[{"status":"public","type":"journal_article","publication":"Math. Ann.","extern":"1","language":[{"iso":"eng"}],"_id":"55279","user_id":"106108","department":[{"_id":"102"}],"year":"2023","citation":{"short":"P. Minelli, A. Sourmelidis, M. Technau, Math. Ann. 387 (2023) 291–320.","mla":"Minelli, P., et al. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i>, vol. 387, 2023, pp. 291–320, doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","bibtex":"@article{Minelli_Sourmelidis_Technau_2023, title={Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}, volume={387}, DOI={<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>}, journal={Math. Ann.}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc}, year={2023}, pages={291–320} }","apa":"Minelli, P., Sourmelidis, A., &#38; Technau, M. (2023). Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math. Ann.</i>, <i>387</i>, 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>","chicago":"Minelli, P., A. Sourmelidis, and Marc Technau. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i> 387 (2023): 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>.","ieee":"P. Minelli, A. Sourmelidis, and M. Technau, “Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums,” <i>Math. Ann.</i>, vol. 387, pp. 291–320, 2023, doi: <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","ama":"Minelli P, Sourmelidis A, Technau M. Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math Ann</i>. 2023;387:291–320. doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>"},"intvolume":"       387","page":"291–320","title":"Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums","doi":"10.1007/s00208-022-02452-2","date_updated":"2024-07-24T07:26:05Z","date_created":"2024-07-16T11:09:01Z","author":[{"last_name":"Minelli","full_name":"Minelli, P.","first_name":"P."},{"last_name":"Sourmelidis","full_name":"Sourmelidis, A.","first_name":"A."},{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"}],"volume":387},{"external_id":{"arxiv":["2207.11141"]},"_id":"34803","user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"article_number":"50","language":[{"iso":"eng"}],"type":"journal_article","publication":"BIT Numerical Mathematics","status":"public","publisher":"Springer","date_updated":"2024-08-09T08:48:06Z","author":[{"last_name":"Celledoni","full_name":"Celledoni, Elena","first_name":"Elena"},{"first_name":"Helge","last_name":"Glöckner","id":"178","full_name":"Glöckner, Helge"},{"first_name":"Jørgen","last_name":"Riseth","full_name":"Riseth, Jørgen"},{"first_name":"Alexander","full_name":"Schmeding, Alexander","last_name":"Schmeding"}],"date_created":"2022-12-22T07:37:20Z","volume":63,"title":"Deep neural networks on diffeomorphism groups for optimal shape reparametrization","doi":"10.1007/s10543-023-00989-05","quality_controlled":"1","year":"2023","citation":{"apa":"Celledoni, E., Glöckner, H., Riseth, J., &#38; Schmeding, A. (2023). Deep neural networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>, <i>63</i>, Article 50. <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">https://doi.org/10.1007/s10543-023-00989-05</a>","short":"E. Celledoni, H. Glöckner, J. Riseth, A. Schmeding, BIT Numerical Mathematics 63 (2023).","bibtex":"@article{Celledoni_Glöckner_Riseth_Schmeding_2023, title={Deep neural networks on diffeomorphism groups for optimal shape reparametrization}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>}, number={50}, journal={BIT Numerical Mathematics}, publisher={Springer}, author={Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}, year={2023} }","mla":"Celledoni, Elena, et al. “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.” <i>BIT Numerical Mathematics</i>, vol. 63, 50, Springer, 2023, doi:<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>.","ieee":"E. Celledoni, H. Glöckner, J. Riseth, and A. Schmeding, “Deep neural networks on diffeomorphism groups for optimal shape reparametrization,” <i>BIT Numerical Mathematics</i>, vol. 63, Art. no. 50, 2023, doi: <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>.","chicago":"Celledoni, Elena, Helge Glöckner, Jørgen Riseth, and Alexander Schmeding. “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.” <i>BIT Numerical Mathematics</i> 63 (2023). <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">https://doi.org/10.1007/s10543-023-00989-05</a>.","ama":"Celledoni E, Glöckner H, Riseth J, Schmeding A. Deep neural networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>. 2023;63. doi:<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>"},"intvolume":"        63"},{"page":"343-358","intvolume":"        30","citation":{"chicago":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i> 30, no. 1 (2023): 343–58.","ieee":"H. Glöckner, “Diffeomorphism groups of convex polytopes,” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, pp. 343–358, 2023.","ama":"Glöckner H. Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>. 2023;30(1):343-358.","bibtex":"@article{Glöckner_2023, title={Diffeomorphism groups of convex polytopes}, volume={30}, number={1}, journal={Journal of Convex Analysis}, publisher={Heldermann}, author={Glöckner, Helge}, year={2023}, pages={343–358} }","short":"H. Glöckner, Journal of Convex Analysis 30 (2023) 343–358.","mla":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, Heldermann, 2023, pp. 343–58.","apa":"Glöckner, H. (2023). Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>, <i>30</i>(1), 343–358."},"volume":30,"author":[{"last_name":"Glöckner","id":"178","full_name":"Glöckner, Helge","first_name":"Helge"}],"date_updated":"2024-08-09T08:49:17Z","status":"public","type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","_id":"34805","year":"2023","issue":"1","quality_controlled":"1","title":"Diffeomorphism groups of convex polytopes","date_created":"2022-12-22T07:45:13Z","publisher":"Heldermann","abstract":[{"text":"Let $E$ be a finite-dimensional real vector space and $M\\subseteq E$ be a\r\nconvex polytope with non-empty interior. We turn the group of all\r\n$C^\\infty$-diffeomorphisms of $M$ into a regular Lie group.","lang":"eng"}],"publication":"Journal of Convex Analysis","language":[{"iso":"eng"}],"external_id":{"arxiv":["2203.09285"]}},{"external_id":{"arxiv":["2210.01246"]},"_id":"34801","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","language":[{"iso":"eng"}],"publication":"Journal of Lie Theory","type":"journal_article","status":"public","date_updated":"2024-08-09T08:48:51Z","publisher":"Heldermann","volume":33,"date_created":"2022-12-22T07:23:57Z","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"},{"full_name":"Tárrega, Luis","last_name":"Tárrega","first_name":"Luis"}],"title":"Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ","quality_controlled":"1","issue":"1","year":"2023","page":"271-296","intvolume":"        33","citation":{"ama":"Glöckner H, Tárrega L. Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>. 2023;33(1):271-296.","ieee":"H. Glöckner and L. Tárrega, “Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ,” <i>Journal of Lie Theory</i>, vol. 33, no. 1, pp. 271–296, 2023.","chicago":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i> 33, no. 1 (2023): 271–96.","mla":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i>, vol. 33, no. 1, Heldermann, 2023, pp. 271–96.","bibtex":"@article{Glöckner_Tárrega_2023, title={Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }, volume={33}, number={1}, journal={Journal of Lie Theory}, publisher={Heldermann}, author={Glöckner, Helge and Tárrega, Luis}, year={2023}, pages={271–296} }","short":"H. Glöckner, L. Tárrega, Journal of Lie Theory 33 (2023) 271–296.","apa":"Glöckner, H., &#38; Tárrega, L. (2023). Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>, <i>33</i>(1), 271–296."}},{"citation":{"ieee":"J. Jakob, “Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen.” 2023.","chicago":"Jakob, Johanna. “Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen,” 2023.","ama":"Jakob J. Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen. Published online 2023.","mla":"Jakob, Johanna. <i>Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen</i>. 2023.","short":"J. Jakob, (2023).","bibtex":"@article{Jakob_2023, title={Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen}, author={Jakob, Johanna}, year={2023} }","apa":"Jakob, J. (2023). <i>Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen</i>."},"year":"2023","title":"Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen","date_created":"2024-08-09T09:15:06Z","author":[{"full_name":"Jakob, Johanna","last_name":"Jakob","first_name":"Johanna"}],"date_updated":"2024-08-09T09:27:43Z","status":"public","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","_id":"55575","external_id":{"arxiv":["2307.03473"]}},{"file_date_updated":"2023-08-02T12:04:17Z","_id":"42163","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"department":[{"_id":"636"}],"user_id":"85279","series_title":"Lecture Notes in Computer Science (LNCS)","editor":[{"first_name":"F","last_name":"Nielsen","full_name":"Nielsen, F"},{"first_name":"F","last_name":"Barbaresco","full_name":"Barbaresco, F"}],"status":"public","type":"conference","conference":{"location":"Saint-Malo, Palais du Grand Large, France","end_date":"2023-09-01","start_date":"2023-08-30","name":"  GSI'23 6th International Conference on Geometric Science of Information"},"doi":"10.1007/978-3-031-38271-0_57","date_updated":"2024-08-12T13:46:29Z","oa":"1","volume":14071,"author":[{"last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279","first_name":"Christian"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"}],"intvolume":"     14071","page":"569-579","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>","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>.","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>.","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>.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","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)} }","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>"},"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"has_accepted_license":"1","publication_status":"published","related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/Christian-Offen/LagrangianDensityML"}]},"keyword":["System identification","discrete Lagrangians","travelling waves"],"ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2302.08232 "]},"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."}],"file":[{"relation":"main_file","content_type":"application/pdf","file_id":"46273","access_level":"open_access","file_name":"LDensityLearning.pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","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,"creator":"coffen","date_created":"2023-08-02T12:04:17Z","date_updated":"2023-08-02T12:04:17Z"}],"publication":"Geometric Science of Information","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","publisher":"Springer, Cham.","date_created":"2023-02-16T11:32:48Z","year":"2023","quality_controlled":"1"},{"department":[{"_id":"10"}],"user_id":"30933","_id":"37469","type":"book_editor","status":"public","editor":[{"first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"},{"last_name":"Liebendörfer","full_name":"Liebendörfer, Michael","first_name":"Michael"},{"first_name":"Ghislaine","last_name":"Gueudet","full_name":"Gueudet, Ghislaine"},{"last_name":"Rasmussen","full_name":"Rasmussen, Chris","first_name":"Chris"},{"first_name":"Carl","full_name":"Winsløw, Carl","last_name":"Winsløw"}],"date_created":"2023-01-18T22:17:58Z","date_updated":"2023-01-18T22:47:41Z","publisher":"Springer International Publishing","doi":"10.1007/978-3-031-14175-1","title":"Practice-Oriented Research in Tertiary Mathematics Education","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"publication_status":"published","citation":{"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.","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>.","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} }","short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 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>"},"place":"Cham","year":"2023"},{"language":[{"iso":"eng"}],"article_type":"original","keyword":["extension of differentiable maps"],"user_id":"30905","department":[{"_id":"93"}],"project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"_id":"34814","status":"public","type":"journal_article","publication":"Canadian Journal of Mathematics","doi":"10.4153/s0008414x21000596","title":"A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus","author":[{"last_name":"Hanusch","id":"30905","full_name":"Hanusch, Maximilian","first_name":"Maximilian"}],"date_created":"2022-12-22T09:16:48Z","volume":75,"date_updated":"2023-02-22T11:38:32Z","publisher":"Canadian Mathematical Society","citation":{"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>.","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>","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} }","short":"M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.","mla":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” <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>.","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>"},"page":"170-201","intvolume":"        75","year":"2023","issue":"1","publication_status":"published","publication_identifier":{"issn":["0008-414X","1496-4279"]}},{"department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","_id":"27426","language":[{"iso":"eng"}],"publication":"Journal of Global Optimization","type":"journal_article","status":"public","abstract":[{"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.","lang":"eng"}],"volume":85,"author":[{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"id":"32829","full_name":"Bieker, Katharina","last_name":"Bieker","first_name":"Katharina"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427"}],"date_created":"2021-11-15T09:24:59Z","date_updated":"2023-03-11T17:16:33Z","oa":"1","doi":"10.1007/s10898-022-01223-2","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms","issue":"3","page":"709-741","intvolume":"        85","citation":{"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>","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} }","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>.","short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741."},"year":"2023"},{"file_date_updated":"2023-03-25T10:01:03Z","_id":"31849","user_id":"32202","department":[{"_id":"97"}],"editor":[{"first_name":"Marı́a","last_name":"Trigueros","full_name":"Trigueros, Marı́a"},{"first_name":"Berta","full_name":"Barquero, Berta","last_name":"Barquero"},{"first_name":"Reinhard","full_name":"Hochmuth, Reinhard","last_name":"Hochmuth"},{"last_name":"Peters","full_name":"Peters, Jana","first_name":"Jana"}],"status":"public","type":"conference","main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}],"date_updated":"2023-03-25T10:11:35Z","oa":"1","author":[{"full_name":"Hoffmann, Max","id":"32202","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","first_name":"Max"},{"first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf","id":"16274"}],"place":"Hannover","citation":{"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.","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.","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.","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} }","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.","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.","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."},"publication_status":"published","has_accepted_license":"1","ddc":["370","510"],"keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2023-03-25T10:01:03Z","creator":"maxh","date_created":"2023-03-25T10:01:03Z","file_size":201942,"access_level":"closed","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","file_id":"43096"}],"publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","publisher":"University of Hannover and INDRUM.","date_created":"2022-06-12T11:07:34Z","year":"2023","quality_controlled":"1"},{"title":"Innovations in university teaching based on mathematic education research","date_created":"2023-03-25T10:09:06Z","year":"2023","quality_controlled":"1","ddc":["370","510"],"language":[{"iso":"eng"}],"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","file_id":"43098","access_level":"closed","file_size":642388,"creator":"maxh","date_created":"2023-03-25T10:07:54Z","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)","main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"date_updated":"2023-03-25T10:10:58Z","oa":"1","author":[{"first_name":"Ignasio","last_name":"Florensa","full_name":"Florensa, Ignasio"},{"first_name":"Max","orcid":"0000-0002-6964-7123","last_name":"Hoffmann","full_name":"Hoffmann, Max","id":"32202"},{"full_name":"Romo Vázquez, Avenilde","last_name":"Romo Vázquez","first_name":"Avenilde"},{"first_name":"Michelle","last_name":"Zandieh","full_name":"Zandieh, Michelle"},{"last_name":"Martínez-Planell","full_name":"Martínez-Planell, Rafael","first_name":"Rafael"}],"place":"Hannover","citation":{"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>.","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.","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.","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} }","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.","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.","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."},"has_accepted_license":"1","file_date_updated":"2023-03-25T10:07:54Z","_id":"43097","user_id":"32202","department":[{"_id":"97"}],"editor":[{"first_name":"Marı́a","full_name":"Trigueros, Marı́a","last_name":"Trigueros"},{"first_name":"Berta","last_name":"Barquero","full_name":"Barquero, Berta"},{"first_name":"Reinhard","last_name":"Hochmuth","full_name":"Hochmuth, Reinhard"},{"full_name":"Peters, Jana","last_name":"Peters","first_name":"Jana"}],"status":"public","type":"conference"},{"keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"article_number":"103868","language":[{"iso":"eng"}],"_id":"43105","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"user_id":"23686","status":"public","publication":"Nonlinear Analysis: Real World Applications","type":"journal_article","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","doi":"10.1016/j.nonrwa.2023.103868","publisher":"Elsevier BV","date_updated":"2023-03-27T07:27:03Z","volume":73,"date_created":"2023-03-27T07:25:58Z","author":[{"orcid":"0000-0001-9963-0800","last_name":"Black","full_name":"Black, Tobias","id":"23686","first_name":"Tobias"},{"last_name":"Fuest","full_name":"Fuest, Mario","first_name":"Mario"},{"first_name":"Johannes","full_name":"Lankeit, Johannes","last_name":"Lankeit"},{"last_name":"Mizukami","full_name":"Mizukami, Masaaki","first_name":"Masaaki"}],"year":"2023","intvolume":"        73","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} }","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).","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>.","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>.","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>"},"publication_identifier":{"issn":["1468-1218"]},"publication_status":"published"},{"publication":"Mathematica Didactica, 46","type":"book_chapter","status":"public","_id":"43227","department":[{"_id":"543"}],"user_id":"44184","language":[{"iso":"eng"}],"year":"2023","citation":{"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>","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.","mla":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” <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>.","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>","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>.","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."},"date_updated":"2023-03-30T10:06:53Z","author":[{"full_name":"Vitt, Vivian","last_name":"Vitt","first_name":"Vivian"},{"last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","id":"60267","first_name":"Uta"}],"date_created":"2023-03-30T10:06:24Z","title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","doi":"https://doi.org/10.18716/ojs/md/2023.1671"},{"publication":"Annals of Global Analysis and Geometry","type":"journal_article","status":"public","department":[{"_id":"93"}],"user_id":"30905","_id":"34832","project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"language":[{"iso":"eng"}],"keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"issue":"21","publication_status":"published","intvolume":"        63","citation":{"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>","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>.","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>.","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>.","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} }","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>"},"year":"2023","volume":63,"author":[{"id":"30905","full_name":"Hanusch, Maximilian","last_name":"Hanusch","first_name":"Maximilian"}],"date_created":"2022-12-22T09:45:34Z","date_updated":"2023-04-05T18:18:24Z","doi":"10.1007/s10455-023-09888-y","title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups"},{"type":"journal_article","status":"public","user_id":"15540","department":[{"_id":"542"}],"_id":"44857","publication_status":"published","publication_identifier":{"issn":["0399-0559","2804-7303"]},"citation":{"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>","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.","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>.","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>"},"page":"1045-1058","intvolume":"        57","author":[{"full_name":"Silva, Helmuth O.M.","last_name":"Silva","first_name":"Helmuth O.M."},{"first_name":"Diego P.","full_name":"Rubert, Diego P.","last_name":"Rubert"},{"first_name":"Eloi","full_name":"Araujo, Eloi","last_name":"Araujo"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"last_name":"Doerr","full_name":"Doerr, Daniel","first_name":"Daniel"},{"last_name":"Martinez","full_name":"Martinez, Fábio V.","first_name":"Fábio V."}],"volume":57,"date_updated":"2023-05-16T08:49:30Z","doi":"10.1051/ro/2023052","publication":"RAIRO - Operations Research","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"}],"language":[{"iso":"eng"}],"keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"issue":"3","year":"2023","date_created":"2023-05-16T08:48:22Z","publisher":"EDP Sciences","title":"Algorithms for the genome median under a restricted measure of rearrangement"},{"citation":{"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.","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.","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.","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>.","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} }","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023."},"year":"2023","author":[{"first_name":"Yulai","last_name":"Ma","full_name":"Ma, Yulai","id":"92748"},{"full_name":"Mattiolo, Davide","last_name":"Mattiolo","first_name":"Davide"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","id":"15548","full_name":"Steffen, Eckhard"},{"last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","id":"88145","first_name":"Isaak Hieronymus"}],"date_created":"2023-05-16T10:07:47Z","date_updated":"2023-05-16T11:17:26Z","title":"Sets of r-graphs that color all r-graphs","type":"preprint","publication":"arXiv:2305.08619","status":"public","user_id":"15540","department":[{"_id":"542"}],"external_id":{"arxiv":["2305.08619"]},"_id":"44859","language":[{"iso":"eng"}]},{"status":"public","type":"journal_article","publication":"Indagationes Mathematicae.","language":[{"iso":"eng"}],"keyword":["Lie group actions and analytic 1-submanifolds"],"user_id":"30905","department":[{"_id":"93"}],"_id":"34833","citation":{"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>.","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>.","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} }","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>.","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 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>"},"intvolume":"        34","page":"752-811","year":"2023","issue":"4","publication_status":"published","doi":"10.1016/j.indag.2023.02.003","title":"Decompositions of Analytic 1-Manifolds","author":[{"last_name":"Hanusch","full_name":"Hanusch, Maximilian","id":"30905","first_name":"Maximilian"}],"date_created":"2022-12-22T09:46:36Z","volume":34,"date_updated":"2023-05-25T07:32:38Z"},{"department":[{"_id":"101"}],"user_id":"97359","external_id":{"arxiv":["2306.03320"]},"_id":"45498","language":[{"iso":"eng"}],"publication":"arXiv:2306.03320","type":"preprint","status":"public","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."}],"author":[{"orcid":"0000-0002-8054-2058","last_name":"von der Gracht","id":"97359","full_name":"von der Gracht, Sören","first_name":"Sören"},{"first_name":"Eddie","last_name":"Nijholt","full_name":"Nijholt, Eddie"},{"first_name":"Bob","full_name":"Rink, Bob","last_name":"Rink"}],"date_created":"2023-06-07T07:57:28Z","date_updated":"2023-06-07T07:59:06Z","main_file_link":[{"url":"https://arxiv.org/pdf/2306.03320"}],"title":"A parametrisation method for high-order phase reduction in coupled  oscillator networks","publication_status":"submitted","page":"29","citation":{"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>.","mla":"von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled  Oscillator Networks.” <i>ArXiv:2306.03320</i>.","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).","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} }","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>.","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.","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>. ."},"year":"2023"},{"publisher":"Friedrich Verlag","date_updated":"2023-06-22T09:34:13Z","date_created":"2023-06-22T09:28:22Z","author":[{"last_name":"Häsel-Weide","id":"60267","full_name":"Häsel-Weide, Uta","first_name":"Uta"}],"title":" Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen","issue":"339","related_material":{"link":[{"url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991","relation":"other"}]},"year":"2023","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.","chicago":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” <i>Die Grundschulzeitschrift</i>, no. 339 (2023): 6–11.","ama":"Häsel-Weide U.  Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. <i>Die Grundschulzeitschrift</i>. 2023;(339):6-11.","apa":"Häsel-Weide, U. (2023).  Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. <i>Die Grundschulzeitschrift</i>, <i>339</i>, 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} }","short":"U. Häsel-Weide, Die Grundschulzeitschrift (2023) 6–11."},"page":"6-11","_id":"45712","user_id":"44184","department":[{"_id":"543"}],"language":[{"iso":"ger"}],"type":"journal_article","publication":"Die Grundschulzeitschrift","status":"public"},{"department":[{"_id":"543"}],"user_id":"44184","_id":"45713","language":[{"iso":"ger"}],"publication":"Die Grundschulzeitschrift","type":"journal_article","status":"public","date_created":"2023-06-22T09:33:59Z","author":[{"first_name":"Lara Marie","last_name":"Graf","full_name":"Graf, Lara Marie","id":"89837"},{"last_name":"Wienhues","full_name":"Wienhues, Inga","id":"61635","first_name":"Inga"},{"id":"60267","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta"}],"date_updated":"2023-06-22T09:34:18Z","publisher":"Friedrich Verlag","title":"Addition und Subtraktion verstehen","related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"issue":"339","page":"20-23","citation":{"apa":"Graf, L. M., Wienhues, I., &#38; Häsel-Weide, U. (2023). Addition und Subtraktion verstehen. <i>Die Grundschulzeitschrift</i>, <i>339</i>, 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.","short":"L.M. Graf, I. Wienhues, U. Häsel-Weide, Die Grundschulzeitschrift (2023) 20–23.","ama":"Graf LM, Wienhues I, Häsel-Weide U. Addition und Subtraktion verstehen. <i>Die Grundschulzeitschrift</i>. 2023;(339):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.","chicago":"Graf, Lara Marie, Inga Wienhues, and Uta Häsel-Weide. “Addition und Subtraktion verstehen.” <i>Die Grundschulzeitschrift</i>, no. 339 (2023): 20–23."},"year":"2023"}]