[{"publication":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","issue":"2301","abstract":[{"text":"To model dynamical systems on networks with higher-order (non-pairwise) interactions, we recently introduced a new class of ordinary differential equations (ODEs) on hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady-state branch.","lang":"eng"}],"file":[{"creator":"svdg","date_created":"2025-03-27T10:16:20Z","file_name":"higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf","access_level":"open_access","file_size":820435,"relation":"main_file","date_updated":"2025-03-27T10:19:48Z","file_id":"59172","content_type":"application/pdf"}],"date_created":"2025-03-27T10:15:06Z","keyword":["higher-order interactions","synchrony breaking","network dynamics","coupled cell systems"],"type":"journal_article","department":[{"_id":"101"}],"title":"Higher-order interactions lead to ‘reluctant’ synchrony breaking","year":"2024","author":[{"id":"97359","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"von der Gracht"},{"last_name":"Nijholt","first_name":"Eddie","full_name":"Nijholt, Eddie"},{"full_name":"Rink, Bob","first_name":"Bob","last_name":"Rink"}],"publication_identifier":{"issn":["1364-5021","1471-2946"]},"publication_status":"published","date_updated":"2025-03-27T10:19:56Z","intvolume":"       480","language":[{"iso":"eng"}],"doi":"10.1098/rspa.2023.0945","file_date_updated":"2025-03-27T10:19:48Z","citation":{"ama":"von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2024;480(2301). doi:<a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>","bibtex":"@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={<a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>}, number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2024} }","mla":"von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 480, no. 2301, The Royal Society, 2024, doi:<a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>.","short":"S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480 (2024).","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i> 480, no. 2301 (2024). <a href=\"https://doi.org/10.1098/rspa.2023.0945\">https://doi.org/10.1098/rspa.2023.0945</a>.","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2024). Higher-order interactions lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, <i>480</i>(2301). <a href=\"https://doi.org/10.1098/rspa.2023.0945\">https://doi.org/10.1098/rspa.2023.0945</a>","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead to ‘reluctant’ synchrony breaking,” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 480, no. 2301, 2024, doi: <a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>."},"oa":"1","status":"public","has_accepted_license":"1","_id":"59171","publisher":"The Royal Society","user_id":"97359","ddc":["510"],"volume":480},{"doi":"https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0","user_id":"44184","editor":[{"first_name":"P.","last_name":"Ebers","full_name":"Ebers, P."},{"full_name":"Rösken, F.","last_name":"Rösken","first_name":"F."},{"first_name":"B.","last_name":"Barzel","full_name":"Barzel, B."},{"full_name":"Büchter, A.","last_name":"Büchter","first_name":"A."},{"full_name":"Schacht, F.","last_name":"Schacht","first_name":"F."},{"full_name":"Scherer, P.","first_name":"P.","last_name":"Scherer"}],"page":"207-210","_id":"59581","language":[{"iso":"ger"}],"date_updated":"2025-09-08T07:32:38Z","status":"public","title":" Praktiken der Förderung im inklusiven Mathematikunterricht","year":"2024","author":[{"last_name":"Häsel-Weide","orcid":"0000-0001-6278-4240","first_name":"Uta","full_name":"Häsel-Weide, Uta","id":"60267"},{"first_name":"M.","last_name":"Nührenbörger","full_name":"Nührenbörger, M."}],"type":"book_chapter","department":[{"_id":"543"}],"date_created":"2025-04-15T10:06:42Z","publication":"Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik","citation":{"ama":"Häsel-Weide U, Nührenbörger M.  Praktiken der Förderung im inklusiven Mathematikunterricht. In: Ebers P, Rösken F, Barzel B, Büchter A, Schacht F, Scherer P, eds. <i>Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>. ; 2024:207-210. doi:<a href=\"https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0\">https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0</a>","bibtex":"@inbook{Häsel-Weide_Nührenbörger_2024, title={ Praktiken der Förderung im inklusiven Mathematikunterricht}, DOI={<a href=\"https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0\">https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0</a>}, booktitle={Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Häsel-Weide, Uta and Nührenbörger, M.}, editor={Ebers, P. and Rösken, F. and Barzel, B. and Büchter, A. and Schacht, F. and Scherer, P.}, year={2024}, pages={207–210} }","mla":"Häsel-Weide, Uta, and M. Nührenbörger. “ Praktiken der Förderung im inklusiven Mathematikunterricht.” <i>Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, edited by P. Ebers et al., 2024, pp. 207–10, doi:<a href=\"https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0\">https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0</a>.","short":"U. Häsel-Weide, M. Nührenbörger, in: P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, P. Scherer (Eds.), Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik, 2024, pp. 207–210.","chicago":"Häsel-Weide, Uta, and M. Nührenbörger. “ Praktiken der Förderung im inklusiven Mathematikunterricht.” In <i>Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, edited by P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, and P. Scherer, 207–10, 2024. <a href=\"https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0\">https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0</a>.","apa":"Häsel-Weide, U., &#38; Nührenbörger, M. (2024).  Praktiken der Förderung im inklusiven Mathematikunterricht. In P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, &#38; P. Scherer (Eds.), <i>Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i> (pp. 207–210). <a href=\"https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0\">https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0</a>","ieee":"U. Häsel-Weide and M. Nührenbörger, “ Praktiken der Förderung im inklusiven Mathematikunterricht,” in <i>Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, and P. Scherer, Eds. 2024, pp. 207–210."}},{"citation":{"ieee":"B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces,” <i>arXiv:2411.19782</i>. 2024.","apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>.","chicago":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","short":"B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).","mla":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","bibtex":"@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces}, journal={arXiv:2411.19782}, author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }","ama":"Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024."},"publication":"arXiv:2411.19782","project":[{"_id":"356","name":"TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen"}],"abstract":[{"lang":"eng","text":"We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical. This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder."}],"date_created":"2025-02-28T10:32:30Z","external_id":{"arxiv":["2411.19782"]},"department":[{"_id":"548"}],"type":"preprint","author":[{"id":"70575","full_name":"Delarue, Benjamin","last_name":"Delarue","first_name":"Benjamin"},{"first_name":"Guendalina","last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467"}],"title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces","year":"2024","status":"public","date_updated":"2026-03-30T12:01:12Z","language":[{"iso":"eng"}],"_id":"58873","user_id":"109467"},{"_id":"53542","publisher":"Springer Science and Business Media LLC","volume":24,"user_id":"100325","status":"public","citation":{"short":"E. Papageorgiou, Journal of Evolution Equations 24 (2024).","chicago":"Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal of Evolution Equations</i> 24, no. 2 (2024). <a href=\"https://doi.org/10.1007/s00028-024-00959-6\">https://doi.org/10.1007/s00028-024-00959-6</a>.","ieee":"E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces,” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, Art. no. 34, 2024, doi: <a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>.","apa":"Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces. <i>Journal of Evolution Equations</i>, <i>24</i>(2), Article 34. <a href=\"https://doi.org/10.1007/s00028-024-00959-6\">https://doi.org/10.1007/s00028-024-00959-6</a>","bibtex":"@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}, volume={24}, DOI={<a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>}, number={234}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024} }","ama":"Papageorgiou E. Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces. <i>Journal of Evolution Equations</i>. 2024;24(2). doi:<a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>","mla":"Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, 34, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>."},"language":[{"iso":"eng"}],"article_number":"34","doi":"10.1007/s00028-024-00959-6","publication_identifier":{"issn":["1424-3199","1424-3202"]},"author":[{"id":"100325","full_name":"Papageorgiou, Efthymia","last_name":"Papageorgiou","first_name":"Efthymia"}],"title":"Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces","year":"2024","intvolume":"        24","publication_status":"published","date_updated":"2026-07-03T12:35:54Z","date_created":"2024-04-17T13:18:30Z","department":[{"_id":"555"}],"type":"journal_article","keyword":["Mathematics (miscellaneous)"],"issue":"2","publication":"Journal of Evolution Equations","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>This work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-<jats:italic>K</jats:italic>-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-<jats:italic>K</jats:italic>-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without the assumption of bi-<jats:italic>K</jats:italic>-invariance.</jats:p>","lang":"eng"}]},{"user_id":"47427","volume":149,"_id":"21199","publisher":"Elsevier","status":"public","oa":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"citation":{"chicago":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” <i>Automatica</i> 149 (2023). <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">https://doi.org/10.1016/j.automatica.2022.110840</a>.","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,” <i>Automatica</i>, vol. 149, Art. no. 110840, 2023, doi: <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>.","apa":"Peitz, S., &#38; Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. <i>Automatica</i>, <i>149</i>, Article 110840. <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">https://doi.org/10.1016/j.automatica.2022.110840</a>","bibtex":"@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }","ama":"Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. <i>Automatica</i>. 2023;149. doi:<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>","mla":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” <i>Automatica</i>, vol. 149, 110840, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>."},"doi":"10.1016/j.automatica.2022.110840","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true"}],"article_number":"110840","language":[{"iso":"eng"}],"date_updated":"2023-01-07T12:01:58Z","publication_status":"published","intvolume":"       149","year":"2023","title":"On the Universal Transformation of Data-Driven Models to Control Systems","author":[{"full_name":"Peitz, Sebastian","first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"first_name":"Katharina","last_name":"Bieker","full_name":"Bieker, Katharina","id":"32829"}],"type":"journal_article","department":[{"_id":"101"},{"_id":"655"}],"date_created":"2021-02-10T07:04:15Z","abstract":[{"lang":"eng","text":"As in almost every other branch of science, the major advances in data\r\nscience and machine learning have also resulted in significant improvements\r\nregarding the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays possible to make accurate medium to long-term predictions of highly\r\ncomplex systems such as the weather, the dynamics within a nuclear fusion\r\nreactor, of disease models or the stock market in a very efficient manner. In\r\nmany cases, predictive methods are advertised to ultimately be useful for\r\ncontrol, as the control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge with huge potential in areas such as clean and efficient energy\r\nproduction, or the development of advanced medical devices. However, the\r\nquestion of how to use a predictive model for control is often left unanswered\r\ndue to the associated challenges, namely a significantly higher system\r\ncomplexity, the requirement of much larger data sets and an increased and often\r\nproblem-specific modeling effort. To solve these issues, we present a universal\r\nframework (which we call QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive models into control systems and use them for feedback control. The\r\nadvantages of our approach are a linear increase in data requirements with\r\nrespect to the control dimension, performance guarantees that rely exclusively\r\non the accuracy of the predictive model, and only little prior knowledge\r\nrequirements in control theory to solve complex control problems. In particular\r\nthe latter point is of key importance to enable a large number of researchers\r\nand practitioners to exploit the ever increasing capabilities of predictive\r\nmodels for control in a straight-forward and systematic fashion."}],"publication":"Automatica"},{"user_id":"45445","editor":[{"full_name":"Novotna, J.","first_name":"J.","last_name":"Novotna"},{"first_name":"H.","last_name":"Moraova","full_name":"Moraova, H."}],"page":"346-354","main_file_link":[{"url":"https://semt.cz/proceedings/semt-23.pdf"}],"_id":"46756","language":[{"iso":"eng"}],"publisher":"Charles University","date_updated":"2023-11-24T16:33:37Z","title":"Conceptual understanding of third grades for axial symmetry","year":"2023","status":"public","author":[{"id":"45445","full_name":"Wallner, Melina","first_name":"Melina","last_name":"Wallner"},{"full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta","id":"60267"}],"conference":{"name":"International Symposium in Elementary Mathematics Teaching","location":"Prag"},"type":"conference","department":[{"_id":"543"}],"date_created":"2023-08-30T09:24:29Z","publication":"International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education","citation":{"ieee":"M. Wallner and U. Häsel-Weide, “Conceptual understanding of third grades for axial symmetry,” in <i>International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education</i>, Prag, 2023, pp. 346–354.","apa":"Wallner, M., &#38; Häsel-Weide, U. (2023). Conceptual understanding of third grades for axial symmetry. In J. Novotna &#38; H. Moraova (Eds.), <i>International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education</i> (pp. 346–354). Charles University.","mla":"Wallner, Melina, and Uta Häsel-Weide. “Conceptual Understanding of Third Grades for Axial Symmetry.” <i>International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education</i>, edited by J. Novotna and H. Moraova, Charles University, 2023, pp. 346–54.","bibtex":"@inproceedings{Wallner_Häsel-Weide_2023, title={Conceptual understanding of third grades for axial symmetry}, booktitle={International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}, publisher={Charles University}, author={Wallner, Melina and Häsel-Weide, Uta}, editor={Novotna, J. and Moraova, H.}, year={2023}, pages={346–354} }","short":"M. Wallner, 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. 346–354.","ama":"Wallner M, Häsel-Weide U. Conceptual understanding of third grades for axial symmetry. In: Novotna J, Moraova H, eds. <i>International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education</i>. Charles University; 2023:346-354.","chicago":"Wallner, Melina, and Uta Häsel-Weide. “Conceptual Understanding of Third Grades for Axial Symmetry.” In <i>International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education</i>, edited by J. Novotna and H. Moraova, 346–54. Charles University, 2023."}},{"issue":"6","publication":"SIAM Journal on Applied Mathematics","abstract":[{"text":"Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.","lang":"eng"}],"date_created":"2023-11-29T10:50:05Z","department":[{"_id":"101"}],"type":"journal_article","keyword":["Applied Mathematics"],"author":[{"full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"von der Gracht","id":"97359"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"title":"Hypernetworks: Cluster Synchronization Is a Higher-Order Effect","year":"2023","intvolume":"        83","publication_status":"published","date_updated":"2023-11-29T10:52:23Z","language":[{"iso":"eng"}],"doi":"10.1137/23m1561075","citation":{"ama":"von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(6):2329-2353. doi:<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}, volume={83}, DOI={<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>}, number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }","mla":"von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 6, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2329–53, doi:<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i> 83, no. 6 (2023): 2329–53. <a href=\"https://doi.org/10.1137/23m1561075\">https://doi.org/10.1137/23m1561075</a>.","short":"S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics 83 (2023) 2329–2353.","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2023). Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>, <i>83</i>(6), 2329–2353. <a href=\"https://doi.org/10.1137/23m1561075\">https://doi.org/10.1137/23m1561075</a>","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 6, pp. 2329–2353, 2023, doi: <a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>."},"external_id":{"arxiv":["2302.08974"]},"status":"public","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"49326","page":"2329-2353","volume":83,"user_id":"97359"},{"type":"journal_article","department":[{"_id":"102"}],"date_created":"2023-12-01T09:23:59Z","publication":"La Matematica","citation":{"bibtex":"@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg Extensions}, DOI={<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>}, journal={La Matematica}, publisher={Springer Science and Business Media LLC}, author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }","ama":"Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. <i>La Matematica</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>","short":"J. Klüners, J. Wang, La Matematica (2023).","chicago":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” <i>La Matematica</i>, 2023. <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">https://doi.org/10.1007/s44007-023-00067-w</a>.","ieee":"J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,” <i>La Matematica</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>.","mla":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” <i>La Matematica</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>.","apa":"Klüners, J., &#38; Wang, J. (2023). Idélic Approach in Enumerating Heisenberg Extensions. <i>La Matematica</i>. <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">https://doi.org/10.1007/s44007-023-00067-w</a>"},"doi":"10.1007/s44007-023-00067-w","user_id":"21202","language":[{"iso":"eng"}],"_id":"49372","publisher":"Springer Science and Business Media LLC","date_updated":"2023-12-06T09:50:43Z","publication_status":"published","year":"2023","title":"Idélic Approach in Enumerating Heisenberg Extensions","status":"public","publication_identifier":{"issn":["2730-9657"]},"author":[{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"},{"first_name":"Jiuya","last_name":"Wang","full_name":"Wang, Jiuya"}]},{"publication":"Teachers and Teaching","citation":{"ieee":"S. Seitz, U. Häsel-Weide, Y. Wilke, and M. Wallner, “Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research,” <i>Teachers and Teaching</i>, pp. 1–16, 2023, doi: <a href=\"https://doi.org/10.1080/13540602.2023.2284876 \">https://doi.org/10.1080/13540602.2023.2284876 </a>.","mla":"Seitz, Simone, et al. “Expertise and Professionalism for Inclusive (Mathematics) Teaching and Learning: Reflections on Findings from Interdisciplinary Professionalisation Research.” <i>Teachers and Teaching</i>, 2023, pp. 1–16, doi:<a href=\"https://doi.org/10.1080/13540602.2023.2284876 \">https://doi.org/10.1080/13540602.2023.2284876 </a>.","apa":"Seitz, S., Häsel-Weide, U., Wilke, Y., &#38; Wallner, M. (2023). Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research. <i>Teachers and Teaching</i>, 1–16. <a href=\"https://doi.org/10.1080/13540602.2023.2284876 \">https://doi.org/10.1080/13540602.2023.2284876 </a>","bibtex":"@article{Seitz_Häsel-Weide_Wilke_Wallner_2023, title={Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research}, DOI={<a href=\"https://doi.org/10.1080/13540602.2023.2284876 \">https://doi.org/10.1080/13540602.2023.2284876 </a>}, journal={Teachers and Teaching}, author={Seitz, Simone and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}, year={2023}, pages={1–16} }","chicago":"Seitz, Simone, Uta Häsel-Weide, Yannik Wilke, and Melina Wallner. “Expertise and Professionalism for Inclusive (Mathematics) Teaching and Learning: Reflections on Findings from Interdisciplinary Professionalisation Research.” <i>Teachers and Teaching</i>, 2023, 1–16. <a href=\"https://doi.org/10.1080/13540602.2023.2284876 \">https://doi.org/10.1080/13540602.2023.2284876 </a>.","short":"S. Seitz, U. Häsel-Weide, Y. Wilke, M. Wallner, Teachers and Teaching (2023) 1–16.","ama":"Seitz S, Häsel-Weide U, Wilke Y, Wallner M. Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research. <i>Teachers and Teaching</i>. Published online 2023:1-16. doi:<a href=\"https://doi.org/10.1080/13540602.2023.2284876 \">https://doi.org/10.1080/13540602.2023.2284876 </a>"},"date_created":"2023-12-04T09:45:04Z","type":"journal_article","department":[{"_id":"543"}],"status":"public","year":"2023","title":"Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research","author":[{"first_name":"Simone","last_name":"Seitz","full_name":"Seitz, Simone"},{"id":"60267","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta"},{"last_name":"Wilke","first_name":"Yannik","full_name":"Wilke, Yannik"},{"full_name":"Wallner, Melina","first_name":"Melina","last_name":"Wallner","id":"45445"}],"date_updated":"2023-12-13T12:51:03Z","page":"1-16","language":[{"iso":"eng"}],"_id":"49425","doi":"https://doi.org/10.1080/13540602.2023.2284876 ","user_id":"45445"},{"doi":"10.1016/j.ifacol.2023.10.1457","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-12-29T14:26:00Z","intvolume":"        56","year":"2023","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","author":[{"first_name":"Yana","last_name":"Lishkova","full_name":"Lishkova, Yana"},{"first_name":"Paul","last_name":"Scherer","full_name":"Scherer, Paul"},{"first_name":"Steffen","last_name":"Ridderbusch","full_name":"Ridderbusch, Steffen"},{"full_name":"Jamnik, Mateja","first_name":"Mateja","last_name":"Jamnik"},{"full_name":"Liò, Pietro","first_name":"Pietro","last_name":"Liò"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian","id":"85279"}],"type":"conference","department":[{"_id":"636"}],"file":[{"date_updated":"2023-04-17T08:05:55Z","relation":"main_file","file_size":576115,"access_level":"open_access","file_name":"LNN_project.pdf","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","content_type":"application/pdf","file_id":"44037","creator":"coffen","description":"By one of the most fundamental principles in physics, a dynamical system will\nexhibit those motions which extremise an action functional. This leads to the formation of\nthe Euler-Lagrange equations, which serve as a model of how the system will behave in time.\nIf the dynamics exhibit additional symmetries, then the motion fulfils additional conservation\nlaws, such as conservation of energy (time invariance), momentum (translation invariance), or\nangular momentum (rotational invariance). To learn a system representation, one could learn\nthe discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function\nLd which defines them. Based on ideas from Lie group theory, we introduce a framework to learn\na discrete Lagrangian along with its symmetry group from discrete observations of motions and,\ntherefore, identify conserved quantities. The learning process does not restrict the form of the\nLagrangian, does not require velocity or momentum observations or predictions and incorporates\na cost term which safeguards against unwanted solutions and against potential numerical issues\nin forward simulations. The learnt discrete quantities are related to their continuous analogues\nusing variational backward error analysis and numerical results demonstrate the improvement\nsuch models can have both qualitatively and quantitatively even in the presence of noise.","date_created":"2023-04-17T08:05:55Z"}],"date_created":"2022-11-23T08:17:10Z","related_material":{"link":[{"url":"https://github.com/yanalish/SymDLNN","relation":"software","description":"GitHub"}]},"abstract":[{"lang":"eng","text":"By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise."}],"publication":"IFAC-PapersOnLine","issue":"2","user_id":"85279","ddc":["510"],"volume":56,"page":"3203-3210","_id":"34135","publisher":"Elsevier","has_accepted_license":"1","status":"public","conference":{"end_date":"2023-07-14","name":"The 22nd World Congress of the International Federation of Automatic Control","start_date":"2023-07-09","location":" Yokohama, Japan"},"oa":"1","external_id":{"arxiv":["2211.10830"]},"quality_controlled":"1","file_date_updated":"2023-04-17T08:05:55Z","citation":{"bibtex":"@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023, title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}, volume={56}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>}, number={2}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier}, author={Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={3203–3210} }","ama":"Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. In: <i>IFAC-PapersOnLine</i>. Vol 56. Elsevier; 2023:3203-3210. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>","mla":"Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” <i>IFAC-PapersOnLine</i>, vol. 56, no. 2, Elsevier, 2023, pp. 3203–10, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","short":"Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum, C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210.","chicago":"Lishkova, Yana, Paul Scherer, Steffen Ridderbusch, Mateja Jamnik, Pietro Liò, Sina Ober-Blöbaum, and Christian Offen. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” In <i>IFAC-PapersOnLine</i>, 56:3203–10. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>.","ieee":"Y. Lishkova <i>et al.</i>, “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery,” in <i>IFAC-PapersOnLine</i>,  Yokohama, Japan, 2023, vol. 56, no. 2, pp. 3203–3210, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","apa":"Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum, S., &#38; Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. <i>IFAC-PapersOnLine</i>, <i>56</i>(2), 3203–3210. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>"}},{"intvolume":"         3","publication_status":"published","date_updated":"2024-01-08T14:39:20Z","author":[{"full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe","last_name":"Schmidt"},{"full_name":"Weiß, Charlene","first_name":"Charlene","last_name":"Weiß","id":"70420"}],"status":"public","title":"Packings and Steiner systems in polar spaces","year":"2023","volume":3,"user_id":"70420","doi":"10.5070/c63160424","language":[{"iso":"eng"}],"_id":"50298","abstract":[{"text":"A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces.","lang":"eng"}],"citation":{"short":"K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).","chicago":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” <i>Combinatorial Theory</i> 3, no. 1 (2023). <a href=\"https://doi.org/10.5070/c63160424\">https://doi.org/10.5070/c63160424</a>.","apa":"Schmidt, K.-U., &#38; Weiß, C. (2023). Packings and Steiner systems in polar spaces. <i>Combinatorial Theory</i>, <i>3</i>(1). <a href=\"https://doi.org/10.5070/c63160424\">https://doi.org/10.5070/c63160424</a>","ieee":"K.-U. Schmidt and C. Weiß, “Packings and Steiner systems in polar spaces,” <i>Combinatorial Theory</i>, vol. 3, no. 1, 2023, doi: <a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>.","ama":"Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. <i>Combinatorial Theory</i>. 2023;3(1). doi:<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>","bibtex":"@article{Schmidt_Weiß_2023, title={Packings and Steiner systems in polar spaces}, volume={3}, DOI={<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>}, number={1}, journal={Combinatorial Theory}, author={Schmidt, Kai-Uwe and Weiß, Charlene}, year={2023} }","mla":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” <i>Combinatorial Theory</i>, vol. 3, no. 1, 2023, doi:<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>."},"issue":"1","publication":"Combinatorial Theory","department":[{"_id":"100"}],"type":"journal_article","date_created":"2024-01-08T14:33:54Z"},{"date_created":"2024-01-08T14:25:28Z","type":"journal_article","department":[{"_id":"100"}],"publication":"Journal of Combinatorial Designs","issue":"9","abstract":[{"lang":"eng","text":"We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled."}],"language":[{"iso":"eng"}],"doi":"10.1002/jcd.21903","title":"Existence of small ordered orthogonal arrays","year":"2023","author":[{"full_name":"Schmidt, Kai‐Uwe","last_name":"Schmidt","first_name":"Kai‐Uwe"},{"first_name":"Charlene","last_name":"Weiß","full_name":"Weiß, Charlene","id":"70420"}],"date_updated":"2024-01-08T14:38:53Z","publication_status":"published","intvolume":"        31","citation":{"mla":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” <i>Journal of Combinatorial Designs</i>, vol. 31, no. 9, Wiley, 2023, pp. 422–31, doi:<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>.","bibtex":"@article{Schmidt_Weiß_2023, title={Existence of small ordered orthogonal arrays}, volume={31}, DOI={<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>}, number={9}, journal={Journal of Combinatorial Designs}, publisher={Wiley}, author={Schmidt, Kai‐Uwe and Weiß, Charlene}, year={2023}, pages={422–431} }","ama":"Schmidt K, Weiß C. Existence of small ordered orthogonal arrays. <i>Journal of Combinatorial Designs</i>. 2023;31(9):422-431. doi:<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>","ieee":"K. Schmidt and C. Weiß, “Existence of small ordered orthogonal arrays,” <i>Journal of Combinatorial Designs</i>, vol. 31, no. 9, pp. 422–431, 2023, doi: <a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>.","apa":"Schmidt, K., &#38; Weiß, C. (2023). Existence of small ordered orthogonal arrays. <i>Journal of Combinatorial Designs</i>, <i>31</i>(9), 422–431. <a href=\"https://doi.org/10.1002/jcd.21903\">https://doi.org/10.1002/jcd.21903</a>","chicago":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” <i>Journal of Combinatorial Designs</i> 31, no. 9 (2023): 422–31. <a href=\"https://doi.org/10.1002/jcd.21903\">https://doi.org/10.1002/jcd.21903</a>.","short":"K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431."},"page":"422-431","_id":"50297","publisher":"Wiley","user_id":"70420","volume":31,"status":"public"},{"department":[{"_id":"100"}],"type":"dissertation","date_created":"2024-01-08T14:42:12Z","abstract":[{"text":"Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases.","lang":"eng"}],"citation":{"ieee":"C. Weiß, <i>Linear programming bounds in classical association schemes</i>. 2023.","apa":"Weiß, C. (2023). <i>Linear programming bounds in classical association schemes</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1672\">https://doi.org/10.17619/UNIPB/1-1672</a>","chicago":"Weiß, Charlene. <i>Linear Programming Bounds in Classical Association Schemes</i>, 2023. <a href=\"https://doi.org/10.17619/UNIPB/1-1672\">https://doi.org/10.17619/UNIPB/1-1672</a>.","short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.","mla":"Weiß, Charlene. <i>Linear Programming Bounds in Classical Association Schemes</i>. 2023, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>.","bibtex":"@book{Weiß_2023, title={Linear programming bounds in classical association schemes}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>}, author={Weiß, Charlene}, year={2023} }","ama":"Weiß C. <i>Linear Programming Bounds in Classical Association Schemes</i>.; 2023. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>"},"user_id":"70420","doi":"10.17619/UNIPB/1-1672","_id":"50300","language":[{"iso":"eng"}],"date_updated":"2024-01-08T14:46:14Z","author":[{"id":"70420","full_name":"Weiß, Charlene","last_name":"Weiß","first_name":"Charlene"}],"title":"Linear programming bounds in classical association schemes","status":"public","year":"2023"},{"page":"3203-3210","language":[{"iso":"eng"}],"_id":"51131","user_id":"14931","editor":[{"full_name":"Drijvers, P.","first_name":"P.","last_name":"Drijvers"},{"full_name":"Csapodi, C.","first_name":"C.","last_name":"Csapodi"},{"last_name":"Palmér","first_name":"H.","full_name":"Palmér, H."},{"full_name":"Gosztonyi, K.","first_name":"K.","last_name":"Gosztonyi"},{"last_name":"Kónya","first_name":"E.","full_name":"Kónya, E."}],"title":"Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics","status":"public","year":"2023","author":[{"first_name":"Lara Marie","last_name":"Graf","full_name":"Graf, Lara Marie","id":"89837"},{"full_name":"Häsel-Weide, Uta","first_name":"Uta","last_name":"Häsel-Weide","id":"60267"},{"last_name":"Höveler","first_name":"K.","full_name":"Höveler, K."},{"full_name":"Nührenbörger, M.","last_name":"Nührenbörger","first_name":"M."}],"corporate_editor":["Alfréd Rényi Institute of Mathematics and ERME"],"date_updated":"2024-02-05T08:55:43Z","date_created":"2024-02-05T08:47:35Z","type":"conference","department":[{"_id":"543"}],"publication":"Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)","citation":{"ama":"Graf LM, Häsel-Weide U, Höveler K, Nührenbörger M. Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics. In: Drijvers P, Csapodi C, Palmér H, Gosztonyi K, Kónya E, Alfréd Rényi Institute of Mathematics and ERME, eds. <i>Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)</i>. ; 2023:3203-3210.","bibtex":"@inproceedings{Graf_Häsel-Weide_Höveler_Nührenbörger_2023, title={Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics}, booktitle={Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)}, author={Graf, Lara Marie and Häsel-Weide, Uta and Höveler, K. and Nührenbörger, M.}, editor={Drijvers, P. and Csapodi, C. and Palmér, H. and Gosztonyi, K. and Kónya, E. and Alfréd Rényi Institute of Mathematics and ERME}, year={2023}, pages={3203–3210} }","mla":"Graf, Lara Marie, et al. “Insights into Out-of-Field Teachers’ Self-Reports: Fostering the Understanding of Addition and Subtraction as a Basis for Children to Overcome Difficulties in Mathematics.” <i>Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)</i>, edited by P. Drijvers et al., 2023, pp. 3203–10.","chicago":"Graf, Lara Marie, Uta Häsel-Weide, K. Höveler, and M. Nührenbörger. “Insights into Out-of-Field Teachers’ Self-Reports: Fostering the Understanding of Addition and Subtraction as a Basis for Children to Overcome Difficulties in Mathematics.” In <i>Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)</i>, edited by P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, and Alfréd Rényi Institute of Mathematics and ERME, 3203–10, 2023.","short":"L.M. Graf, U. Häsel-Weide, K. Höveler, M. Nührenbörger, in: P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, Alfréd Rényi Institute of Mathematics and ERME (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), 2023, pp. 3203–3210.","apa":"Graf, L. M., Häsel-Weide, U., Höveler, K., &#38; Nührenbörger, M. (2023). Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, &#38; Alfréd Rényi Institute of Mathematics and ERME (Eds.), <i>Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)</i> (pp. 3203–3210).","ieee":"L. M. Graf, U. Häsel-Weide, K. Höveler, and M. Nührenbörger, “Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics,” in <i>Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)</i>, 2023, pp. 3203–3210."}},{"external_id":{"arxiv":["2205.03167"]},"date_created":"2022-05-11T10:38:11Z","type":"journal_article","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"publication":"Communications in Mathematical Physics","citation":{"ieee":"T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric  spaces,” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","apa":"Weich, T., &#38; Wolf, L. L. (2023). Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>, <i>403</i>. <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","bibtex":"@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher rank locally symmetric  spaces}, volume={403}, DOI={<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>}, journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2023} }","short":"T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).","ama":"Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>. 2023;403. doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i> 403 (2023). <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>."},"abstract":[{"text":"Given a geometrically finite hyperbolic surface of infinite volume it is a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding principal eigenvalues. A large class of examples fulfilling these\r\nassumptions are the non-compact quotients by Anosov subgroups.","lang":"eng"}],"language":[{"iso":"eng"}],"_id":"31189","user_id":"49178","doi":"https://doi.org/10.1007/s00220-023-04819-1","volume":403,"year":"2023","title":"Absence of principal eigenvalues for higher rank locally symmetric  spaces","status":"public","publication_identifier":{"unknown":["1275-1295"]},"author":[{"id":"49178","full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"},{"id":"45027","full_name":"Wolf, Lasse Lennart","first_name":"Lasse Lennart","last_name":"Wolf"}],"date_updated":"2024-02-06T20:52:40Z","intvolume":"       403"},{"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"preprint","date_created":"2024-02-06T20:58:35Z","external_id":{"arxiv":["2308.13463"]},"abstract":[{"lang":"eng","text":"We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the connection between invariant Ruelle distributions and residues\r\nof meromorphically continued weighted zeta functions established by the authors\r\ntogether with Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer operator has to include a contracting direction which\r\nwe account for with techniques developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed for our algorithm in the case of surfaces with\r\nadditional symmetries by proving and applying a symmetry reduction of weighted\r\nzeta functions."}],"citation":{"mla":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","bibtex":"@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463}, author={Schütte, Philipp and Weich, Tobias}, year={2023} }","ama":"Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. <i>arXiv:230813463</i>. Published online 2023.","ieee":"P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions,” <i>arXiv:2308.13463</i>. 2023.","apa":"Schütte, P., &#38; Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. In <i>arXiv:2308.13463</i>.","chicago":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","short":"P. Schütte, T. Weich, ArXiv:2308.13463 (2023)."},"publication":"arXiv:2308.13463","user_id":"49178","_id":"51206","language":[{"iso":"eng"}],"date_updated":"2024-02-11T19:56:01Z","author":[{"full_name":"Schütte, Philipp","first_name":"Philipp","last_name":"Schütte","id":"50168"},{"last_name":"Weich","first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"}],"title":"Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions","year":"2023","status":"public"},{"volume":337,"user_id":"15540","publisher":"Elsevier BV","_id":"51351","page":"185-189","status":"public","citation":{"short":"E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.","chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i> 337 (2023): 185–89. <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">https://doi.org/10.1016/j.dam.2023.05.008</a>.","apa":"Steffen, E., &#38; Wolf, I. H. (2023). Bounds for the chromatic index of signed multigraphs. <i>Discrete Applied Mathematics</i>, <i>337</i>, 185–189. <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">https://doi.org/10.1016/j.dam.2023.05.008</a>","ieee":"E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,” <i>Discrete Applied Mathematics</i>, vol. 337, pp. 185–189, 2023, doi: <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>.","ama":"Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. <i>Discrete Applied Mathematics</i>. 2023;337:185-189. doi:<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>","bibtex":"@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed multigraphs}, volume={337}, DOI={<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>}, journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i>, vol. 337, Elsevier BV, 2023, pp. 185–89, doi:<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>."},"doi":"10.1016/j.dam.2023.05.008","language":[{"iso":"eng"}],"intvolume":"       337","publication_status":"published","date_updated":"2024-02-14T17:33:59Z","author":[{"id":"15548","first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard"},{"id":"88145","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","last_name":"Wolf"}],"publication_identifier":{"issn":["0166-218X"]},"year":"2023","title":"Bounds for the chromatic index of signed multigraphs","department":[{"_id":"542"}],"type":"journal_article","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"date_created":"2024-02-14T17:33:29Z","publication":"Discrete Applied Mathematics"},{"publication_identifier":{"isbn":["9783031261039","9783031261046"]},"author":[{"full_name":"Cappello, Chiara","last_name":"Cappello","first_name":"Chiara","id":"72874"},{"id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen"}],"status":"public","year":"2023","title":"Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks","publication_status":"published","date_updated":"2024-02-16T07:42:38Z","language":[{"iso":"eng"}],"_id":"45190","publisher":"Springer International Publishing","page":"93--110","user_id":"15540","doi":"10.1007/978-3-031-26104-6_5","citation":{"short":"C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International Publishing, Cham, 2023, pp. 93--110.","chicago":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” In <i>The Digital Twin of Humans</i>, 93--110. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">https://doi.org/10.1007/978-3-031-26104-6_5</a>.","apa":"Cappello, C., &#38; Steffen, E. (2023). Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In <i>The Digital Twin of Humans</i> (pp. 93--110). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">https://doi.org/10.1007/978-3-031-26104-6_5</a>","ieee":"C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks,” in <i>The Digital Twin of Humans</i>, Cham: Springer International Publishing, 2023, pp. 93--110.","ama":"Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In: <i>The Digital Twin of Humans</i>. Springer International Publishing; 2023:93--110. doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>","bibtex":"@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>}, booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing}, author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }","mla":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” <i>The Digital Twin of Humans</i>, Springer International Publishing, 2023, pp. 93--110, doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>."},"publication":"The Digital Twin of Humans","date_created":"2023-05-22T10:22:21Z","place":"Cham","department":[{"_id":"542"}],"type":"book_chapter"},{"doi":"10.1016/j.disc.2023.113457","user_id":"15540","article_number":"113457","publisher":"Elsevier BV","_id":"51357","language":[{"iso":"eng"}],"date_updated":"2024-02-16T08:45:10Z","publication_status":"published","year":"2023","title":"Rotation r-graphs","status":"public","publication_identifier":{"issn":["0012-365X"]},"author":[{"id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen"},{"last_name":"Wolf","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus","id":"88145"}],"keyword":["Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"type":"journal_article","department":[{"_id":"542"}],"date_created":"2024-02-16T08:44:50Z","publication":"Discrete Mathematics","citation":{"ieee":"E. Steffen and I. H. Wolf, “Rotation r-graphs,” <i>Discrete Mathematics</i>, Art. no. 113457, 2023, doi: <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>.","apa":"Steffen, E., &#38; Wolf, I. H. (2023). Rotation r-graphs. <i>Discrete Mathematics</i>, Article 113457. <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">https://doi.org/10.1016/j.disc.2023.113457</a>","short":"E. Steffen, I.H. Wolf, Discrete Mathematics (2023).","chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete Mathematics</i>, 2023. <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">https://doi.org/10.1016/j.disc.2023.113457</a>.","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete Mathematics</i>, 113457, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>.","bibtex":"@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>}, number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","ama":"Steffen E, Wolf IH. Rotation r-graphs. <i>Discrete Mathematics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>"}},{"status":"public","volume":10,"user_id":"49063","_id":"31210","page":"335-403","citation":{"apa":"Arends, C., &#38; Hilgert, J. (2023). Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. <i>Journal de l’École Polytechnique — Mathématiques</i>, <i>10</i>, 335–403. <a href=\"https://doi.org/10.5802/jep.220\">https://doi.org/10.5802/jep.220</a>","ieee":"C. Arends and J. Hilgert, “Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters,” <i>Journal de l’École polytechnique — Mathématiques</i>, vol. 10, pp. 335–403, 2023, doi: <a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>.","chicago":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” <i>Journal de l’École Polytechnique — Mathématiques</i> 10 (2023): 335–403. <a href=\"https://doi.org/10.5802/jep.220\">https://doi.org/10.5802/jep.220</a>.","short":"C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","mla":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” <i>Journal de l’École Polytechnique — Mathématiques</i>, vol. 10, 2023, pp. 335–403, doi:<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>.","ama":"Arends C, Hilgert J. Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. <i>Journal de l’École polytechnique — Mathématiques</i>. 2023;10:335-403. doi:<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>","bibtex":"@article{Arends_Hilgert_2023, title={Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}, volume={10}, DOI={<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>}, journal={Journal de l’École polytechnique — Mathématiques}, author={Arends, Christian and Hilgert, Joachim}, year={2023}, pages={335–403} }"},"external_id":{"arxiv":["2112.11073"]},"intvolume":"        10","date_updated":"2024-02-19T06:30:26Z","publication_status":"published","publication_identifier":{"issn":["2429-7100"],"eissn":["2270-518X"]},"author":[{"id":"43994","last_name":"Arends","first_name":"Christian","full_name":"Arends, Christian"},{"full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim","id":"220"}],"year":"2023","title":"Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters","doi":"10.5802/jep.220","language":[{"iso":"eng"}],"abstract":[{"text":"In this paper we complete the program of relating the Laplace spectrum for\r\nrank one compact locally symmetric spaces with the first band Ruelle-Pollicott\r\nresonances of the geodesic flow on its sphere bundle. This program was started\r\nby Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and\r\nGuillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for\r\ngeneral rank one spaces. Except for the case of hyperbolic surfaces a countable\r\nset of exceptional spectral parameters always left untreated since the\r\ncorresponding Poisson transforms are neither injective nor surjective. We use\r\nvector valued Poisson transforms to treat also the exceptional spectral\r\nparameters. For surfaces the exceptional spectral parameters lead to discrete\r\nseries representations of $\\mathrm{SL}(2,\\mathbb R)$. In higher dimensions the\r\nsituation is more complicated, but can be described completely.","lang":"eng"}],"publication":"Journal de l’École polytechnique — Mathématiques","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"keyword":["Ruelle resonances","Poisson transforms","locally symmetric spaces","principal series representations"],"type":"journal_article","date_created":"2022-05-11T12:27:00Z"}]