[{"user_id":"99427","volume":528,"status":"public","date_created":"2023-07-20T05:08:49Z","publisher":"Elsevier BV","author":[{"last_name":"Hinrichs","id":"99427","first_name":"Benjamin","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin"},{"last_name":"Janssen","full_name":"Janssen, Daan W.","first_name":"Daan W."},{"last_name":"Ziebell","first_name":"Jobst","full_name":"Ziebell, Jobst"}],"publication":"Journal of Mathematical Analysis and Applications","keyword":["Applied Mathematics","Analysis"],"article_number":"127558","issue":"1","_id":"46100","intvolume":" 528","year":"2023","type":"journal_article","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."},"title":"Super-Gaussian decay of exponentials: A sufficient condition","external_id":{"arxiv":["2205.09189"]},"publication_identifier":{"issn":["0022-247X"]},"publication_status":"published","department":[{"_id":"799"}],"doi":"10.1016/j.jmaa.2023.127558","date_updated":"2023-07-20T05:11:12Z","language":[{"iso":"eng"}]},{"date_updated":"2023-07-24T07:53:29Z","_id":"46117","language":[{"iso":"eng"}],"citation":{"chicago":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” ArXiv:2304.09573, 2023.","ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. arXiv:230409573. Published online 2023.","apa":"Weich, T., & Wolf, L. L. (2023). Temperedness of locally symmetric spaces: The product case. In arXiv:2304.09573.","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.","short":"T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023).","ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” arXiv:2304.09573. 2023."},"type":"preprint","year":"2023","user_id":"45027","title":"Temperedness of locally symmetric spaces: The product case","external_id":{"arxiv":["2304.09573"]},"abstract":[{"text":"Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$.","lang":"eng"}],"status":"public","date_created":"2023-07-24T07:52:23Z","author":[{"last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"},{"last_name":"Wolf","first_name":"Lasse L.","full_name":"Wolf, Lasse L."}],"publication":"arXiv:2304.09573","department":[{"_id":"10"}]},{"language":[{"iso":"eng"}],"doi":"10.1016/j.tate.2023.104270","date_updated":"2023-07-26T08:57:01Z","publication_identifier":{"issn":["0742-051X"]},"publication_status":"published","department":[{"_id":"611"}],"title":"Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?","citation":{"ama":"Bruns J, Hagena M, Gasteiger H. Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects? Teaching and Teacher Education. 2023;132. doi:10.1016/j.tate.2023.104270","apa":"Bruns, J., Hagena, M., & Gasteiger, H. (2023). Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects? Teaching and Teacher Education, 132, Article 104270. https://doi.org/10.1016/j.tate.2023.104270","chicago":"Bruns, Julia, Maike Hagena, and Hedwig Gasteiger. “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?” Teaching and Teacher Education 132 (2023). https://doi.org/10.1016/j.tate.2023.104270.","mla":"Bruns, Julia, et al. “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?” Teaching and Teacher Education, vol. 132, 104270, Elsevier BV, 2023, doi:10.1016/j.tate.2023.104270.","bibtex":"@article{Bruns_Hagena_Gasteiger_2023, title={Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?}, volume={132}, DOI={10.1016/j.tate.2023.104270}, number={104270}, journal={Teaching and Teacher Education}, publisher={Elsevier BV}, author={Bruns, Julia and Hagena, Maike and Gasteiger, Hedwig}, year={2023} }","short":"J. Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023).","ieee":"J. Bruns, M. Hagena, and H. Gasteiger, “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?,” Teaching and Teacher Education, vol. 132, Art. no. 104270, 2023, doi: 10.1016/j.tate.2023.104270."},"year":"2023","type":"journal_article","article_number":"104270","intvolume":" 132","_id":"46155","status":"public","date_created":"2023-07-26T08:55:26Z","volume":132,"author":[{"full_name":"Bruns, Julia","first_name":"Julia","last_name":"Bruns"},{"last_name":"Hagena","first_name":"Maike","full_name":"Hagena, Maike"},{"first_name":"Hedwig","full_name":"Gasteiger, Hedwig","last_name":"Gasteiger"}],"publisher":"Elsevier BV","publication":"Teaching and Teacher Education","keyword":["Education"],"user_id":"72183"},{"doi":"10.1007/978-3-031-14175-1","date_updated":"2023-07-26T10:17:43Z","_id":"46157","year":"2023","type":"book_editor","citation":{"mla":"Biehler, Rolf, et al., editors. Practice-Oriented Research in Tertiary Mathematics Education. 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Springer International Publishing; 2023. doi:10.1007/978-3-031-14175-1","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."},"language":[{"iso":"eng"}],"title":"Practice-Oriented Research in Tertiary Mathematics Education","user_id":"37888","place":"Cham","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"publication_status":"published","editor":[{"full_name":"Biehler, Rolf","first_name":"Rolf","id":"16274","last_name":"Biehler"},{"last_name":"Liebendörfer","id":"30933","first_name":"Michael","orcid":"0000-0001-9887-2074","full_name":"Liebendörfer, Michael"},{"full_name":"Gueudet, Ghislaine","first_name":"Ghislaine","last_name":"Gueudet"},{"full_name":"Rasmussen, Chris","first_name":"Chris","last_name":"Rasmussen"},{"last_name":"Winsløw","full_name":"Winsløw, Carl","first_name":"Carl"}],"date_created":"2023-07-26T10:16:08Z","status":"public","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publisher":"Springer International Publishing"},{"keyword":["General Mathematics"],"publication":"SIAM Journal on Discrete Mathematics","publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"first_name":"Yulai","full_name":"Ma, Yulai","last_name":"Ma","id":"92748"},{"full_name":"Mattiolo, Davide","first_name":"Davide","last_name":"Mattiolo"},{"id":"15548","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard"},{"full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","id":"88145","last_name":"Wolf"}],"volume":37,"date_created":"2023-08-01T10:08:32Z","status":"public","user_id":"15540","page":"1548-1565","type":"journal_article","citation":{"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.","mla":"Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }","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.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. doi:10.1137/22m1500654","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654"},"year":"2023","_id":"46256","intvolume":" 37","issue":"3","department":[{"_id":"542"}],"publication_identifier":{"issn":["0895-4801","1095-7146"]},"publication_status":"published","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"},{"editor":[{"last_name":"Nielsen","full_name":"Nielsen, F","first_name":"F"},{"last_name":"Barbaresco","first_name":"F","full_name":"Barbaresco, F"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"publication_status":"published","department":[{"_id":"636"}],"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianDensityML","relation":"software","description":"GitHub"}]},"external_id":{"arxiv":["2302.08232 "]},"language":[{"iso":"eng"}],"series_title":"Lecture Notes in Computer Science (LNCS)","doi":"10.1007/978-3-031-38271-0_57","oa":"1","date_updated":"2023-08-10T08:34:04Z","volume":14071,"status":"public","has_accepted_license":"1","date_created":"2023-02-16T11:32:48Z","publisher":"Springer, Cham.","author":[{"last_name":"Offen","id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian"},{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"quality_controlled":"1","keyword":["System identification","discrete Lagrangians","travelling waves"],"file_date_updated":"2023-08-02T12:04:17Z","publication":"Geometric Science of Information","file":[{"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.","date_updated":"2023-08-02T12:04:17Z","content_type":"application/pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","creator":"coffen","file_id":"46273","file_size":1938962,"access_level":"open_access","file_name":"LDensityLearning.pdf","date_created":"2023-08-02T12:04:17Z"}],"ddc":["510"],"user_id":"85279","abstract":[{"lang":"eng","text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE."}],"year":"2023","citation":{"short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in Geometric Science of Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.","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.","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57."},"type":"conference","page":"569-579","intvolume":" 14071","_id":"42163","conference":{"end_date":"2023-09-01","location":"Saint-Malo, Palais du Grand Large, France","name":" GSI'23 6th International Conference on Geometric Science of Information","start_date":"2023-08-30"}},{"intvolume":" 421","_id":"29240","page":"114780","type":"journal_article","citation":{"bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics, vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780.","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","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” Journal of Computational and Applied Mathematics, vol. 421, p. 114780, 2023, doi: 10.1016/j.cam.2022.114780.","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780."},"year":"2023","user_id":"85279","ddc":["510"],"abstract":[{"text":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\r\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.","lang":"eng"}],"article_type":"original","date_created":"2022-01-11T13:24:00Z","has_accepted_license":"1","status":"public","volume":421,"file":[{"file_id":"32274","creator":"coffen","content_type":"application/pdf","date_updated":"2022-06-28T15:25:50Z","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.","date_created":"2022-06-28T15:25:50Z","file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","access_level":"open_access","file_size":3640770,"title":"Variational Learning of Euler–Lagrange Dynamics from Data"}],"file_date_updated":"2022-06-28T15:25:50Z","publication":"Journal of Computational and Applied Mathematics","keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"quality_controlled":"1","publisher":"Elsevier","author":[{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"},{"id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian"}],"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_identifier":{"issn":["0377-0427"]},"publication_status":"epub_ahead","department":[{"_id":"636"}]},{"ddc":["510"],"user_id":"85279","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"}],"volume":15,"has_accepted_license":"1","status":"public","date_created":"2022-01-11T12:48:39Z","quality_controlled":"1","publisher":"AIMS Press","author":[{"last_name":"McLachlan","full_name":"McLachlan, Robert","first_name":"Robert"},{"id":"85279","last_name":"Offen","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian"}],"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"],"file":[{"file_size":827030,"title":"Backward error analysis for conjugate symplectic methods","file_name":"BEA_MultiStep_Matrix.pdf","date_created":"2022-08-12T16:48:59Z","access_level":"open_access","file_id":"32801","creator":"coffen","content_type":"application/pdf","date_updated":"2022-08-12T16:48:59Z","description":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","relation":"main_file"}],"issue":"1","intvolume":" 15","_id":"29236","year":"2023","citation":{"chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115. https://doi.org/10.3934/jgm.2023005.","apa":"McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115. https://doi.org/10.3934/jgm.2023005","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005","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.","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."},"type":"journal_article","page":"98-115","title":"Backward error analysis for conjugate symplectic methods","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/BEAConjugateSymplectic"}]},"external_id":{"arxiv":["2201.03911"]},"publication_status":"published","department":[{"_id":"636"}],"doi":"10.3934/jgm.2023005","oa":"1","date_updated":"2023-08-10T08:40:30Z","language":[{"iso":"eng"}]},{"intvolume":" 33","_id":"37654","article_number":"063115","issue":"6","citation":{"chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos 33, no. 6 (2023). https://doi.org/10.1063/5.0142969.","apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos, 33(6), Article 063115. https://doi.org/10.1063/5.0142969","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969","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} }","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."},"year":"2023","type":"journal_article","article_type":"original","abstract":[{"text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered.","lang":"eng"}],"ddc":["510"],"user_id":"85279","author":[{"first_name":"Eva","full_name":"Dierkes, Eva","last_name":"Dierkes"},{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"},{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"}],"publisher":"AIP Publishing","file_date_updated":"2023-04-26T16:20:56Z","publication":"Chaos","file":[{"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","file_size":5200111,"access_level":"open_access","file_name":"JournalPaper_main.pdf","date_created":"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","date_updated":"2023-04-26T16:20:56Z","content_type":"application/pdf","creator":"coffen","file_id":"44205"}],"volume":33,"status":"public","has_accepted_license":"1","date_created":"2023-01-20T09:10:06Z","date_updated":"2023-08-10T08:37:01Z","doi":"10.1063/5.0142969","oa":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2301.07928"]},"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"department":[{"_id":"636"}],"publication_identifier":{"issn":["1054-1500"]},"publication_status":"published"},{"date_created":"2021-08-17T12:25:09Z","status":"public","volume":33,"publication":"Journal of Nonlinear Science","author":[{"full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","first_name":"Feliks","id":"81513","last_name":"Nüske"},{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"last_name":"Philipp","first_name":"Friedrich","full_name":"Philipp, Friedrich"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"full_name":"Worthmann, Karl","first_name":"Karl","last_name":"Worthmann"}],"user_id":"47427","abstract":[{"lang":"eng","text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled."}],"type":"journal_article","year":"2023","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).","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.","bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","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","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","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."},"main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"article_number":"14","_id":"23428","intvolume":" 33","publication_status":"published","department":[{"_id":"101"},{"_id":"655"}],"title":"Finite-data error bounds for Koopman-based prediction and control","language":[{"iso":"eng"}],"oa":"1","doi":"10.1007/s00332-022-09862-1","date_updated":"2023-08-24T07:50:12Z"},{"language":[{"iso":"eng"}],"doi":"10.1137/21M1412682","date_updated":"2023-08-25T09:24:50Z","publication_status":"published","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"title":"Efficient time stepping for numerical integration using reinforcement learning","related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/lueckem/quadrature-ML"}]},"external_id":{"arxiv":["arXiv:2104.03562"]},"citation":{"chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing, 45(2), A579–A595. https://doi.org/10.1137/21M1412682","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing. 2023;45(2):A579-A595. doi:10.1137/21M1412682","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement learning}, volume={45}, DOI={10.1137/21M1412682}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol. 45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.","short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.","ieee":"M. Dellnitz et al., “Efficient time stepping for numerical integration using reinforcement learning,” SIAM Journal on Scientific Computing, vol. 45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682."},"year":"2023","type":"journal_article","page":"A579-A595","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"issue":"2","_id":"21600","intvolume":" 45","volume":45,"status":"public","has_accepted_license":"1","date_created":"2021-04-09T07:59:19Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Hüllermeier, Eyke","first_name":"Eyke","id":"48129","last_name":"Hüllermeier"},{"full_name":"Lücke, Marvin","first_name":"Marvin","last_name":"Lücke"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"last_name":"Offen","id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"first_name":"Karlson","orcid":"0000-0001-9407-7903","full_name":"Pfannschmidt, Karlson","last_name":"Pfannschmidt","id":"13472"}],"publication":"SIAM Journal on Scientific Computing","ddc":["510"],"user_id":"47427","abstract":[{"text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.","lang":"eng"}]},{"_id":"46757","date_updated":"2023-08-30T09:55:41Z","conference":{"name":"International Symposium in Elementary Mathematics Teaching","location":"Prag"},"language":[{"iso":"eng"}],"year":"2023","citation":{"ieee":"I. Schwerin and U. Häsel-Weide, “Second grader´s understanding of doubling and halfing in various representations,” in International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, Prag, 2023, pp. 297–305.","short":"I. Schwerin, U. Häsel-Weide, in: J. Novotna, H. Moraova (Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, Charles University, 2023, pp. 297–305.","mla":"Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of Doubling and Halfing in Various Representations.” International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, edited by J. Novotna and H. Moraova, Charles University, 2023, pp. 297–305.","bibtex":"@inproceedings{Schwerin_Häsel-Weide_2023, title={Second grader´s understanding of doubling and halfing in various representations}, booktitle={International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}, publisher={Charles University}, author={Schwerin, Imke and Häsel-Weide, Uta}, editor={Novotna, J. and Moraova, H.}, year={2023}, pages={297–305} }","ama":"Schwerin I, Häsel-Weide U. Second grader´s understanding of doubling and halfing in various representations. In: Novotna J, Moraova H, eds. International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education. Charles University; 2023:297-305.","apa":"Schwerin, I., & Häsel-Weide, U. (2023). Second grader´s understanding of doubling and halfing in various representations. In J. Novotna & H. Moraova (Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education (pp. 297–305). Charles University.","chicago":"Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of Doubling and Halfing in Various Representations.” In International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education, edited by J. Novotna and H. Moraova, 297–305. Charles University, 2023."},"type":"conference","page":"297-305","user_id":"44184","title":"Second grader´s understanding of doubling and halfing in various representations","status":"public","date_created":"2023-08-30T09:40:23Z","editor":[{"last_name":"Novotna","full_name":"Novotna, J.","first_name":"J."},{"last_name":"Moraova","first_name":"H.","full_name":"Moraova, H."}],"author":[{"first_name":"Imke","full_name":"Schwerin, Imke","last_name":"Schwerin","id":"48912"},{"id":"60267","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","first_name":"Uta"}],"publisher":"Charles University","department":[{"_id":"543"}],"publication":"International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education"},{"language":[{"iso":"ger"}],"page":"297-318","type":"book_chapter","year":"2023","citation":{"ieee":"R. Schmidt, C. Tenberge, and U. Häsel-Weide, “Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern,” in Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, N. Vöing, R. Schmidt, and I. Neiske, Eds. Visual Ink Publishing, 2023, pp. 297–318.","short":"R. Schmidt, C. Tenberge, U. Häsel-Weide, in: N. Vöing, R. Schmidt, I. Neiske (Eds.), Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, Visual Ink Publishing, 2023, pp. 297–318.","mla":"Schmidt, Rebekka, et al. “Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern.” Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, edited by N. Vöing et al., Visual Ink Publishing, 2023, pp. 297–318.","bibtex":"@inbook{Schmidt_Tenberge_Häsel-Weide_2023, title={Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern}, booktitle={Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre}, publisher={Visual Ink Publishing}, author={Schmidt, Rebekka and Tenberge, Claudia and Häsel-Weide, Uta}, editor={Vöing, N. and Schmidt, R. and Neiske, I.}, year={2023}, pages={297–318} }","chicago":"Schmidt, Rebekka, Claudia Tenberge, and Uta Häsel-Weide. “Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern.” In Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, edited by N. Vöing, R. Schmidt, and I. Neiske, 297–318. Visual Ink Publishing, 2023.","ama":"Schmidt R, Tenberge C, Häsel-Weide U. Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern. In: Vöing N, Schmidt R, Neiske I, eds. Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre. Visual Ink Publishing; 2023:297-318.","apa":"Schmidt, R., Tenberge, C., & Häsel-Weide, U. (2023). Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern. In N. Vöing, R. Schmidt, & I. Neiske (Eds.), Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre (pp. 297–318). Visual Ink Publishing."},"date_updated":"2023-08-30T09:55:46Z","_id":"46758","department":[{"_id":"543"}],"publication":"Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre","publisher":"Visual Ink Publishing","author":[{"full_name":"Schmidt, Rebekka","first_name":"Rebekka","id":"58565","last_name":"Schmidt"},{"id":"67302","last_name":"Tenberge","full_name":"Tenberge, Claudia","first_name":"Claudia"},{"last_name":"Häsel-Weide","id":"60267","first_name":"Uta","full_name":"Häsel-Weide, Uta"}],"date_created":"2023-08-30T09:54:47Z","status":"public","editor":[{"last_name":"Vöing","first_name":"N.","full_name":"Vöing, N."},{"full_name":"Schmidt, R.","first_name":"R.","last_name":"Schmidt"},{"full_name":"Neiske, I.","first_name":"I.","last_name":"Neiske"}],"user_id":"44184","title":"Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern"},{"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"Handbuch der Mathematikdidaktik","publisher":"Springer","author":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"first_name":"Joachim","full_name":"Engel, Joachim","last_name":"Engel"},{"first_name":"Daniel","full_name":"Frischemeier, Daniel","last_name":"Frischemeier"}],"date_created":"2023-09-25T11:15:18Z","status":"public","publication_identifier":{"isbn":["9783662666036","9783662666043"]},"publication_status":"published","editor":[{"last_name":"Bruder","first_name":"Regina","full_name":"Bruder, Regina"},{"full_name":"Büchter, A.","first_name":"A.","last_name":"Büchter"},{"first_name":"H.","full_name":"Gasteiger, H.","last_name":"Gasteiger"},{"last_name":"Schmidt-Thieme","first_name":"B.","full_name":"Schmidt-Thieme, B."},{"full_name":"Weigand, HG.","first_name":"HG.","last_name":"Weigand"}],"place":"Berlin, Heidelberg","user_id":"37888","title":"Stochastik: Leitidee Daten und Zufall","language":[{"iso":"eng"}],"type":"book_chapter","citation":{"short":"R. Biehler, J. Engel, D. Frischemeier, in: R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, HG. Weigand (Eds.), Handbuch Der Mathematikdidaktik, Springer, Berlin, Heidelberg, 2023.","ieee":"R. Biehler, J. Engel, and D. Frischemeier, “Stochastik: Leitidee Daten und Zufall,” in Handbuch der Mathematikdidaktik, R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, and HG. Weigand, Eds. Berlin, Heidelberg: Springer, 2023.","apa":"Biehler, R., Engel, J., & Frischemeier, D. (2023). Stochastik: Leitidee Daten und Zufall. In R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, & HG. Weigand (Eds.), Handbuch der Mathematikdidaktik. Springer. https://doi.org/10.1007/978-3-662-66604-3_8","ama":"Biehler R, Engel J, Frischemeier D. Stochastik: Leitidee Daten und Zufall. In: Bruder R, Büchter A, Gasteiger H, Schmidt-Thieme B, Weigand HG, eds. Handbuch Der Mathematikdidaktik. Springer; 2023. doi:10.1007/978-3-662-66604-3_8","chicago":"Biehler, Rolf, Joachim Engel, and Daniel Frischemeier. “Stochastik: Leitidee Daten Und Zufall.” In Handbuch Der Mathematikdidaktik, edited by Regina Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, and HG. Weigand. Berlin, Heidelberg: Springer, 2023. https://doi.org/10.1007/978-3-662-66604-3_8.","bibtex":"@inbook{Biehler_Engel_Frischemeier_2023, place={Berlin, Heidelberg}, title={Stochastik: Leitidee Daten und Zufall}, DOI={10.1007/978-3-662-66604-3_8}, booktitle={Handbuch der Mathematikdidaktik}, publisher={Springer}, author={Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel}, editor={Bruder, Regina and Büchter, A. and Gasteiger, H. and Schmidt-Thieme, B. and Weigand, HG.}, year={2023} }","mla":"Biehler, Rolf, et al. “Stochastik: Leitidee Daten Und Zufall.” Handbuch Der Mathematikdidaktik, edited by Regina Bruder et al., Springer, 2023, doi:10.1007/978-3-662-66604-3_8."},"year":"2023","date_updated":"2023-09-25T11:18:19Z","_id":"47416","doi":"10.1007/978-3-662-66604-3_8"},{"_id":"47534","date_updated":"2023-10-02T06:22:55Z","citation":{"short":"B. Hinrichs, O. Matte, ArXiv:2309.09005 (2023).","ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions,” arXiv:2309.09005. 2023.","apa":"Hinrichs, B., & Matte, O. (2023). Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions. In arXiv:2309.09005.","ama":"Hinrichs B, Matte O. Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions. arXiv:230909005. Published online 2023.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson Model in Two Spatial Dimensions.” ArXiv:2309.09005, 2023.","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson Model in Two Spatial Dimensions.” ArXiv:2309.09005, 2023.","bibtex":"@article{Hinrichs_Matte_2023, title={Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions}, journal={arXiv:2309.09005}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023} }"},"year":"2023","type":"preprint","language":[{"iso":"eng"}],"external_id":{"arxiv":["2309.09005"]},"abstract":[{"text":"In this proceeding we consider a translation invariant Nelson type model in\r\ntwo spatial dimensions modeling a scalar relativistic particle in interaction\r\nwith a massive radiation field. As is well-known, the corresponding Hamiltonian\r\ncan be defined with the help of an energy renormalization. First, we review a\r\nFeynman-Kac formula for the semigroup generated by this Hamiltonian proven by\r\nthe authors in a recent preprint (where several matter particles and exterior\r\npotentials are treated as well). After that, we employ a few technical key\r\nrelations and estimates obtained in our preprint to present an otherwise\r\nself-contained derivation of new Feynman-Kac formulas for the fiber\r\nHamiltonians attached to fixed total momenta of the translation invariant\r\nsystem. We conclude by inferring an alternative derivation of the Feynman-Kac\r\nformula for the full translation invariant Hamiltonian.","lang":"eng"}],"title":"Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions","user_id":"99427","publication":"arXiv:2309.09005","department":[{"_id":"799"},{"_id":"623"}],"author":[{"orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","first_name":"Benjamin","id":"99427","last_name":"Hinrichs"},{"full_name":"Matte, Oliver","first_name":"Oliver","last_name":"Matte"}],"date_created":"2023-10-02T06:21:37Z","project":[{"_id":"266","name":"PhoQC: PhoQC: Photonisches Quantencomputing"}],"status":"public"},{"place":"Cham","user_id":"37888","title":"Impacts of Digitalization on Content and Goals of Statistics Education","author":[{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"full_name":"Frischemeier, Daniel","first_name":"Daniel","last_name":"Frischemeier"},{"last_name":"Gould","first_name":"Ronald","full_name":"Gould, Ronald"},{"last_name":"Pfannkuch","full_name":"Pfannkuch, Maxine","first_name":"Maxine"}],"publisher":"Springer International Publishing","publication":"Handbook of Digital Resources in Mathematics Education","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"status":"public","date_created":"2023-10-12T11:31:22Z","editor":[{"full_name":"Pepin, Birgit","first_name":"Birgit","last_name":"Pepin"},{"first_name":"Ghislaine","full_name":"Gueudet, Ghislaine","last_name":"Gueudet"},{"full_name":"Choppin, Jeffrey","first_name":"Jeffrey","last_name":"Choppin"}],"date_updated":"2023-10-12T11:31:47Z","_id":"48042","language":[{"iso":"eng"}],"type":"book_chapter","year":"2023","citation":{"mla":"Biehler, Rolf, et al. “Impacts of Digitalization on Content and Goals of Statistics Education.” Handbook of Digital Resources in Mathematics Education, edited by Birgit Pepin et al., Springer International Publishing, 2023.","bibtex":"@inbook{Biehler_Frischemeier_Gould_Pfannkuch_2023, place={Cham}, title={Impacts of Digitalization on Content and Goals of Statistics Education}, booktitle={Handbook of Digital Resources in Mathematics Education}, publisher={Springer International Publishing}, author={Biehler, Rolf and Frischemeier, Daniel and Gould, Ronald and Pfannkuch, Maxine}, editor={Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeffrey}, year={2023} }","apa":"Biehler, R., Frischemeier, D., Gould, R., & Pfannkuch, M. 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