[{"citation":{"ieee":"J. Jakob, “Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen.” 2023.","apa":"Jakob, J. (2023). <i>Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen</i>.","short":"J. Jakob, (2023).","chicago":"Jakob, Johanna. “Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen,” 2023.","mla":"Jakob, Johanna. <i>Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen</i>. 2023.","bibtex":"@article{Jakob_2023, title={Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen}, author={Jakob, Johanna}, year={2023} }","ama":"Jakob J. Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen. Published online 2023."},"date_created":"2024-08-09T09:15:06Z","external_id":{"arxiv":["2307.03473"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"preprint","author":[{"full_name":"Jakob, Johanna","first_name":"Johanna","last_name":"Jakob"}],"status":"public","year":"2023","title":"Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen","date_updated":"2024-08-09T09:27:43Z","language":[{"iso":"eng"}],"_id":"55575","user_id":"178"},{"external_id":{"arxiv":["2302.08232 "]},"oa":"1","citation":{"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. <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>","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={<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>}, 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.” <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen &#38; F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp. 569–579). Springer, Cham. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in <i>Geometric Science of Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>."},"file_date_updated":"2023-08-02T12:04:17Z","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"quality_controlled":"1","publisher":"Springer, Cham.","_id":"42163","page":"569-579","volume":14071,"editor":[{"full_name":"Nielsen, F","first_name":"F","last_name":"Nielsen"},{"full_name":"Barbaresco, F","last_name":"Barbaresco","first_name":"F"}],"user_id":"85279","ddc":["510"],"conference":{"name":"  GSI'23 6th International Conference on Geometric Science of Information","start_date":"2023-08-30","location":"Saint-Malo, Palais du Grand Large, France","end_date":"2023-09-01"},"status":"public","has_accepted_license":"1","date_created":"2023-02-16T11:32:48Z","file":[{"creator":"coffen","date_created":"2023-08-02T12:04:17Z","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.","file_size":1938962,"access_level":"open_access","file_name":"LDensityLearning.pdf","date_updated":"2023-08-02T12:04:17Z","relation":"main_file","content_type":"application/pdf","file_id":"46273","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves"}],"department":[{"_id":"636"}],"keyword":["System identification","discrete Lagrangians","travelling waves"],"type":"conference","publication":"Geometric Science of Information","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML","description":"GitHub"}]},"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."}],"language":[{"iso":"eng"}],"series_title":"Lecture Notes in Computer Science (LNCS)","doi":"10.1007/978-3-031-38271-0_57","publication_identifier":{"eisbn":["978-3-031-38271-0"]},"author":[{"id":"85279","last_name":"Offen","first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"year":"2023","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","intvolume":"     14071","publication_status":"published","date_updated":"2024-08-12T13:46:29Z"},{"editor":[{"first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"},{"first_name":"Michael","last_name":"Liebendörfer","full_name":"Liebendörfer, Michael"},{"first_name":"Ghislaine","last_name":"Gueudet","full_name":"Gueudet, Ghislaine"},{"full_name":"Rasmussen, Chris","last_name":"Rasmussen","first_name":"Chris"},{"last_name":"Winsløw","first_name":"Carl","full_name":"Winsløw, Carl"}],"doi":"10.1007/978-3-031-14175-1","user_id":"30933","publisher":"Springer International Publishing","_id":"37469","date_updated":"2023-01-18T22:47:41Z","publication_status":"published","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"year":"2023","status":"public","title":"Practice-Oriented Research in Tertiary Mathematics Education","department":[{"_id":"10"}],"type":"book_editor","place":"Cham","date_created":"2023-01-18T22:17:58Z","citation":{"bibtex":"@book{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>}, publisher={Springer International Publishing}, year={2023} }","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing; 2023. doi:<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>","mla":"Biehler, Rolf, et al., editors. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing, 2023, doi:<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>.","short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-14175-1\">https://doi.org/10.1007/978-3-031-14175-1</a>.","ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Cham: Springer International Publishing, 2023.","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., &#38; Winsløw, C. (Eds.). (2023). <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-14175-1\">https://doi.org/10.1007/978-3-031-14175-1</a>"}},{"citation":{"bibtex":"@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}, volume={75}, DOI={<a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>}, number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }","ama":"Hanusch M. A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. <i>Canadian Journal of Mathematics</i>. 2023;75(1):170-201. doi:<a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>","mla":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, Canadian Mathematical Society, 2023, pp. 170–201, doi:<a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>.","short":"M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.","chicago":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” <i>Canadian Journal of Mathematics</i> 75, no. 1 (2023): 170–201. <a href=\"https://doi.org/10.4153/s0008414x21000596\">https://doi.org/10.4153/s0008414x21000596</a>.","ieee":"M. Hanusch, “A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus,” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, pp. 170–201, 2023, doi: <a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>.","apa":"Hanusch, M. (2023). A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. <i>Canadian Journal of Mathematics</i>, <i>75</i>(1), 170–201. <a href=\"https://doi.org/10.4153/s0008414x21000596\">https://doi.org/10.4153/s0008414x21000596</a>"},"project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"status":"public","page":"170-201","_id":"34814","publisher":"Canadian Mathematical Society","user_id":"30905","volume":75,"issue":"1","publication":"Canadian Journal of Mathematics","date_created":"2022-12-22T09:16:48Z","keyword":["extension of differentiable maps"],"type":"journal_article","department":[{"_id":"93"}],"year":"2023","title":"A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus","author":[{"full_name":"Hanusch, Maximilian","last_name":"Hanusch","first_name":"Maximilian","id":"30905"}],"publication_identifier":{"issn":["0008-414X","1496-4279"]},"publication_status":"published","date_updated":"2023-02-22T11:38:32Z","article_type":"original","intvolume":"        75","language":[{"iso":"eng"}],"doi":"10.4153/s0008414x21000596"},{"oa":"1","citation":{"short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” <i>Journal of Global Optimization</i> 85, no. 3 (2023): 709–41. <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">https://doi.org/10.1007/s10898-022-01223-2</a>.","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” <i>Journal of Global Optimization</i>, vol. 85, no. 3, pp. 709–741, 2023, doi: <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>.","apa":"Gebken, B., Bieker, K., &#38; Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. <i>Journal of Global Optimization</i>, <i>85</i>(3), 709–741. <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">https://doi.org/10.1007/s10898-022-01223-2</a>","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. <i>Journal of Global Optimization</i>. 2023;85(3):709-741. doi:<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” <i>Journal of Global Optimization</i>, vol. 85, no. 3, 2023, pp. 709–41, doi:<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>."},"_id":"27426","page":"709-741","volume":85,"user_id":"47427","status":"public","date_created":"2021-11-15T09:24:59Z","department":[{"_id":"101"},{"_id":"655"}],"type":"journal_article","publication":"Journal of Global Optimization","issue":"3","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."}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"doi":"10.1007/s10898-022-01223-2","author":[{"last_name":"Gebken","first_name":"Bennet","full_name":"Gebken, Bennet","id":"32643"},{"last_name":"Bieker","first_name":"Katharina","full_name":"Bieker, Katharina","id":"32829"},{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian","full_name":"Peitz, Sebastian"}],"year":"2023","title":"On the structure of regularization paths for piecewise differentiable regularization terms","intvolume":"        85","date_updated":"2023-03-11T17:16:33Z"},{"keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"type":"conference","department":[{"_id":"97"}],"file":[{"success":1,"content_type":"application/pdf","file_id":"43096","date_updated":"2023-03-25T10:01:03Z","relation":"main_file","file_size":201942,"access_level":"closed","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","date_created":"2023-03-25T10:01:03Z","creator":"maxh"}],"date_created":"2022-06-12T11:07:34Z","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-03-25T10:11:35Z","year":"2023","title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","author":[{"id":"32202","orcid":"0000-0002-6964-7123","last_name":"Hoffmann","first_name":"Max","full_name":"Hoffmann, Max"},{"id":"16274","last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"}],"oa":"1","place":"Hannover","quality_controlled":"1","file_date_updated":"2023-03-25T10:01:03Z","citation":{"mla":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros et al., University of Hannover and INDRUM., 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. <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>. 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} }","apa":"Hoffmann, M., &#38; Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth, &#38; J. Peters (Eds.), <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>. University of Hannover and INDRUM.","ieee":"M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry,” in <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, 2023.","short":"M. Hoffmann, R. Biehler, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), University of Hannover and INDRUM., Hannover, 2023.","chicago":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” In <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023."},"user_id":"32202","ddc":["370","510"],"editor":[{"full_name":"Trigueros, Marı́a","first_name":"Marı́a","last_name":"Trigueros"},{"full_name":"Barquero, Berta","first_name":"Berta","last_name":"Barquero"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"full_name":"Peters, Jana","last_name":"Peters","first_name":"Jana"}],"publisher":"University of Hannover and INDRUM.","_id":"31849","has_accepted_license":"1","status":"public"},{"oa":"1","place":"Hannover","quality_controlled":"1","citation":{"ama":"Florensa I, Hoffmann M, Romo Vázquez A, Zandieh M, Martínez-Planell R. Innovations in university teaching based on mathematic education research. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>. ; 2023.","bibtex":"@inproceedings{Florensa_Hoffmann_Romo Vázquez_Zandieh_Martínez-Planell_2023, place={Hannover}, title={Innovations in university teaching based on mathematic education research}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, author={Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde and Zandieh, Michelle and Martínez-Planell, Rafael}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","mla":"Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic Education Research.” <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros et al., 2023.","short":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, R. Martínez-Planell, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), Hannover, 2023.","chicago":"Florensa, Ignasio, Max Hoffmann, Avenilde Romo Vázquez, Michelle Zandieh, and Rafael Martínez-Planell. “Innovations in University Teaching Based on Mathematic Education Research.” In <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover, 2023.","apa":"Florensa, I., Hoffmann, M., Romo Vázquez, A., Zandieh, M., &#38; Martínez-Planell, R. (2023). Innovations in university teaching based on mathematic education research. In M. Trigueros, B. Barquero, R. Hochmuth, &#38; J. Peters (Eds.), <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>.","ieee":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, and R. Martínez-Planell, “Innovations in university teaching based on mathematic education research,” in <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, 2023."},"file_date_updated":"2023-03-25T10:07:54Z","editor":[{"full_name":"Trigueros, Marı́a","first_name":"Marı́a","last_name":"Trigueros"},{"full_name":"Barquero, Berta","last_name":"Barquero","first_name":"Berta"},{"full_name":"Hochmuth, Reinhard","last_name":"Hochmuth","first_name":"Reinhard"},{"full_name":"Peters, Jana","last_name":"Peters","first_name":"Jana"}],"ddc":["370","510"],"user_id":"32202","_id":"43097","has_accepted_license":"1","status":"public","department":[{"_id":"97"}],"type":"conference","date_created":"2023-03-25T10:09:06Z","file":[{"content_type":"application/pdf","success":1,"file_id":"43098","access_level":"closed","file_size":642388,"file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","date_updated":"2023-03-25T10:07:54Z","relation":"main_file","date_created":"2023-03-25T10:07:54Z","creator":"maxh"}],"publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}],"date_updated":"2023-03-25T10:10:58Z","author":[{"last_name":"Florensa","first_name":"Ignasio","full_name":"Florensa, Ignasio"},{"full_name":"Hoffmann, Max","last_name":"Hoffmann","first_name":"Max","orcid":"0000-0002-6964-7123","id":"32202"},{"full_name":"Romo Vázquez, Avenilde","first_name":"Avenilde","last_name":"Romo Vázquez"},{"last_name":"Zandieh","first_name":"Michelle","full_name":"Zandieh, Michelle"},{"full_name":"Martínez-Planell, Rafael","last_name":"Martínez-Planell","first_name":"Rafael"}],"title":"Innovations in university teaching based on mathematic education research","year":"2023"},{"citation":{"mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, 103868, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>}, 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} }","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>. 2023;73. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, Art. no. 103868, 2023, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","apa":"Black, T., Fuest, M., Lankeit, J., &#38; Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>, <i>73</i>, Article 103868. <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i> 73 (2023). <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>.","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023)."},"publisher":"Elsevier BV","_id":"43105","user_id":"23686","volume":73,"status":"public","date_created":"2023-03-27T07:25:58Z","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Nonlinear Analysis: Real World Applications","article_number":"103868","language":[{"iso":"eng"}],"doi":"10.1016/j.nonrwa.2023.103868","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","year":"2023","publication_identifier":{"issn":["1468-1218"]},"author":[{"full_name":"Black, Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias","id":"23686"},{"full_name":"Fuest, Mario","first_name":"Mario","last_name":"Fuest"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"},{"last_name":"Mizukami","first_name":"Masaaki","full_name":"Mizukami, Masaaki"}],"publication_status":"published","date_updated":"2023-03-27T07:27:03Z","intvolume":"        73"},{"user_id":"44184","doi":"https://doi.org/10.18716/ojs/md/2023.1671","language":[{"iso":"eng"}],"_id":"43227","date_updated":"2023-03-30T10:06:53Z","author":[{"full_name":"Vitt, Vivian","last_name":"Vitt","first_name":"Vivian"},{"first_name":"Uta","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","id":"60267"}],"title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","status":"public","year":"2023","department":[{"_id":"543"}],"type":"book_chapter","date_created":"2023-03-30T10:06:24Z","citation":{"chicago":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In <i>Mathematica Didactica, 46</i>, 2023. <a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>.","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 <i>Mathematica Didactica, 46</i>, 2023.","apa":"Vitt, V., &#38; Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In <i>Mathematica Didactica, 46</i>. <a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>","bibtex":"@inbook{Vitt_Häsel-Weide_2023, title={Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}, DOI={<a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>}, booktitle={Mathematica Didactica, 46}, author={Vitt, Vivian and Häsel-Weide, Uta}, year={2023} }","ama":"Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In: <i>Mathematica Didactica, 46</i>. ; 2023. doi:<a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>","mla":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” <i>Mathematica Didactica, 46</i>, 2023, doi:<a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>."},"publication":"Mathematica Didactica, 46"},{"project":[{"_id":"161","name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)"}],"citation":{"chicago":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” <i>Annals of Global Analysis and Geometry</i> 63, no. 21 (2023). <a href=\"https://doi.org/10.1007/s10455-023-09888-y\">https://doi.org/10.1007/s10455-023-09888-y</a>.","short":"M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).","apa":"Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. <i>Annals of Global Analysis and Geometry</i>, <i>63</i>(21). <a href=\"https://doi.org/10.1007/s10455-023-09888-y\">https://doi.org/10.1007/s10455-023-09888-y</a>","ieee":"M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups,” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 21, 2023, doi: <a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>.","ama":"Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. <i>Annals of Global Analysis and Geometry</i>. 2023;63(21). doi:<a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>","bibtex":"@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>}, number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch, Maximilian}, year={2023} }","mla":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 21, 2023, doi:<a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>."},"publication":"Annals of Global Analysis and Geometry","issue":"21","department":[{"_id":"93"}],"keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"type":"journal_article","date_created":"2022-12-22T09:45:34Z","intvolume":"        63","date_updated":"2023-04-05T18:18:24Z","publication_status":"published","author":[{"first_name":"Maximilian","last_name":"Hanusch","full_name":"Hanusch, Maximilian","id":"30905"}],"title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups","status":"public","year":"2023","volume":63,"doi":"10.1007/s10455-023-09888-y","user_id":"30905","language":[{"iso":"eng"}],"_id":"34832"},{"citation":{"mla":"Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” <i>RAIRO - Operations Research</i>, vol. 57, no. 3, EDP Sciences, 2023, pp. 1045–58, doi:<a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>.","ama":"Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. <i>RAIRO - Operations Research</i>. 2023;57(3):1045-1058. doi:<a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>","bibtex":"@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms for the genome median under a restricted measure of rearrangement}, volume={57}, DOI={<a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>}, number={3}, journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }","apa":"Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., &#38; Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. <i>RAIRO - Operations Research</i>, <i>57</i>(3), 1045–1058. <a href=\"https://doi.org/10.1051/ro/2023052\">https://doi.org/10.1051/ro/2023052</a>","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,” <i>RAIRO - Operations Research</i>, vol. 57, no. 3, pp. 1045–1058, 2023, doi: <a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>.","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.” <i>RAIRO - Operations Research</i> 57, no. 3 (2023): 1045–58. <a href=\"https://doi.org/10.1051/ro/2023052\">https://doi.org/10.1051/ro/2023052</a>.","short":"H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058."},"status":"public","page":"1045-1058","_id":"44857","publisher":"EDP Sciences","user_id":"15540","volume":57,"publication":"RAIRO - Operations Research","issue":"3","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_created":"2023-05-16T08:48:22Z","keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"type":"journal_article","department":[{"_id":"542"}],"year":"2023","title":"Algorithms for the genome median under a restricted measure of rearrangement","author":[{"last_name":"Silva","first_name":"Helmuth O.M.","full_name":"Silva, Helmuth O.M."},{"last_name":"Rubert","first_name":"Diego P.","full_name":"Rubert, Diego P."},{"full_name":"Araujo, Eloi","first_name":"Eloi","last_name":"Araujo"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"first_name":"Daniel","last_name":"Doerr","full_name":"Doerr, Daniel"},{"full_name":"Martinez, Fábio V.","first_name":"Fábio V.","last_name":"Martinez"}],"publication_identifier":{"issn":["0399-0559","2804-7303"]},"date_updated":"2023-05-16T08:49:30Z","publication_status":"published","intvolume":"        57","language":[{"iso":"eng"}],"doi":"10.1051/ro/2023052"},{"citation":{"mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs. <i>arXiv:230508619</i>. Published online 2023.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In <i>arXiv:2305.08619</i>.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” <i>arXiv:2305.08619</i>. 2023.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023."},"publication":"arXiv:2305.08619","date_created":"2023-05-16T10:07:47Z","external_id":{"arxiv":["2305.08619"]},"department":[{"_id":"542"}],"type":"preprint","author":[{"id":"92748","full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen"},{"id":"88145","last_name":"Wolf","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus"}],"status":"public","title":"Sets of r-graphs that color all r-graphs","year":"2023","date_updated":"2023-05-16T11:17:26Z","_id":"44859","language":[{"iso":"eng"}],"user_id":"15540"},{"keyword":["Lie group actions and analytic 1-submanifolds"],"type":"journal_article","department":[{"_id":"93"}],"date_created":"2022-12-22T09:46:36Z","publication":"Indagationes Mathematicae.","issue":"4","citation":{"mla":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes Mathematicae.</i>, vol. 34, no. 4, 2023, pp. 752–811, doi:<a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>.","ama":"Hanusch M. Decompositions of Analytic 1-Manifolds. <i>Indagationes Mathematicae</i>. 2023;34(4):752-811. doi:<a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>","bibtex":"@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds}, volume={34}, DOI={<a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>}, number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian}, year={2023}, pages={752–811} }","apa":"Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. <i>Indagationes Mathematicae.</i>, <i>34</i>(4), 752–811. <a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">https://doi.org/10.1016/j.indag.2023.02.003</a>","ieee":"M. Hanusch, “Decompositions of Analytic 1-Manifolds,” <i>Indagationes Mathematicae.</i>, vol. 34, no. 4, pp. 752–811, 2023, doi: <a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>.","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.","chicago":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes Mathematicae.</i> 34, no. 4 (2023): 752–811. <a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">https://doi.org/10.1016/j.indag.2023.02.003</a>."},"user_id":"30905","doi":"10.1016/j.indag.2023.02.003","volume":34,"page":"752-811","language":[{"iso":"eng"}],"_id":"34833","publication_status":"published","date_updated":"2023-05-25T07:32:38Z","intvolume":"        34","year":"2023","title":"Decompositions of Analytic 1-Manifolds","status":"public","author":[{"id":"30905","full_name":"Hanusch, Maximilian","last_name":"Hanusch","first_name":"Maximilian"}]},{"user_id":"97359","language":[{"iso":"eng"}],"_id":"45498","main_file_link":[{"url":"https://arxiv.org/pdf/2306.03320"}],"page":"29","date_updated":"2023-06-07T07:59:06Z","publication_status":"submitted","author":[{"full_name":"von der Gracht, Sören","last_name":"von der Gracht","first_name":"Sören","orcid":"0000-0002-8054-2058","id":"97359"},{"last_name":"Nijholt","first_name":"Eddie","full_name":"Nijholt, Eddie"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"}],"status":"public","year":"2023","title":"A parametrisation method for high-order phase reduction in coupled  oscillator networks","department":[{"_id":"101"}],"type":"preprint","date_created":"2023-06-07T07:57:28Z","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."}],"citation":{"ama":"von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order phase reduction in coupled  oscillator networks. <i>arXiv:230603320</i>.","bibtex":"@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for high-order phase reduction in coupled  oscillator networks}, journal={arXiv:2306.03320}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }","mla":"von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled  Oscillator Networks.” <i>ArXiv:2306.03320</i>.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation Method for High-Order Phase Reduction in Coupled  Oscillator Networks.” <i>ArXiv:2306.03320</i>, n.d.","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (n.d.). A parametrisation method for high-order phase reduction in coupled  oscillator networks. In <i>arXiv:2306.03320</i>.","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for high-order phase reduction in coupled  oscillator networks,” <i>arXiv:2306.03320</i>. ."},"publication":"arXiv:2306.03320"},{"date_updated":"2023-06-22T09:34:13Z","year":"2023","status":"public","title":" Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen","author":[{"id":"60267","full_name":"Häsel-Weide, Uta","first_name":"Uta","last_name":"Häsel-Weide"}],"user_id":"44184","page":"6-11","_id":"45712","publisher":"Friedrich Verlag","language":[{"iso":"ger"}],"related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"publication":"Die Grundschulzeitschrift","issue":"339","citation":{"ieee":"U. Häsel-Weide, “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen,” <i>Die Grundschulzeitschrift</i>, no. 339, pp. 6–11, 2023.","apa":"Häsel-Weide, U. (2023).  Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. <i>Die Grundschulzeitschrift</i>, <i>339</i>, 6–11.","short":"U. Häsel-Weide, Die Grundschulzeitschrift (2023) 6–11.","chicago":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” <i>Die Grundschulzeitschrift</i>, no. 339 (2023): 6–11.","mla":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” <i>Die Grundschulzeitschrift</i>, 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} }","ama":"Häsel-Weide U.  Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. <i>Die Grundschulzeitschrift</i>. 2023;(339):6-11."},"type":"journal_article","department":[{"_id":"543"}],"date_created":"2023-06-22T09:28:22Z"},{"related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"issue":"339","publication":"Die Grundschulzeitschrift","citation":{"chicago":"Graf, Lara Marie, Inga Wienhues, and Uta Häsel-Weide. “Addition und Subtraktion verstehen.” <i>Die Grundschulzeitschrift</i>, no. 339 (2023): 20–23.","short":"L.M. Graf, I. Wienhues, U. Häsel-Weide, Die Grundschulzeitschrift (2023) 20–23.","apa":"Graf, L. M., Wienhues, I., &#38; Häsel-Weide, U. (2023). Addition und Subtraktion verstehen. <i>Die Grundschulzeitschrift</i>, <i>339</i>, 20–23.","ieee":"L. M. Graf, I. Wienhues, and U. Häsel-Weide, “Addition und Subtraktion verstehen,” <i>Die Grundschulzeitschrift</i>, no. 339, pp. 20–23, 2023.","ama":"Graf LM, Wienhues I, Häsel-Weide U. Addition und Subtraktion verstehen. <i>Die Grundschulzeitschrift</i>. 2023;(339):20-23.","bibtex":"@article{Graf_Wienhues_Häsel-Weide_2023, title={Addition und Subtraktion verstehen}, number={339}, journal={Die Grundschulzeitschrift}, publisher={Friedrich Verlag}, author={Graf, Lara Marie and Wienhues, Inga and Häsel-Weide, Uta}, year={2023}, pages={20–23} }","mla":"Graf, Lara Marie, et al. “Addition und Subtraktion verstehen.” <i>Die Grundschulzeitschrift</i>, no. 339, Friedrich Verlag, 2023, pp. 20–23."},"type":"journal_article","department":[{"_id":"543"}],"date_created":"2023-06-22T09:33:59Z","date_updated":"2023-06-22T09:34:18Z","year":"2023","status":"public","title":"Addition und Subtraktion verstehen","author":[{"full_name":"Graf, Lara Marie","last_name":"Graf","first_name":"Lara Marie","id":"89837"},{"id":"61635","first_name":"Inga","last_name":"Wienhues","full_name":"Wienhues, Inga"},{"full_name":"Häsel-Weide, Uta","first_name":"Uta","last_name":"Häsel-Weide","id":"60267"}],"user_id":"44184","page":"20-23","_id":"45713","publisher":"Friedrich Verlag","language":[{"iso":"ger"}]},{"date_updated":"2023-07-24T07:53:29Z","author":[{"full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich"},{"first_name":"Lasse L.","last_name":"Wolf","full_name":"Wolf, Lasse L."}],"year":"2023","status":"public","title":"Temperedness of locally symmetric spaces: The product case","user_id":"45027","language":[{"iso":"eng"}],"_id":"46117","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"}],"citation":{"apa":"Weich, T., &#38; Wolf, L. L. (2023). Temperedness of locally symmetric spaces: The product case. In <i>arXiv:2304.09573</i>.","ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” <i>arXiv:2304.09573</i>. 2023.","short":"T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023).","chicago":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>ArXiv:2304.09573</i>, 2023.","mla":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>ArXiv:2304.09573</i>, 2023.","ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. <i>arXiv:230409573</i>. Published online 2023.","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} }"},"publication":"arXiv:2304.09573","department":[{"_id":"10"}],"type":"preprint","date_created":"2023-07-24T07:52:23Z","external_id":{"arxiv":["2304.09573"]}},{"citation":{"ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3, pp. 1548–1565, 2023, doi: <a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>.","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>, <i>37</i>(3), 1548–1565. <a href=\"https://doi.org/10.1137/22m1500654\">https://doi.org/10.1137/22m1500654</a>","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i> 37, no. 3 (2023): 1548–65. <a href=\"https://doi.org/10.1137/22m1500654\">https://doi.org/10.1137/22m1500654</a>.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565.","mla":"Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>. 2023;37(3):1548-1565. doi:<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>"},"volume":37,"user_id":"15540","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"46256","page":"1548-1565","status":"public","department":[{"_id":"542"}],"type":"journal_article","keyword":["General Mathematics"],"date_created":"2023-08-01T10:08:32Z","issue":"3","publication":"SIAM Journal on Discrete Mathematics","doi":"10.1137/22m1500654","language":[{"iso":"eng"}],"intvolume":"        37","publication_status":"published","date_updated":"2023-08-01T10:09:35Z","author":[{"full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai","id":"92748"},{"full_name":"Mattiolo, Davide","first_name":"Davide","last_name":"Mattiolo"},{"last_name":"Steffen","orcid":"0000-0002-9808-7401","first_name":"Eckhard","full_name":"Steffen, Eckhard","id":"15548"},{"id":"88145","last_name":"Wolf","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus"}],"publication_identifier":{"issn":["0895-4801","1095-7146"]},"year":"2023","title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs"},{"volume":421,"user_id":"85279","ddc":["510"],"publisher":"Elsevier","_id":"29240","page":"114780","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["2112.12619"]},"quality_controlled":"1","citation":{"short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i> 421 (2023): 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>.","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, p. 114780, 2023, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","apa":"Ober-Blöbaum, S., &#38; Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>, <i>421</i>, 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>","bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>. 2023;421:114780. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, Elsevier, 2023, p. 114780, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>."},"file_date_updated":"2022-06-28T15:25:50Z","doi":"10.1016/j.cam.2022.114780","language":[{"iso":"eng"}],"article_type":"original","intvolume":"       421","publication_status":"epub_ahead","date_updated":"2023-08-10T08:42:39Z","publication_identifier":{"issn":["0377-0427"]},"author":[{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"}],"title":"Variational Learning of Euler–Lagrange Dynamics from Data","year":"2023","department":[{"_id":"636"}],"type":"journal_article","keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"date_created":"2022-01-11T13:24:00Z","file":[{"creator":"coffen","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.","date_created":"2022-06-28T15:25:50Z","relation":"main_file","date_updated":"2022-06-28T15:25:50Z","file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","access_level":"open_access","file_size":3640770,"title":"Variational Learning of Euler–Lagrange Dynamics from Data","file_id":"32274","content_type":"application/pdf"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianShadowIntegration","relation":"software"}]},"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."}],"publication":"Journal of Computational and Applied Mathematics"},{"doi":"10.3934/jgm.2023005","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-08-10T08:40:30Z","article_type":"original","intvolume":"        15","title":"Backward error analysis for conjugate symplectic methods","year":"2023","author":[{"full_name":"McLachlan, Robert","last_name":"McLachlan","first_name":"Robert"},{"full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279"}],"keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"type":"journal_article","department":[{"_id":"636"}],"file":[{"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.","date_created":"2022-08-12T16:48:59Z","creator":"coffen","title":"Backward error analysis for conjugate symplectic methods","content_type":"application/pdf","file_id":"32801","date_updated":"2022-08-12T16:48:59Z","relation":"main_file","access_level":"open_access","file_size":827030,"file_name":"BEA_MultiStep_Matrix.pdf"}],"date_created":"2022-01-11T12:48:39Z","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"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/BEAConjugateSymplectic"}]},"issue":"1","publication":"Journal of Geometric Mechanics","user_id":"85279","ddc":["510"],"volume":15,"page":"98-115","publisher":"AIMS Press","_id":"29236","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["2201.03911"]},"quality_controlled":"1","file_date_updated":"2022-08-12T16:48:59Z","citation":{"mla":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>. 2023;15(1):98-115. doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>","bibtex":"@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }","apa":"McLachlan, R., &#38; Offen, C. (2023). Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>, <i>15</i>(1), 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>","ieee":"R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, pp. 98–115, 2023, doi: <a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","short":"R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.","chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i> 15, no. 1 (2023): 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>."}}]