[{"oa":"1","date_updated":"2023-12-21T09:47:22Z","_id":"32097","language":[{"iso":"eng"}],"citation":{"short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127 (2024).","ieee":"T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov Actions,” Journal of Differential Geometry (to appear) -- arXiv:2103.12127, 2024.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions. Journal of Differential Geometry (to appear) -- arXiv:210312127. Published online 2024.","apa":"Weich, T., Guedes Bonthonneau, Y., & Guillarmou, C. (2024). SRB Measures of Anosov Actions. Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127.","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127, 2024.","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures of Anosov Actions}, journal={Journal of Differential Geometry (to appear) -- arXiv:2103.12127}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}, year={2024} }","mla":"Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127, 2024."},"year":"2024","type":"journal_article","user_id":"49178","ddc":["510"],"title":"SRB Measures of Anosov Actions","external_id":{"arxiv":["https://arxiv.org/abs/2103.12127"]},"status":"public","has_accepted_license":"1","date_created":"2022-06-22T09:56:23Z","file":[{"access_level":"open_access","file_name":"2103.12127.pdf","date_created":"2022-06-22T09:56:08Z","relation":"main_file","date_updated":"2022-06-22T09:56:08Z","content_type":"application/pdf","file_id":"32098","creator":"weich","file_size":745870}],"author":[{"last_name":"Weich","id":"49178","first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias"},{"last_name":"Guedes Bonthonneau","first_name":"Yannick","full_name":"Guedes Bonthonneau, Yannick"},{"last_name":"Guillarmou","first_name":"Colin","full_name":"Guillarmou, Colin"}],"file_date_updated":"2022-06-22T09:56:08Z","publication":"Journal of Differential Geometry (to appear) -- arXiv:2103.12127","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}]},{"year":"2024","type":"journal_article","citation":{"ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. Chaos. 2024;34(1). doi:10.1063/5.0172287","apa":"Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287"},"issue":"1","article_number":"013104","intvolume":" 34","_id":"46469","status":"public","has_accepted_license":"1","date_created":"2023-08-10T08:24:48Z","volume":34,"file":[{"access_level":"open_access","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","date_created":"2024-01-09T10:48:38Z","relation":"main_file","date_updated":"2024-01-09T10:48:38Z","content_type":"application/pdf","title":"Accepted Manuscript Chaos","file_id":"50376","creator":"coffen","file_size":13222105},{"access_level":"open_access","file_name":"LDensityPDE_AIP.pdf","date_created":"2024-01-09T11:19:49Z","date_updated":"2024-01-09T11:19:49Z","content_type":"application/pdf","description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation.","relation":"main_file","file_size":12960884,"creator":"coffen","file_id":"50390","title":"Learning of discrete models of variational PDEs from data"}],"publisher":"AIP Publishing","author":[{"first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","last_name":"Offen","id":"85279"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"}],"quality_controlled":"1","file_date_updated":"2024-01-09T11:19:49Z","publication":"Chaos","user_id":"85279","ddc":["510"],"article_type":"original","abstract":[{"text":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as travelling waves. This is possible even when travelling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation. ","lang":"eng"}],"language":[{"iso":"eng"}],"oa":"1","doi":"10.1063/5.0172287","date_updated":"2024-01-09T11:29:06Z","publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","department":[{"_id":"636"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/DLNN_pde","relation":"software","description":"GitHub"}]},"title":"Learning of discrete models of variational PDEs from data","external_id":{"arxiv":["2308.05082 "]}},{"user_id":"37888","status":"public","date_created":"2024-01-17T10:58:04Z","volume":"Band 3","publisher":"DE GRUYTER","author":[{"full_name":"Prediger, Susanne","first_name":"Susanne","last_name":"Prediger"},{"id":"85190","last_name":"Wessel","full_name":"Wessel, Lena","first_name":"Lena"}],"publication":"Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis","_id":"50554","type":"book_chapter","citation":{"ieee":"S. Prediger and L. Wessel, “31 Sprachbildung im berufsbezogenen Mathematikunterricht.,” in Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, vol. Band 3, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin: DE GRUYTER, 2024, pp. 363–372.","short":"S. Prediger, L. Wessel, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, DE GRUYTER, Berlin, 2024, pp. 363–372.","bibtex":"@inbook{Prediger_Wessel_2024, place={Berlin}, series={DaZ-Handbücher}, title={31 Sprachbildung im berufsbezogenen Mathematikunterricht.}, volume={Band 3}, booktitle={Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}, publisher={DE GRUYTER}, author={Prediger, Susanne and Wessel, Lena}, editor={Efing, Christian and Kalkavan-Aydin, Zeynep}, year={2024}, pages={363–372}, collection={DaZ-Handbücher} }","mla":"Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.” Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, vol. Band 3, DE GRUYTER, 2024, pp. 363–72.","ama":"Prediger S, Wessel L. 31 Sprachbildung im berufsbezogenen Mathematikunterricht. In: Efing C, Kalkavan-Aydin Z, eds. Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis. Vol Band 3. DaZ-Handbücher. DE GRUYTER; 2024:363-372.","apa":"Prediger, S., & Wessel, L. (2024). 31 Sprachbildung im berufsbezogenen Mathematikunterricht. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis: Vol. Band 3 (pp. 363–372). DE GRUYTER.","chicago":"Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.” In Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, Band 3:363–72. DaZ-Handbücher. Berlin: DE GRUYTER, 2024."},"year":"2024","page":"363-372","main_file_link":[{"open_access":"1","url":"https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381"}],"title":"31 Sprachbildung im berufsbezogenen Mathematikunterricht.","place":"Berlin","editor":[{"full_name":"Efing, Christian","first_name":"Christian","last_name":"Efing"},{"first_name":"Zeynep","full_name":"Kalkavan-Aydin, Zeynep","last_name":"Kalkavan-Aydin"}],"publication_identifier":{"isbn":["978-3-11-074544-3"]},"publication_status":"published","department":[{"_id":"34"},{"_id":"10"},{"_id":"643"}],"oa":"1","date_updated":"2024-01-17T11:07:21Z","language":[{"iso":"ger"}],"series_title":"DaZ-Handbücher"},{"date_updated":"2024-02-08T08:05:54Z","_id":"51208","doi":"10.1007/s10589-024-00552-0","language":[{"iso":"eng"}],"year":"2024","citation":{"apa":"Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. https://doi.org/10.1007/s10589-024-00552-0","ama":"Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. Published online 2024. doi:10.1007/s10589-024-00552-0","chicago":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” Computational Optimization and Applications, 2024. https://doi.org/10.1007/s10589-024-00552-0.","mla":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” Computational Optimization and Applications, Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.","bibtex":"@article{Gebken_2024, title={A note on the convergence of deterministic gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Gebken, Bennet}, year={2024} }","short":"B. Gebken, Computational Optimization and Applications (2024).","ieee":"B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” Computational Optimization and Applications, 2024, doi: 10.1007/s10589-024-00552-0."},"type":"journal_article","abstract":[{"lang":"eng","text":"AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions."}],"user_id":"32643","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"publication":"Computational Optimization and Applications","department":[{"_id":"101"}],"publisher":"Springer Science and Business Media LLC","author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"}],"date_created":"2024-02-07T07:23:23Z","status":"public","publication_status":"published","publication_identifier":{"issn":["0926-6003","1573-2894"]}},{"status":"public","date_created":"2024-02-06T20:35:36Z","author":[{"first_name":"Christopher","full_name":"Lutsko, Christopher","last_name":"Lutsko"},{"last_name":"Weich","full_name":"Weich, Tobias","first_name":"Tobias"},{"first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart","last_name":"Wolf","id":"45027"}],"publication":"arXiv:2402.02530","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","title":"Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces","external_id":{"arxiv":["2402.02530"]},"abstract":[{"lang":"eng","text":"Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant differential operators, and the decay of matrix coefficients. In\r\nparticular, this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash G)$ in this general setting."}],"language":[{"iso":"eng"}],"year":"2024","citation":{"ieee":"C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces,” arXiv:2402.02530. 2024.","mla":"Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” ArXiv:2402.02530, 2024.","bibtex":"@article{Lutsko_Weich_Wolf_2024, title={Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces}, journal={arXiv:2402.02530}, author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2024} }","short":"C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).","apa":"Lutsko, C., Weich, T., & Wolf, L. L. (2024). Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces. In arXiv:2402.02530.","ama":"Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces. arXiv:240202530. Published online 2024.","chicago":"Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” ArXiv:2402.02530, 2024."},"type":"preprint","date_updated":"2024-02-11T19:56:35Z","_id":"51204"},{"external_id":{"arxiv":["2302.06998"]},"title":"Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively","department":[{"_id":"799"}],"publication_identifier":{"issn":["0022-1236"]},"publication_status":"published","date_updated":"2024-02-18T12:32:23Z","doi":"10.1016/j.jfa.2024.110319","language":[{"iso":"eng"}],"extern":"1","user_id":"99427","keyword":["Analysis"],"publication":"Journal of Functional Analysis","author":[{"first_name":"David","full_name":"Hasler, David","last_name":"Hasler"},{"last_name":"Hinrichs","id":"99427","first_name":"Benjamin","full_name":"Hinrichs, Benjamin","orcid":"0000-0001-9074-1205"},{"last_name":"Siebert","first_name":"Oliver","full_name":"Siebert, Oliver"}],"publisher":"Elsevier BV","date_created":"2024-02-18T12:31:28Z","status":"public","volume":286,"intvolume":" 286","_id":"51374","issue":"7","article_number":"110319","year":"2024","type":"journal_article","citation":{"short":"D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024).","ieee":"D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively,” Journal of Functional Analysis, vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.","apa":"Hasler, D., Hinrichs, B., & Siebert, O. (2024). Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. Journal of Functional Analysis, 286(7), Article 110319. https://doi.org/10.1016/j.jfa.2024.110319","ama":"Hasler D, Hinrichs B, Siebert O. Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. Journal of Functional Analysis. 2024;286(7). doi:10.1016/j.jfa.2024.110319","chicago":"Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319.","bibtex":"@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively}, volume={286}, DOI={10.1016/j.jfa.2024.110319}, number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024} }","mla":"Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis, vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:10.1016/j.jfa.2024.110319."}},{"oa":"1","date_updated":"2024-02-19T06:25:13Z","_id":"32101","language":[{"iso":"eng"}],"type":"journal_article","year":"2024","citation":{"mla":"Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, pp. 1–36.","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor resonaces of Anosov actions}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={1–36} }","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim Hilgert. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, 1–36.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonaces of Anosov actions. J Europ Math Soc. Published online 2024:1-36.","apa":"Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024). Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 1–36.","ieee":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor resonaces of Anosov actions,” J. Europ. Math. Soc., pp. 1–36, 2024.","short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 1–36."},"page":"1-36","user_id":"49063","ddc":["510"],"title":"Ruelle-Taylor resonaces of Anosov actions","has_accepted_license":"1","status":"public","date_created":"2022-06-22T09:56:51Z","publication_status":"published","file":[{"date_created":"2022-06-22T09:56:47Z","file_name":"2007.14275.pdf","access_level":"open_access","file_size":796410,"creator":"weich","file_id":"32102","date_updated":"2022-06-22T09:56:47Z","content_type":"application/pdf","relation":"main_file"}],"author":[{"id":"49178","last_name":"Weich","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"full_name":"Guedes Bonthonneau, Yannick","first_name":"Yannick","last_name":"Guedes Bonthonneau"},{"full_name":"Guillarmou, Colin","first_name":"Colin","last_name":"Guillarmou"},{"last_name":"Hilgert","id":"220","first_name":"Joachim","full_name":"Hilgert, Joachim"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"file_date_updated":"2022-06-22T09:56:47Z","publication":"J. Europ. Math. Soc."},{"user_id":"49063","title":"Quantum-Classical Correspondences for Locally Symmetric Spaces","status":"public","date_created":"2024-02-19T10:31:51Z","publication_status":"published","author":[{"first_name":"Joachim","full_name":"Hilgert, Joachim","last_name":"Hilgert","id":"220"}],"department":[{"_id":"91"}],"oa":"1","_id":"51501","date_updated":"2024-02-19T10:32:07Z","language":[{"iso":"eng"}],"citation":{"ieee":"J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.” 2024.","short":"J. Hilgert, (2024).","bibtex":"@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }","mla":"Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric Spaces. 2024.","chicago":"Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces,” 2024.","apa":"Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric Spaces.","ama":"Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces. Published online 2024."},"year":"2024","type":"preprint","main_file_link":[{"url":"https://arxiv.org/pdf/2303.00578.pdf","open_access":"1"}]},{"title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","user_id":"56399","abstract":[{"text":"We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent.","lang":"eng"}],"publication_status":"published","date_created":"2023-07-12T06:35:58Z","status":"public","publication":"Journal of Optimization Theory and Applications","department":[{"_id":"101"},{"_id":"655"}],"publisher":"Springer","author":[{"first_name":"Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","last_name":"Sonntag","id":"56399"},{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"}],"doi":"10.1007/s10957-024-02389-3","oa":"1","_id":"46019","date_updated":"2024-02-21T10:13:33Z","citation":{"ieee":"K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory and Applications, 2024, doi: 10.1007/s10957-024-02389-3.","short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3}, journal={Journal of Optimization Theory and Applications}, publisher={Springer}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.","apa":"Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3","ama":"Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. Published online 2024. doi:10.1007/s10957-024-02389-3"},"type":"journal_article","year":"2024","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}]},{"has_accepted_license":"1","status":"public","date_created":"2024-02-13T09:35:26Z","author":[{"first_name":"Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","last_name":"Sonntag","id":"56399"},{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"},{"last_name":"Müller","full_name":"Müller, Georg","first_name":"Georg"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"full_name":"Volkwein, Stefan","first_name":"Stefan","last_name":"Volkwein"}],"department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2402.06376","title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces","user_id":"56399","abstract":[{"lang":"eng","text":"The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem."}],"external_id":{"arxiv":["\t2402.06376"]},"type":"preprint","citation":{"ieee":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376. 2024.","short":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024).","mla":"Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.","bibtex":"@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376}, author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}, year={2024} }","chicago":"Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.","apa":"Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In arXiv:2402.06376.","ama":"Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published online 2024."},"year":"2024","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"oa":"1","_id":"51334","date_updated":"2024-02-21T10:21:03Z"},{"user_id":"32202","ddc":["510","370"],"article_type":"original","abstract":[{"text":"athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.","lang":"ger"}],"status":"public","has_accepted_license":"1","date_created":"2024-02-25T20:58:51Z","volume":242,"file":[{"file_size":1410541,"file_id":"51842","creator":"maxh","date_updated":"2024-02-25T20:55:29Z","content_type":"application/pdf","relation":"main_file","success":1,"file_name":"Barzel_etal_2024_DigitalisierungalsChancefrallePrinzipiengut.pdf","date_created":"2024-02-25T20:55:29Z","access_level":"closed"}],"author":[{"last_name":"Barzel","first_name":"Bärbel","full_name":"Barzel, Bärbel"},{"first_name":"Gilbert","full_name":"Greefrath, Gilbert","last_name":"Greefrath"},{"last_name":"Nagel","full_name":"Nagel, Mareike","first_name":"Mareike"},{"id":"32202","last_name":"Hoffmann","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123","first_name":"Max"}],"file_date_updated":"2024-02-25T20:55:29Z","publication":"mathematik lehren","intvolume":" 242","_id":"51841","citation":{"apa":"Barzel, B., Greefrath, G., Nagel, M., & Hoffmann, M. (2024). Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren, 242, 42–47.","ama":"Barzel B, Greefrath G, Nagel M, Hoffmann M. Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren. 2024;242:42-47.","chicago":"Barzel, Bärbel, Gilbert Greefrath, Mareike Nagel, and Max Hoffmann. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren 242 (2024): 42–47.","mla":"Barzel, Bärbel, et al. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren, vol. 242, 2024, pp. 42–47.","bibtex":"@article{Barzel_Greefrath_Nagel_Hoffmann_2024, title={Digitalisierung als Chance für alle Prinzipien guten Unterrichts}, volume={242}, journal={mathematik lehren}, author={Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and Hoffmann, Max}, year={2024}, pages={42–47} }","short":"B. Barzel, G. Greefrath, M. Nagel, M. Hoffmann, mathematik lehren 242 (2024) 42–47.","ieee":"B. Barzel, G. Greefrath, M. Nagel, and M. Hoffmann, “Digitalisierung als Chance für alle Prinzipien guten Unterrichts,” mathematik lehren, vol. 242, pp. 42–47, 2024."},"year":"2024","type":"journal_article","page":"42 - 47","main_file_link":[{"open_access":"1","url":"https://www.friedrich-verlag.de/shop/mwdownloads/download/link/id/114555/"}],"title":"Digitalisierung als Chance für alle Prinzipien guten Unterrichts","publication_status":"published","department":[{"_id":"97"},{"_id":"643"}],"oa":"1","date_updated":"2024-02-25T21:01:03Z","language":[{"iso":"ger"}]},{"date_updated":"2024-03-07T08:50:33Z","_id":"52342","language":[{"iso":"eng"}],"year":"2024","type":"preprint","citation":{"short":"C. Dalfó, M.A. Fiol, E. Steffen, ArXiv:2403.02924 (2024).","ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” arXiv:2403.02924. 2024.","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.","apa":"Dalfó, C., Fiol, M. A., & Steffen, E. (2024). On token signed graphs. In arXiv:2403.02924.","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. arXiv:240302924. Published online 2024.","mla":"Dalfó, C., et al. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.","bibtex":"@article{Dalfó_Fiol_Steffen_2024, title={On token signed graphs}, journal={arXiv:2403.02924}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2024} }"},"external_id":{"arxiv":["2403.02924"]},"abstract":[{"lang":"eng","text":"We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs. "}],"user_id":"15540","title":"On token signed graphs","author":[{"full_name":"Dalfó, C.","first_name":"C.","last_name":"Dalfó"},{"first_name":"M. A.","full_name":"Fiol, M. A.","last_name":"Fiol"},{"orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard","id":"15548","last_name":"Steffen"}],"department":[{"_id":"542"}],"publication":"arXiv:2403.02924","status":"public","date_created":"2024-03-07T08:48:39Z"},{"date_updated":"2024-03-20T14:56:50Z","_id":"52691","language":[{"iso":"eng"}],"type":"preprint","year":"2024","citation":{"ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains,” arXiv:2403.12147. 2024.","short":"B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024).","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.” ArXiv:2403.12147, 2024.","bibtex":"@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains}, journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024} }","ama":"Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains. arXiv:240312147. Published online 2024.","apa":"Hinrichs, B., & Matte, O. (2024). Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains. In arXiv:2403.12147.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.” ArXiv:2403.12147, 2024."},"user_id":"99427","title":"Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains","abstract":[{"lang":"eng","text":"We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics. The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical electrons moving in a polarizable crystal and interacting with the\r\nquantized phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We also include possibly very singular magnetic vector potentials and\r\nelectrostatic potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative functionals and can be applied to every vector\r\nin the underlying Hilbert space. In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac formulas are known, the analysis of the\r\ncreation and annihilation terms in the multiplicative functionals requires\r\nnovel ideas to overcome difficulties caused by the phonon dispersion relation\r\nbeing constant. Getting these terms under control and generalizing other\r\nconstruction steps so as to cover confined systems are the main achievements of\r\nthis article."}],"external_id":{"arxiv":["2403.12147"]},"date_created":"2024-03-20T14:56:05Z","status":"public","department":[{"_id":"799"}],"publication":"arXiv:2403.12147","author":[{"id":"99427","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin","orcid":"0000-0001-9074-1205","first_name":"Benjamin"},{"last_name":"Matte","first_name":"Oliver","full_name":"Matte, Oliver"}]},{"language":[{"iso":"eng"}],"doi":"10.1093/comnet/cnae009","oa":"1","date_updated":"2024-03-22T09:11:53Z","publication_identifier":{"issn":["2051-1329"]},"publication_status":"published","department":[{"_id":"101"}],"title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","external_id":{"arxiv":["2309.02006"]},"citation":{"mla":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks, vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.","bibtex":"@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009}, number={2}, journal={Journal of Complex Networks}, publisher={Oxford University Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024} }","ama":"Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems with higher-order interactions. Journal of Complex Networks. 2024;12(2). doi:10.1093/comnet/cnae009","apa":"Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network dynamical systems with higher-order interactions. Journal of Complex Networks, 12(2). https://doi.org/10.1093/comnet/cnae009","chicago":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks 12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.","ieee":"C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical systems with higher-order interactions,” Journal of Complex Networks, vol. 12, no. 2, 2024, doi: 10.1093/comnet/cnae009.","short":"C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024)."},"type":"journal_article","year":"2024","main_file_link":[{"open_access":"1","url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf"}],"issue":"2","intvolume":" 12","_id":"52726","volume":12,"has_accepted_license":"1","status":"public","date_created":"2024-03-22T09:04:57Z","author":[{"last_name":"Bick","first_name":"Christian","full_name":"Bick, Christian"},{"id":"97359","last_name":"von der Gracht","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören"}],"publisher":"Oxford University Press (OUP)","publication":"Journal of Complex Networks","file_date_updated":"2024-03-22T09:06:07Z","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"file":[{"success":1,"relation":"main_file","date_updated":"2024-03-22T09:06:07Z","content_type":"application/pdf","creator":"svdg","file_id":"52728","file_size":649155,"access_level":"closed","date_created":"2024-03-22T09:06:07Z","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf"}],"ddc":["510"],"user_id":"97359","article_type":"original","abstract":[{"lang":"eng","text":"Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures."}]},{"user_id":"15540","abstract":[{"text":"For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \u0003 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l.","lang":"eng"}],"date_created":"2023-12-20T10:31:27Z","status":"public","volume":44,"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"publication":"Combinatorica","author":[{"last_name":"Ma","id":"92748","first_name":"Yulai","full_name":"Ma, Yulai"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"last_name":"Steffen","id":"15548","first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard"},{"id":"88145","last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus"}],"publisher":"Springer Science and Business Media LLC","intvolume":" 44","_id":"49905","page":"429-440","citation":{"ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica, 44, 429–440. https://doi.org/10.1007/s00493-023-00078-9","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.","mla":"Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2024}, pages={429–440} }","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44, pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9."},"year":"2024","type":"journal_article","title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","publication_status":"published","publication_identifier":{"issn":["0209-9683","1439-6912"]},"department":[{"_id":"542"}],"doi":"10.1007/s00493-023-00078-9","date_updated":"2024-03-22T12:11:35Z","language":[{"iso":"eng"}]},{"date_updated":"2024-03-28T16:07:34Z","doi":"10.3934/jcd.2024017","oa":"1","language":[{"iso":"eng"}],"title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","department":[{"_id":"636"}],"publication_identifier":{"issn":["2158-2491","2158-2505"]},"publication_status":"published","_id":"53101","issue":"0","main_file_link":[{"open_access":"1","url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017"}],"year":"2024","type":"journal_article","citation":{"mla":"Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational Dynamics, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:10.3934/jcd.2024017.","bibtex":"@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A new Lagrangian approach to control affine systems with a quadratic Lagrange term}, volume={0}, DOI={10.3934/jcd.2024017}, number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}, year={2024}, pages={0–0} }","ama":"Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO. A new Lagrangian approach to control affine systems with a quadratic Lagrange term. Journal of Computational Dynamics. 2024;0(0):0-0. doi:10.3934/jcd.2024017","apa":"Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de, & Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems with a quadratic Lagrange term. Journal of Computational Dynamics, 0(0), 0–0. https://doi.org/10.3934/jcd.2024017","chicago":"Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T. Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational Dynamics 0, no. 0 (2024): 0–0. https://doi.org/10.3934/jcd.2024017.","ieee":"S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro, and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with a quadratic Lagrange term,” Journal of Computational Dynamics, vol. 0, no. 0, pp. 0–0, 2024, doi: 10.3934/jcd.2024017.","short":"S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O. Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0."},"page":"0-0","article_type":"original","abstract":[{"lang":"eng","text":"In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way."}],"ddc":["510"],"user_id":"87909","author":[{"last_name":"Leyendecker","full_name":"Leyendecker, Sigrid","first_name":"Sigrid"},{"last_name":"Maslovskaya","id":"87909","first_name":"Sofya","full_name":"Maslovskaya, Sofya"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"last_name":"Almagro","first_name":"Rodrigo T. Sato Martín de","full_name":"Almagro, Rodrigo T. Sato Martín de"},{"last_name":"Szemenyei","full_name":"Szemenyei, Flóra Orsolya","first_name":"Flóra Orsolya"}],"publisher":"American Institute of Mathematical Sciences (AIMS)","publication":"Journal of Computational Dynamics","keyword":["Optimal control problem","Lagrangian system","Hamiltonian system","Variations","Pontryagin's maximum principle."],"volume":"0","has_accepted_license":"1","status":"public","date_created":"2024-03-28T15:58:02Z"},{"article_number":"110840","intvolume":" 149","_id":"21199","citation":{"ama":"Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840","apa":"Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840","chicago":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840.","bibtex":"@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }","mla":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier, 2023, doi:10.1016/j.automatica.2022.110840.","short":"S. Peitz, K. Bieker, Automatica 149 (2023).","ieee":"S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi: 10.1016/j.automatica.2022.110840."},"type":"journal_article","year":"2023","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true","open_access":"1"}],"user_id":"47427","abstract":[{"lang":"eng","text":"As in almost every other branch of science, the major advances in data\r\nscience and machine learning have also resulted in significant improvements\r\nregarding the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays possible to make accurate medium to long-term predictions of highly\r\ncomplex systems such as the weather, the dynamics within a nuclear fusion\r\nreactor, of disease models or the stock market in a very efficient manner. In\r\nmany cases, predictive methods are advertised to ultimately be useful for\r\ncontrol, as the control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge with huge potential in areas such as clean and efficient energy\r\nproduction, or the development of advanced medical devices. However, the\r\nquestion of how to use a predictive model for control is often left unanswered\r\ndue to the associated challenges, namely a significantly higher system\r\ncomplexity, the requirement of much larger data sets and an increased and often\r\nproblem-specific modeling effort. To solve these issues, we present a universal\r\nframework (which we call QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive models into control systems and use them for feedback control. The\r\nadvantages of our approach are a linear increase in data requirements with\r\nrespect to the control dimension, performance guarantees that rely exclusively\r\non the accuracy of the predictive model, and only little prior knowledge\r\nrequirements in control theory to solve complex control problems. In particular\r\nthe latter point is of key importance to enable a large number of researchers\r\nand practitioners to exploit the ever increasing capabilities of predictive\r\nmodels for control in a straight-forward and systematic fashion."}],"status":"public","date_created":"2021-02-10T07:04:15Z","volume":149,"publisher":"Elsevier","author":[{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"first_name":"Katharina","full_name":"Bieker, Katharina","last_name":"Bieker","id":"32829"}],"publication":"Automatica","oa":"1","doi":"10.1016/j.automatica.2022.110840","date_updated":"2023-01-07T12:01:58Z","language":[{"iso":"eng"}],"title":"On the Universal Transformation of Data-Driven Models to Control Systems","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication_status":"published","department":[{"_id":"101"},{"_id":"655"}]},{"title":"Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences","user_id":"37888","place":"Cham","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"publication_status":"published","date_created":"2023-01-10T09:03:11Z","status":"public","publication":"Practice-Oriented Research in Tertiary Mathematics Education","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publisher":"Springer International Publishing","author":[{"full_name":"Ostsieker, Laura","first_name":"Laura","last_name":"Ostsieker"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"}],"doi":"10.1007/978-3-031-14175-1_9","date_updated":"2023-01-11T08:19:24Z","_id":"35697","page":"181-201","type":"book_chapter","year":"2023","citation":{"bibtex":"@inbook{Ostsieker_Biehler_2023, place={Cham}, title={Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences}, DOI={10.1007/978-3-031-14175-1_9}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Ostsieker, Laura and Biehler, Rolf}, year={2023}, pages={181–201} }","mla":"Ostsieker, Laura, and Rolf Biehler. “Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences.” Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, 2023, pp. 181–201, doi:10.1007/978-3-031-14175-1_9.","ama":"Ostsieker L, Biehler R. Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences. In: Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023:181-201. doi:10.1007/978-3-031-14175-1_9","apa":"Ostsieker, L., & Biehler, R. (2023). Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences. In Practice-Oriented Research in Tertiary Mathematics Education (pp. 181–201). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_9","chicago":"Ostsieker, Laura, and Rolf Biehler. “Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences.” In Practice-Oriented Research in Tertiary Mathematics Education, 181–201. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_9.","ieee":"L. Ostsieker and R. 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Biehler, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 181–201."},"language":[{"iso":"eng"}]},{"place":"Cham","title":"Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses","user_id":"37888","publication":"Practice-Oriented Research in Tertiary Mathematics Education","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publisher":"Springer International Publishing","author":[{"full_name":"Kortemeyer, Jörg","first_name":"Jörg","last_name":"Kortemeyer"},{"full_name":"Biehler, Rolf","first_name":"Rolf","id":"16274","last_name":"Biehler"}],"publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"publication_status":"published","date_created":"2023-01-10T08:53:44Z","status":"public","_id":"35678","date_updated":"2023-01-11T08:20:40Z","doi":"10.1007/978-3-031-14175-1_32","page":"669-692","citation":{"chicago":"Kortemeyer, Jörg, and Rolf Biehler. “Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses.” In Practice-Oriented Research in Tertiary Mathematics Education, 669–92. 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Liebendörfer, C. Büdenbender-Kuklinski, E. Lankeit, M. Schürmann, R. Biehler, N. Schaper, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 91–117.","ieee":"M. Liebendörfer, C. Büdenbender-Kuklinski, E. Lankeit, M. Schürmann, R. Biehler, and N. Schaper, “Framing Goals of Mathematics Support Measures,” in Practice-Oriented Research in Tertiary Mathematics Education, Cham: Springer International Publishing, 2023, pp. 91–117.","ama":"Liebendörfer M, Büdenbender-Kuklinski C, Lankeit E, Schürmann M, Biehler R, Schaper N. Framing Goals of Mathematics Support Measures. In: Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023:91-117. doi:10.1007/978-3-031-14175-1_5","apa":"Liebendörfer, M., Büdenbender-Kuklinski, C., Lankeit, E., Schürmann, M., Biehler, R., & Schaper, N. (2023). Framing Goals of Mathematics Support Measures. In Practice-Oriented Research in Tertiary Mathematics Education (pp. 91–117). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_5","chicago":"Liebendörfer, Michael, Christiane Büdenbender-Kuklinski, Elisa Lankeit, Mirko Schürmann, Rolf Biehler, and Niclas Schaper. “Framing Goals of Mathematics Support Measures.” In Practice-Oriented Research in Tertiary Mathematics Education, 91–117. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_5.","bibtex":"@inbook{Liebendörfer_Büdenbender-Kuklinski_Lankeit_Schürmann_Biehler_Schaper_2023, place={Cham}, title={Framing Goals of Mathematics Support Measures}, DOI={10.1007/978-3-031-14175-1_5}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Liebendörfer, Michael and Büdenbender-Kuklinski, Christiane and Lankeit, Elisa and Schürmann, Mirko and Biehler, Rolf and Schaper, Niclas}, year={2023}, pages={91–117} }","mla":"Liebendörfer, Michael, et al. “Framing Goals of Mathematics Support Measures.” Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, 2023, pp. 91–117, doi:10.1007/978-3-031-14175-1_5."},"page":"91-117","place":"Cham","user_id":"14931","title":"Framing Goals of Mathematics Support Measures","author":[{"last_name":"Liebendörfer","id":"30933","first_name":"Michael","orcid":"0000-0001-9887-2074","full_name":"Liebendörfer, Michael"},{"last_name":"Büdenbender-Kuklinski","first_name":"Christiane","full_name":"Büdenbender-Kuklinski, Christiane"},{"first_name":"Elisa","full_name":"Lankeit, Elisa","last_name":"Lankeit"},{"first_name":"Mirko","orcid":"0000-0003-2646-085X","full_name":"Schürmann, Mirko","last_name":"Schürmann","id":"59707"},{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler","id":"16274"},{"last_name":"Schaper","full_name":"Schaper, Niclas","first_name":"Niclas"}],"publisher":"Springer International Publishing","publication":"Practice-Oriented Research in Tertiary Mathematics Education","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"},{"_id":"423"}],"status":"public","date_created":"2023-01-10T08:55:08Z","publication_identifier":{"isbn":["9783031141744","9783031141751"],"issn":["1869-4918","1869-4926"]},"publication_status":"published"},{"publisher":"Springer International Publishing","department":[{"_id":"10"}],"editor":[{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"},{"last_name":"Liebendörfer","first_name":"Michael","full_name":"Liebendörfer, Michael"},{"last_name":"Gueudet","full_name":"Gueudet, Ghislaine","first_name":"Ghislaine"},{"last_name":"Rasmussen","full_name":"Rasmussen, Chris","first_name":"Chris"},{"last_name":"Winsløw","first_name":"Carl","full_name":"Winsløw, Carl"}],"publication_status":"published","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"status":"public","date_created":"2023-01-18T22:17:58Z","place":"Cham","title":"Practice-Oriented Research in Tertiary Mathematics Education","user_id":"30933","year":"2023","citation":{"ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023.","short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","mla":"Biehler, Rolf, et al., editors. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing, 2023, doi:10.1007/978-3-031-14175-1.","bibtex":"@book{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education}, DOI={10.1007/978-3-031-14175-1}, publisher={Springer International Publishing}, year={2023} }","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1.","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (Eds.). (2023). Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. Practice-Oriented Research in Tertiary Mathematics Education. 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Rösler, Transaction of the American Mathematical Society (n.d.).","bibtex":"@article{Brennecken_Rösler, title={The Dunkl-Laplace transform and Macdonald’s hypergeometric series}, DOI={10.1090/tran/8860}, journal={Transaction of the American Mathematical Society}, publisher={ American Mathematical Society}, author={Brennecken, Dominik and Rösler, Margit} }","mla":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” Transaction of the American Mathematical Society, American Mathematical Society, doi:10.1090/tran/8860.","apa":"Brennecken, D., & Rösler, M. (n.d.). The Dunkl-Laplace transform and Macdonald’s hypergeometric series. Transaction of the American Mathematical Society. https://doi.org/10.1090/tran/8860","ama":"Brennecken D, Rösler M. The Dunkl-Laplace transform and Macdonald’s hypergeometric series. Transaction of the American Mathematical Society. doi:10.1090/tran/8860","chicago":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” Transaction of the American Mathematical Society, n.d. https://doi.org/10.1090/tran/8860."},"year":"2023","language":[{"iso":"eng"}],"date_updated":"2023-01-24T22:14:22Z","_id":"36294","doi":"10.1090/tran/8860"},{"page":"170-201","type":"journal_article","citation":{"ieee":"M. Hanusch, “A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus,” Canadian Journal of Mathematics, vol. 75, no. 1, pp. 170–201, 2023, doi: 10.4153/s0008414x21000596.","short":"M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.","mla":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” Canadian Journal of Mathematics, vol. 75, no. 1, Canadian Mathematical Society, 2023, pp. 170–201, doi:10.4153/s0008414x21000596.","bibtex":"@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}, volume={75}, DOI={10.4153/s0008414x21000596}, number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }","chicago":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” Canadian Journal of Mathematics 75, no. 1 (2023): 170–201. https://doi.org/10.4153/s0008414x21000596.","ama":"Hanusch M. A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. 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Canadian Journal of Mathematics, 75(1), 170–201. https://doi.org/10.4153/s0008414x21000596"},"year":"2023","issue":"1","_id":"34814","intvolume":" 75","volume":75,"date_created":"2022-12-22T09:16:48Z","status":"public","publication":"Canadian Journal of Mathematics","keyword":["extension of differentiable maps"],"publisher":"Canadian Mathematical Society","author":[{"full_name":"Hanusch, Maximilian","first_name":"Maximilian","id":"30905","last_name":"Hanusch"}],"user_id":"30905","article_type":"original","language":[{"iso":"eng"}],"doi":"10.4153/s0008414x21000596","date_updated":"2023-02-22T11:38:32Z","publication_identifier":{"issn":["0008-414X","1496-4279"]},"publication_status":"published","project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"department":[{"_id":"93"}],"title":"A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus"},{"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"page":"709-741","year":"2023","citation":{"ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.","short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2","apa":"Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2."},"type":"journal_article","intvolume":" 85","_id":"27426","issue":"3","publication":"Journal of Global Optimization","author":[{"first_name":"Bennet","full_name":"Gebken, Bennet","last_name":"Gebken","id":"32643"},{"full_name":"Bieker, Katharina","first_name":"Katharina","id":"32829","last_name":"Bieker"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"date_created":"2021-11-15T09:24:59Z","status":"public","volume":85,"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"}],"user_id":"47427","language":[{"iso":"eng"}],"date_updated":"2023-03-11T17:16:33Z","oa":"1","doi":"10.1007/s10898-022-01223-2","department":[{"_id":"101"},{"_id":"655"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms"},{"date_created":"2022-06-12T11:07:34Z","has_accepted_license":"1","status":"public","file":[{"creator":"maxh","file_id":"43096","file_size":201942,"relation":"main_file","success":1,"date_updated":"2023-03-25T10:01:03Z","content_type":"application/pdf","date_created":"2023-03-25T10:01:03Z","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","access_level":"closed"}],"publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file_date_updated":"2023-03-25T10:01:03Z","keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"quality_controlled":"1","author":[{"last_name":"Hoffmann","id":"32202","first_name":"Max","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"}],"publisher":"University of Hannover and INDRUM.","user_id":"32202","ddc":["370","510"],"year":"2023","citation":{"ieee":"M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry,” in Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023.","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.","bibtex":"@inproceedings{Hoffmann_Biehler_2023, place={Hannover}, title={Student Teachers ’ Knowledge of Congruence before a University Course on Geometry}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, publisher={University of Hannover and INDRUM.}, author={Hoffmann, Max and Biehler, Rolf}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","mla":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., University of Hannover and INDRUM., 2023.","chicago":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023.","apa":"Hoffmann, M., & Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). University of Hannover and INDRUM.","ama":"Hoffmann M, Biehler R. Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). University of Hannover and INDRUM.; 2023."},"type":"conference","main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"_id":"31849","publication_status":"published","editor":[{"last_name":"Trigueros","full_name":"Trigueros, Marı́a","first_name":"Marı́a"},{"first_name":"Berta","full_name":"Barquero, Berta","last_name":"Barquero"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"last_name":"Peters","full_name":"Peters, Jana","first_name":"Jana"}],"department":[{"_id":"97"}],"title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","place":"Hannover","language":[{"iso":"eng"}],"oa":"1","date_updated":"2023-03-25T10:11:35Z"},{"oa":"1","date_updated":"2023-03-25T10:10:58Z","language":[{"iso":"eng"}],"title":"Innovations in university teaching based on mathematic education research","place":"Hannover","editor":[{"first_name":"Marı́a","full_name":"Trigueros, Marı́a","last_name":"Trigueros"},{"first_name":"Berta","full_name":"Barquero, Berta","last_name":"Barquero"},{"first_name":"Reinhard","full_name":"Hochmuth, Reinhard","last_name":"Hochmuth"},{"last_name":"Peters","first_name":"Jana","full_name":"Peters, Jana"}],"department":[{"_id":"97"}],"_id":"43097","type":"conference","citation":{"apa":"Florensa, I., Hoffmann, M., Romo Vázquez, A., Zandieh, M., & Martínez-Planell, R. (2023). Innovations in university teaching based on mathematic education research. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022).","ama":"Florensa I, Hoffmann M, Romo Vázquez A, Zandieh M, Martínez-Planell R. Innovations in university teaching based on mathematic education research. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). ; 2023.","chicago":"Florensa, Ignasio, Max Hoffmann, Avenilde Romo Vázquez, Michelle Zandieh, and Rafael Martínez-Planell. “Innovations in University Teaching Based on Mathematic Education Research.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover, 2023.","mla":"Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic Education Research.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., 2023.","bibtex":"@inproceedings{Florensa_Hoffmann_Romo Vázquez_Zandieh_Martínez-Planell_2023, place={Hannover}, title={Innovations in university teaching based on mathematic education research}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, author={Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde and Zandieh, Michelle and Martínez-Planell, Rafael}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","short":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, R. Martínez-Planell, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), Hannover, 2023.","ieee":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, and R. Martínez-Planell, “Innovations in university teaching based on mathematic education research,” in Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023."},"year":"2023","main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}],"ddc":["370","510"],"user_id":"32202","date_created":"2023-03-25T10:09:06Z","has_accepted_license":"1","status":"public","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file_date_updated":"2023-03-25T10:07:54Z","author":[{"first_name":"Ignasio","full_name":"Florensa, Ignasio","last_name":"Florensa"},{"last_name":"Hoffmann","id":"32202","first_name":"Max","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123"},{"first_name":"Avenilde","full_name":"Romo Vázquez, Avenilde","last_name":"Romo Vázquez"},{"full_name":"Zandieh, Michelle","first_name":"Michelle","last_name":"Zandieh"},{"first_name":"Rafael","full_name":"Martínez-Planell, Rafael","last_name":"Martínez-Planell"}],"quality_controlled":"1","file":[{"file_id":"43098","creator":"maxh","file_size":642388,"relation":"main_file","success":1,"date_updated":"2023-03-25T10:07:54Z","content_type":"application/pdf","file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","date_created":"2023-03-25T10:07:54Z","access_level":"closed"}]},{"citation":{"short":"R. Biehler, M. Liebendörfer, A. Schmitz, Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023) 8–12.","ieee":"R. Biehler, M. Liebendörfer, and A. Schmitz, “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos,” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, pp. 8–12, 2023.","apa":"Biehler, R., Liebendörfer, M., & Schmitz, A. (2023). Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik, 114, 8–12.","ama":"Biehler R, Liebendörfer M, Schmitz A. Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik. 2023;114:8-12.","chicago":"Biehler, Rolf, Michael Liebendörfer, and A. Schmitz. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023): 8–12.","mla":"Biehler, Rolf, et al. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, 2023, pp. 8–12.","bibtex":"@article{Biehler_Liebendörfer_Schmitz_2023, title={Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos}, volume={114}, journal={Mitteilungen der Gesellschaft für Didaktik der Mathematik}, author={Biehler, Rolf and Liebendörfer, Michael and Schmitz, A.}, year={2023}, pages={8–12} }"},"type":"journal_article","year":"2023","page":"8-12","language":[{"iso":"ger"}],"_id":"43504","intvolume":" 114","date_updated":"2023-04-14T09:25:27Z","volume":114,"status":"public","date_created":"2023-04-14T09:25:18Z","author":[{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler","id":"16274"},{"last_name":"Liebendörfer","id":"30933","first_name":"Michael","full_name":"Liebendörfer, Michael","orcid":"0000-0001-9887-2074"},{"first_name":"A.","full_name":"Schmitz, A.","last_name":"Schmitz"}],"publication":"Mitteilungen der Gesellschaft für Didaktik der Mathematik","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"title":"Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos","user_id":"37888"},{"language":[{"iso":"eng"}],"date_updated":"2023-03-27T07:27:03Z","doi":"10.1016/j.nonrwa.2023.103868","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","citation":{"mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications, vol. 73, 103868, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2023.103868.","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={10.1016/j.nonrwa.2023.103868}, number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}, year={2023} }","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real World Applications. 2023;73. doi:10.1016/j.nonrwa.2023.103868","apa":"Black, T., Fuest, M., Lankeit, J., & Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real World Applications, 73, Article 103868. https://doi.org/10.1016/j.nonrwa.2023.103868","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications 73 (2023). https://doi.org/10.1016/j.nonrwa.2023.103868.","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” Nonlinear Analysis: Real World Applications, vol. 73, Art. no. 103868, 2023, doi: 10.1016/j.nonrwa.2023.103868.","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023)."},"year":"2023","type":"journal_article","intvolume":" 73","_id":"43105","article_number":"103868","publication":"Nonlinear Analysis: Real World Applications","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"publisher":"Elsevier BV","author":[{"orcid":"0000-0001-9963-0800","full_name":"Black, Tobias","first_name":"Tobias","id":"23686","last_name":"Black"},{"full_name":"Fuest, Mario","first_name":"Mario","last_name":"Fuest"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"},{"first_name":"Masaaki","full_name":"Mizukami, Masaaki","last_name":"Mizukami"}],"date_created":"2023-03-27T07:25:58Z","status":"public","volume":73,"user_id":"23686"},{"author":[{"first_name":"Vivian","full_name":"Vitt, Vivian","last_name":"Vitt"},{"full_name":"Häsel-Weide, Uta","first_name":"Uta","id":"60267","last_name":"Häsel-Weide"}],"department":[{"_id":"543"}],"publication":"Mathematica Didactica, 46","status":"public","date_created":"2023-03-30T10:06:24Z","title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","user_id":"44184","citation":{"chicago":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1671.","ama":"Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1671","apa":"Vitt, V., & Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1671","bibtex":"@inbook{Vitt_Häsel-Weide_2023, title={Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}, DOI={https://doi.org/10.18716/ojs/md/2023.1671}, booktitle={Mathematica Didactica, 46}, author={Vitt, Vivian and Häsel-Weide, Uta}, year={2023} }","mla":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1671.","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.","ieee":"V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46, 2023."},"type":"book_chapter","year":"2023","language":[{"iso":"eng"}],"_id":"43227","date_updated":"2023-03-30T10:06:53Z","doi":"https://doi.org/10.18716/ojs/md/2023.1671"},{"user_id":"44184","title":"Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.","status":"public","date_created":"2023-03-30T10:04:31Z","author":[{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"},{"last_name":"Nührenbörger","first_name":"M.","full_name":"Nührenbörger, M."}],"department":[{"_id":"543"}],"publication":"Mathematica Didactica, 46","doi":"https://doi.org/10.18716/ojs/md/2023.1670","_id":"43226","date_updated":"2023-03-30T10:06:49Z","language":[{"iso":"eng"}],"year":"2023","citation":{"chicago":"Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter Förderung Im Mathematikunterricht.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1670.","apa":"Häsel-Weide, U., & Nührenbörger, M. (2023). Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1670","ama":"Häsel-Weide U, Nührenbörger M. Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1670","bibtex":"@inbook{Häsel-Weide_Nührenbörger_2023, title={Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.}, DOI={https://doi.org/10.18716/ojs/md/2023.1670}, booktitle={Mathematica Didactica, 46}, author={Häsel-Weide, Uta and Nührenbörger, M.}, year={2023} }","mla":"Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter Förderung Im Mathematikunterricht.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1670.","short":"U. Häsel-Weide, M. Nührenbörger, in: Mathematica Didactica, 46, 2023.","ieee":"U. Häsel-Weide and M. Nührenbörger, “Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.,” in Mathematica Didactica, 46, 2023."},"type":"book_chapter"},{"language":[{"iso":"eng"}],"year":"2023","type":"journal_article","citation":{"mla":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023, doi:10.1007/s10455-023-09888-y.","bibtex":"@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}, volume={63}, DOI={10.1007/s10455-023-09888-y}, number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch, Maximilian}, year={2023} }","chicago":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” Annals of Global Analysis and Geometry 63, no. 21 (2023). https://doi.org/10.1007/s10455-023-09888-y.","apa":"Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. Annals of Global Analysis and Geometry, 63(21). https://doi.org/10.1007/s10455-023-09888-y","ama":"Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. Annals of Global Analysis and Geometry. 2023;63(21). doi:10.1007/s10455-023-09888-y","ieee":"M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups,” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023, doi: 10.1007/s10455-023-09888-y.","short":"M. Hanusch, Annals of Global Analysis and Geometry 63 (2023)."},"_id":"34832","date_updated":"2023-04-05T18:18:24Z","intvolume":" 63","issue":"21","doi":"10.1007/s10455-023-09888-y","author":[{"last_name":"Hanusch","id":"30905","first_name":"Maximilian","full_name":"Hanusch, Maximilian"}],"publication":"Annals of Global Analysis and Geometry","department":[{"_id":"93"}],"keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"status":"public","project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"date_created":"2022-12-22T09:45:34Z","publication_status":"published","volume":63,"user_id":"30905","title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups"},{"date_created":"2023-05-05T06:52:39Z","status":"public","publication":"arXiv:2304.10243","department":[{"_id":"542"}],"author":[{"last_name":"Cappello","id":"72874","first_name":"Chiara","full_name":"Cappello, Chiara"},{"last_name":"Naserasr","full_name":"Naserasr, Reza","first_name":"Reza"},{"last_name":"Steffen","id":"15548","first_name":"Eckhard","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401"},{"last_name":"Wang","full_name":"Wang, Zhouningxin","first_name":"Zhouningxin"}],"title":"Critically 3-frustrated signed graphs","user_id":"15540","abstract":[{"lang":"eng","text":"Extending the notion of maxcut, the study of the frustration index of signed graphs is one of the basic questions in the theory of signed graphs. Recently two of the authors initiated the study of critically frustrated signed graphs. That is a signed graph whose frustration index decreases with the removal of any edge. The main focus of this study is on critical signed graphs which are not edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable signed graphs) and which are not built from other critically frustrated signed graphs by subdivision. We conjecture that for any given k there are only finitely many critically k-frustrated signed graphs of this kind.\r\nProviding support for this conjecture we show that there are only two of such critically 3-frustrated signed graphs where there is no pair of edge-disjoint negative cycles. Similarly, we show that there are exactly ten critically 3-frustrated signed planar graphs that are neither decomposable nor subdivisions of other critically frustrated signed graphs. We present a method for building non-decomposable critically frustrated signed graphs based on two given such signed graphs. We also show that the condition of being non-decomposable is necessary for our conjecture. "}],"external_id":{"arxiv":["2304.10243"]},"citation":{"mla":"Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","bibtex":"@article{Cappello_Naserasr_Steffen_Wang_2023, title={Critically 3-frustrated signed graphs}, journal={arXiv:2304.10243}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2023} }","apa":"Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically 3-frustrated signed graphs. In arXiv:2304.10243.","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. arXiv:230410243. Published online 2023.","chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” arXiv:2304.10243. 2023.","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023)."},"type":"preprint","year":"2023","language":[{"iso":"eng"}],"date_updated":"2023-05-05T06:53:47Z","_id":"44501"},{"citation":{"ieee":"H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V. Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,” RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi: 10.1051/ro/2023052.","short":"H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058.","mla":"Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3, EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052.","bibtex":"@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms for the genome median under a restricted measure of rearrangement}, volume={57}, DOI={10.1051/ro/2023052}, number={3}, journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }","chicago":"Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023): 1045–58. https://doi.org/10.1051/ro/2023052.","ama":"Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052","apa":"Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052"},"year":"2023","type":"journal_article","page":"1045-1058","issue":"3","_id":"44857","intvolume":" 57","status":"public","date_created":"2023-05-16T08:48:22Z","volume":57,"publisher":"EDP Sciences","author":[{"last_name":"Silva","full_name":"Silva, Helmuth O.M.","first_name":"Helmuth O.M."},{"last_name":"Rubert","first_name":"Diego P.","full_name":"Rubert, Diego P."},{"first_name":"Eloi","full_name":"Araujo, Eloi","last_name":"Araujo"},{"orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"last_name":"Doerr","first_name":"Daniel","full_name":"Doerr, Daniel"},{"last_name":"Martinez","first_name":"Fábio V.","full_name":"Martinez, Fábio V."}],"publication":"RAIRO - Operations Research","keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"user_id":"15540","abstract":[{"lang":"eng","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."}],"language":[{"iso":"eng"}],"doi":"10.1051/ro/2023052","date_updated":"2023-05-16T08:49:30Z","publication_status":"published","publication_identifier":{"issn":["0399-0559","2804-7303"]},"department":[{"_id":"542"}],"title":"Algorithms for the genome median under a restricted measure of rearrangement"},{"date_updated":"2023-05-16T11:17:26Z","_id":"44859","language":[{"iso":"eng"}],"year":"2023","type":"preprint","citation":{"ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” arXiv:2305.08619. 2023.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs. arXiv:230508619. Published online 2023.","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In arXiv:2305.08619.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023."},"user_id":"15540","title":"Sets of r-graphs that color all r-graphs","external_id":{"arxiv":["2305.08619"]},"date_created":"2023-05-16T10:07:47Z","status":"public","department":[{"_id":"542"}],"publication":"arXiv:2305.08619","author":[{"last_name":"Ma","id":"92748","first_name":"Yulai","full_name":"Ma, Yulai"},{"full_name":"Mattiolo, Davide","first_name":"Davide","last_name":"Mattiolo"},{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","last_name":"Steffen","id":"15548"},{"last_name":"Wolf","id":"88145","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus"}]},{"user_id":"30905","title":"Decompositions of Analytic 1-Manifolds","status":"public","date_created":"2022-12-22T09:46:36Z","publication_status":"published","volume":34,"author":[{"full_name":"Hanusch, Maximilian","first_name":"Maximilian","id":"30905","last_name":"Hanusch"}],"department":[{"_id":"93"}],"publication":"Indagationes Mathematicae.","keyword":["Lie group actions and analytic 1-submanifolds"],"issue":"4","doi":"10.1016/j.indag.2023.02.003","intvolume":" 34","_id":"34833","date_updated":"2023-05-25T07:32:38Z","language":[{"iso":"eng"}],"citation":{"chicago":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes Mathematicae. 34, no. 4 (2023): 752–811. https://doi.org/10.1016/j.indag.2023.02.003.","ama":"Hanusch M. Decompositions of Analytic 1-Manifolds. Indagationes Mathematicae. 2023;34(4):752-811. doi:10.1016/j.indag.2023.02.003","apa":"Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. Indagationes Mathematicae., 34(4), 752–811. https://doi.org/10.1016/j.indag.2023.02.003","mla":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes Mathematicae., vol. 34, no. 4, 2023, pp. 752–811, doi:10.1016/j.indag.2023.02.003.","bibtex":"@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds}, volume={34}, DOI={10.1016/j.indag.2023.02.003}, number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian}, year={2023}, pages={752–811} }","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.","ieee":"M. Hanusch, “Decompositions of Analytic 1-Manifolds,” Indagationes Mathematicae., vol. 34, no. 4, pp. 752–811, 2023, doi: 10.1016/j.indag.2023.02.003."},"type":"journal_article","year":"2023","page":"752-811"},{"main_file_link":[{"url":"https://arxiv.org/pdf/2306.03320"}],"year":"2023","citation":{"short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320. .","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.","ama":"von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order phase reduction in coupled oscillator networks. arXiv:230603320.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320, n.d.","mla":"von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.","bibtex":"@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }"},"type":"preprint","page":"29","language":[{"iso":"eng"}],"_id":"45498","date_updated":"2023-06-07T07:59:06Z","author":[{"first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","last_name":"von der Gracht","id":"97359"},{"first_name":"Eddie","full_name":"Nijholt, Eddie","last_name":"Nijholt"},{"full_name":"Rink, Bob","first_name":"Bob","last_name":"Rink"}],"department":[{"_id":"101"}],"publication":"arXiv:2306.03320","publication_status":"submitted","status":"public","date_created":"2023-06-07T07:57:28Z","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."}],"external_id":{"arxiv":["2306.03320"]},"title":"A parametrisation method for high-order phase reduction in coupled oscillator networks","user_id":"97359"},{"publisher":"Friedrich Verlag","author":[{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"}],"publication":"Die Grundschulzeitschrift","department":[{"_id":"543"}],"status":"public","date_created":"2023-06-22T09:28:22Z","related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"user_id":"44184","title":" Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen","language":[{"iso":"ger"}],"citation":{"chicago":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift, no. 339 (2023): 6–11.","ama":"Häsel-Weide U. Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift. 2023;(339):6-11.","apa":"Häsel-Weide, U. (2023). Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift, 339, 6–11.","mla":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift, no. 339, Friedrich Verlag, 2023, pp. 6–11.","bibtex":"@article{Häsel-Weide_2023, title={ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen}, number={339}, journal={Die Grundschulzeitschrift}, publisher={Friedrich Verlag}, author={Häsel-Weide, Uta}, year={2023}, pages={6–11} }","short":"U. Häsel-Weide, Die Grundschulzeitschrift (2023) 6–11.","ieee":"U. Häsel-Weide, “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen,” Die Grundschulzeitschrift, no. 339, pp. 6–11, 2023."},"type":"journal_article","year":"2023","page":"6-11","date_updated":"2023-06-22T09:34:13Z","_id":"45712","issue":"339"},{"status":"public","date_created":"2023-06-22T09:33:59Z","publisher":"Friedrich Verlag","author":[{"full_name":"Graf, Lara Marie","first_name":"Lara Marie","id":"89837","last_name":"Graf"},{"first_name":"Inga","full_name":"Wienhues, Inga","last_name":"Wienhues","id":"61635"},{"id":"60267","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","first_name":"Uta"}],"department":[{"_id":"543"}],"publication":"Die Grundschulzeitschrift","title":"Addition und Subtraktion verstehen","related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"user_id":"44184","type":"journal_article","citation":{"bibtex":"@article{Graf_Wienhues_Häsel-Weide_2023, title={Addition und Subtraktion verstehen}, number={339}, journal={Die Grundschulzeitschrift}, publisher={Friedrich Verlag}, author={Graf, Lara Marie and Wienhues, Inga and Häsel-Weide, Uta}, year={2023}, pages={20–23} }","mla":"Graf, Lara Marie, et al. “Addition und Subtraktion verstehen.” Die Grundschulzeitschrift, no. 339, Friedrich Verlag, 2023, pp. 20–23.","ama":"Graf LM, Wienhues I, Häsel-Weide U. Addition und Subtraktion verstehen. Die Grundschulzeitschrift. 2023;(339):20-23.","apa":"Graf, L. M., Wienhues, I., & Häsel-Weide, U. (2023). Addition und Subtraktion verstehen. Die Grundschulzeitschrift, 339, 20–23.","chicago":"Graf, Lara Marie, Inga Wienhues, and Uta Häsel-Weide. “Addition und Subtraktion verstehen.” Die Grundschulzeitschrift, no. 339 (2023): 20–23.","ieee":"L. M. Graf, I. Wienhues, and U. Häsel-Weide, “Addition und Subtraktion verstehen,” Die Grundschulzeitschrift, no. 339, pp. 20–23, 2023.","short":"L.M. Graf, I. Wienhues, U. Häsel-Weide, Die Grundschulzeitschrift (2023) 20–23."},"year":"2023","page":"20-23","language":[{"iso":"ger"}],"issue":"339","date_updated":"2023-06-22T09:34:18Z","_id":"45713"},{"oa":"1","doi":"10.1007/s11858-023-01505-3","date_updated":"2023-07-13T09:41:20Z","language":[{"iso":"eng"}],"title":"Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course","publication_status":"published","publication_identifier":{"issn":["1863-9690","1863-9704"]},"department":[{"_id":"97"},{"_id":"643"}],"_id":"45786","type":"journal_article","citation":{"chicago":"Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM – Mathematics Education, 2023. https://doi.org/10.1007/s11858-023-01505-3.","apa":"Hoffmann, M., & Biehler, R. (2023). Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-023-01505-3","ama":"Hoffmann M, Biehler R. Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. Published online 2023. doi:10.1007/s11858-023-01505-3","bibtex":"@article{Hoffmann_Biehler_2023, title={Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}, DOI={10.1007/s11858-023-01505-3}, journal={ZDM – Mathematics Education}, publisher={Springer}, author={Hoffmann, Max and Biehler, Rolf}, year={2023} }","mla":"Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM – Mathematics Education, Springer, 2023, doi:10.1007/s11858-023-01505-3.","short":"M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2023).","ieee":"M. Hoffmann and R. Biehler, “Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01505-3."},"year":"2023","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/s11858-023-01505-3"}],"user_id":"32202","ddc":["510","370"],"abstract":[{"lang":"eng","text":"Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers."}],"article_type":"original","date_created":"2023-06-27T11:45:25Z","status":"public","has_accepted_license":"1","file":[{"date_created":"2023-07-13T09:40:02Z","file_name":"s11858-023-01505-3.pdf","access_level":"closed","file_id":"46041","creator":"maxh","file_size":1460246,"success":1,"relation":"main_file","content_type":"application/pdf","date_updated":"2023-07-13T09:40:02Z"}],"file_date_updated":"2023-07-13T09:40:02Z","publication":"ZDM – Mathematics Education","keyword":["General Mathematics","Education"],"quality_controlled":"1","publisher":"Springer","author":[{"full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123","first_name":"Max","id":"32202","last_name":"Hoffmann"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"}]},{"publication_status":"published","publication_identifier":{"issn":["0022-247X"]},"department":[{"_id":"799"}],"title":"Super-Gaussian decay of exponentials: A sufficient condition","external_id":{"arxiv":["2205.09189"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.jmaa.2023.127558","date_updated":"2023-07-20T05:11:12Z","volume":528,"status":"public","date_created":"2023-07-20T05:08:49Z","publisher":"Elsevier BV","author":[{"full_name":"Hinrichs, Benjamin","orcid":"0000-0001-9074-1205","first_name":"Benjamin","id":"99427","last_name":"Hinrichs"},{"full_name":"Janssen, Daan W.","first_name":"Daan W.","last_name":"Janssen"},{"last_name":"Ziebell","first_name":"Jobst","full_name":"Ziebell, Jobst"}],"publication":"Journal of Mathematical Analysis and Applications","keyword":["Applied Mathematics","Analysis"],"user_id":"99427","year":"2023","citation":{"ieee":"B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials: A sufficient condition,” Journal of Mathematical Analysis and Applications, vol. 528, no. 1, Art. no. 127558, 2023, doi: 10.1016/j.jmaa.2023.127558.","short":"B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and Applications 528 (2023).","mla":"Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” Journal of Mathematical Analysis and Applications, vol. 528, no. 1, 127558, Elsevier BV, 2023, doi:10.1016/j.jmaa.2023.127558.","bibtex":"@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of exponentials: A sufficient condition}, volume={528}, DOI={10.1016/j.jmaa.2023.127558}, number={1127558}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}, year={2023} }","apa":"Hinrichs, B., Janssen, D. W., & Ziebell, J. (2023). Super-Gaussian decay of exponentials: A sufficient condition. Journal of Mathematical Analysis and Applications, 528(1), Article 127558. https://doi.org/10.1016/j.jmaa.2023.127558","ama":"Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A sufficient condition. Journal of Mathematical Analysis and Applications. 2023;528(1). doi:10.1016/j.jmaa.2023.127558","chicago":"Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” Journal of Mathematical Analysis and Applications 528, no. 1 (2023). https://doi.org/10.1016/j.jmaa.2023.127558."},"type":"journal_article","article_number":"127558","issue":"1","_id":"46100","intvolume":" 528"},{"language":[{"iso":"eng"}],"type":"preprint","year":"2023","citation":{"bibtex":"@article{Weich_Wolf_2023, title={Temperedness of locally symmetric spaces: The product case}, journal={arXiv:2304.09573}, author={Weich, Tobias and Wolf, Lasse L.}, year={2023} }","mla":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” ArXiv:2304.09573, 2023.","chicago":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” ArXiv:2304.09573, 2023.","apa":"Weich, T., & Wolf, L. L. (2023). Temperedness of locally symmetric spaces: The product case. In arXiv:2304.09573.","ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. arXiv:230409573. Published online 2023.","ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” arXiv:2304.09573. 2023.","short":"T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023)."},"_id":"46117","date_updated":"2023-07-24T07:53:29Z","department":[{"_id":"10"}],"publication":"arXiv:2304.09573","author":[{"last_name":"Weich","full_name":"Weich, Tobias","first_name":"Tobias"},{"last_name":"Wolf","full_name":"Wolf, Lasse L.","first_name":"Lasse L."}],"date_created":"2023-07-24T07:52:23Z","status":"public","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"}],"external_id":{"arxiv":["2304.09573"]},"user_id":"45027","title":"Temperedness of locally symmetric spaces: The product case"},{"title":"Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?","publication_identifier":{"issn":["0742-051X"]},"publication_status":"published","department":[{"_id":"611"}],"doi":"10.1016/j.tate.2023.104270","date_updated":"2023-07-26T08:57:01Z","language":[{"iso":"eng"}],"user_id":"72183","volume":132,"date_created":"2023-07-26T08:55:26Z","status":"public","publication":"Teaching and Teacher Education","keyword":["Education"],"author":[{"last_name":"Bruns","full_name":"Bruns, Julia","first_name":"Julia"},{"full_name":"Hagena, Maike","first_name":"Maike","last_name":"Hagena"},{"last_name":"Gasteiger","full_name":"Gasteiger, Hedwig","first_name":"Hedwig"}],"publisher":"Elsevier BV","article_number":"104270","intvolume":" 132","_id":"46155","year":"2023","type":"journal_article","citation":{"apa":"Bruns, J., Hagena, M., & Gasteiger, H. 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Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023).","ieee":"J. Bruns, M. Hagena, and H. Gasteiger, “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?,” Teaching and Teacher Education, vol. 132, Art. no. 104270, 2023, doi: 10.1016/j.tate.2023.104270."}},{"year":"2023","type":"book_editor","citation":{"ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023.","short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","bibtex":"@book{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education}, DOI={10.1007/978-3-031-14175-1}, publisher={Springer International Publishing}, year={2023} }","mla":"Biehler, Rolf, et al., editors. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing, 2023, doi:10.1007/978-3-031-14175-1.","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1.","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023. doi:10.1007/978-3-031-14175-1","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (Eds.). (2023). Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1"},"language":[{"iso":"eng"}],"_id":"46157","date_updated":"2023-07-26T10:17:43Z","doi":"10.1007/978-3-031-14175-1","publisher":"Springer International Publishing","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"editor":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"last_name":"Liebendörfer","id":"30933","first_name":"Michael","full_name":"Liebendörfer, Michael","orcid":"0000-0001-9887-2074"},{"last_name":"Gueudet","first_name":"Ghislaine","full_name":"Gueudet, Ghislaine"},{"first_name":"Chris","full_name":"Rasmussen, Chris","last_name":"Rasmussen"},{"last_name":"Winsløw","full_name":"Winsløw, Carl","first_name":"Carl"}],"publication_status":"published","publication_identifier":{"isbn":["9783031141744","9783031141751"],"issn":["1869-4918","1869-4926"]},"status":"public","date_created":"2023-07-26T10:16:08Z","place":"Cham","title":"Practice-Oriented Research in Tertiary Mathematics Education","user_id":"37888"},{"department":[{"_id":"542"}],"publication_status":"published","publication_identifier":{"issn":["0895-4801","1095-7146"]},"title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs","language":[{"iso":"eng"}],"date_updated":"2023-08-01T10:09:35Z","doi":"10.1137/22m1500654","author":[{"full_name":"Ma, Yulai","first_name":"Yulai","id":"92748","last_name":"Ma"},{"last_name":"Mattiolo","first_name":"Davide","full_name":"Mattiolo, Davide"},{"last_name":"Steffen","id":"15548","first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard"},{"id":"88145","last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus"}],"publisher":"Society for Industrial & Applied Mathematics (SIAM)","publication":"SIAM Journal on Discrete Mathematics","keyword":["General Mathematics"],"volume":37,"status":"public","date_created":"2023-08-01T10:08:32Z","user_id":"15540","year":"2023","type":"journal_article","citation":{"bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }","mla":"Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. doi:10.1137/22m1500654","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565."},"page":"1548-1565","_id":"46256","intvolume":" 37","issue":"3"},{"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."}],"ddc":["510"],"user_id":"85279","quality_controlled":"1","author":[{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"publisher":"Springer, Cham.","publication":"Geometric Science of Information","file_date_updated":"2023-08-02T12:04:17Z","keyword":["System identification","discrete Lagrangians","travelling waves"],"file":[{"access_level":"open_access","file_name":"LDensityLearning.pdf","date_created":"2023-08-02T12:04:17Z","content_type":"application/pdf","date_updated":"2023-08-02T12:04:17Z","relation":"main_file","description":"The article shows how to learn models of dynamical systems\nfrom data which are governed by an unknown variational PDE. Rather\nthan employing reduction techniques, we learn a discrete field theory\ngoverned by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is\nnecessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of\nthe discrete Euler–Lagrange equations. Secondly, we develop a method to\nfind solutions to machine learned discrete field theories which constitute\ntravelling waves of the underlying continuous PDE.","file_size":1938962,"creator":"coffen","file_id":"46273","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves"}],"volume":14071,"has_accepted_license":"1","status":"public","date_created":"2023-02-16T11:32:48Z","intvolume":" 14071","_id":"42163","conference":{"location":"Saint-Malo, Palais du Grand Large, France","start_date":"2023-08-30","name":" GSI'23 6th International Conference on Geometric Science of Information","end_date":"2023-09-01"},"type":"conference","year":"2023","citation":{"mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57.","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","apa":"Offen, C., & Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen & F. Barbaresco (Eds.), Geometric Science of Information (Vol. 14071, pp. 569–579). Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_57","ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. Geometric Science of Information. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:10.1007/978-3-031-38271-0_57","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In Geometric Science of Information, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. https://doi.org/10.1007/978-3-031-38271-0_57.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in Geometric Science of Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579."},"page":"569-579","external_id":{"arxiv":["2302.08232 "]},"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML"}]},"department":[{"_id":"636"}],"editor":[{"last_name":"Nielsen","full_name":"Nielsen, F","first_name":"F"},{"first_name":"F","full_name":"Barbaresco, F","last_name":"Barbaresco"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"publication_status":"published","date_updated":"2023-08-10T08:34:04Z","doi":"10.1007/978-3-031-38271-0_57","oa":"1","series_title":"Lecture Notes in Computer Science (LNCS)","language":[{"iso":"eng"}]},{"intvolume":" 421","_id":"29240","page":"114780","type":"journal_article","citation":{"short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” Journal of Computational and Applied Mathematics, vol. 421, p. 114780, 2023, doi: 10.1016/j.cam.2022.114780.","chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics 421 (2023): 114780. https://doi.org/10.1016/j.cam.2022.114780.","apa":"Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics, 421, 114780. https://doi.org/10.1016/j.cam.2022.114780","ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics. 2023;421:114780. doi:10.1016/j.cam.2022.114780","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics, vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780.","bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }"},"year":"2023","user_id":"85279","ddc":["510"],"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."}],"article_type":"original","date_created":"2022-01-11T13:24:00Z","status":"public","has_accepted_license":"1","volume":421,"file":[{"file_size":3640770,"title":"Variational Learning of Euler–Lagrange Dynamics from Data","file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","date_created":"2022-06-28T15:25:50Z","access_level":"open_access","creator":"coffen","file_id":"32274","date_updated":"2022-06-28T15:25:50Z","content_type":"application/pdf","relation":"main_file","description":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions\nconnecting two points in a phase space, the system will exhibit those motions which extremise an action functional.\nMany qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-\ntions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms\nfor dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features\nwith the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-\ntions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position\ndata of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no\nprior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward\nerror analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the\nlearned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of\nvariational backward error analysis. (3) Finally, we introduce a method to perform system identification from position\nobservations only, based on variational backward error analysis."}],"keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"file_date_updated":"2022-06-28T15:25:50Z","publication":"Journal of Computational and Applied Mathematics","author":[{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","id":"85279","last_name":"Offen"}],"publisher":"Elsevier","quality_controlled":"1","oa":"1","doi":"10.1016/j.cam.2022.114780","date_updated":"2023-08-10T08:42:39Z","language":[{"iso":"eng"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianShadowIntegration","relation":"software"}]},"title":"Variational Learning of Euler–Lagrange Dynamics from Data","external_id":{"arxiv":["2112.12619"]},"publication_status":"epub_ahead","publication_identifier":{"issn":["0377-0427"]},"department":[{"_id":"636"}]},{"external_id":{"arxiv":["2201.03911"]},"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/BEAConjugateSymplectic"}]},"title":"Backward error analysis for conjugate symplectic methods","department":[{"_id":"636"}],"publication_status":"published","date_updated":"2023-08-10T08:40:30Z","oa":"1","doi":"10.3934/jgm.2023005","language":[{"iso":"eng"}],"article_type":"original","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"}],"user_id":"85279","ddc":["510"],"file":[{"relation":"main_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.","content_type":"application/pdf","date_updated":"2022-08-12T16:48:59Z","file_id":"32801","creator":"coffen","access_level":"open_access","file_name":"BEA_MultiStep_Matrix.pdf","date_created":"2022-08-12T16:48:59Z","title":"Backward error analysis for conjugate symplectic methods","file_size":827030}],"quality_controlled":"1","author":[{"full_name":"McLachlan, Robert","first_name":"Robert","last_name":"McLachlan"},{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"}],"publisher":"AIMS Press","file_date_updated":"2022-08-12T16:48:59Z","publication":"Journal of Geometric Mechanics","keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"has_accepted_license":"1","status":"public","date_created":"2022-01-11T12:48:39Z","volume":15,"intvolume":" 15","_id":"29236","issue":"1","year":"2023","citation":{"short":"R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.","ieee":"R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” Journal of Geometric Mechanics, vol. 15, no. 1, pp. 98–115, 2023, doi: 10.3934/jgm.2023005.","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005","apa":"McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115. https://doi.org/10.3934/jgm.2023005","chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115. https://doi.org/10.3934/jgm.2023005.","bibtex":"@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={10.3934/jgm.2023005}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }","mla":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:10.3934/jgm.2023005."},"type":"journal_article","page":"98-115"},{"year":"2023","citation":{"short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","ieee":"E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art. no. 063115, 2023, doi: 10.1063/5.0142969.","apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos, 33(6), Article 063115. https://doi.org/10.1063/5.0142969","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969","chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos 33, no. 6 (2023). https://doi.org/10.1063/5.0142969.","mla":"Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.","bibtex":"@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }"},"type":"journal_article","article_number":"063115","issue":"6","_id":"37654","intvolume":" 33","volume":33,"has_accepted_license":"1","status":"public","date_created":"2023-01-20T09:10:06Z","publisher":"AIP Publishing","author":[{"full_name":"Dierkes, Eva","first_name":"Eva","last_name":"Dierkes"},{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"}],"publication":"Chaos","file_date_updated":"2023-04-26T16:20:56Z","file":[{"file_name":"JournalPaper_main.pdf","date_created":"2023-04-26T16:20:56Z","access_level":"open_access","file_size":5200111,"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","file_id":"44205","creator":"coffen","content_type":"application/pdf","date_updated":"2023-04-26T16:20:56Z","description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously.","relation":"main_file"}],"ddc":["510"],"user_id":"85279","article_type":"original","abstract":[{"lang":"eng","text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered."}],"language":[{"iso":"eng"}],"doi":"10.1063/5.0142969","oa":"1","date_updated":"2023-08-10T08:37:01Z","publication_status":"published","publication_identifier":{"issn":["1054-1500"]},"department":[{"_id":"636"}],"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"external_id":{"arxiv":["2301.07928"]}},{"department":[{"_id":"101"},{"_id":"655"}],"publication_status":"published","title":"Finite-data error bounds for Koopman-based prediction and control","language":[{"iso":"eng"}],"date_updated":"2023-08-24T07:50:12Z","doi":"10.1007/s00332-022-09862-1","oa":"1","publication":"Journal of Nonlinear Science","author":[{"first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","last_name":"Nüske","id":"81513"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"full_name":"Philipp, Friedrich","first_name":"Friedrich","last_name":"Philipp"},{"last_name":"Schaller","full_name":"Schaller, Manuel","first_name":"Manuel"},{"last_name":"Worthmann","first_name":"Karl","full_name":"Worthmann, Karl"}],"volume":33,"date_created":"2021-08-17T12:25:09Z","status":"public","abstract":[{"text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.","lang":"eng"}],"user_id":"47427","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"citation":{"ieee":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” Journal of Nonlinear Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.","short":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023).","bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.","chicago":"Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.","apa":"Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1","ama":"Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-022-09862-1"},"year":"2023","type":"journal_article","intvolume":" 33","_id":"23428","article_number":"14"}]