[{"main_file_link":[{"open_access":"1","url":"https://www.friedrich-verlag.de/shop/mwdownloads/download/link/id/114555/"}],"type":"journal_article","year":"2024","citation":{"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.","short":"B. Barzel, G. Greefrath, M. Nagel, M. Hoffmann, mathematik lehren 242 (2024) 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} }","mla":"Barzel, Bärbel, et al. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren, vol. 242, 2024, pp. 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.","apa":"Barzel, B., Greefrath, G., Nagel, M., & Hoffmann, M. (2024). Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren, 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."},"page":"42 - 47","intvolume":" 242","_id":"51841","file":[{"file_size":1410541,"file_id":"51842","creator":"maxh","date_updated":"2024-02-25T20:55:29Z","content_type":"application/pdf","success":1,"relation":"main_file","date_created":"2024-02-25T20:55:29Z","file_name":"Barzel_etal_2024_DigitalisierungalsChancefrallePrinzipiengut.pdf","access_level":"closed"}],"author":[{"full_name":"Barzel, Bärbel","first_name":"Bärbel","last_name":"Barzel"},{"first_name":"Gilbert","full_name":"Greefrath, Gilbert","last_name":"Greefrath"},{"last_name":"Nagel","full_name":"Nagel, Mareike","first_name":"Mareike"},{"last_name":"Hoffmann","id":"32202","first_name":"Max","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123"}],"file_date_updated":"2024-02-25T20:55:29Z","publication":"mathematik lehren","status":"public","has_accepted_license":"1","date_created":"2024-02-25T20:58:51Z","volume":242,"article_type":"original","abstract":[{"lang":"ger","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."}],"user_id":"32202","ddc":["510","370"],"language":[{"iso":"ger"}],"date_updated":"2024-02-25T21:01:03Z","oa":"1","department":[{"_id":"97"},{"_id":"643"}],"publication_status":"published","title":"Digitalisierung als Chance für alle Prinzipien guten Unterrichts"},{"language":[{"iso":"eng"}],"type":"preprint","citation":{"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} }","mla":"Dalfó, C., et al. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. arXiv:240302924. Published online 2024.","apa":"Dalfó, C., Fiol, M. A., & Steffen, E. (2024). On token signed graphs. In arXiv:2403.02924.","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.","ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” arXiv:2403.02924. 2024.","short":"C. Dalfó, M.A. Fiol, E. Steffen, ArXiv:2403.02924 (2024)."},"year":"2024","date_updated":"2024-03-07T08:50:33Z","_id":"52342","author":[{"full_name":"Dalfó, C.","first_name":"C.","last_name":"Dalfó"},{"last_name":"Fiol","first_name":"M. A.","full_name":"Fiol, M. A."},{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","last_name":"Steffen","id":"15548"}],"department":[{"_id":"542"}],"publication":"arXiv:2403.02924","status":"public","date_created":"2024-03-07T08:48:39Z","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. "}],"external_id":{"arxiv":["2403.02924"]},"user_id":"15540","title":"On token signed graphs"},{"publication":"arXiv:2403.12147","department":[{"_id":"799"}],"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":"2024-03-20T14:56:05Z","status":"public","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"]},"title":"Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains","user_id":"99427","year":"2024","type":"preprint","citation":{"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} }","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.","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.","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.","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)."},"language":[{"iso":"eng"}],"date_updated":"2024-03-20T14:56:50Z","_id":"52691"},{"issue":"2","_id":"52726","intvolume":" 12","type":"journal_article","citation":{"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).","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."},"year":"2024","main_file_link":[{"open_access":"1","url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf"}],"user_id":"97359","ddc":["510"],"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."}],"article_type":"original","date_created":"2024-03-22T09:04:57Z","has_accepted_license":"1","status":"public","volume":12,"file":[{"date_created":"2024-03-22T09:06:07Z","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","access_level":"closed","file_size":649155,"file_id":"52728","creator":"svdg","content_type":"application/pdf","date_updated":"2024-03-22T09:06:07Z","relation":"main_file","success":1}],"publication":"Journal of Complex Networks","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"file_date_updated":"2024-03-22T09:06:07Z","publisher":"Oxford University Press (OUP)","author":[{"first_name":"Christian","full_name":"Bick, Christian","last_name":"Bick"},{"last_name":"von der Gracht","id":"97359","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören"}],"oa":"1","doi":"10.1093/comnet/cnae009","date_updated":"2024-03-22T09:11:53Z","language":[{"iso":"eng"}],"title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","external_id":{"arxiv":["2309.02006"]},"publication_identifier":{"issn":["2051-1329"]},"publication_status":"published","department":[{"_id":"101"}]},{"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"},{"orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","id":"88145","last_name":"Wolf"}],"publisher":"Springer Science and Business Media LLC","volume":44,"date_created":"2023-12-20T10:31:27Z","status":"public","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"}],"user_id":"15540","page":"429-440","type":"journal_article","citation":{"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.","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.","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","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} }","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."},"year":"2024","intvolume":" 44","_id":"49905","department":[{"_id":"542"}],"publication_status":"published","publication_identifier":{"issn":["0209-9683","1439-6912"]},"title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","language":[{"iso":"eng"}],"date_updated":"2024-03-22T12:11:35Z","doi":"10.1007/s00493-023-00078-9"},{"language":[{"iso":"eng"}],"oa":"1","doi":"10.3934/jcd.2024017","date_updated":"2024-03-28T16:07:34Z","publication_identifier":{"issn":["2158-2491","2158-2505"]},"publication_status":"published","department":[{"_id":"636"}],"title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","type":"journal_article","citation":{"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.","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} }","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.","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.","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"},"year":"2024","page":"0-0","main_file_link":[{"open_access":"1","url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017"}],"issue":"0","_id":"53101","has_accepted_license":"1","status":"public","date_created":"2024-03-28T15:58:02Z","volume":"0","author":[{"last_name":"Leyendecker","first_name":"Sigrid","full_name":"Leyendecker, Sigrid"},{"id":"87909","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Almagro","first_name":"Rodrigo T. Sato Martín de","full_name":"Almagro, Rodrigo T. Sato Martín de"},{"first_name":"Flóra Orsolya","full_name":"Szemenyei, Flóra Orsolya","last_name":"Szemenyei"}],"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."],"user_id":"87909","ddc":["510"],"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."}]},{"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"}],"oa":"1","doi":"10.1016/j.automatica.2022.110840","date_updated":"2023-01-07T12:01:58Z","language":[{"iso":"eng"}],"user_id":"47427","abstract":[{"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.","lang":"eng"}],"status":"public","date_created":"2021-02-10T07:04:15Z","volume":149,"publisher":"Elsevier","author":[{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X"},{"first_name":"Katharina","full_name":"Bieker, Katharina","last_name":"Bieker","id":"32829"}],"publication":"Automatica","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.","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.","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} }","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"}]},{"language":[{"iso":"eng"}],"page":"181-201","type":"book_chapter","citation":{"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.","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","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","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.","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} }","short":"L. Ostsieker, R. Biehler, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 181–201.","ieee":"L. Ostsieker and R. 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Rösler, “The Dunkl-Laplace transform and Macdonald’s hypergeometric series,” Transaction of the American Mathematical Society, doi: 10.1090/tran/8860.","apa":"Brennecken, D., & Rösler, M. (n.d.). The Dunkl-Laplace transform and Macdonald’s hypergeometric series. Transaction of the American Mathematical Society. https://doi.org/10.1090/tran/8860","ama":"Brennecken D, Rösler M. The Dunkl-Laplace transform and Macdonald’s hypergeometric series. 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A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. Canadian Journal of Mathematics. 2023;75(1):170-201. doi:10.4153/s0008414x21000596","apa":"Hanusch, M. (2023). A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. Canadian Journal of Mathematics, 75(1), 170–201. https://doi.org/10.4153/s0008414x21000596","bibtex":"@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}, volume={75}, DOI={10.4153/s0008414x21000596}, number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }","mla":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” Canadian Journal of Mathematics, vol. 75, no. 1, Canadian Mathematical Society, 2023, pp. 170–201, doi:10.4153/s0008414x21000596.","short":"M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.","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."},"type":"journal_article","page":"170-201","intvolume":" 75","_id":"34814","issue":"1"},{"year":"2023","type":"journal_article","citation":{"short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.","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.","apa":"Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }"},"page":"709-741","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"issue":"3","_id":"27426","intvolume":" 85","volume":85,"status":"public","date_created":"2021-11-15T09:24:59Z","author":[{"first_name":"Bennet","full_name":"Gebken, Bennet","last_name":"Gebken","id":"32643"},{"last_name":"Bieker","id":"32829","first_name":"Katharina","full_name":"Bieker, Katharina"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"}],"publication":"Journal of Global Optimization","user_id":"47427","abstract":[{"lang":"eng","text":"Regularization is used in many different areas of optimization when solutions\r\nare sought which not only minimize a given function, but also possess a certain\r\ndegree of regularity. Popular applications are image denoising, sparse\r\nregression and machine learning. Since the choice of the regularization\r\nparameter is crucial but often difficult, path-following methods are used to\r\napproximate the entire regularization path, i.e., the set of all possible\r\nsolutions for all regularization parameters. Due to their nature, the\r\ndevelopment of these methods requires structural results about the\r\nregularization path. The goal of this article is to derive these results for\r\nthe case of a smooth objective function which is penalized by a piecewise\r\ndifferentiable regularization term. We do this by treating regularization as a\r\nmultiobjective optimization problem. Our results suggest that even in this\r\ngeneral case, the regularization path is piecewise smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features that occur in between\r\nsmooth parts. This is demonstrated in two applications, namely support-vector\r\nmachines and exact penalty methods."}],"language":[{"iso":"eng"}],"doi":"10.1007/s10898-022-01223-2","oa":"1","date_updated":"2023-03-11T17:16:33Z","department":[{"_id":"101"},{"_id":"655"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms"},{"place":"Hannover","title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","department":[{"_id":"97"}],"editor":[{"last_name":"Trigueros","first_name":"Marı́a","full_name":"Trigueros, Marı́a"},{"full_name":"Barquero, Berta","first_name":"Berta","last_name":"Barquero"},{"full_name":"Hochmuth, Reinhard","first_name":"Reinhard","last_name":"Hochmuth"},{"full_name":"Peters, Jana","first_name":"Jana","last_name":"Peters"}],"publication_status":"published","date_updated":"2023-03-25T10:11:35Z","oa":"1","language":[{"iso":"eng"}],"user_id":"32202","ddc":["370","510"],"file":[{"date_updated":"2023-03-25T10:01:03Z","content_type":"application/pdf","relation":"main_file","success":1,"file_size":201942,"file_id":"43096","creator":"maxh","access_level":"closed","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","date_created":"2023-03-25T10:01:03Z"}],"quality_controlled":"1","author":[{"last_name":"Hoffmann","id":"32202","first_name":"Max","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123"},{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler","id":"16274"}],"publisher":"University of Hannover and INDRUM.","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"file_date_updated":"2023-03-25T10:01:03Z","status":"public","has_accepted_license":"1","date_created":"2022-06-12T11:07:34Z","_id":"31849","main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"type":"conference","citation":{"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.","chicago":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023.","bibtex":"@inproceedings{Hoffmann_Biehler_2023, place={Hannover}, title={Student Teachers ’ Knowledge of Congruence before a University Course on Geometry}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, publisher={University of Hannover and INDRUM.}, author={Hoffmann, Max and Biehler, Rolf}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","mla":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., University of Hannover and INDRUM., 2023.","short":"M. Hoffmann, R. Biehler, in: M. Trigueros, B. Barquero, R. Hochmuth, J. 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Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, R. Martínez-Planell, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), Hannover, 2023.","mla":"Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic Education Research.” 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} }","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.","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.","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)."},"ddc":["370","510"],"user_id":"32202","quality_controlled":"1","author":[{"last_name":"Florensa","first_name":"Ignasio","full_name":"Florensa, Ignasio"},{"orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max","first_name":"Max","id":"32202","last_name":"Hoffmann"},{"last_name":"Romo Vázquez","first_name":"Avenilde","full_name":"Romo Vázquez, Avenilde"},{"last_name":"Zandieh","first_name":"Michelle","full_name":"Zandieh, Michelle"},{"first_name":"Rafael","full_name":"Martínez-Planell, Rafael","last_name":"Martínez-Planell"}],"file_date_updated":"2023-03-25T10:07:54Z","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file":[{"creator":"maxh","file_id":"43098","file_size":642388,"relation":"main_file","success":1,"content_type":"application/pdf","date_updated":"2023-03-25T10:07:54Z","file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","date_created":"2023-03-25T10:07:54Z","access_level":"closed"}],"status":"public","has_accepted_license":"1","date_created":"2023-03-25T10:09:06Z","date_updated":"2023-03-25T10:10:58Z","oa":"1","language":[{"iso":"eng"}],"place":"Hannover","title":"Innovations in university teaching based on mathematic education research","department":[{"_id":"97"}],"editor":[{"last_name":"Trigueros","full_name":"Trigueros, Marı́a","first_name":"Marı́a"},{"last_name":"Barquero","first_name":"Berta","full_name":"Barquero, Berta"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"last_name":"Peters","full_name":"Peters, Jana","first_name":"Jana"}]},{"user_id":"37888","title":"Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos","date_created":"2023-04-14T09:25:18Z","status":"public","volume":114,"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"Mitteilungen der Gesellschaft für Didaktik der Mathematik","author":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"first_name":"Michael","orcid":"0000-0001-9887-2074","full_name":"Liebendörfer, Michael","last_name":"Liebendörfer","id":"30933"},{"last_name":"Schmitz","first_name":"A.","full_name":"Schmitz, A."}],"intvolume":" 114","_id":"43504","date_updated":"2023-04-14T09:25:27Z","language":[{"iso":"ger"}],"page":"8-12","citation":{"chicago":"Biehler, Rolf, Michael Liebendörfer, and A. 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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","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={10.1016/j.nonrwa.2023.103868}, number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}, year={2023} }","mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications, vol. 73, 103868, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2023.103868."},"type":"journal_article","year":"2023","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"doi":"10.1016/j.nonrwa.2023.103868","date_updated":"2023-03-27T07:27:03Z","language":[{"iso":"eng"}]},{"year":"2023","citation":{"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.","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} }","chicago":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1671.","apa":"Vitt, V., & Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1671","ama":"Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1671","ieee":"V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46, 2023.","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023."},"type":"book_chapter","language":[{"iso":"eng"}],"doi":"https://doi.org/10.18716/ojs/md/2023.1671","date_updated":"2023-03-30T10:06:53Z","_id":"43227","status":"public","date_created":"2023-03-30T10:06:24Z","author":[{"full_name":"Vitt, Vivian","first_name":"Vivian","last_name":"Vitt"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"department":[{"_id":"543"}],"publication":"Mathematica Didactica, 46","title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","user_id":"44184"},{"user_id":"44184","title":"Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.","status":"public","date_created":"2023-03-30T10:04:31Z","author":[{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"},{"last_name":"Nührenbörger","first_name":"M.","full_name":"Nührenbörger, M."}],"publication":"Mathematica Didactica, 46","department":[{"_id":"543"}],"doi":"https://doi.org/10.18716/ojs/md/2023.1670","_id":"43226","date_updated":"2023-03-30T10:06:49Z","language":[{"iso":"eng"}],"citation":{"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.","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","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.","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.","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} }"},"type":"book_chapter","year":"2023"},{"language":[{"iso":"eng"}],"type":"journal_article","year":"2023","citation":{"short":"M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).","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.","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","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","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.","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} }"},"issue":"21","doi":"10.1007/s10455-023-09888-y","date_updated":"2023-04-05T18:18:24Z","_id":"34832","intvolume":" 63","status":"public","project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"date_created":"2022-12-22T09:45:34Z","volume":63,"publication_status":"published","author":[{"first_name":"Maximilian","full_name":"Hanusch, Maximilian","last_name":"Hanusch","id":"30905"}],"department":[{"_id":"93"}],"publication":"Annals of Global Analysis and Geometry","keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"user_id":"30905","title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups"},{"title":"Critically 3-frustrated signed graphs","user_id":"15540","abstract":[{"text":"Extending the notion of maxcut, the study of the frustration index of signed graphs is one of the basic questions in the theory of signed graphs. Recently two of the authors initiated the study of critically frustrated signed graphs. That is a signed graph whose frustration index decreases with the removal of any edge. The main focus of this study is on critical signed graphs which are not edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable signed graphs) and which are not built from other critically frustrated signed graphs by subdivision. We conjecture that for any given k there are only finitely many critically k-frustrated signed graphs of this kind.\r\nProviding support for this conjecture we show that there are only two of such critically 3-frustrated signed graphs where there is no pair of edge-disjoint negative cycles. Similarly, we show that there are exactly ten critically 3-frustrated signed planar graphs that are neither decomposable nor subdivisions of other critically frustrated signed graphs. We present a method for building non-decomposable critically frustrated signed graphs based on two given such signed graphs. We also show that the condition of being non-decomposable is necessary for our conjecture. ","lang":"eng"}],"external_id":{"arxiv":["2304.10243"]},"status":"public","date_created":"2023-05-05T06:52:39Z","author":[{"last_name":"Cappello","id":"72874","first_name":"Chiara","full_name":"Cappello, Chiara"},{"last_name":"Naserasr","first_name":"Reza","full_name":"Naserasr, Reza"},{"first_name":"Eckhard","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548"},{"last_name":"Wang","full_name":"Wang, Zhouningxin","first_name":"Zhouningxin"}],"publication":"arXiv:2304.10243","department":[{"_id":"542"}],"date_updated":"2023-05-05T06:53:47Z","_id":"44501","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} }","chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 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.","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)."},"year":"2023","type":"preprint","language":[{"iso":"eng"}]},{"volume":57,"date_created":"2023-05-16T08:48:22Z","status":"public","keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"publication":"RAIRO - Operations Research","author":[{"first_name":"Helmuth O.M.","full_name":"Silva, Helmuth O.M.","last_name":"Silva"},{"first_name":"Diego P.","full_name":"Rubert, Diego P.","last_name":"Rubert"},{"first_name":"Eloi","full_name":"Araujo, Eloi","last_name":"Araujo"},{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","last_name":"Steffen","id":"15548"},{"last_name":"Doerr","first_name":"Daniel","full_name":"Doerr, Daniel"},{"last_name":"Martinez","full_name":"Martinez, Fábio V.","first_name":"Fábio V."}],"publisher":"EDP Sciences","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."}],"page":"1045-1058","citation":{"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} }","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.","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.","apa":"Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052","ama":"Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052","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."},"year":"2023","type":"journal_article","issue":"3","intvolume":" 57","_id":"44857","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","language":[{"iso":"eng"}],"doi":"10.1051/ro/2023052","date_updated":"2023-05-16T08:49:30Z"},{"author":[{"first_name":"Yulai","full_name":"Ma, Yulai","last_name":"Ma","id":"92748"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf","id":"88145"}],"publication":"arXiv:2305.08619","department":[{"_id":"542"}],"status":"public","date_created":"2023-05-16T10:07:47Z","external_id":{"arxiv":["2305.08619"]},"user_id":"15540","title":"Sets of r-graphs that color all r-graphs","language":[{"iso":"eng"}],"year":"2023","type":"preprint","citation":{"chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs. arXiv:230508619. Published online 2023.","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In arXiv:2305.08619.","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” arXiv:2305.08619. 2023."},"_id":"44859","date_updated":"2023-05-16T11:17:26Z"},{"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"],"status":"public","date_created":"2022-12-22T09:46:36Z","volume":34,"publication_status":"published","user_id":"30905","title":"Decompositions of Analytic 1-Manifolds","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","bibtex":"@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds}, volume={34}, DOI={10.1016/j.indag.2023.02.003}, number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian}, year={2023}, pages={752–811} }","mla":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes Mathematicae., vol. 34, no. 4, 2023, pp. 752–811, doi:10.1016/j.indag.2023.02.003.","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.","ieee":"M. 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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."},"year":"2023","page":"29","language":[{"iso":"eng"}],"external_id":{"arxiv":["2306.03320"]},"abstract":[{"lang":"eng","text":"We present a novel method for high-order phase reduction in networks of\r\nweakly coupled oscillators and, more generally, perturbations of reducible\r\nnormally hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic expansion for an embedding of the perturbed invariant torus, as well\r\nas for the reduced phase dynamics in local coordinates. Both can be determined\r\nto arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly be obtained in normal form. We apply the method to predict remote\r\nsynchronisation in a chain of coupled Stuart-Landau oscillators."}],"title":"A parametrisation method for high-order phase reduction in coupled oscillator networks","user_id":"97359","author":[{"last_name":"von der Gracht","id":"97359","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören"},{"last_name":"Nijholt","full_name":"Nijholt, Eddie","first_name":"Eddie"},{"last_name":"Rink","first_name":"Bob","full_name":"Rink, Bob"}],"publication":"arXiv:2306.03320","department":[{"_id":"101"}],"publication_status":"submitted","status":"public","date_created":"2023-06-07T07:57:28Z"},{"title":" Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen","user_id":"44184","related_material":{"link":[{"relation":"other","url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991"}]},"publication":"Die Grundschulzeitschrift","department":[{"_id":"543"}],"author":[{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"publisher":"Friedrich Verlag","date_created":"2023-06-22T09:28:22Z","status":"public","_id":"45712","date_updated":"2023-06-22T09:34:13Z","issue":"339","page":"6-11","type":"journal_article","citation":{"ieee":"U. Häsel-Weide, “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen,” Die Grundschulzeitschrift, no. 339, pp. 6–11, 2023.","short":"U. Häsel-Weide, Die Grundschulzeitschrift (2023) 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} }","mla":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift, no. 339, Friedrich Verlag, 2023, pp. 6–11.","apa":"Häsel-Weide, U. (2023). Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift, 339, 6–11.","ama":"Häsel-Weide U. Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift. 2023;(339):6-11.","chicago":"Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift, no. 339 (2023): 6–11."},"year":"2023","language":[{"iso":"ger"}]},{"publication":"Die Grundschulzeitschrift","department":[{"_id":"543"}],"publisher":"Friedrich Verlag","author":[{"first_name":"Lara Marie","full_name":"Graf, Lara Marie","last_name":"Graf","id":"89837"},{"full_name":"Wienhues, Inga","first_name":"Inga","id":"61635","last_name":"Wienhues"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"date_created":"2023-06-22T09:33:59Z","status":"public","user_id":"44184","related_material":{"link":[{"url":"https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991","relation":"other"}]},"title":"Addition und Subtraktion verstehen","language":[{"iso":"ger"}],"page":"20-23","year":"2023","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."},"type":"journal_article","_id":"45713","date_updated":"2023-06-22T09:34:18Z","issue":"339"},{"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_identifier":{"issn":["1863-9690","1863-9704"]},"publication_status":"published","department":[{"_id":"97"},{"_id":"643"}],"doi":"10.1007/s11858-023-01505-3","oa":"1","date_updated":"2023-07-13T09:41:20Z","language":[{"iso":"eng"}],"ddc":["510","370"],"user_id":"32202","article_type":"original","abstract":[{"text":"Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers.","lang":"eng"}],"has_accepted_license":"1","status":"public","date_created":"2023-06-27T11:45:25Z","publisher":"Springer","quality_controlled":"1","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"}],"file_date_updated":"2023-07-13T09:40:02Z","keyword":["General Mathematics","Education"],"publication":"ZDM – Mathematics Education","file":[{"access_level":"closed","file_name":"s11858-023-01505-3.pdf","date_created":"2023-07-13T09:40:02Z","success":1,"relation":"main_file","date_updated":"2023-07-13T09:40:02Z","content_type":"application/pdf","creator":"maxh","file_id":"46041","file_size":1460246}],"_id":"45786","citation":{"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.","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","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","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.","ieee":"M. Hoffmann and R. Biehler, “Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01505-3.","short":"M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2023)."},"year":"2023","type":"journal_article","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s11858-023-01505-3","open_access":"1"}]},{"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"}],"user_id":"99427","volume":528,"status":"public","date_created":"2023-07-20T05:08:49Z","author":[{"orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","first_name":"Benjamin","id":"99427","last_name":"Hinrichs"},{"first_name":"Daan W.","full_name":"Janssen, Daan W.","last_name":"Janssen"},{"first_name":"Jobst","full_name":"Ziebell, Jobst","last_name":"Ziebell"}],"publisher":"Elsevier BV","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":{"short":"B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and Applications 528 (2023).","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.","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.","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","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","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} }"}},{"type":"preprint","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."},"year":"2023","language":[{"iso":"eng"}],"date_updated":"2023-07-24T07:53:29Z","_id":"46117","status":"public","date_created":"2023-07-24T07:52:23Z","author":[{"last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"},{"full_name":"Wolf, Lasse L.","first_name":"Lasse L.","last_name":"Wolf"}],"publication":"arXiv:2304.09573","department":[{"_id":"10"}],"title":"Temperedness of locally symmetric spaces: The product case","user_id":"45027","abstract":[{"lang":"eng","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$\\Gamma$."}],"external_id":{"arxiv":["2304.09573"]}},{"doi":"10.1016/j.tate.2023.104270","date_updated":"2023-07-26T08:57:01Z","language":[{"iso":"eng"}],"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"}],"article_number":"104270","intvolume":" 132","_id":"46155","citation":{"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} }","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.","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","ieee":"J. Bruns, M. Hagena, and H. Gasteiger, “Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?,” Teaching and Teacher Education, vol. 132, Art. no. 104270, 2023, doi: 10.1016/j.tate.2023.104270.","short":"J. Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023)."},"type":"journal_article","year":"2023","user_id":"72183","volume":132,"date_created":"2023-07-26T08:55:26Z","status":"public","keyword":["Education"],"publication":"Teaching and Teacher Education","author":[{"first_name":"Julia","full_name":"Bruns, Julia","last_name":"Bruns"},{"full_name":"Hagena, Maike","first_name":"Maike","last_name":"Hagena"},{"last_name":"Gasteiger","full_name":"Gasteiger, Hedwig","first_name":"Hedwig"}],"publisher":"Elsevier BV"},{"publisher":"Springer International Publishing","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"status":"public","date_created":"2023-07-26T10:16:08Z","editor":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"orcid":"0000-0001-9887-2074","full_name":"Liebendörfer, Michael","first_name":"Michael","id":"30933","last_name":"Liebendörfer"},{"last_name":"Gueudet","first_name":"Ghislaine","full_name":"Gueudet, Ghislaine"},{"last_name":"Rasmussen","full_name":"Rasmussen, Chris","first_name":"Chris"},{"full_name":"Winsløw, Carl","first_name":"Carl","last_name":"Winsløw"}],"publication_status":"published","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"place":"Cham","user_id":"37888","title":"Practice-Oriented Research in Tertiary Mathematics Education","language":[{"iso":"eng"}],"citation":{"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.","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","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."},"type":"book_editor","year":"2023","_id":"46157","date_updated":"2023-07-26T10:17:43Z","doi":"10.1007/978-3-031-14175-1"},{"date_created":"2023-08-01T10:08:32Z","status":"public","volume":37,"publication":"SIAM Journal on Discrete Mathematics","keyword":["General Mathematics"],"publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"last_name":"Ma","id":"92748","first_name":"Yulai","full_name":"Ma, Yulai"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","first_name":"Eckhard","id":"15548","last_name":"Steffen"},{"last_name":"Wolf","id":"88145","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus"}],"user_id":"15540","page":"1548-1565","citation":{"ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. doi:10.1137/22m1500654","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.","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.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654."},"type":"journal_article","year":"2023","issue":"3","intvolume":" 37","_id":"46256","publication_status":"published","publication_identifier":{"issn":["0895-4801","1095-7146"]},"department":[{"_id":"542"}],"title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs","language":[{"iso":"eng"}],"doi":"10.1137/22m1500654","date_updated":"2023-08-01T10:09:35Z"},{"type":"conference","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.","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)} }"},"page":"569-579","intvolume":" 14071","_id":"42163","conference":{"name":" GSI'23 6th International Conference on Geometric Science of Information","start_date":"2023-08-30","location":"Saint-Malo, Palais du Grand Large, France","end_date":"2023-09-01"},"file":[{"date_created":"2023-08-02T12:04:17Z","file_name":"LDensityLearning.pdf","access_level":"open_access","file_size":1938962,"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","creator":"coffen","file_id":"46273","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."}],"publisher":"Springer, Cham.","author":[{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"}],"quality_controlled":"1","file_date_updated":"2023-08-02T12:04:17Z","keyword":["System identification","discrete Lagrangians","travelling waves"],"publication":"Geometric Science of Information","status":"public","has_accepted_license":"1","date_created":"2023-02-16T11:32:48Z","volume":14071,"abstract":[{"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.","lang":"eng"}],"user_id":"85279","ddc":["510"],"series_title":"Lecture Notes in Computer Science (LNCS)","language":[{"iso":"eng"}],"date_updated":"2023-08-10T08:34:04Z","oa":"1","doi":"10.1007/978-3-031-38271-0_57","department":[{"_id":"636"}],"editor":[{"first_name":"F","full_name":"Nielsen, F","last_name":"Nielsen"},{"last_name":"Barbaresco","first_name":"F","full_name":"Barbaresco, F"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"publication_status":"published","external_id":{"arxiv":["2302.08232 "]},"related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianDensityML","description":"GitHub","relation":"software"}]},"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves"},{"page":"114780","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.","ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics. 2023;421:114780. doi:10.1016/j.cam.2022.114780","apa":"Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics, 421, 114780. https://doi.org/10.1016/j.cam.2022.114780","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.","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","type":"journal_article","intvolume":" 421","_id":"29240","date_created":"2022-01-11T13:24:00Z","status":"public","has_accepted_license":"1","volume":421,"file":[{"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_id":"32274","creator":"coffen","content_type":"application/pdf","date_updated":"2022-06-28T15:25:50Z","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.","relation":"main_file"}],"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","publisher":"Elsevier","author":[{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","id":"85279","last_name":"Offen"}],"quality_controlled":"1","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","language":[{"iso":"eng"}],"oa":"1","doi":"10.1016/j.cam.2022.114780","date_updated":"2023-08-10T08:42:39Z","publication_identifier":{"issn":["0377-0427"]},"publication_status":"epub_ahead","department":[{"_id":"636"}],"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"]}},{"volume":15,"date_created":"2022-01-11T12:48:39Z","has_accepted_license":"1","status":"public","publication":"Journal of Geometric Mechanics","file_date_updated":"2022-08-12T16:48:59Z","keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"quality_controlled":"1","author":[{"last_name":"McLachlan","full_name":"McLachlan, Robert","first_name":"Robert"},{"orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","first_name":"Christian","id":"85279","last_name":"Offen"}],"publisher":"AIMS Press","file":[{"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","file_id":"32801","creator":"coffen","file_size":827030,"title":"Backward error analysis for conjugate symplectic methods","access_level":"open_access","date_created":"2022-08-12T16:48:59Z","file_name":"BEA_MultiStep_Matrix.pdf"}],"ddc":["510"],"user_id":"85279","abstract":[{"lang":"eng","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."}],"article_type":"original","page":"98-115","citation":{"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","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.","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.","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} }","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."},"year":"2023","type":"journal_article","issue":"1","intvolume":" 15","_id":"29236","publication_status":"published","department":[{"_id":"636"}],"title":"Backward error analysis for conjugate symplectic methods","related_material":{"link":[{"url":"https://github.com/Christian-Offen/BEAConjugateSymplectic","relation":"software"}]},"external_id":{"arxiv":["2201.03911"]},"language":[{"iso":"eng"}],"doi":"10.3934/jgm.2023005","oa":"1","date_updated":"2023-08-10T08:40:30Z"},{"intvolume":" 33","_id":"37654","issue":"6","article_number":"063115","citation":{"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} }","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.","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","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","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.","short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023)."},"year":"2023","type":"journal_article","abstract":[{"text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered.","lang":"eng"}],"article_type":"original","user_id":"85279","ddc":["510"],"file":[{"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","file_size":5200111,"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","date_created":"2023-04-26T16:20:56Z","file_name":"JournalPaper_main.pdf","access_level":"open_access"}],"file_date_updated":"2023-04-26T16:20:56Z","publication":"Chaos","author":[{"first_name":"Eva","full_name":"Dierkes, Eva","last_name":"Dierkes"},{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","id":"85279","last_name":"Offen"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"full_name":"Flaßkamp, Kathrin","first_name":"Kathrin","last_name":"Flaßkamp"}],"publisher":"AIP Publishing","date_created":"2023-01-20T09:10:06Z","status":"public","has_accepted_license":"1","volume":33,"date_updated":"2023-08-10T08:37:01Z","oa":"1","doi":"10.1063/5.0142969","language":[{"iso":"eng"}],"external_id":{"arxiv":["2301.07928"]},"related_material":{"link":[{"url":"https://github.com/eva-dierkes/HNN_withSymmetries","description":"GitHub","relation":"software"}]},"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","department":[{"_id":"636"}],"publication_identifier":{"issn":["1054-1500"]},"publication_status":"published"},{"language":[{"iso":"eng"}],"date_updated":"2023-08-24T07:50:12Z","doi":"10.1007/s00332-022-09862-1","oa":"1","department":[{"_id":"101"},{"_id":"655"}],"publication_status":"published","title":"Finite-data error bounds for Koopman-based prediction and control","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf","open_access":"1"}],"year":"2023","type":"journal_article","citation":{"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.","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","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.","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)."},"_id":"23428","intvolume":" 33","article_number":"14","author":[{"last_name":"Nüske","id":"81513","first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"full_name":"Schaller, Manuel","first_name":"Manuel","last_name":"Schaller"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"}],"publication":"Journal of Nonlinear Science","volume":33,"status":"public","date_created":"2021-08-17T12:25:09Z","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"},{"publication_status":"published","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"title":"Efficient time stepping for numerical integration using reinforcement learning","related_material":{"link":[{"url":"https://github.com/lueckem/quadrature-ML","relation":"software","description":"GitHub"}]},"external_id":{"arxiv":["arXiv:2104.03562"]},"language":[{"iso":"eng"}],"doi":"10.1137/21M1412682","date_updated":"2023-08-25T09:24:50Z","volume":45,"has_accepted_license":"1","status":"public","date_created":"2021-04-09T07:59:19Z","author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"first_name":"Eyke","full_name":"Hüllermeier, Eyke","last_name":"Hüllermeier","id":"48129"},{"last_name":"Lücke","full_name":"Lücke, Marvin","first_name":"Marvin"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","last_name":"Offen","id":"85279"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X"},{"orcid":"0000-0001-9407-7903","full_name":"Pfannschmidt, Karlson","first_name":"Karlson","id":"13472","last_name":"Pfannschmidt"}],"publication":"SIAM Journal on Scientific Computing","ddc":["510"],"user_id":"47427","abstract":[{"lang":"eng","text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML."}],"year":"2023","type":"journal_article","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.","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing. 2023;45(2):A579-A595. doi:10.1137/21M1412682","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing, 45(2), A579–A595. https://doi.org/10.1137/21M1412682","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.","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} }","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."},"page":"A579-A595","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"issue":"2","intvolume":" 45","_id":"21600"},{"_id":"46757","date_updated":"2023-08-30T09:55:41Z","conference":{"location":"Prag","name":"International Symposium in Elementary Mathematics Teaching"},"language":[{"iso":"eng"}],"type":"conference","citation":{"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} }","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.","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.","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."},"year":"2023","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","first_name":"J.","full_name":"Novotna, J."},{"last_name":"Moraova","full_name":"Moraova, H.","first_name":"H."}],"author":[{"first_name":"Imke","full_name":"Schwerin, Imke","last_name":"Schwerin","id":"48912"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"publisher":"Charles University","publication":"International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education","department":[{"_id":"543"}]},{"title":"Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern","user_id":"44184","editor":[{"full_name":"Vöing, N.","first_name":"N.","last_name":"Vöing"},{"first_name":"R.","full_name":"Schmidt, R.","last_name":"Schmidt"},{"full_name":"Neiske, I.","first_name":"I.","last_name":"Neiske"}],"date_created":"2023-08-30T09:54:47Z","status":"public","department":[{"_id":"543"}],"publication":"Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre","publisher":"Visual Ink Publishing","author":[{"id":"58565","last_name":"Schmidt","full_name":"Schmidt, Rebekka","first_name":"Rebekka"},{"first_name":"Claudia","full_name":"Tenberge, Claudia","last_name":"Tenberge","id":"67302"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"}],"date_updated":"2023-08-30T09:55:46Z","_id":"46758","page":"297-318","type":"book_chapter","year":"2023","citation":{"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.","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.","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.","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.","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} }","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."},"language":[{"iso":"ger"}]},{"doi":"10.1007/978-3-662-66604-3_8","_id":"47416","date_updated":"2023-09-25T11:18:19Z","language":[{"iso":"eng"}],"citation":{"chicago":"Biehler, Rolf, Joachim Engel, and Daniel Frischemeier. “Stochastik: Leitidee Daten Und Zufall.” In Handbuch Der Mathematikdidaktik, edited by Regina Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, and HG. Weigand. Berlin, Heidelberg: Springer, 2023. https://doi.org/10.1007/978-3-662-66604-3_8.","apa":"Biehler, R., Engel, J., & Frischemeier, D. (2023). Stochastik: Leitidee Daten und Zufall. In R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, & HG. Weigand (Eds.), Handbuch der Mathematikdidaktik. Springer. https://doi.org/10.1007/978-3-662-66604-3_8","ama":"Biehler R, Engel J, Frischemeier D. Stochastik: Leitidee Daten und Zufall. In: Bruder R, Büchter A, Gasteiger H, Schmidt-Thieme B, Weigand HG, eds. Handbuch Der Mathematikdidaktik. Springer; 2023. doi:10.1007/978-3-662-66604-3_8","mla":"Biehler, Rolf, et al. “Stochastik: Leitidee Daten Und Zufall.” Handbuch Der Mathematikdidaktik, edited by Regina Bruder et al., Springer, 2023, doi:10.1007/978-3-662-66604-3_8.","bibtex":"@inbook{Biehler_Engel_Frischemeier_2023, place={Berlin, Heidelberg}, title={Stochastik: Leitidee Daten und Zufall}, DOI={10.1007/978-3-662-66604-3_8}, booktitle={Handbuch der Mathematikdidaktik}, publisher={Springer}, author={Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel}, editor={Bruder, Regina and Büchter, A. and Gasteiger, H. and Schmidt-Thieme, B. and Weigand, HG.}, year={2023} }","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."},"type":"book_chapter","year":"2023","user_id":"37888","title":"Stochastik: Leitidee Daten und Zufall","place":"Berlin, Heidelberg","date_created":"2023-09-25T11:15:18Z","status":"public","publication_identifier":{"isbn":["9783662666036","9783662666043"]},"publication_status":"published","editor":[{"full_name":"Bruder, Regina","first_name":"Regina","last_name":"Bruder"},{"last_name":"Büchter","first_name":"A.","full_name":"Büchter, A."},{"full_name":"Gasteiger, H.","first_name":"H.","last_name":"Gasteiger"},{"first_name":"B.","full_name":"Schmidt-Thieme, B.","last_name":"Schmidt-Thieme"},{"last_name":"Weigand","first_name":"HG.","full_name":"Weigand, HG."}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"Handbuch der Mathematikdidaktik","author":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"},{"full_name":"Engel, Joachim","first_name":"Joachim","last_name":"Engel"},{"last_name":"Frischemeier","first_name":"Daniel","full_name":"Frischemeier, Daniel"}],"publisher":"Springer"},{"_id":"47534","date_updated":"2023-10-02T06:22:55Z","language":[{"iso":"eng"}],"citation":{"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.","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.","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} }","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."},"year":"2023","type":"preprint","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"}],"user_id":"99427","title":"Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions","department":[{"_id":"799"},{"_id":"623"}],"publication":"arXiv:2309.09005","author":[{"last_name":"Hinrichs","id":"99427","first_name":"Benjamin","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin"},{"first_name":"Oliver","full_name":"Matte, Oliver","last_name":"Matte"}],"date_created":"2023-10-02T06:21:37Z","project":[{"name":"PhoQC: PhoQC: Photonisches Quantencomputing","_id":"266"}],"status":"public"},{"language":[{"iso":"eng"}],"citation":{"ieee":"R. Biehler, D. Frischemeier, R. Gould, and M. Pfannkuch, “Impacts of Digitalization on Content and Goals of Statistics Education,” in Handbook of Digital Resources in Mathematics Education, B. Pepin, G. Gueudet, and J. Choppin, Eds. Cham: Springer International Publishing, 2023.","short":"R. Biehler, D. Frischemeier, R. Gould, M. Pfannkuch, in: B. Pepin, G. Gueudet, J. Choppin (Eds.), Handbook of Digital Resources in Mathematics Education, Springer International Publishing, Cham, 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} }","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.","apa":"Biehler, R., Frischemeier, D., Gould, R., & Pfannkuch, M. 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