieee":"J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,” La Matematica, 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","ama":"Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. La Matematica. Published online 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.","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."},"year":"2023","type":"journal_article","doi":"10.1007/s44007-023-00067-w","date_updated":"2023-12-06T09:50:43Z","_id":"49372"},{"title":"Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research","user_id":"45445","status":"public","date_created":"2023-12-04T09:45:04Z","author":[{"full_name":"Seitz, Simone","first_name":"Simone","last_name":"Seitz"},{"id":"60267","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","first_name":"Uta"},{"full_name":"Wilke, Yannik","first_name":"Yannik","last_name":"Wilke"},{"full_name":"Wallner, Melina","first_name":"Melina","id":"45445","last_name":"Wallner"}],"publication":"Teachers and Teaching","department":[{"_id":"543"}],"doi":"https://doi.org/10.1080/13540602.2023.2284876 ","_id":"49425","date_updated":"2023-12-13T12:51:03Z","type":"journal_article","year":"2023","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."},"page":"1-16","language":[{"iso":"eng"}]},{"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"year":"2023","type":"conference","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.","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.","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} }","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","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."},"page":"3203-3210","_id":"34135","intvolume":" 56","conference":{"start_date":"2023-07-09","name":"The 22nd World Congress of the International Federation of Automatic Control","location":" Yokohama, Japan","end_date":"2023-07-14"},"issue":"2","file":[{"title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","file_size":576115,"access_level":"open_access","file_name":"LNN_project.pdf","date_created":"2023-04-17T08:05:55Z","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.","relation":"main_file","date_updated":"2023-04-17T08:05:55Z","content_type":"application/pdf","creator":"coffen","file_id":"44037"}],"author":[{"last_name":"Lishkova","first_name":"Yana","full_name":"Lishkova, Yana"},{"last_name":"Scherer","full_name":"Scherer, Paul","first_name":"Paul"},{"first_name":"Steffen","full_name":"Ridderbusch, Steffen","last_name":"Ridderbusch"},{"last_name":"Jamnik","full_name":"Jamnik, Mateja","first_name":"Mateja"},{"full_name":"Liò, Pietro","first_name":"Pietro","last_name":"Liò"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"last_name":"Offen","id":"85279","first_name":"Christian","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057"}],"publisher":"Elsevier","quality_controlled":"1","publication":"IFAC-PapersOnLine","file_date_updated":"2023-04-17T08:05:55Z","status":"public","has_accepted_license":"1","date_created":"2022-11-23T08:17:10Z","volume":56,"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."}],"user_id":"85279","ddc":["510"],"language":[{"iso":"eng"}],"date_updated":"2023-12-29T14:26:00Z","oa":"1","doi":"10.1016/j.ifacol.2023.10.1457","department":[{"_id":"636"}],"publication_status":"published","external_id":{"arxiv":["2211.10830"]},"related_material":{"link":[{"url":"https://github.com/yanalish/SymDLNN","description":"GitHub","relation":"software"}]},"title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery"},{"keyword":["Dynamical Systems","Coupled Systems","Distributed Computing","Robot Swarms","Autonomous Mobile Robots","Gathering"],"publication":"arXiv:2305.06632","author":[{"first_name":"Raphael","full_name":"Gerlach, Raphael","last_name":"Gerlach","id":"32655"},{"first_name":"Sören","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht","id":"97359"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"date_created":"2023-05-12T10:16:06Z","status":"public","abstract":[{"lang":"eng","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."}],"user_id":"32655","main_file_link":[{"url":"https://arxiv.org/abs/2305.06632"}],"page":"38","type":"preprint","year":"2023","citation":{"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.","ama":"Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. arXiv:230506632.","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.","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} }","mla":"Gerlach, Raphael, et al. “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.).","ieee":"R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies,” arXiv:2305.06632. ."},"_id":"44840","department":[{"_id":"101"}],"publication_status":"submitted","project":[{"grant_number":"453112019","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme","_id":"106"}],"external_id":{"arxiv":["2305.06632"]},"title":"On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies","related_material":{"link":[{"url":"https://math.uni-paderborn.de/en/ag/chair-of-applied-mathematics/research/research-projects/swarmdynamics","relation":"supplementary_material"}]},"language":[{"iso":"eng"}],"date_updated":"2024-01-03T17:00:48Z"},{"language":[{"iso":"eng"}],"citation":{"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.","short":"K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).","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} }","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.","ama":"Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. Combinatorial Theory. 2023;3(1). doi: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"},"year":"2023","type":"journal_article","issue":"1","doi":"10.5070/c63160424","date_updated":"2024-01-08T14:39:20Z","_id":"50298","intvolume":" 3","status":"public","date_created":"2024-01-08T14:33:54Z","volume":3,"publication_status":"published","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"}],"publication":"Combinatorial Theory","department":[{"_id":"100"}],"user_id":"70420","title":"Packings and Steiner systems in polar spaces","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."}]},{"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","author":[{"last_name":"Schmidt","first_name":"Kai‐Uwe","full_name":"Schmidt, Kai‐Uwe"},{"last_name":"Weiß","id":"70420","first_name":"Charlene","full_name":"Weiß, Charlene"}],"publisher":"Wiley","publication":"Journal of Combinatorial Designs","volume":31,"status":"public","date_created":"2024-01-08T14:25:28Z","intvolume":" 31","_id":"50297","issue":"9","year":"2023","type":"journal_article","citation":{"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","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} }","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.","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."},"page":"422-431","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"}]},{"language":[{"iso":"eng"}],"citation":{"short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.","ieee":"C. Weiß, Linear programming bounds in classical association schemes. 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","bibtex":"@book{Weiß_2023, title={Linear programming bounds in classical association schemes}, DOI={10.17619/UNIPB/1-1672}, author={Weiß, Charlene}, year={2023} }","mla":"Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes. 2023, doi:10.17619/UNIPB/1-1672."},"type":"dissertation","year":"2023","doi":"10.17619/UNIPB/1-1672","_id":"50300","date_updated":"2024-01-08T14:46:14Z","status":"public","date_created":"2024-01-08T14:42:12Z","author":[{"last_name":"Weiß","id":"70420","first_name":"Charlene","full_name":"Weiß, Charlene"}],"department":[{"_id":"100"}],"user_id":"70420","title":"Linear programming bounds in classical association schemes","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"}]},{"_id":"50299","date_updated":"2024-01-08T14:41:18Z","language":[{"iso":"eng"}],"year":"2023","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.).","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” ArXiv:2311.08288.","bibtex":"@article{Weiß, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, journal={arXiv:2311.08288}, author={Weiß, Charlene} }","ama":"Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. arXiv:231108288.","apa":"Weiß, C. (n.d.). Nontrivial $t$-designs in polar spaces exist for all $t$. In arXiv:2311.08288.","chicago":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” ArXiv:2311.08288, n.d."},"type":"preprint","external_id":{"arxiv":["2311.08288"]},"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."}],"user_id":"70420","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","author":[{"full_name":"Weiß, Charlene","first_name":"Charlene","id":"70420","last_name":"Weiß"}],"department":[{"_id":"100"}],"publication":"arXiv:2311.08288","status":"public","date_created":"2024-01-08T14:39:54Z","publication_status":"submitted"}]