[{"date_updated":"2024-12-24T16:58:38Z","intvolume":"       252","status":"public","year":"2025","title":"Lie groups of real analytic diffeomorphisms are L^1-regular","author":[{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"}],"user_id":"178","doi":"10.1016/j.na.2024.113690","volume":252,"article_number":"113690","_id":"34807","language":[{"iso":"eng"}],"abstract":[{"text":"Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all\r\nreal-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space\r\n${\\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of\r\ntime-dependent real-analytic vector fields on $M$ which are integrable\r\nfunctions in time, and their dependence on the time-dependent vector field.\r\nNotably, we show that the Lie group $G$ is $L^1$-regular in the sense that each\r\n$[\\gamma]$ in $L^1([0,1],{\\mathfrak g})$ has an evolution which is an\r\nabsolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\\gamma]$.\r\nAs tools for the proof, we develop several new results concerning\r\n$L^p$-regularity of infinite-dimensional Lie groups, for $1\\leq p\\leq \\infty$,\r\nwhich will be useful also for the discussion of other classes of groups.\r\nMoreover, we obtain new results concerning the continuity and complex\r\nanalyticity of non-linear mappings on open subsets of locally convex direct\r\nlimits.","lang":"eng"}],"quality_controlled":"1","publication":"Nonlinear Analysis","citation":{"bibtex":"@article{Glöckner_2025, title={Lie groups of real analytic diffeomorphisms are L^1-regular}, volume={252}, DOI={<a href=\"https://doi.org/10.1016/j.na.2024.113690\">10.1016/j.na.2024.113690</a>}, number={113690}, journal={Nonlinear Analysis}, author={Glöckner, Helge}, year={2025} }","short":"H. Glöckner, Nonlinear Analysis 252 (2025).","ama":"Glöckner H. Lie groups of real analytic diffeomorphisms are L^1-regular. <i>Nonlinear Analysis</i>. 2025;252. doi:<a href=\"https://doi.org/10.1016/j.na.2024.113690\">10.1016/j.na.2024.113690</a>","chicago":"Glöckner, Helge. “Lie Groups of Real Analytic Diffeomorphisms Are L^1-Regular.” <i>Nonlinear Analysis</i> 252 (2025). <a href=\"https://doi.org/10.1016/j.na.2024.113690\">https://doi.org/10.1016/j.na.2024.113690</a>.","ieee":"H. Glöckner, “Lie groups of real analytic diffeomorphisms are L^1-regular,” <i>Nonlinear Analysis</i>, vol. 252, Art. no. 113690, 2025, doi: <a href=\"https://doi.org/10.1016/j.na.2024.113690\">10.1016/j.na.2024.113690</a>.","apa":"Glöckner, H. (2025). Lie groups of real analytic diffeomorphisms are L^1-regular. <i>Nonlinear Analysis</i>, <i>252</i>, Article 113690. <a href=\"https://doi.org/10.1016/j.na.2024.113690\">https://doi.org/10.1016/j.na.2024.113690</a>","mla":"Glöckner, Helge. “Lie Groups of Real Analytic Diffeomorphisms Are L^1-Regular.” <i>Nonlinear Analysis</i>, vol. 252, 113690, 2025, doi:<a href=\"https://doi.org/10.1016/j.na.2024.113690\">10.1016/j.na.2024.113690</a>."},"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"date_created":"2022-12-22T07:49:32Z"},{"user_id":"97359","volume":324,"editor":[{"full_name":"Bonomi, Silvia","first_name":"Silvia","last_name":"Bonomi"},{"last_name":"Galletta","first_name":"Letterio","full_name":"Galletta, Letterio"},{"first_name":" Etienne","last_name":"Rivière","full_name":"Rivière,  Etienne"},{"full_name":"Schiavoni,  Valerio","last_name":"Schiavoni","first_name":" Valerio"}],"publisher":"Schloss Dagstuhl -- Leibniz-Zentrum für Informatik","_id":"56298","status":"public","conference":{"end_date":"2024-12-13","location":"Lucca, Italy","name":"28th International Conference on Principles of Distributed Systems (OPODIS 2024)","start_date":"2024-12-11"},"oa":"1","external_id":{"arxiv":["2409.19277"]},"project":[{"name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme","grant_number":"453112019","_id":"106"}],"citation":{"short":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, P. Kling, in: S. Bonomi, L. Galletta,  Etienne Rivière,  Valerio Schiavoni (Eds.), 28th International Conference on Principles of Distributed Systems (OPODIS 2024), Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025.","chicago":"Gerlach, Raphael, Sören von der Gracht, Christopher Hahn, Jonas Harbig, and Peter Kling. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” In <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, edited by Silvia Bonomi, Letterio Galletta,  Etienne Rivière, and  Valerio Schiavoni, Vol. 324. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">https://doi.org/10.4230/LIPIcs.OPODIS.2024.13</a>.","apa":"Gerlach, R., von der Gracht, S., Hahn, C., Harbig, J., &#38; Kling, P. (2025). Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In S. Bonomi, L. Galletta,  Etienne Rivière, &#38;  Valerio Schiavoni (Eds.), <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i> (Vol. 324). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">https://doi.org/10.4230/LIPIcs.OPODIS.2024.13</a>","ieee":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, and P. Kling, “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility,” in <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, Lucca, Italy, 2025, vol. 324, doi: <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>.","ama":"Gerlach R, von der Gracht S, Hahn C, Harbig J, Kling P. Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In: Bonomi S, Galletta L, Rivière  Etienne, Schiavoni  Valerio, eds. <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>. Vol 324. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>","bibtex":"@inproceedings{Gerlach_von der Gracht_Hahn_Harbig_Kling_2025, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility}, volume={324}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>}, booktitle={28th International Conference on Principles of Distributed Systems (OPODIS 2024)}, publisher={Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}, author={Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig, Jonas and Kling, Peter}, editor={Bonomi, Silvia and Galletta, Letterio and Rivière,  Etienne and Schiavoni,  Valerio}, year={2025}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","mla":"Gerlach, Raphael, et al. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, edited by Silvia Bonomi et al., vol. 324, Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>."},"doi":"10.4230/LIPIcs.OPODIS.2024.13","main_file_link":[{"url":"https://arxiv.org/abs/2409.19277","open_access":"1"}],"series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-01-09T11:39:19Z","intvolume":"       324","year":"2025","title":"Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility","author":[{"full_name":"Gerlach, Raphael","orcid":"0009-0002-4750-2051","first_name":"Raphael","last_name":"Gerlach","id":"32655"},{"id":"97359","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"von der Gracht"},{"full_name":"Hahn, Christopher","first_name":"Christopher","last_name":"Hahn"},{"full_name":"Harbig, Jonas","last_name":"Harbig","first_name":"Jonas","id":"47213"},{"full_name":"Kling, Peter","first_name":"Peter","last_name":"Kling"}],"publication_identifier":{"isbn":["978-3-95977-360-7"],"issn":["1868-8969"]},"keyword":["Swarm Algorithm","Swarm Robots","Distributed Algorithm","Pattern Formation","Limited Visibility","Oblivious"],"type":"conference","department":[{"_id":"101"}],"date_created":"2024-10-01T13:29:43Z","abstract":[{"text":"In the general pattern formation (GPF) problem, a swarm of simple autonomous,\r\ndisoriented robots must form a given pattern. The robots' simplicity imply a\r\nstrong limitation: When the initial configuration is rotationally symmetric,\r\nonly patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS\r\n2010]. The only known algorithm to form large patterns with limited visibility\r\nand without memory requires the robots to start in a near-gathering (a swarm of\r\nconstant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know\r\nany near-gathering algorithm guaranteed to preserve symmetry but most natural\r\ngathering strategies trivially increase symmetries [Castenow et al.; OPODIS\r\n2022].\r\n  Thus, we study near-gathering without changing the swarm's rotational\r\nsymmetry for disoriented, oblivious robots with limited visibility (the\r\nOBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on\r\nthe theory of dynamical systems to analyze how a given algorithm affects\r\nsymmetry and provide sufficient conditions for symmetry preservation. Until\r\nnow, it was unknown whether the considered OBLOT-model allows for any\r\nnon-trivial algorithm that always preserves symmetry. Our first result shows\r\nthat a variant of Go-to-the-Average always preserves symmetry but may sometimes\r\nlead to multiple, unconnected near-gathering clusters. Our second result is a\r\nsymmetry-preserving near-gathering algorithm that works on swarms with a convex\r\nboundary (the outer boundary of the unit disc graph) and without holes (circles\r\nof diameter 1 inside the boundary without any robots).","lang":"eng"}],"publication":"28th International Conference on Principles of Distributed Systems (OPODIS 2024)"},{"publication":"arXiv","citation":{"apa":"Bullerjahn, N. (2025). Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions. <i>ArXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">https://doi.org/10.48550/ARXIV.2502.03847</a>","mla":"Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.” <i>ArXiv</i>, 2025, doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>.","ieee":"N. Bullerjahn, “Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions,” <i>arXiv</i>, 2025, doi: <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>.","chicago":"Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.” <i>ArXiv</i>, 2025. <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">https://doi.org/10.48550/ARXIV.2502.03847</a>.","ama":"Bullerjahn N. Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions. <i>arXiv</i>. Published online 2025. doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>","short":"N. Bullerjahn, ArXiv (2025).","bibtex":"@article{Bullerjahn_2025, title={Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>}, journal={arXiv}, author={Bullerjahn, Nils}, year={2025} }"},"type":"journal_article","department":[{"_id":"841"}],"date_created":"2025-02-07T08:27:10Z","date_updated":"2025-02-07T08:28:48Z","status":"public","year":"2025","title":"Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions","author":[{"first_name":"Nils","orcid":"https://orcid.org/0009-0003-8460-1574","last_name":"Bullerjahn","full_name":"Bullerjahn, Nils","id":"103797"}],"user_id":"103797","doi":"10.48550/ARXIV.2502.03847","_id":"58532","language":[{"iso":"eng"}]},{"user_id":"85279","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.05123","open_access":"1"}],"language":[{"iso":"eng"}],"_id":"58544","date_updated":"2025-02-10T08:36:12Z","publication_status":"submitted","title":"Multiphoton, multimode state classification for nonlinear optical circuits ","status":"public","year":"2025","author":[{"full_name":"Kopylov, Denis","first_name":"Denis","last_name":"Kopylov","id":"98502"},{"last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian","full_name":"Offen, Christian","id":"85279"},{"full_name":"Ares, Laura","first_name":"Laura","last_name":"Ares"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"orcid":"0000-0001-8864-2072","last_name":"Meier","first_name":"Torsten","full_name":"Meier, Torsten","id":"344"},{"id":"60286","full_name":"Sharapova, Polina","first_name":"Polina","last_name":"Sharapova"},{"last_name":"Sperling","orcid":"0000-0002-5844-3205","first_name":"Jan","full_name":"Sperling, Jan","id":"75127"}],"type":"preprint","oa":"1","department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"external_id":{"arxiv":["2502.05123"]},"date_created":"2025-02-10T08:26:45Z","abstract":[{"text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. ","lang":"eng"}],"citation":{"ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” .","apa":"Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state classification for nonlinear optical circuits </i>.","chicago":"Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits ,” n.d.","short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling, title={Multiphoton, multimode state classification for nonlinear optical circuits }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan} }","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits ."}},{"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"98"},{"_id":"360"}],"date_created":"2025-03-10T10:46:07Z","publication":"The Journal of Mathematical Behavior","citation":{"ieee":"K. Krüger and G. Werth, “Mathematics education for girls in Prussia 1890–1925,” <i>The Journal of Mathematical Behavior</i>, vol. 79, Art. no. 101242, 2025, doi: <a href=\"https://doi.org/10.1016/j.jmathb.2025.101242\">10.1016/j.jmathb.2025.101242</a>.","apa":"Krüger, K., &#38; Werth, G. (2025). Mathematics education for girls in Prussia 1890–1925. <i>The Journal of Mathematical Behavior</i>, <i>79</i>, Article 101242. <a href=\"https://doi.org/10.1016/j.jmathb.2025.101242\">https://doi.org/10.1016/j.jmathb.2025.101242</a>","mla":"Krüger, Katja, and Gerda Werth. “Mathematics Education for Girls in Prussia 1890–1925.” <i>The Journal of Mathematical Behavior</i>, vol. 79, 101242, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.jmathb.2025.101242\">10.1016/j.jmathb.2025.101242</a>.","bibtex":"@article{Krüger_Werth_2025, title={Mathematics education for girls in Prussia 1890–1925}, volume={79}, DOI={<a href=\"https://doi.org/10.1016/j.jmathb.2025.101242\">10.1016/j.jmathb.2025.101242</a>}, number={101242}, journal={The Journal of Mathematical Behavior}, publisher={Elsevier BV}, author={Krüger, Katja and Werth, Gerda}, year={2025} }","chicago":"Krüger, Katja, and Gerda Werth. “Mathematics Education for Girls in Prussia 1890–1925.” <i>The Journal of Mathematical Behavior</i> 79 (2025). <a href=\"https://doi.org/10.1016/j.jmathb.2025.101242\">https://doi.org/10.1016/j.jmathb.2025.101242</a>.","short":"K. Krüger, G. Werth, The Journal of Mathematical Behavior 79 (2025).","ama":"Krüger K, Werth G. Mathematics education for girls in Prussia 1890–1925. <i>The Journal of Mathematical Behavior</i>. 2025;79. doi:<a href=\"https://doi.org/10.1016/j.jmathb.2025.101242\">10.1016/j.jmathb.2025.101242</a>"},"user_id":"578","doi":"10.1016/j.jmathb.2025.101242","volume":79,"article_number":"101242","_id":"58947","publisher":"Elsevier BV","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-03-10T10:54:03Z","intvolume":"        79","status":"public","year":"2025","title":"Mathematics education for girls in Prussia 1890–1925","publication_identifier":{"issn":["0732-3123"]},"author":[{"full_name":"Krüger, Katja","first_name":"Katja","last_name":"Krüger"},{"full_name":"Werth, Gerda","first_name":"Gerda","last_name":"Werth","id":"578"}]},{"language":[{"iso":"eng"}],"date_updated":"2025-03-11T08:53:02Z","author":[{"orcid":"0009-0002-4750-2051","first_name":"Raphael","last_name":"Gerlach","full_name":"Gerlach, Raphael","id":"32655"},{"first_name":"Sören","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","id":"97359"}],"title":"Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems","year":"2025","department":[{"_id":"101"}],"keyword":["dynamical systems","coupled systems","distributed computing","robot swarms","autonomous mobile robots","symmetry","equivariant dynamics"],"type":"preprint","date_created":"2025-03-11T08:21:05Z","file":[{"file_id":"58954","content_type":"application/pdf","file_name":"Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf","file_size":812198,"access_level":"open_access","relation":"main_file","date_updated":"2025-03-11T08:27:32Z","date_created":"2025-03-11T08:27:32Z","creator":"svdg"}],"abstract":[{"lang":"eng","text":"In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze their collective Fsync dynamics using of equivariant dynamical systems theory. To this end, we show that the corresponding evolution function commutes with rotational and reflective transformations of R^2. These form a group that is isomorphic to O(2) x S_n, the product group of the orthogonal group and the permutation on n elements. The theory of equivariant dynamical systems is used to deduce a hierarchy along which symmetries of a robot swarm can potentially increase following an arbitrary protocol. By decoupling the Look phase from the Compute and Move phases in the mathematical description of an LCM cycle, this hierarchy can be characterized in terms of automorphisms of connectivity graphs. In particular, we find all possible types of symmetry increase, if the decoupled Compute and Move phase is invertible. Finally, we apply our results to protocols which induce state-dependent linear dynamics, where the reduced system consisting of only the Compute and Move phase is linear."}],"publication":"arXiv:2503.07576","ddc":["004"],"user_id":"97359","_id":"58953","page":"23","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["2503.07576"]},"project":[{"grant_number":"453112019","_id":"106","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"citation":{"chicago":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","ama":"Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. <i>arXiv:250307576</i>. Published online 2025.","short":"R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).","bibtex":"@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems}, journal={arXiv:2503.07576}, author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }","mla":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","apa":"Gerlach, R., &#38; von der Gracht, S. (2025). Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. In <i>arXiv:2503.07576</i>.","ieee":"R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems,” <i>arXiv:2503.07576</i>. 2025."},"file_date_updated":"2025-03-11T08:27:32Z"},{"author":[{"first_name":"Daniel","last_name":"Frischemeier","full_name":"Frischemeier, Daniel"},{"id":"16274","full_name":"Biehler, Rolf","last_name":"Biehler","first_name":"Rolf"}],"status":"public","year":"2025","title":"Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten","intvolume":"        45","date_updated":"2025-03-17T09:03:05Z","language":[{"iso":"ger"}],"_id":"59053","page":"22-33","volume":45,"user_id":"37888","citation":{"chicago":"Frischemeier, Daniel, and Rolf Biehler. “Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten.” <i>Stochastik in der Schule</i> 45, no. 1 (2025): 22–33.","short":"D. Frischemeier, R. Biehler, Stochastik in der Schule 45 (2025) 22–33.","apa":"Frischemeier, D., &#38; Biehler, R. (2025). Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten. <i>Stochastik in der Schule</i>, <i>45</i>(1), 22–33.","ieee":"D. Frischemeier and R. Biehler, “Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten,” <i>Stochastik in der Schule</i>, vol. 45, no. 1, pp. 22–33, 2025.","ama":"Frischemeier D, Biehler R. Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten. <i>Stochastik in der Schule</i>. 2025;45(1):22-33.","bibtex":"@article{Frischemeier_Biehler_2025, title={Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten}, volume={45}, number={1}, journal={Stochastik in der Schule}, author={Frischemeier, Daniel and Biehler, Rolf}, year={2025}, pages={22–33} }","mla":"Frischemeier, Daniel, and Rolf Biehler. “Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten.” <i>Stochastik in der Schule</i>, vol. 45, no. 1, 2025, pp. 22–33."},"issue":"1","publication":"Stochastik in der Schule","date_created":"2025-03-17T09:02:59Z","department":[{"_id":"363"}],"type":"journal_article"},{"citation":{"short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 45 (2025).","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i> 45, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-Graphs that Color All r-Graphs,” <i>Combinatorica</i>, vol. 45, no. 2, Art. no. 16, 2025, doi: <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>.","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2025). Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>, <i>45</i>(2), Article 16. <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2025, title={Sets of r-Graphs that Color All r-Graphs}, volume={45}, DOI={<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>}, number={216}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak H.}, year={2025} }","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>. 2025;45(2). doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i>, vol. 45, no. 2, 16, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>."},"status":"public","_id":"59169","publisher":"Springer Science and Business Media LLC","volume":45,"user_id":"15540","issue":"2","publication":"Combinatorica","abstract":[{"text":"An r-regular graph is an r-graph, if every odd set of vertices is connected to its complement by at least r edges. Let G and H be r-graphs. An H-coloring of G is a mapping such that each r adjacent edges of G are mapped to r adjacent edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs, such that for every connected r-graph G there is an which colors G. The Petersen Coloring Conjecture states that consists of the Petersen graph P. We show that if true, then this is a very exclusive situation. Our main result is that either or is an infinite set and if , then is an infinite set. In particular, for all , is unique. We first characterize and then prove that if contains more than one element, then it is an infinite set. To obtain our main result we show that contains the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and we determine the smallest r-graphs of class 2.","lang":"eng"}],"date_created":"2025-03-27T09:46:34Z","department":[{"_id":"542"}],"type":"journal_article","publication_identifier":{"issn":["0209-9683","1439-6912"]},"author":[{"full_name":"Ma, Yulai","first_name":"Yulai","last_name":"Ma"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"last_name":"Wolf","first_name":"Isaak H.","full_name":"Wolf, Isaak H."}],"year":"2025","title":"Sets of r-Graphs that Color All r-Graphs","intvolume":"        45","publication_status":"published","date_updated":"2025-03-27T09:48:48Z","language":[{"iso":"eng"}],"article_number":"16","doi":"10.1007/s00493-025-00144-4"},{"user_id":"23686","doi":"10.1016/j.jde.2025.113555","volume":443,"article_number":"113555","publisher":"Elsevier BV","_id":"60205","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-06-13T11:13:22Z","intvolume":"       443","year":"2025","status":"public","title":"Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system","publication_identifier":{"issn":["0022-0396"]},"author":[{"id":"23686","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","full_name":"Black, Tobias"}],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2025-06-13T11:12:23Z","publication":"Journal of Differential Equations","citation":{"mla":"Black, Tobias. “Very Mild Diffusion Enhancement and Singular Sensitivity: Existence of Bounded Weak Solutions in a Two-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Differential Equations</i>, vol. 443, 113555, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>.","bibtex":"@article{Black_2025, title={Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system}, volume={443}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>}, number={113555}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Black, Tobias}, year={2025} }","ama":"Black T. Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system. <i>Journal of Differential Equations</i>. 2025;443. doi:<a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>","ieee":"T. Black, “Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system,” <i>Journal of Differential Equations</i>, vol. 443, Art. no. 113555, 2025, doi: <a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>.","apa":"Black, T. (2025). Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system. <i>Journal of Differential Equations</i>, <i>443</i>, Article 113555. <a href=\"https://doi.org/10.1016/j.jde.2025.113555\">https://doi.org/10.1016/j.jde.2025.113555</a>","short":"T. Black, Journal of Differential Equations 443 (2025).","chicago":"Black, Tobias. “Very Mild Diffusion Enhancement and Singular Sensitivity: Existence of Bounded Weak Solutions in a Two-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Differential Equations</i> 443 (2025). <a href=\"https://doi.org/10.1016/j.jde.2025.113555\">https://doi.org/10.1016/j.jde.2025.113555</a>."}},{"title":"Box-Covariances of Hyperuniform Point Processes","year":"2025","status":"public","author":[{"id":"113768","full_name":"Jalowy, Jonas","orcid":"0000-0001-9624-2685","last_name":"Jalowy","first_name":"Jonas"},{"full_name":"Stange, Hanna","first_name":"Hanna","last_name":"Stange"}],"date_updated":"2025-06-22T08:03:20Z","_id":"60293","language":[{"iso":"eng"}],"user_id":"113768","publication":"arXiv:2506.13661","citation":{"ieee":"J. Jalowy and H. Stange, “Box-Covariances of Hyperuniform Point Processes,” <i>arXiv:2506.13661</i>. 2025.","apa":"Jalowy, J., &#38; Stange, H. (2025). Box-Covariances of Hyperuniform Point Processes. In <i>arXiv:2506.13661</i>.","short":"J. Jalowy, H. Stange, ArXiv:2506.13661 (2025).","chicago":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025.","mla":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025.","bibtex":"@article{Jalowy_Stange_2025, title={Box-Covariances of Hyperuniform Point Processes}, journal={arXiv:2506.13661}, author={Jalowy, Jonas and Stange, Hanna}, year={2025} }","ama":"Jalowy J, Stange H. Box-Covariances of Hyperuniform Point Processes. <i>arXiv:250613661</i>. Published online 2025."},"abstract":[{"text":"In this work, we present a complete characterization of the covariance\r\nstructure of number statistics in boxes for hyperuniform point processes. Under\r\na standard integrability assumption, the covariance depends solely on the\r\noverlap of the faces of the box. Beyond this assumption, a novel interpolating\r\ncovariance structure emerges. This enables us to identify a limiting Gaussian\r\n'coarse-grained' process, counting the number of points in large boxes as a\r\nfunction of the box position. Depending on the integrability assumption, this\r\nprocess may be continuous or discontinuous, e.g. in d=1 it is given by an\r\nincrement process of a fractional Brownian motion.","lang":"eng"}],"external_id":{"arxiv":["2506.13661"]},"date_created":"2025-06-22T08:02:28Z","type":"preprint","department":[{"_id":"94"}]},{"abstract":[{"text":"<jats:p>This article is a short summary of the report of survey team 3, presented to the 15th International Congress on Mathematical Education (ICME-15) in Sydney in July 2024.</jats:p>","lang":"eng"}],"citation":{"ieee":"R. Biehler, T. Kawakami, E. Lampen, T. Weiland, and L. Zapata-Cardona, “Statistics and data science education as a vehicle for empowering citizens – short summary of a survey,” <i>European Mathematical Society Magazine</i>, 2025, doi: <a href=\"https://doi.org/10.4171/mag/257\">10.4171/mag/257</a>.","apa":"Biehler, R., Kawakami, T., Lampen, E., Weiland, T., &#38; Zapata-Cardona, L. (2025). Statistics and data science education as a vehicle for empowering citizens – short summary of a survey. <i>European Mathematical Society Magazine</i>. <a href=\"https://doi.org/10.4171/mag/257\">https://doi.org/10.4171/mag/257</a>","short":"R. Biehler, T. Kawakami, E. Lampen, T. Weiland, L. Zapata-Cardona, European Mathematical Society Magazine (2025).","chicago":"Biehler, Rolf, Takashi Kawakami, Erna Lampen, Travis Weiland, and Lucía Zapata-Cardona. “Statistics and Data Science Education as a Vehicle for Empowering Citizens – Short Summary of a Survey.” <i>European Mathematical Society Magazine</i>, 2025. <a href=\"https://doi.org/10.4171/mag/257\">https://doi.org/10.4171/mag/257</a>.","mla":"Biehler, Rolf, et al. “Statistics and Data Science Education as a Vehicle for Empowering Citizens – Short Summary of a Survey.” <i>European Mathematical Society Magazine</i>, European Mathematical Society - EMS - Publishing House GmbH, 2025, doi:<a href=\"https://doi.org/10.4171/mag/257\">10.4171/mag/257</a>.","bibtex":"@article{Biehler_Kawakami_Lampen_Weiland_Zapata-Cardona_2025, title={Statistics and data science education as a vehicle for empowering citizens – short summary of a survey}, DOI={<a href=\"https://doi.org/10.4171/mag/257\">10.4171/mag/257</a>}, journal={European Mathematical Society Magazine}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Biehler, Rolf and Kawakami, Takashi and Lampen, Erna and Weiland, Travis and Zapata-Cardona, Lucía}, year={2025} }","ama":"Biehler R, Kawakami T, Lampen E, Weiland T, Zapata-Cardona L. Statistics and data science education as a vehicle for empowering citizens – short summary of a survey. <i>European Mathematical Society Magazine</i>. Published online 2025. doi:<a href=\"https://doi.org/10.4171/mag/257\">10.4171/mag/257</a>"},"publication":"European Mathematical Society Magazine","department":[{"_id":"363"}],"oa":"1","type":"journal_article","date_created":"2025-06-24T06:58:17Z","publication_status":"published","date_updated":"2025-06-24T06:59:42Z","author":[{"id":"16274","last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"},{"first_name":"Takashi","last_name":"Kawakami","full_name":"Kawakami, Takashi"},{"last_name":"Lampen","first_name":"Erna","full_name":"Lampen, Erna"},{"first_name":"Travis","last_name":"Weiland","full_name":"Weiland, Travis"},{"full_name":"Zapata-Cardona, Lucía","last_name":"Zapata-Cardona","first_name":"Lucía"}],"publication_identifier":{"issn":["2747-7894","2747-7908"]},"status":"public","year":"2025","title":"Statistics and data science education as a vehicle for empowering citizens – short summary of a survey","user_id":"37888","doi":"10.4171/mag/257","_id":"60351","publisher":"European Mathematical Society - EMS - Publishing House GmbH","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.4171/MAG/257","open_access":"1"}]},{"has_accepted_license":"1","status":"public","ddc":["510"],"user_id":"85279","publisher":"American Mathematical Society","_id":"53805","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"quality_controlled":"1","citation":{"mla":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, American Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>.","ama":"Offen C. Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>","bibtex":"@article{Offen_2025, title={Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification}, DOI={<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>}, journal={Mathematics of Computation}, publisher={American Mathematical Society}, author={Offen, Christian}, year={2025} }","apa":"Offen, C. (2025). Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>","ieee":"C. Offen, “Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification,” <i>Mathematics of Computation</i>, 2025, doi: <a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>.","chicago":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, 2025. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>.","short":"C. Offen, Mathematics of Computation (2025)."},"file_date_updated":"2025-05-02T13:20:31Z","oa":"1","external_id":{"arxiv":["arXiv:2404.19626"]},"article_type":"original","date_updated":"2025-06-29T13:03:55Z","publication_status":"epub_ahead","author":[{"id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"}],"year":"2025","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification","doi":"10.1090/mcom/4120","language":[{"iso":"eng"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/Lagrangian_GP","description":"GitHub"}]},"abstract":[{"text":"The article introduces a method to learn dynamical systems that are governed by Euler–Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian, including of Hamiltonian functions (energy) and symplectic structures, which is of interest in the context of system identification. The article overcomes major practical and theoretical difficulties related to the ill-posedness of the identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex minimisation problems in reproducing kernel Hilbert spaces.","lang":"eng"}],"publication":"Mathematics of Computation","department":[{"_id":"636"}],"type":"journal_article","date_created":"2024-04-30T16:04:40Z","file":[{"date_created":"2025-05-02T13:20:31Z","description":"The article introduces a method to learn dynamical systems that\nare governed by Euler–Lagrange equations from data. The method is based on\nGaussian process regression and identifies continuous or discrete Lagrangians\nand is, therefore, structure preserving by design. A rigorous proof of con-\nvergence as the distance between observation data points converges to zero\nand lower bounds for convergence rates are provided. Next to convergence\nguarantees, the method allows for quantification of model uncertainty, which\ncan provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,\nincluding of Hamiltonian functions (energy) and symplectic structures, which\nis of interest in the context of system identification. The article overcomes\nmajor practical and theoretical difficulties related to the ill-posedness of the\nidentification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex\nminimisation problems in reproducing kernel Hilbert spaces.","creator":"coffen","file_id":"59759","content_type":"application/pdf","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification ","file_name":"L_Collocation_ODE_mcom-l-template.pdf","file_size":1819189,"access_level":"open_access","relation":"main_file","date_updated":"2025-05-02T13:20:31Z"}]},{"_id":"60495","language":[{"iso":"ger"}],"page":"9-16","volume":45,"user_id":"37888","author":[{"id":"30619","full_name":"Podworny, Susanne","first_name":"Susanne","orcid":"0000-0002-6313-5987","last_name":"Podworny"},{"full_name":"Fleischer, Yannik","last_name":"Fleischer","orcid":"https://orcid.org/0000-0003-0318-0329","first_name":"Yannik","id":"42660"},{"full_name":"Biehler, Rolf","last_name":"Biehler","first_name":"Rolf","id":"16274"}],"year":"2025","status":"public","title":"Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten","intvolume":"        45","publication_status":"published","date_updated":"2025-07-02T09:45:22Z","date_created":"2025-07-02T09:45:14Z","department":[{"_id":"363"}],"type":"journal_article","citation":{"mla":"Podworny, Susanne, et al. “Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten.” <i>Stochastik in der Schule</i>, vol. 45, no. 2, 2025, pp. 9–16.","apa":"Podworny, S., Fleischer, Y., &#38; Biehler, R. (2025). Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten. <i>Stochastik in der Schule</i>, <i>45</i>(2), 9–16.","ieee":"S. Podworny, Y. Fleischer, and R. Biehler, “Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten,” <i>Stochastik in der Schule</i>, vol. 45, no. 2, pp. 9–16, 2025.","ama":"Podworny S, Fleischer Y, Biehler R. Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten. <i>Stochastik in der Schule</i>. 2025;45(2):9-16.","short":"S. Podworny, Y. Fleischer, R. Biehler, Stochastik in der Schule 45 (2025) 9–16.","chicago":"Podworny, Susanne, Yannik Fleischer, and Rolf Biehler. “Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten.” <i>Stochastik in der Schule</i> 45, no. 2 (2025): 9–16.","bibtex":"@article{Podworny_Fleischer_Biehler_2025, title={Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten}, volume={45}, number={2}, journal={Stochastik in der Schule}, author={Podworny, Susanne and Fleischer, Yannik and Biehler, Rolf}, year={2025}, pages={9–16} }"},"publication":"Stochastik in der Schule","issue":"2"},{"main_file_link":[{"open_access":"1","url":"https://openreview.net/forum?id=TGsuaghKD3"}],"_id":"60532","language":[{"iso":"eng"}],"user_id":"37888","title":"Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines.","status":"public","year":"2025","author":[{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf","id":"16274"},{"full_name":"Schulte, Carsten","first_name":"Carsten","last_name":"Schulte","id":"60311"}],"date_updated":"2025-07-07T07:24:35Z","date_created":"2025-07-07T07:24:30Z","type":"book_chapter","department":[{"_id":"363"}],"oa":"1","publication":"Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria","citation":{"mla":"Biehler, Rolf, and Carsten Schulte. “Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines.” <i>Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria</i>, 2025.","ama":"Biehler R, Schulte C. Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines. In: <i>Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria</i>. ; 2025.","bibtex":"@inbook{Biehler_Schulte_2025, title={Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines.}, booktitle={Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria}, author={Biehler, Rolf and Schulte, Carsten}, year={2025} }","apa":"Biehler, R., &#38; Schulte, C. (2025). Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines. In <i>Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria</i>.","ieee":"R. Biehler and C. Schulte, “Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines.,” in <i>Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria</i>, 2025.","short":"R. Biehler, C. Schulte, in: Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria, 2025.","chicago":"Biehler, Rolf, and Carsten Schulte. “Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines.” In <i>Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria</i>, 2025."}},{"date_created":"2025-07-29T09:30:04Z","department":[{"_id":"543"}],"type":"book_chapter","citation":{"bibtex":"@inbook{Häsel-Weide_Hußmann_Nührenbörger_2025, title={ Flexibles Addieren und Subtrahieren im Zahlenraum bis 100}, booktitle={Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule}, publisher={Klett Kallmeyer}, author={Häsel-Weide, Uta and Hußmann, S. and Nührenbörger, M.}, editor={Rechtsteiner, C.}, year={2025}, pages={71–80} }","ama":"Häsel-Weide U, Hußmann S, Nührenbörger M.  Flexibles Addieren und Subtrahieren im Zahlenraum bis 100. In: Rechtsteiner C, ed. <i>Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule</i>. Klett Kallmeyer; 2025:71-80.","mla":"Häsel-Weide, Uta, et al. “ Flexibles Addieren und Subtrahieren im Zahlenraum bis 100.” <i>Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule</i>, edited by C. Rechtsteiner, Klett Kallmeyer, 2025, pp. 71–80.","chicago":"Häsel-Weide, Uta, S. Hußmann, and M. Nührenbörger. “ Flexibles Addieren und Subtrahieren im Zahlenraum bis 100.” In <i>Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule</i>, edited by C. Rechtsteiner, 71–80. Klett Kallmeyer, 2025.","short":"U. Häsel-Weide, S. Hußmann, M. Nührenbörger, in: C. Rechtsteiner (Ed.), Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule, Klett Kallmeyer, 2025, pp. 71–80.","ieee":"U. Häsel-Weide, S. Hußmann, and M. Nührenbörger, “ Flexibles Addieren und Subtrahieren im Zahlenraum bis 100,” in <i>Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule</i>, C. Rechtsteiner, Ed. Klett Kallmeyer, 2025, pp. 71–80.","apa":"Häsel-Weide, U., Hußmann, S., &#38; Nührenbörger, M. (2025).  Flexibles Addieren und Subtrahieren im Zahlenraum bis 100. In C. Rechtsteiner (Ed.), <i>Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule</i> (pp. 71–80). Klett Kallmeyer."},"publication":"Rechnen richtig  lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule","_id":"60816","language":[{"iso":"ger"}],"publisher":"Klett Kallmeyer","page":"71-80","editor":[{"last_name":"Rechtsteiner","first_name":"C.","full_name":"Rechtsteiner, C."}],"user_id":"44184","author":[{"first_name":"Uta","orcid":"0000-0001-6278-4240","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","id":"60267"},{"full_name":"Hußmann, S.","last_name":"Hußmann","first_name":"S."},{"first_name":"M.","last_name":"Nührenbörger","full_name":"Nührenbörger, M."}],"status":"public","year":"2025","title":" Flexibles Addieren und Subtrahieren im Zahlenraum bis 100","date_updated":"2025-07-29T09:30:28Z"},{"publication":"Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 ","citation":{"chicago":"Fleischer, Franz Yannik, and Rolf Biehler. “ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM.” In <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 </i>, edited by C. Cornejo, P. Felmer, D.M. Gomez, P. Dartnell, P. Araya, A. Peri, and V. Randolph, 267–74, 2025.","short":"F.Y. Fleischer, R. Biehler, in: C. Cornejo, P. Felmer, D.M. Gomez, P. Dartnell, P. Araya, A. Peri, V. Randolph (Eds.), Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 , 2025, pp. 267–274.","ama":"Fleischer FY, Biehler R. ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM. In: Cornejo C, Felmer P, Gomez DM, et al., eds. <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 </i>. ; 2025:267-274.","bibtex":"@inproceedings{Fleischer_Biehler_2025, title={ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM}, booktitle={Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 }, author={Fleischer, Franz Yannik and Biehler, Rolf}, editor={Cornejo, C. and Felmer, P. and Gomez, D.M. and Dartnell, P. and Araya, P. and Peri, A. and Randolph, V.}, year={2025}, pages={267–274} }","apa":"Fleischer, F. Y., &#38; Biehler, R. (2025). ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM. In C. Cornejo, P. Felmer, D. M. Gomez, P. Dartnell, P. Araya, A. Peri, &#38; V. Randolph (Eds.), <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 </i> (pp. 267–274).","mla":"Fleischer, Franz Yannik, and Rolf Biehler. “ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM.” <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 </i>, edited by C. Cornejo et al., 2025, pp. 267–74.","ieee":"F. Y. Fleischer and R. Biehler, “ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM,” in <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 </i>, 2025, pp. 267–274."},"date_created":"2025-08-04T07:15:39Z","type":"conference","department":[{"_id":"363"}],"status":"public","year":"2025","title":"ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM","author":[{"id":"42660","full_name":"Fleischer, Franz Yannik","first_name":"Franz Yannik","orcid":"https://orcid.org/0000-0003-0318-0329","last_name":"Fleischer"},{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler","id":"16274"}],"date_updated":"2025-08-04T07:17:59Z","page":"267-274","_id":"60860","language":[{"iso":"eng"}],"user_id":"37888","editor":[{"last_name":"Cornejo","first_name":"C.","full_name":"Cornejo, C."},{"full_name":"Felmer, P.","first_name":"P.","last_name":"Felmer"},{"first_name":"D.M.","last_name":"Gomez","full_name":"Gomez, D.M."},{"first_name":"P.","last_name":"Dartnell","full_name":"Dartnell, P."},{"full_name":"Araya, P.","first_name":"P.","last_name":"Araya"},{"first_name":"A.","last_name":"Peri","full_name":"Peri, A."},{"last_name":"Randolph","first_name":"V.","full_name":"Randolph, V."}]},{"status":"public","_id":"61042","publisher":"Springer Science and Business Media LLC","user_id":"15540","volume":62,"citation":{"short":"C. Dalfó, M.A. Fiol, E. Steffen, Journal of Algebraic Combinatorics 62 (2025).","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i> 62, no. 1 (2025). <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>.","ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, Art. no. 7, 2025, doi: <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","apa":"Dalfó, C., Fiol, M. A., &#38; Steffen, E. (2025). On token signed graphs. <i>Journal of Algebraic Combinatorics</i>, <i>62</i>(1), Article 7. <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>","bibtex":"@article{Dalfó_Fiol_Steffen_2025, title={On token signed graphs}, volume={62}, DOI={<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>}, number={17}, journal={Journal of Algebraic Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2025} }","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. <i>Journal of Algebraic Combinatorics</i>. 2025;62(1). doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>","mla":"Dalfó, C., et al. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, 7, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>."},"year":"2025","title":"On token signed graphs","publication_identifier":{"issn":["0925-9899","1572-9192"]},"author":[{"last_name":"Dalfó","first_name":"C.","full_name":"Dalfó, C."},{"last_name":"Fiol","first_name":"M. A.","full_name":"Fiol, M. A."},{"id":"15548","orcid":"0000-0002-9808-7401","first_name":"Eckhard","last_name":"Steffen","full_name":"Steffen, Eckhard"}],"date_updated":"2025-08-28T07:57:27Z","publication_status":"published","intvolume":"        62","article_number":"7","language":[{"iso":"eng"}],"doi":"10.1007/s10801-025-01416-4","issue":"1","publication":"Journal of Algebraic Combinatorics","abstract":[{"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.","lang":"eng"}],"date_created":"2025-08-28T07:50:03Z","type":"journal_article","department":[{"_id":"542"}]},{"language":[{"iso":"ger"}],"main_file_link":[{"url":"https://doi.org/10.1515/dmvm-2025-0053","open_access":"1"}],"author":[{"id":"16274","first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"},{"full_name":"Liebendörfer, Michael","last_name":"Liebendörfer","first_name":"Michael"},{"full_name":"Schmitz, Angela","last_name":"Schmitz","first_name":"Angela"},{"last_name":"Reich","first_name":"Birte","full_name":"Reich, Birte"}],"year":"2025","title":"studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar","intvolume":"        33","date_updated":"2025-09-04T09:25:03Z","publication_status":"published","date_created":"2025-09-04T09:23:47Z","department":[{"_id":"363"}],"type":"journal_article","publication":"Mitteilungen der Deutschen Mathematiker-Vereinigung","issue":"3","_id":"61125","publisher":"De Gruyter","page":"170–171","volume":33,"user_id":"37888","status":"public","oa":"1","citation":{"ieee":"R. Biehler, M. Liebendörfer, A. Schmitz, and B. Reich, “studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar,” <i>Mitteilungen der Deutschen Mathematiker-Vereinigung</i>, vol. 33, no. 3, pp. 170–171, 2025.","apa":"Biehler, R., Liebendörfer, M., Schmitz, A., &#38; Reich, B. (2025). studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar. <i>Mitteilungen der Deutschen Mathematiker-Vereinigung</i>, <i>33</i>(3), 170–171.","mla":"Biehler, Rolf, et al. “studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar.” <i>Mitteilungen der Deutschen Mathematiker-Vereinigung</i>, vol. 33, no. 3, De Gruyter, 2025, pp. 170–171.","bibtex":"@article{Biehler_Liebendörfer_Schmitz_Reich_2025, title={studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar}, volume={33}, number={3}, journal={Mitteilungen der Deutschen Mathematiker-Vereinigung}, publisher={De Gruyter}, author={Biehler, Rolf and Liebendörfer, Michael and Schmitz, Angela and Reich, Birte}, year={2025}, pages={170–171} }","chicago":"Biehler, Rolf, Michael Liebendörfer, Angela Schmitz, and Birte Reich. “studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar.” <i>Mitteilungen der Deutschen Mathematiker-Vereinigung</i> 33, no. 3 (2025): 170–171.","ama":"Biehler R, Liebendörfer M, Schmitz A, Reich B. studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar. <i>Mitteilungen der Deutschen Mathematiker-Vereinigung</i>. 2025;33(3):170–171.","short":"R. Biehler, M. Liebendörfer, A. Schmitz, B. Reich, Mitteilungen der Deutschen Mathematiker-Vereinigung 33 (2025) 170–171."}},{"doi":"https://doi.org/10.1026/2191-9186/a000712","user_id":"72183","volume":14,"page":"72-78","_id":"54970","language":[{"iso":"ger"}],"date_updated":"2026-03-11T14:31:13Z","intvolume":"        14","title":"Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte","year":"2025","status":"public","author":[{"id":"77311","last_name":"Quack","first_name":"Carolin","full_name":"Quack, Carolin"},{"orcid":"https://orcid.org/0000-0002-6604-5864","first_name":"Julia","last_name":"Bruns","full_name":"Bruns, Julia","id":"72183"}],"type":"journal_article","department":[{"_id":"611"}],"date_created":"2024-07-02T07:31:26Z","publication":"Frühe Bildung","issue":"2","citation":{"ama":"Quack C, Bruns J. Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte. <i>Frühe Bildung</i>. 2025;14(2):72-78. doi:<a href=\"https://doi.org/10.1026/2191-9186/a000712\">https://doi.org/10.1026/2191-9186/a000712</a>","bibtex":"@article{Quack_Bruns_2025, title={Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte}, volume={14}, DOI={<a href=\"https://doi.org/10.1026/2191-9186/a000712\">https://doi.org/10.1026/2191-9186/a000712</a>}, number={2}, journal={Frühe Bildung}, author={Quack, Carolin and Bruns, Julia}, year={2025}, pages={72–78} }","mla":"Quack, Carolin, and Julia Bruns. “Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte.” <i>Frühe Bildung</i>, vol. 14, no. 2, 2025, pp. 72–78, doi:<a href=\"https://doi.org/10.1026/2191-9186/a000712\">https://doi.org/10.1026/2191-9186/a000712</a>.","short":"C. Quack, J. Bruns, Frühe Bildung 14 (2025) 72–78.","chicago":"Quack, Carolin, and Julia Bruns. “Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte.” <i>Frühe Bildung</i> 14, no. 2 (2025): 72–78. <a href=\"https://doi.org/10.1026/2191-9186/a000712\">https://doi.org/10.1026/2191-9186/a000712</a>.","apa":"Quack, C., &#38; Bruns, J. (2025). Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte. <i>Frühe Bildung</i>, <i>14</i>(2), 72–78. <a href=\"https://doi.org/10.1026/2191-9186/a000712\">https://doi.org/10.1026/2191-9186/a000712</a>","ieee":"C. Quack and J. Bruns, “Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte,” <i>Frühe Bildung</i>, vol. 14, no. 2, pp. 72–78, 2025, doi: <a href=\"https://doi.org/10.1026/2191-9186/a000712\">https://doi.org/10.1026/2191-9186/a000712</a>."}},{"type":"journal_article","department":[{"_id":"94"}],"date_created":"2025-11-24T13:55:55Z","abstract":[{"lang":"eng","text":"In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real-rooted polynomials, as the degree goes to $\\infty$. In this note, we aim to apply it to a vast range of examples of polynomials providing a unifying source for limiting empirical zero distributions.\n We cover Touchard, Fubini, Eulerian, Narayana and little $q$-Laguerre polynomials as well as hypergeometric polynomials including the classical Hermite, Laguerre and Jacobi polynomials. We construct polynomials whose empirical zero distributions converge to the free multiplicative normal and Poisson distributions. Furthermore, we study polynomials generated by some differential operators. As one inverse result, we derive coefficient asymptotics of the characteristic polynomial of random covariance matrices."}],"citation":{"ieee":"“Zeros and exponential profiles of polynomials II: Examples,” 2025, doi: <a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>.","apa":"<i>Zeros and exponential profiles of polynomials II: Examples</i>. (2025). <a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">https://doi.org/10.48550/ARXIV.2509.11248</a>","mla":"<i>Zeros and Exponential Profiles of Polynomials II: Examples</i>. 2025, doi:<a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>.","bibtex":"@article{Zeros and exponential profiles of polynomials II: Examples_2025, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>}, year={2025} }","chicago":"“Zeros and Exponential Profiles of Polynomials II: Examples,” 2025. <a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">https://doi.org/10.48550/ARXIV.2509.11248</a>.","ama":"Zeros and exponential profiles of polynomials II: Examples. Published online 2025. doi:<a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>","short":"(2025)."},"doi":"10.48550/ARXIV.2509.11248","user_id":"113768","_id":"62291","date_updated":"2026-03-19T14:45:35Z","status":"public","title":"Zeros and exponential profiles of polynomials II: Examples","year":"2025"}]