[{"_id":"32338","user_id":"85821","department":[{"_id":"98"},{"_id":"543"}],"language":[{"iso":"ger"}],"type":"journal_article","publication":"QfI - Qualifizierung für Inklusion","status":"public","date_updated":"2022-07-11T05:31:41Z","author":[{"first_name":"K.","last_name":"Hähn","full_name":"Hähn, K."},{"last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","id":"60267","first_name":"Uta"},{"full_name":"Scherer, P.","last_name":"Scherer","first_name":"P."}],"date_created":"2022-07-11T05:13:52Z","volume":3,"title":"Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.","publication_status":"published","issue":"2","related_material":{"link":[{"url":"https://doi.org/10.21248/qfi.72","relation":"contains"}]},"year":"2022","citation":{"chicago":"Hähn, K., Uta Häsel-Weide, and P. Scherer. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i> 3, no. 2 (2022).","ieee":"K. Hähn, U. Häsel-Weide, and P. Scherer, “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.,” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2, 2022.","ama":"Hähn K, Häsel-Weide U, Scherer P. Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>. 2022;3(2).","bibtex":"@article{Hähn_Häsel-Weide_Scherer_2022, title={Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.}, volume={3}, number={2}, journal={QfI - Qualifizierung für Inklusion}, author={Hähn, K. and Häsel-Weide, Uta and Scherer, P.}, year={2022} }","mla":"Hähn, K., et al. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2, 2022.","short":"K. Hähn, U. Häsel-Weide, P. Scherer, QfI - Qualifizierung für Inklusion 3 (2022).","apa":"Hähn, K., Häsel-Weide, U., &#38; Scherer, P. (2022). Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>, <i>3</i>(2)."},"intvolume":"         3"},{"oa":"1","date_updated":"2022-07-18T14:26:41Z","volume":55,"author":[{"full_name":"Klus, Stefan","last_name":"Klus","first_name":"Stefan"},{"id":"81513","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","first_name":"Feliks"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"}],"doi":"10.1088/1751-8121/ac7d22","main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf","open_access":"1"}],"publication_status":"published","page":"314002","intvolume":"        55","citation":{"apa":"Klus, S., Nüske, F., &#38; Peitz, S. (2022). Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(31), 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }","mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002.","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(31):314002. doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>","ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, p. 314002, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 31 (2022): 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>."},"_id":"29673","department":[{"_id":"655"},{"_id":"101"}],"user_id":"47427","type":"journal_article","status":"public","publisher":"IOP Publishing Ltd.","date_created":"2022-01-31T09:49:40Z","title":"Koopman analysis of quantum systems","issue":"31","year":"2022","external_id":{"arxiv":["2201.12062"]},"language":[{"iso":"eng"}],"publication":"Journal of Physics A: Mathematical and Theoretical","abstract":[{"lang":"eng","text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science."}]},{"status":"public","abstract":[{"lang":"eng","text":"In this article, we show how second-order derivative information can be\r\nincorporated into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order information we consider is essentially the set of coefficients of\r\nall second-order Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based on this concept, we define a model of the objective as the\r\nmaximum of these Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed ball) results in a simple descent method, for which\r\nwe prove convergence to minimal points in case the objective is convex. To\r\nobtain an implementable method, we construct an approximation scheme for the\r\nsecond-order information based on sampling objective values, gradients and\r\nHessian matrices at finitely many points. Using a set of test problems, we\r\ncompare the resulting method to five other available solvers. Considering the\r\nnumber of function evaluations, the results suggest that the method we propose\r\nis superior to the standard gradient sampling method, and competitive compared\r\nto other methods."}],"type":"preprint","publication":"arXiv:2210.04579","language":[{"iso":"eng"}],"user_id":"32643","department":[{"_id":"101"}],"_id":"34618","external_id":{"arxiv":["2210.04579"]},"citation":{"chicago":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.","ieee":"B. Gebken, “Using second-order information in gradient sampling methods for  nonsmooth optimization,” <i>arXiv:2210.04579</i>. 2022.","ama":"Gebken B. Using second-order information in gradient sampling methods for  nonsmooth optimization. <i>arXiv:221004579</i>. Published online 2022.","bibtex":"@article{Gebken_2022, title={Using second-order information in gradient sampling methods for  nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken, Bennet}, year={2022} }","mla":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.","short":"B. Gebken, ArXiv:2210.04579 (2022).","apa":"Gebken, B. (2022). Using second-order information in gradient sampling methods for  nonsmooth optimization. In <i>arXiv:2210.04579</i>."},"year":"2022","main_file_link":[{"url":"https://arxiv.org/pdf/2210.04579","open_access":"1"}],"title":"Using second-order information in gradient sampling methods for  nonsmooth optimization","date_created":"2022-12-20T15:25:17Z","author":[{"first_name":"Bennet","id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken"}],"oa":"1","date_updated":"2022-12-20T15:28:54Z"},{"page":"138–144","intvolume":"        14","citation":{"ama":"Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic. <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>. 2022;14(2):138–144. doi:<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>","ieee":"H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive characteristic,” <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>, vol. 14, no. 2, pp. 138–144, 2022, doi: <a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>.","chicago":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i> 14, no. 2 (2022): 138–144. <a href=\"https://doi.org/10.1134/S2070046622020042\">https://doi.org/10.1134/S2070046622020042</a>.","apa":"Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive characteristic. <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>, <i>14</i>(2), 138–144. <a href=\"https://doi.org/10.1134/S2070046622020042\">https://doi.org/10.1134/S2070046622020042</a>","bibtex":"@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local fields of positive characteristic}, volume={14}, DOI={<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>}, number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications}, author={Glöckner, Helge}, year={2022}, pages={138–144} }","short":"H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022) 138–144.","mla":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>, vol. 14, no. 2, 2022, pp. 138–144, doi:<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>."},"year":"2022","issue":"2","quality_controlled":"1","publication_identifier":{"issn":["2070-0466"]},"doi":"10.1134/S2070046622020042","title":"Non-Lie subgroups in Lie groups over local fields of positive characteristic","volume":14,"date_created":"2022-12-21T19:27:51Z","author":[{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"}],"date_updated":"2022-12-21T19:30:25Z","status":"public","publication":"p-Adic Numbers, Ultrametric Analysis, and Applications","type":"journal_article","language":[{"iso":"eng"}],"keyword":["20Exx","22Exx","32Cxx"],"article_type":"original","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","_id":"34792"},{"keyword":["58D15","22E65","26E15","26E20","46E40","46T20","58A05"],"article_type":"original","language":[{"iso":"eng"}],"_id":"34791","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","status":"public","publication":"Annals of Global Analysis and Geometry","type":"journal_article","title":"Manifolds of mappings on Cartesian products","doi":"10.1007/s10455-021-09816-y","date_updated":"2022-12-21T19:27:09Z","volume":61,"date_created":"2022-12-21T19:24:48Z","author":[{"full_name":"Glöckner, Helge","id":"178","last_name":"Glöckner","first_name":"Helge"},{"first_name":"Alexander","full_name":"Schmeding, Alexander","last_name":"Schmeding"}],"year":"2022","page":"359–398","intvolume":"        61","citation":{"mla":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, 2022, pp. 359–398, doi:<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>.","bibtex":"@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian products}, volume={61}, DOI={<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>}, number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner, Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }","short":"H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022) 359–398.","apa":"Glöckner, H., &#38; Schmeding, A. (2022). Manifolds of mappings on Cartesian products. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(2), 359–398. <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">https://doi.org/10.1007/s10455-021-09816-y</a>","ama":"Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. <i>Annals of Global Analysis and Geometry</i>. 2022;61(2):359–398. doi:<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>","chicago":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” <i>Annals of Global Analysis and Geometry</i> 61, no. 2 (2022): 359–398. <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">https://doi.org/10.1007/s10455-021-09816-y</a>.","ieee":"H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, pp. 359–398, 2022, doi: <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>."},"quality_controlled":"1","publication_identifier":{"issn":["0232-704X"]},"issue":"2"},{"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34796","language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","publication":"Axioms","status":"public","abstract":[{"lang":"eng","text":"We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E&times;E is a kR-space."}],"author":[{"last_name":"Glöckner","id":"178","full_name":"Glöckner, Helge","first_name":"Helge"}],"date_created":"2022-12-21T20:02:29Z","volume":11,"date_updated":"2022-12-22T07:31:55Z","doi":"10.3390/axioms11050221","title":"Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces","issue":"5","quality_controlled":"1","publication_identifier":{"issn":["2075-1680"]},"citation":{"apa":"Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href=\"https://doi.org/10.3390/axioms11050221\">https://doi.org/10.3390/axioms11050221</a>","short":"H. Glöckner, Axioms 11 (2022).","mla":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022, doi:<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>.","bibtex":"@article{Glöckner_2022, title={Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11}, DOI={<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>}, number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }","chicago":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i> 11, no. 5 (2022). <a href=\"https://doi.org/10.3390/axioms11050221\">https://doi.org/10.3390/axioms11050221</a>.","ieee":"H. Glöckner, “Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022, doi: <a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>.","ama":"Glöckner H. Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. <i>Axioms</i>. 2022;11(5). doi:<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>"},"intvolume":"        11","year":"2022"},{"language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","_id":"34804","external_id":{"arxiv":["2206.11711"]},"status":"public","abstract":[{"lang":"eng","text":"Starting with a finite-dimensional complex Lie algebra, we extend scalars\r\nusing suitable commutative topological algebras. We study Birkhoff\r\ndecompositions for the corresponding loop groups. Some results remain valid for\r\nloop groups with valued in complex Banach-Lie groups."}],"publication":"arXiv:2206.11711","type":"preprint","title":"Birkhoff decompositions for loop groups with coefficient algebras","date_created":"2022-12-22T07:42:07Z","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"}],"date_updated":"2022-12-22T07:44:08Z","citation":{"ama":"Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras. <i>arXiv:220611711</i>. Published online 2022.","chicago":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” <i>ArXiv:2206.11711</i>, 2022.","ieee":"H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,” <i>arXiv:2206.11711</i>. 2022.","bibtex":"@article{Glöckner_2022, title={Birkhoff decompositions for loop groups with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge}, year={2022} }","mla":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” <i>ArXiv:2206.11711</i>, 2022.","short":"H. Glöckner, ArXiv:2206.11711 (2022).","apa":"Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient algebras. In <i>arXiv:2206.11711</i>."},"year":"2022"},{"abstract":[{"lang":"ger","text":"Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten. Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor gefunden werden soll, für den die Datenpunkte kritisch sind."},{"lang":"eng","text":"Multiobjective optimization is concerned with the simultaneous optimization of multiple scalar-valued functions. In this case, a point is optimal if there is no other point that is at least as good in all objectives and better in at least one objective. A necessary condition for optimality can be derived based on first-order information of the objectives. The set of points that satisfy this necessary condition is called the Pareto critical set. This thesis presents new results about Pareto critical sets for smooth and nonsmooth multiobjective optimization problems, both in terms of their efficient computation and structural properties. In the smooth case they are computed via a continuation method and in the nonsmooth case via a descent method. Afterwards, the structure of the boundary of the Pareto critical set is analyzed, which consists of Pareto critical sets of smaller subproblems. Finally, inverse problems are considered, where a data set is given and an objective vector is sought for which the data points are critical."}],"status":"public","type":"dissertation","language":[{"iso":"eng"}],"_id":"31556","user_id":"32643","department":[{"_id":"101"}],"year":"2022","citation":{"ieee":"B. Gebken, <i>Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization</i>. 2022.","chicago":"Gebken, Bennet. <i>Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization</i>, 2022. <a href=\"https://doi.org/10.17619/UNIPB/1-1327\">https://doi.org/10.17619/UNIPB/1-1327</a>.","ama":"Gebken B. <i>Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization</i>.; 2022. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1327\">10.17619/UNIPB/1-1327</a>","apa":"Gebken, B. (2022). <i>Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1327\">https://doi.org/10.17619/UNIPB/1-1327</a>","mla":"Gebken, Bennet. <i>Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization</i>. 2022, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1327\">10.17619/UNIPB/1-1327</a>.","bibtex":"@book{Gebken_2022, title={Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1327\">10.17619/UNIPB/1-1327</a>}, author={Gebken, Bennet}, year={2022} }","short":"B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization, 2022."},"title":"Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization","main_file_link":[{"url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779","open_access":"1"}],"doi":"10.17619/UNIPB/1-1327","oa":"1","date_updated":"2022-06-01T07:13:09Z","date_created":"2022-06-01T06:48:08Z","supervisor":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"author":[{"last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet","first_name":"Bennet"}]},{"_id":"33150","external_id":{"arxiv":["2208.12094"]},"user_id":"47427","department":[{"_id":"101"},{"_id":"655"}],"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2208.12094","abstract":[{"lang":"eng","text":"In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem."}],"status":"public","date_updated":"2022-08-26T06:12:10Z","oa":"1","date_created":"2022-08-26T06:08:06Z","author":[{"first_name":"Manuel Bastian","full_name":"Berkemeier, Manuel Bastian","id":"51701","last_name":"Berkemeier"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X"}],"title":"Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients","main_file_link":[{"url":"https://arxiv.org/pdf/2208.12094","open_access":"1"}],"year":"2022","citation":{"ama":"Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. <i>arXiv:220812094</i>. Published online 2022.","ieee":"M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients,” <i>arXiv:2208.12094</i>. 2022.","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>, 2022.","apa":"Berkemeier, M. B., &#38; Peitz, S. (2022). Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. In <i>arXiv:2208.12094</i>.","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>, 2022.","short":"M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).","bibtex":"@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }"}},{"year":"2022","issue":"11","title":"On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation","publisher":"IEEE","date_created":"2020-12-15T07:46:36Z","abstract":[{"text":"We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach.","lang":"eng"}],"file":[{"date_updated":"2021-09-25T11:59:15Z","creator":"speitz","date_created":"2021-09-25T11:59:15Z","file_size":7990831,"access_level":"closed","file_name":"On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf","file_id":"25040","content_type":"application/pdf","success":1,"relation":"main_file"}],"publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","ddc":["510"],"language":[{"iso":"eng"}],"intvolume":"        44","page":"7797-7808","citation":{"short":"K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (2022) 7797–7808.","mla":"Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 44, no. 11, IEEE, 2022, pp. 7797–808, doi:<a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>.","bibtex":"@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44}, DOI={<a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>}, number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian}, year={2022}, pages={7797–7808} }","apa":"Bieker, K., Gebken, B., &#38; Peitz, S. (2022). On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, <i>44</i>(11), 7797–7808. <a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">https://doi.org/10.1109/TPAMI.2021.3114962</a>","ieee":"K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 44, no. 11, pp. 7797–7808, 2022, doi: <a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>.","chicago":"Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i> 44, no. 11 (2022): 7797–7808. <a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">https://doi.org/10.1109/TPAMI.2021.3114962</a>.","ama":"Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 2022;44(11):7797-7808. doi:<a href=\"https://doi.org/10.1109/TPAMI.2021.3114962\">10.1109/TPAMI.2021.3114962</a>"},"has_accepted_license":"1","publication_status":"epub_ahead","doi":"10.1109/TPAMI.2021.3114962","main_file_link":[{"open_access":"1","url":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772"}],"oa":"1","date_updated":"2022-10-21T12:27:16Z","volume":44,"author":[{"first_name":"Katharina","full_name":"Bieker, Katharina","id":"32829","last_name":"Bieker"},{"first_name":"Bennet","full_name":"Gebken, Bennet","id":"32643","last_name":"Gebken"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"status":"public","type":"journal_article","article_type":"original","file_date_updated":"2021-09-25T11:59:15Z","_id":"20731","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"user_id":"47427"},{"citation":{"ama":"Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>. 2022;24(3):851-923. doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>","chicago":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i> 24, no. 3 (2022): 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>.","ieee":"Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds with hyperbolic cusps,” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, pp. 851–923, 2022, doi: <a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","apa":"Guedes Bonthonneau, Y., &#38; Weich, T. (2022). Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>, <i>24</i>(3), 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>","mla":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 851–923, doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","short":"Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.","bibtex":"@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}, volume={24}, DOI={<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>}, number={3}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau, Yannick and Weich, Tobias}, year={2022}, pages={851–923} }"},"intvolume":"        24","page":"851-923","publication_status":"published","publication_identifier":{"issn":["1435-9855"]},"doi":"10.4171/jems/1103","author":[{"first_name":"Yannick","full_name":"Guedes Bonthonneau, Yannick","last_name":"Guedes Bonthonneau"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"}],"volume":24,"date_updated":"2023-01-06T08:47:35Z","status":"public","type":"journal_article","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"_id":"35306","year":"2022","issue":"3","title":"Ruelle–Pollicott resonances for manifolds with hyperbolic cusps","date_created":"2023-01-05T16:23:34Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH","publication":"Journal of the European Mathematical Society","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"]},{"doi":"10.1016/j.cam.2022.114118","title":"L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data","author":[{"first_name":"Kerstin","full_name":"Hesse, Kerstin","id":"42608","orcid":"0000-0003-4125-1941","last_name":"Hesse"},{"first_name":"Quoc Thong","last_name":"Le Gia","full_name":"Le Gia, Quoc Thong"}],"date_created":"2022-12-20T17:37:16Z","volume":408,"publisher":"Elsevier BV","date_updated":"2023-01-09T08:23:56Z","citation":{"apa":"Hesse, K., &#38; Le Gia, Q. T. (2022). L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. <i>Journal of Computational and Applied Mathematics</i>, <i>408</i>, Article 114118. <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">https://doi.org/10.1016/j.cam.2022.114118</a>","mla":"Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 408, 114118, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>.","bibtex":"@article{Hesse_Le Gia_2022, title={L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}, volume={408}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>}, number={114118}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier BV}, author={Hesse, Kerstin and Le Gia, Quoc Thong}, year={2022} }","short":"K. Hesse, Q.T. Le Gia, Journal of Computational and Applied Mathematics 408 (2022).","chicago":"Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.” <i>Journal of Computational and Applied Mathematics</i> 408 (2022). <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">https://doi.org/10.1016/j.cam.2022.114118</a>.","ieee":"K. Hesse and Q. T. Le Gia, “L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 408, Art. no. 114118, 2022, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>.","ama":"Hesse K, Le Gia QT. L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. <i>Journal of Computational and Applied Mathematics</i>. 2022;408. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114118\">10.1016/j.cam.2022.114118</a>"},"intvolume":"       408","year":"2022","publication_status":"published","publication_identifier":{"issn":["0377-0427"]},"language":[{"iso":"eng"}],"article_number":"114118","keyword":["Applied Mathematics","Computational Mathematics"],"user_id":"14931","department":[{"_id":"10"}],"_id":"34633","status":"public","type":"journal_article","publication":"Journal of Computational and Applied Mathematics"},{"year":"2022","issue":"1","title":"Regularity of Lie groups","date_created":"2022-12-22T09:19:43Z","publisher":"International Press of Boston","publication":"Communications in Analysis and Geometry","language":[{"iso":"eng"}],"keyword":["regularity of Lie groups"],"intvolume":"        30","page":"53-152","citation":{"ama":"Hanusch M. Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>. 2022;30(1):53-152. doi:<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>","ieee":"M. Hanusch, “Regularity of Lie groups,” <i>Communications in Analysis and Geometry</i>, vol. 30, no. 1, pp. 53–152, 2022, doi: <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>.","chicago":"Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis and Geometry</i> 30, no. 1 (2022): 53–152. <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>.","short":"M. Hanusch, Communications in Analysis and Geometry 30 (2022) 53–152.","bibtex":"@article{Hanusch_2022, title={Regularity of Lie groups}, volume={30}, DOI={<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>}, number={1}, journal={Communications in Analysis and Geometry}, publisher={International Press of Boston}, author={Hanusch, Maximilian}, year={2022}, pages={53–152} }","mla":"Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis and Geometry</i>, vol. 30, no. 1, International Press of Boston, 2022, pp. 53–152, doi:<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>.","apa":"Hanusch, M. (2022). Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>, <i>30</i>(1), 53–152. <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>"},"publication_identifier":{"issn":["1019-8385","1944-9992"]},"publication_status":"published","doi":"10.4310/cag.2022.v30.n1.a2","volume":30,"author":[{"first_name":"Maximilian","last_name":"Hanusch","full_name":"Hanusch, Maximilian","id":"30905"}],"date_updated":"2023-01-09T18:07:30Z","status":"public","type":"journal_article","extern":"1","article_type":"original","department":[{"_id":"93"}],"user_id":"30905","_id":"34817"},{"language":[{"iso":"ger"}],"department":[{"_id":"93"}],"user_id":"30905","_id":"34856","status":"public","type":"working_paper","title":"Analysis 1 und 2 Skript/Buch","author":[{"last_name":"Hanusch","full_name":"Hanusch, Maximilian","id":"30905","first_name":"Maximilian"}],"date_created":"2022-12-22T17:06:02Z","date_updated":"2023-01-09T18:07:00Z","publisher":"https://maximilianhanusch.wixsite.com/my-site/lehre-teaching","page":"385","citation":{"ama":"Hanusch M. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching","chicago":"Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching, n.d.","ieee":"M. Hanusch, <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","mla":"Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","bibtex":"@book{Hanusch, title={Analysis 1 und 2 Skript/Buch}, publisher={https://maximilianhanusch.wixsite.com/my-site/lehre-teaching}, author={Hanusch, Maximilian} }","short":"M. Hanusch, Analysis 1 und 2 Skript/Buch, https://maximilianhanusch.wixsite.com/my-site/lehre-teaching, n.d.","apa":"Hanusch, M. (n.d.). <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching."},"year":"2022","publication_status":"draft"},{"year":"2022","page":"717-744","intvolume":"        67","citation":{"short":"M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.","mla":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability and Its Applications</i>, vol. 67, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 717–44.","bibtex":"@article{Kolb_Klump_2022, title={Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary}, volume={67}, number={4}, journal={Theory of Probability and its Applications}, publisher={Society for Industrial and Applied Mathematics}, author={Kolb, Martin and Klump, Alexander}, year={2022}, pages={717–744} }","apa":"Kolb, M., &#38; Klump, A. (2022). Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and Its Applications</i>, <i>67</i>(4), 717–744.","ama":"Kolb M, Klump A. Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and its Applications</i>. 2022;67(4):717-744.","ieee":"M. Kolb and A. Klump, “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary,” <i>Theory of Probability and its Applications</i>, vol. 67, no. 4, pp. 717–744, 2022.","chicago":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability and Its Applications</i> 67, no. 4 (2022): 717–44."},"publication_status":"published","issue":"4","title":"Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary","publisher":"Society for Industrial and Applied Mathematics","date_updated":"2023-01-10T08:13:30Z","volume":67,"date_created":"2023-01-10T08:13:17Z","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"first_name":"Alexander","id":"45067","full_name":"Klump, Alexander","last_name":"Klump"}],"status":"public","publication":"Theory of Probability and its Applications","type":"journal_article","language":[{"iso":"eng"}],"_id":"35644","department":[{"_id":"96"}],"user_id":"85821"},{"doi":"https://doi.org/10.1214/22-EJP866","title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","author":[{"last_name":"Kolb","full_name":"Kolb, Martin","id":"48880","first_name":"Martin"},{"last_name":"Liesenfeld","full_name":"Liesenfeld, Matthias","first_name":"Matthias"}],"date_created":"2023-01-10T08:19:25Z","date_updated":"2023-01-10T08:19:38Z","publisher":"Institute of Mathematical Statistics","citation":{"ama":"Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model with Bessel drift. <i>Electronic Journal of Probability</i>. 2022;(27):1-28. doi:<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>","chicago":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27 (2022): 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","ieee":"M. Kolb and M. Liesenfeld, “On non-extinction in a Fleming-Viot-type particle model with Bessel drift,” <i>Electronic Journal of Probability</i>, no. 27, pp. 1–28, 2022, doi: <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","bibtex":"@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type particle model with Bessel drift}, DOI={<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>}, number={27}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2022}, pages={1–28} }","short":"M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.","mla":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27, Institute of Mathematical Statistics, 2022, pp. 1–28, doi:<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","apa":"Kolb, M., &#38; Liesenfeld, M. (2022). On non-extinction in a Fleming-Viot-type particle model with Bessel drift. <i>Electronic Journal of Probability</i>, <i>27</i>, 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>"},"page":"1-28","year":"2022","issue":"27","publication_status":"published","language":[{"iso":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"35649","status":"public","abstract":[{"text":"Motivated by the work [6] of Mariusz Bieniek, Krzysztof Burdzy and Soumik Pal we study a Fleming-Viot-type particle system consisting of independently moving particles each driven by generalized Bessel processes on the positive real line. Upon hitting the boundary {0} this particle is killed and an uniformly chosen different one branches into two particles. Using the symmetry of the model and the self similarity property of Bessel processes, we obtain a criterion to decide whether the particles converge to the origin at a finite time. This addresses open problem 1.4 in [6]. Specifically, inspired by [6, Open Problem 1.5], we investigate the case of three moving particles and refine the general result of [6, Theorem 1.1(ii)] extending the regime of drift parameters, where convergence does not occur – even to values, where it does occur when considering the case of only two particles.","lang":"eng"}],"type":"journal_article","publication":"Electronic Journal of Probability"},{"publication":"Electronic Journal of Probability","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"We consider autoregressive sequences Xn = aXn−1 + ξn and\r\nMn = max{aMn−1 , ξn} with a constant a ∈ (0, 1) and with positive, in-\r\ndependent and identically distributed innovations {ξk }. It is known that if\r\nP(ξ1 > x) ∼ d\r\nlog x with some d ∈ (0, − log a) then the chains {Xn} and {Mn}\r\nare null recurrent. We investigate the tail behaviour of recurrence times in this\r\ncase of logarithmically decaying tails. More precisely, we show that the tails\r\nof recurrence times are regularly varying of index −1 − d/ log a. We also prove\r\nlimit theorems for {Xn} and {Mn} conditioned to stay over a fixed level x0.\r\nFurthermore, we study tail asymptotics for recurrence times of {Xn} and {Mn}\r\nin the case when these chains are positive recurrent and the tail of log ξ1 is\r\nsubexponential."}],"department":[{"_id":"96"}],"user_id":"85821","_id":"35650","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"        27","page":"1-43","citation":{"short":"D. Denisov, G. Hinrichs, M. Kolb, V. Wachtel, Electronic Journal of Probability 27 (2022) 1–43.","mla":"Denisov, Denis, et al. “Persistence of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–43, doi:<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","bibtex":"@article{Denisov_Hinrichs_Kolb_Wachtel_2022, title={Persistence of autoregressive sequences with logarithmic tails}, volume={27}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Denisov, Denis and Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2022}, pages={1–43} }","apa":"Denisov, D., Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2022). Persistence of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>, <i>27</i>, 1–43. <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>","ama":"Denisov D, Hinrichs G, Kolb M, Wachtel V. Persistence of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>. 2022;27:1-43. doi:<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>","chicago":"Denisov, Denis, Günter Hinrichs, Martin Kolb, and Vitali Wachtel. “Persistence of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of Probability</i> 27 (2022): 1–43. <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","ieee":"D. Denisov, G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of autoregressive sequences with logarithmic tails,” <i>Electronic Journal of Probability</i>, vol. 27, pp. 1–43, 2022, doi: <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>."},"year":"2022","volume":27,"date_created":"2023-01-10T08:28:12Z","author":[{"first_name":"Denis","full_name":"Denisov, Denis","last_name":"Denisov"},{"full_name":"Hinrichs, Günter","last_name":"Hinrichs","first_name":"Günter"},{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"},{"full_name":"Wachtel, Vitali","last_name":"Wachtel","first_name":"Vitali"}],"publisher":"Institute of Mathematical Statistics","date_updated":"2023-01-10T08:29:02Z","doi":"https://doi.org/10.48550/arXiv.2203.14772","title":"Persistence of autoregressive sequences with logarithmic tails"},{"_id":"31367","department":[{"_id":"97"}],"user_id":"32202","language":[{"iso":"ger"}],"publication":" Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen ","type":"conference","editor":[{"first_name":"Stefan","last_name":"Halverscheid","full_name":"Halverscheid, Stefan"},{"full_name":"Kersten, Ina","last_name":"Kersten","first_name":"Ina"},{"first_name":"Barbara","full_name":"Schmidt-Thieme, Barbara","last_name":"Schmidt-Thieme"}],"status":"public","publisher":"Springer Spektrum","date_updated":"2023-01-11T15:28:21Z","author":[{"first_name":"Max","id":"32202","full_name":"Hoffmann, Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123"},{"full_name":"Biehler, Rolf","id":"16274","last_name":"Biehler","first_name":"Rolf"}],"date_created":"2022-05-22T14:16:52Z","title":"Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.","quality_controlled":"1","publication_status":"published","place":"Wiesbaden","year":"2022","page":"351-368","citation":{"apa":"Hoffmann, M., &#38; Biehler, R. (2022). Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie. In S. Halverscheid, I. Kersten, &#38; B. Schmidt-Thieme (Eds.), <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i> (pp. 351–368). Springer Spektrum.","bibtex":"@inproceedings{Hoffmann_Biehler_2022, place={Wiesbaden}, title={Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.}, booktitle={ Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen }, publisher={Springer Spektrum}, author={Hoffmann, Max and Biehler, Rolf}, editor={Halverscheid, Stefan and Kersten, Ina and Schmidt-Thieme, Barbara}, year={2022}, pages={351–368} }","mla":"Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.” <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>, edited by Stefan Halverscheid et al., Springer Spektrum, 2022, pp. 351–68.","short":"M. Hoffmann, R. Biehler, in: S. Halverscheid, I. Kersten, B. Schmidt-Thieme (Eds.),  Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen , Springer Spektrum, Wiesbaden, 2022, pp. 351–368.","ieee":"M. Hoffmann and R. Biehler, “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.,” in <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>, 2022, pp. 351–368.","chicago":"Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.” In <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>, edited by Stefan Halverscheid, Ina Kersten, and Barbara Schmidt-Thieme, 351–68. Wiesbaden: Springer Spektrum, 2022.","ama":"Hoffmann M, Biehler R. Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie. In: Halverscheid S, Kersten I, Schmidt-Thieme B, eds. <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>. Springer Spektrum; 2022:351-368."}},{"publication":" Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik","language":[{"iso":"ger"}],"year":"2022","quality_controlled":"1","title":"Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium","publisher":"Springer","date_created":"2022-05-22T14:03:58Z","editor":[{"full_name":"Isaev, Viktor","last_name":"Isaev","first_name":"Viktor"},{"first_name":"Andreas","last_name":"Eichler","full_name":"Eichler, Andreas"},{"first_name":"Frank","last_name":"Loose","full_name":"Loose, Frank"}],"status":"public","type":"conference","_id":"31365","user_id":"32202","department":[{"_id":"97"}],"place":"Berlin, Heidelberg","citation":{"bibtex":"@inproceedings{Biehler_Hoffmann_2022, place={Berlin, Heidelberg}, title={Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>}, booktitle={ Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik}, publisher={Springer}, author={Biehler, Rolf and Hoffmann, Max}, editor={Isaev, Viktor and Eichler, Andreas and Loose, Frank}, year={2022}, pages={49–72} }","short":"R. Biehler, M. Hoffmann, in: V. Isaev, A. Eichler, F. Loose (Eds.),  Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik, Springer, Berlin, Heidelberg, 2022, pp. 49–72.","mla":"Biehler, Rolf, and Max Hoffmann. “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.” <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>, edited by Viktor Isaev et al., Springer, 2022, pp. 49–72, doi:<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>.","apa":"Biehler, R., &#38; Hoffmann, M. (2022). Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium. In V. Isaev, A. Eichler, &#38; F. Loose (Eds.), <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i> (pp. 49–72). Springer. <a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">https://doi.org/10.1007/978-3-662-63948-1_4</a>","ama":"Biehler R, Hoffmann M. Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium. In: Isaev V, Eichler A, Loose F, eds. <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>. Springer; 2022:49–72. doi:<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>","ieee":"R. Biehler and M. Hoffmann, “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium,” in <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>, 2022, pp. 49–72, doi: <a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>.","chicago":"Biehler, Rolf, and Max Hoffmann. “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.” In <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>, edited by Viktor Isaev, Andreas Eichler, and Frank Loose, 49–72. Berlin, Heidelberg: Springer, 2022. <a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">https://doi.org/10.1007/978-3-662-63948-1_4</a>."},"page":" 49–72","publication_status":"published","publication_identifier":{"isbn":["9783662639474","9783662639481"],"issn":["2197-8751","2197-876X"]},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-662-63948-1_4"}],"doi":"10.1007/978-3-662-63948-1_4","date_updated":"2023-01-11T15:29:09Z","author":[{"first_name":"Rolf","full_name":"Biehler, Rolf","id":"16274","last_name":"Biehler"},{"first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","id":"32202","full_name":"Hoffmann, Max"}]},{"date_created":"2023-05-31T06:22:21Z","author":[{"id":"85820","full_name":"Dröse, Jennifer","last_name":"Dröse","first_name":"Jennifer"},{"full_name":"Neugebauer, P.","last_name":"Neugebauer","first_name":"P."},{"last_name":"Delucchi Danhier","full_name":"Delucchi Danhier, R.","first_name":"R."},{"last_name":"Mertins","full_name":"Mertins, B.","first_name":"B."}],"date_updated":"2023-11-02T08:07:31Z","doi":"https://doi.org/10.1007/978-3-662-63214-7","title":"Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen","quality_controlled":"1","citation":{"apa":"Dröse, J., Neugebauer, P., Delucchi Danhier, R., &#38; Mertins, B. (2022). Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In P. Kleine, N. Graulich, J. Kuhn, &#38; M. Schindler (Eds.), <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i> (pp. 209–225). <a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>","short":"J. Dröse, P. Neugebauer, R. Delucchi Danhier, B. Mertins, in: P. Kleine, N. Graulich, J. Kuhn, M. Schindler (Eds.), Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, 2022, pp. 209–225.","mla":"Dröse, Jennifer, et al. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>, edited by P. Kleine et al., 2022, pp. 209–25, doi:<a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>.","bibtex":"@inbook{Dröse_Neugebauer_Delucchi Danhier_Mertins_2022, title={Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>}, booktitle={Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis}, author={Dröse, Jennifer and Neugebauer, P. and Delucchi Danhier, R. and Mertins, B.}, editor={Kleine, P. and Graulich, N. and Kuhn, J. and Schindler, M.}, year={2022}, pages={209–225} }","ieee":"J. Dröse, P. Neugebauer, R. Delucchi Danhier, and B. Mertins, “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen,” in <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>, P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, Eds. 2022, pp. 209–225.","chicago":"Dröse, Jennifer, P. Neugebauer, R. Delucchi Danhier, and B. Mertins. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” In <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>, edited by P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, 209–25, 2022. <a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>.","ama":"Dröse J, Neugebauer P, Delucchi Danhier R, Mertins B. Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In: Kleine P, Graulich N, Kuhn J, Schindler M, eds. <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>. ; 2022:209-225. doi:<a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>"},"page":"209-225","year":"2022","user_id":"85820","department":[{"_id":"98"}],"_id":"45373","language":[{"iso":"ger"}],"type":"book_chapter","publication":"Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis","status":"public","editor":[{"first_name":"P.","full_name":"Kleine, P.","last_name":"Kleine"},{"last_name":"Graulich","full_name":"Graulich, N.","first_name":"N."},{"first_name":"J.","full_name":"Kuhn, J.","last_name":"Kuhn"},{"first_name":"M.","full_name":"Schindler, M.","last_name":"Schindler"}]}]