@unpublished{46578, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".}}, author = {{Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}}, booktitle = {{arXiv:2308.01113}}, title = {{{Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}}}, year = {{2023}}, } @article{34803, author = {{Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}}, journal = {{BIT Numerical Mathematics}}, publisher = {{Springer}}, title = {{{Deep neural networks on diffeomorphism groups for optimal shape reparametrization}}}, doi = {{10.1007/s10543-023-00989-05}}, volume = {{63}}, year = {{2023}}, } @article{34793, author = {{Glöckner, Helge and Hilgert, Joachim}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{22E65, 28B05, 34A12, 34H05, 46E30, 46E40}}, pages = {{186–232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, doi = {{10.1016/j.jde.2022.10.001}}, volume = {{343}}, year = {{2023}}, } @article{34805, abstract = {{Let $E$ be a finite-dimensional real vector space and $M\subseteq E$ be a convex polytope with non-empty interior. We turn the group of all $C^\infty$-diffeomorphisms of $M$ into a regular Lie group.}}, author = {{Glöckner, Helge}}, journal = {{Journal of Convex Analysis}}, number = {{1}}, pages = {{343--358}}, publisher = {{Heldermann}}, title = {{{Diffeomorphism groups of convex polytopes}}}, volume = {{30}}, year = {{2023}}, } @article{34801, author = {{Glöckner, Helge and Tárrega, Luis}}, journal = {{Journal of Lie Theory}}, number = {{1}}, pages = {{271--296}}, publisher = {{Heldermann}}, title = {{{Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }}}, volume = {{33}}, year = {{2023}}, } @book{45191, editor = {{Gräßler, Iris and Maier, Günter W. and Steffen, Eckhard and Roesmann, Daniel}}, isbn = {{9783031261039}}, publisher = {{Springer International Publishing}}, title = {{{The Digital Twin of Humans}}}, doi = {{10.1007/978-3-031-26104-6}}, year = {{2023}}, } @article{52806, author = {{Gilbert, H. and Schürmann, M. and Liebendörfer, M. and Lawson, D. and Hodds, M.}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, pages = {{1--26}}, publisher = {{Informa UK Limited}}, title = {{{Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland}}}, doi = {{10.1080/0020739x.2023.2184282}}, year = {{2023}}, } @inbook{52811, author = {{Biehler, Rolf and Guntermann, Dominik and Liebendörfer, Michael and Krämer, Sandra and Schlüter, Sarah}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{407–410}}, publisher = {{WTM}}, title = {{{Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{1}}, year = {{2023}}, } @inbook{52810, author = {{Göller, Robin and Gildehaus, Lara and Liebendörfer, Michael and Besser, Michael}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum}}, editor = {{Härterich, Jörg and Kallweit, Michael and Rolka, Katrin and Skill, Thomas}}, isbn = {{978-3-95987-264-5}}, pages = {{66–80}}, publisher = {{WTM}}, title = {{{Erfassung und Vergleich (mathematischer) Eingangsvoraussetzungen angehender Studierender verschiedener mathematikhaltiger Studiengänge}}}, year = {{2023}}, } @inbook{52809, author = {{Kempen, Leander and Liebendörfer, Michael}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum}}, editor = {{Härterich, Jörg and Kallweit, Michael and Rolka, Katrin and Skill, Thomas}}, isbn = {{978-3-95987-264-5}}, pages = {{91–106}}, publisher = {{WTM}}, title = {{{Zu digital - zu viel - zu schwer? Qualitative Einsichten in das Erleben und Handeln von Erstsemester-Studierenden der Mathematik während der Corona-Pandemie}}}, year = {{2023}}, } @inbook{52813, author = {{Schlüter, Sarah and Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{1177–1180}}, publisher = {{WTM}}, title = {{{Bearbeitungsmuster von Studierenden im Umgang mit formalen Definitionen im Kontext konstanter Folgen}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{2}}, year = {{2023}}, } @inbook{52812, author = {{Krämer, Sandra and Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{949–952}}, publisher = {{WTM}}, title = {{{Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{2}}, year = {{2023}}, } @article{52807, abstract = {{Many preservice mathematics teachers lose their motivation during their first year at university. This phenomenon has been repeatedly described in recent years but is not yet fully under­stood. Since motivation may relate to different objects such as mathematics or teaching, we aim to qualitatively reconstruct different facets of the central motivational constructs of Situated-Expectancy-Value theory (intrinsic value, attainment value, utility value, cost, and expectancy of success) for preservice mathematics teachers. The analysis of longitudinal group interviews of 14 pre­service higher-secondary mathematic teachers from a German university revealed different objects of motivation (e.g., teaching mathematics, scientific mathematics, procedural mathematics, or proof-based mathematics) in preservice teachers' values and expectancy of success. Furthermore, relations between those values and expectancy of success were identified that played a significant role in preservice teachers’ motivational development over their first semester (e.g., relations of attain­ment value for scientific mathematics and psychological cost). Theoretical and practical implications towards a teaching-specific conceptualization of expectancy of success and values and value interventions are being discussed.}}, title = {{{Preservice teachers’ mathematics-related values and expectancy in the transition from school to university}}}, doi = {{10.48489/QUADRANTE.31191}}, year = {{2023}}, } @inbook{16296, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate as is the case for models governed by partial differential equations (PDEs). To decrease the numerical effort to an affordable amount, surrogate models can be used to replace the expensive PDE evaluations. Existing multiobjective optimization methods using model reduction are limited either to low parameter dimensions or to few (ideally two) objectives. In this article, we present a combination of the reduced basis model reduction method with a continuation approach using inexact gradients. The resulting approach can handle an arbitrary number of objectives while yielding a significant reduction in computing time.}}, author = {{Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}}, booktitle = {{Non-Smooth and Complementarity-Based Distributed Parameter Systems}}, editor = {{Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}}, isbn = {{978-3-030-79392-0}}, pages = {{43--76}}, publisher = {{Springer}}, title = {{{ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}}}, doi = {{10.1007/978-3-030-79393-7_3}}, year = {{2022}}, } @inbook{30294, abstract = {{With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios.}}, author = {{Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}}, booktitle = {{German Success Stories in Industrial Mathematics}}, editor = {{Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}}, isbn = {{9783030814540}}, issn = {{1612-3956}}, publisher = {{Springer International Publishing}}, title = {{{Efficient Virtual Design and Testing of Autonomous Vehicles}}}, doi = {{10.1007/978-3-030-81455-7_23}}, volume = {{35}}, year = {{2022}}, } @article{30490, author = {{Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}}, journal = {{AIMS}}, pages = {{57--89}}, title = {{{Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations}}}, volume = {{14(1)}}, year = {{2022}}, } @article{30861, abstract = {{AbstractWe consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.}}, author = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}}, issn = {{0022-3239}}, journal = {{Journal of Optimization Theory and Applications}}, keywords = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Turnpike Property in Optimal Microbial Metabolite Production}}}, doi = {{10.1007/s10957-022-02023-0}}, year = {{2022}}, } @article{31982, abstract = {{AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $$\Sigma $$ Σ with Betti number $$b_1$$ b 1 , the order of vanishing of the Ruelle zeta function at zero equals $$4-b_1$$ 4 - b 1 , while in the hyperbolic case it is equal to $$4-2b_1$$ 4 - 2 b 1 . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle $$S\Sigma $$ S Σ with harmonic 1-forms on $$\Sigma $$ Σ .}}, author = {{Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}}, issn = {{0020-9910}}, journal = {{Inventiones mathematicae}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{303--394}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}}}, doi = {{10.1007/s00222-022-01108-x}}, volume = {{229}}, year = {{2022}}, } @inbook{32233, author = {{Häsel-Weide, Uta and Wallner, Melina and Hattermann, M.}}, booktitle = {{Anfangsunterricht für alle Kinder - Willkommen in der Schule!}}, editor = {{Gutzmann, M. and Carle, U.}}, pages = {{200--215}}, title = {{{Symmetrieverständnis von Anfang an}}}, year = {{2022}}, } @inbook{32339, author = {{Häsel-Weide, Uta and Seitz, S. and Wallner, Melina and Wilke, Y.}}, booktitle = {{Qualifizierung für Inklusion. Sekundarstufe}}, editor = {{Lutz, D. and Becker, J. and Buchhaupt, F. and Katzenbach, D. and Strecker, A. and Urban, M.}}, pages = {{83--100}}, publisher = {{Waxmann}}, title = {{{Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe}}}, year = {{2022}}, } @article{32338, author = {{Hähn, K. and Häsel-Weide, Uta and Scherer, P.}}, journal = {{QfI - Qualifizierung für Inklusion}}, number = {{2}}, title = {{{Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.}}}, volume = {{3}}, year = {{2022}}, } @article{29673, abstract = {{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.}}, author = {{Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}}, journal = {{Journal of Physics A: Mathematical and Theoretical}}, number = {{31}}, pages = {{314002}}, publisher = {{IOP Publishing Ltd.}}, title = {{{Koopman analysis of quantum systems}}}, doi = {{10.1088/1751-8121/ac7d22}}, volume = {{55}}, year = {{2022}}, } @unpublished{34618, abstract = {{In this article, we show how second-order derivative information can be incorporated into gradient sampling methods for nonsmooth optimization. The second-order information we consider is essentially the set of coefficients of all second-order Taylor expansions of the objective in a closed ball around a given point. Based on this concept, we define a model of the objective as the maximum of these Taylor expansions. Iteratively minimizing this model (constrained to the closed ball) results in a simple descent method, for which we prove convergence to minimal points in case the objective is convex. To obtain an implementable method, we construct an approximation scheme for the second-order information based on sampling objective values, gradients and Hessian matrices at finitely many points. Using a set of test problems, we compare the resulting method to five other available solvers. Considering the number of function evaluations, the results suggest that the method we propose is superior to the standard gradient sampling method, and competitive compared to other methods.}}, author = {{Gebken, Bennet}}, booktitle = {{arXiv:2210.04579}}, title = {{{Using second-order information in gradient sampling methods for nonsmooth optimization}}}, year = {{2022}}, } @article{34792, author = {{Glöckner, Helge}}, issn = {{2070-0466}}, journal = {{p-Adic Numbers, Ultrametric Analysis, and Applications}}, keywords = {{20Exx, 22Exx, 32Cxx}}, number = {{2}}, pages = {{138–144}}, title = {{{Non-Lie subgroups in Lie groups over local fields of positive characteristic}}}, doi = {{10.1134/S2070046622020042}}, volume = {{14}}, year = {{2022}}, } @article{34791, author = {{Glöckner, Helge and Schmeding, Alexander}}, issn = {{0232-704X}}, journal = {{Annals of Global Analysis and Geometry}}, keywords = {{58D15, 22E65, 26E15, 26E20, 46E40, 46T20, 58A05}}, number = {{2}}, pages = {{359–398}}, title = {{{Manifolds of mappings on Cartesian products}}}, doi = {{10.1007/s10455-021-09816-y}}, volume = {{61}}, year = {{2022}}, } @article{34796, abstract = {{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×E is a kR-space.}}, author = {{Glöckner, Helge}}, issn = {{2075-1680}}, journal = {{Axioms}}, number = {{5}}, title = {{{Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}}}, doi = {{10.3390/axioms11050221}}, volume = {{11}}, year = {{2022}}, } @unpublished{34804, abstract = {{Starting with a finite-dimensional complex Lie algebra, we extend scalars using suitable commutative topological algebras. We study Birkhoff decompositions for the corresponding loop groups. Some results remain valid for loop groups with valued in complex Banach-Lie groups.}}, author = {{Glöckner, Helge}}, booktitle = {{arXiv:2206.11711}}, title = {{{Birkhoff decompositions for loop groups with coefficient algebras}}}, year = {{2022}}, } @phdthesis{31556, abstract = {{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.}}, author = {{Gebken, Bennet}}, title = {{{Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization}}}, doi = {{10.17619/UNIPB/1-1327}}, year = {{2022}}, } @unpublished{33150, abstract = {{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.}}, author = {{Berkemeier, Manuel Bastian and Peitz, Sebastian}}, booktitle = {{arXiv:2208.12094}}, title = {{{Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients}}}, year = {{2022}}, } @article{20731, abstract = {{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.}}, author = {{Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian}}, journal = {{IEEE Transactions on Pattern Analysis and Machine Intelligence}}, number = {{11}}, pages = {{7797--7808}}, publisher = {{IEEE}}, title = {{{On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}}}, doi = {{10.1109/TPAMI.2021.3114962}}, volume = {{44}}, year = {{2022}}, } @article{31193, abstract = {{AbstractThe kinetic Brownian motion on the sphere bundle of a Riemannian manifold $$\mathbb {M}$$ M is a stochastic process that models a random perturbation of the geodesic flow. If $$\mathbb {M}$$ M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the $$L^2$$ L 2 -spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.}}, author = {{Kolb, Martin and Weich, Tobias and Wolf, Lasse Lennart}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}}, number = {{4}}, pages = {{1283--1296}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}}}, doi = {{10.1007/s00023-021-01121-5}}, volume = {{23}}, year = {{2022}}, } @article{35306, author = {{Guedes Bonthonneau, Yannick and Weich, Tobias}}, issn = {{1435-9855}}, journal = {{Journal of the European Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{3}}, pages = {{851--923}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}}}, doi = {{10.4171/jems/1103}}, volume = {{24}}, year = {{2022}}, } @article{34633, author = {{Hesse, Kerstin and Le Gia, Quoc Thong}}, issn = {{0377-0427}}, journal = {{Journal of Computational and Applied Mathematics}}, keywords = {{Applied Mathematics, Computational Mathematics}}, publisher = {{Elsevier BV}}, title = {{{L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}}}, doi = {{10.1016/j.cam.2022.114118}}, volume = {{408}}, year = {{2022}}, } @article{34817, author = {{Hanusch, Maximilian}}, issn = {{1019-8385}}, journal = {{Communications in Analysis and Geometry}}, keywords = {{regularity of Lie groups}}, number = {{1}}, pages = {{53--152}}, publisher = {{International Press of Boston}}, title = {{{Regularity of Lie groups}}}, doi = {{10.4310/cag.2022.v30.n1.a2}}, volume = {{30}}, year = {{2022}}, } @techreport{34856, author = {{Hanusch, Maximilian}}, pages = {{385}}, publisher = {{https://maximilianhanusch.wixsite.com/my-site/lehre-teaching}}, title = {{{Analysis 1 und 2 Skript/Buch}}}, year = {{2022}}, } @article{35644, author = {{Kolb, Martin and Klump, Alexander}}, journal = {{Theory of Probability and its Applications}}, number = {{4}}, pages = {{717--744}}, publisher = {{Society for Industrial and Applied Mathematics}}, title = {{{Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary}}}, volume = {{67}}, year = {{2022}}, } @article{35649, abstract = {{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.}}, author = {{Kolb, Martin and Liesenfeld, Matthias}}, journal = {{Electronic Journal of Probability}}, number = {{27}}, pages = {{1--28}}, publisher = {{Institute of Mathematical Statistics}}, title = {{{On non-extinction in a Fleming-Viot-type particle model with Bessel drift}}}, doi = {{https://doi.org/10.1214/22-EJP866}}, year = {{2022}}, } @article{35650, abstract = {{We consider autoregressive sequences Xn = aXn−1 + ξn and Mn = max{aMn−1 , ξn} with a constant a ∈ (0, 1) and with positive, in- dependent and identically distributed innovations {ξk }. It is known that if P(ξ1 > x) ∼ d log x with some d ∈ (0, − log a) then the chains {Xn} and {Mn} are null recurrent. We investigate the tail behaviour of recurrence times in this case of logarithmically decaying tails. More precisely, we show that the tails of recurrence times are regularly varying of index −1 − d/ log a. We also prove limit theorems for {Xn} and {Mn} conditioned to stay over a fixed level x0. Furthermore, we study tail asymptotics for recurrence times of {Xn} and {Mn} in the case when these chains are positive recurrent and the tail of log ξ1 is subexponential.}}, author = {{Denisov, Denis and Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}}, journal = {{Electronic Journal of Probability}}, pages = {{1--43}}, publisher = {{Institute of Mathematical Statistics}}, title = {{{Persistence of autoregressive sequences with logarithmic tails}}}, doi = {{https://doi.org/10.48550/arXiv.2203.14772}}, volume = {{27}}, year = {{2022}}, } @article{35685, author = {{Liebendörfer, Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, number = {{5}}, pages = {{1133--1152}}, publisher = {{Informa UK Limited}}, title = {{{The role of learning strategies for performance in mathematics courses for engineers}}}, doi = {{10.1080/0020739x.2021.2023772}}, volume = {{53}}, year = {{2022}}, } @article{35718, author = {{Biehler, Rolf and Langlotz, Hubert and Zappe, Wilfried}}, journal = {{mathematik lehren}}, number = {{232}}, pages = {{41–45}}, publisher = {{Friedrich Verlag}}, title = {{{Alles normal?! Daten auf Normalverteilung prüfen–mit schulischen Mitteln}}}, volume = {{2022}}, year = {{2022}}, } @inbook{35696, abstract = {{The data age has led to curriculum developments promoting the relevance of stochastics in mathematics education. This has resulted in an increased demand for teacher professional development (PD) courses, and thus in a rising number of facilitators for this purpose. Their expertise, however, remains under-researched, even though facilitators are the crucial factor in PD success. Our study aims at revealing how one aspect of facilitator expertise, orientation, is connected to other aspects: views on content goals, perception of possible challenges, and attitude towards teaching resources. The explorations reveal differing orientations and learning goals with identical teaching resources for two facilitators who had also been working as a team for the re-design of the PD course for years.}}, author = {{Nieszporek, Ralf and Griese, Birgit and Biehler, Rolf}}, booktitle = {{Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics}}, editor = {{Peters, S. A. and Zapata-Cardona, L. and Bonafini, F. and Fan, A.}}, publisher = {{International Association for Statistical Education}}, title = {{{Facilitators’ Orientations Towards Learning Goals, Perceived Challenges, and Teaching Resources for a PD Course on Conditional Probability}}}, doi = {{10.52041/iase.icots11.t4b2}}, year = {{2022}}, } @inproceedings{34919, abstract = {{Fundamental ideas (Burrill & Biehler, 2011) have been specified to structure the curriculum across different age levels and to focus on and revisit the most important ideas. Such ideas must be based on an epistemological analysis of the scientific domain of statistics and its applications. Because these domains are changing, fundamental ideas have to be revisited from time to time. In particular, data science and machine learning have led to new methods and applications in society that must be considered for updating fundamental ideas.}}, author = {{Biehler, Rolf}}, booktitle = {{Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics}}, editor = {{Peters, S. A. and Zapata-Cardona, L. and Bonafini, F. and Fan, A.}}, publisher = {{International Association for Statistical Education}}, title = {{{Revisiting Fundamental Ideas for Statistics Education From the Perspective of Machine Learning and Its Applications}}}, doi = {{10.52041/iase.icots11.t1a2}}, year = {{2022}}, } @article{34920, abstract = {{A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on data science education. Our hope is to give an overview of selected theoretical thoughts and empirical studies on data science education from a statistics education research perspective. Data science education is rapidly developing but research into data science education is still in its infancy. The current issue presents a snapshot of this developing field.}}, author = {{Biehler, Rolf and De Veaux, Richard and Engel, Joachim and Kazak, Sibel and Frischemeier, Daniel}}, issn = {{1570-1824}}, journal = {{Statistics Education Research Journal}}, keywords = {{Education, Statistics and Probability}}, number = {{2}}, publisher = {{International Association for Statistical Education}}, title = {{{Editorial: Research on Data Science Education}}}, doi = {{10.52041/serj.v21i2.606}}, volume = {{21}}, year = {{2022}}, } @article{35926, author = {{Biehler, Rolf and Griese, Birgit}}, journal = {{mathematik lehren}}, number = {{232}}, pages = {{2–6}}, publisher = {{Friedrich Verlag}}, title = {{{Modellieren im Stochastikunterricht: Annahmen hinterfragen, Ergebnisse validieren}}}, volume = {{2022}}, year = {{2022}}, } @inproceedings{31367, author = {{Hoffmann, Max and Biehler, Rolf}}, booktitle = {{ Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen }}, editor = {{Halverscheid, Stefan and Kersten, Ina and Schmidt-Thieme, Barbara}}, pages = {{351--368}}, publisher = {{Springer Spektrum}}, title = {{{Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.}}}, year = {{2022}}, } @inproceedings{31365, author = {{Biehler, Rolf and Hoffmann, Max}}, booktitle = {{ Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik}}, editor = {{Isaev, Viktor and Eichler, Andreas and Loose, Frank}}, isbn = {{9783662639474}}, issn = {{2197-8751}}, pages = {{ 49–72}}, publisher = {{Springer}}, title = {{{Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium}}}, doi = {{10.1007/978-3-662-63948-1_4}}, year = {{2022}}, } @misc{35698, author = {{Schürmann, Mirko and Büdenbender-Kuklinski, C. and Lankeit, Elisa and Liebendörfer, Michael and Hochmuth, R. and Biehler, Rolf and Schaper, N.}}, publisher = {{LibreCat University}}, title = {{{Dokumentation der Erhebungsinstrumente des Projekts WiGeMath}}}, doi = {{10.17170/KOBRA-202205176188}}, year = {{2022}}, } @article{37470, abstract = {{AbstractWhen the COVID-19 pandemic began, many universities switched to fully online teaching. This unexpected switching to online teaching was challenging for both teachers and students, and restrictions that were put in place because of pandemic made this challenge even greater. However, new ways of teaching might also open new opportunities for students’ learning. The research question driving our study was as follows: how do students regulate their learning and specifically their choice of resources and peer learning in university mathematics classes that are fully taught online as offered during the COVID-19 pandemic? We report on a longitudinal, qualitative study in which students recorded a brief audio diary twice a week over one whole semester (14 weeks). We focused on three students who completed 70 interviews in total and finished the semester with varying degrees of success. The results show how the students structured their studying (e.g., the roles that deadlines or synchronous teaching events played). They illustrate the strengths and limitations of digital materials provided by the lecturer and the use of complementary media. Further, the pandemic uncovered the double-edged role of simple, often anonymous exchanges (e.g., via Discord servers), with few binding forces for either side, and the significance of stable learning partnerships for students’ success. Our research highlights aspects that should be focal points when comparing traditional instruction and online instruction during the pandemic from a self-regulatory perspective. Practical implications refer to how these aspects can be combined sensibly in fully online courses, but also in blended learning contexts.}}, author = {{Liebendörfer, Michael and Kempen, Leander and Schukajlow, Stanislaw}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, keywords = {{General Mathematics, Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{First-year university students' self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study}}}, doi = {{10.1007/s11858-022-01444-5}}, year = {{2022}}, } @article{37472, abstract = {{AbstractAs earlier research results suggest that many mathematics teaching students criticize a missing relevance in their studies, we explore explanations and interrelationships of their relevance assessments. We aim at finding out how one could support the students in attributing relevance to their study programs. A two-fold model for relevance assessments in mathematics teacher education is proposed, consisting of relevance content and relevance reasons. We investigate students' relevance perceptions of mathematical topics and of topics’ complexities, as well as their rating of individual and societal/ vocational relevance reasons, all in relation to their perception of the relevance of their overall program of study. Contrary to earlier research findings, our results suggest that mathematics teaching students already do attribute relevance to many content areas and that a preparation for the teaching profession is not the only reason for them to assign relevance. There also seem to be many students who would attribute relevance if they could develop as individuals and pursue their interests. We suggest that giving students opportunities to set individual priorities in their studies could hence support their relevance assessments. As low relevance assessments seem to be connected to students’ motivational problems, students might profit from motivational support, as well.}}, author = {{Büdenbender-Kuklinski, Christiane and Hochmuth, Reinhard and Liebendörfer, Michael}}, issn = {{2198-9745}}, journal = {{International Journal of Research in Undergraduate Mathematics Education}}, keywords = {{Education, Mathematics (miscellaneous)}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students}}}, doi = {{10.1007/s40753-022-00188-7}}, year = {{2022}}, } @article{35577, author = {{Winkler, Michael}}, journal = {{Calculus of Variations and Partial Differential Equations}}, title = {{{Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar.}}}, volume = {{61}}, year = {{2022}}, }