TY - GEN AB - To model dynamical systems on networks with higher order (non-pairwise) interactions, we recently introduced a new class of ODEs on hypernetworks. Here we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady state branch "reluctant" if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady state branch. AU - von der Gracht, Sören AU - Nijholt, Eddie AU - Rink, Bob ID - 49371 T2 - arXiv:2311.17186 TI - Higher order interactions lead to "reluctant" synchrony breaking ER - TY - JOUR AU - Klüners, Jürgen AU - Wang, Jiuya ID - 49372 JF - La Matematica SN - 2730-9657 TI - Idélic Approach in Enumerating Heisenberg Extensions ER - TY - JOUR AU - Seitz, Simone AU - Häsel-Weide, Uta AU - Wilke, Yannik AU - Wallner, Melina ID - 49425 JF - Teachers and Teaching TI - Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research ER - TY - CONF AB - By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise. AU - Lishkova, Yana AU - Scherer, Paul AU - Ridderbusch, Steffen AU - Jamnik, Mateja AU - Liò, Pietro AU - Ober-Blöbaum, Sina AU - Offen, Christian ID - 34135 IS - 2 T2 - IFAC-PapersOnLine TI - Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery VL - 56 ER - TY - GEN AB - In this article we investigate the convergence behavior of gathering protocols with fixed circulant topologies using tools form dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we model a gathering protocol as a system of ordinary differential equations whose equilibria are exactly all possible gathering points. Then, we find necessary and sufficient conditions for the structure of the underlying interaction graph such that the protocol is stable and converging, i.e., gathering, in the distributive computing sense by using tools from dynamical systems. Moreover, these tools allow for a more fine grained analysis in terms of speed of convergence in the dynamical systems sense. In fact, we derive a decomposition of the state space into stable invariant subspaces with different convergence rates. In particular, this decomposition is identical for every (linear) circulant gathering protocol, whereas only the convergence rates depend on the weights in interaction graph itself. AU - Gerlach, Raphael AU - von der Gracht, Sören AU - Dellnitz, Michael ID - 44840 KW - Dynamical Systems KW - Coupled Systems KW - Distributed Computing KW - Robot Swarms KW - Autonomous Mobile Robots KW - Gathering T2 - arXiv:2305.06632 TI - On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies ER - TY - JOUR AB - A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces. AU - Schmidt, Kai-Uwe AU - Weiß, Charlene ID - 50298 IS - 1 JF - Combinatorial Theory TI - Packings and Steiner systems in polar spaces VL - 3 ER - TY - JOUR AB - We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled. AU - Schmidt, Kai‐Uwe AU - Weiß, Charlene ID - 50297 IS - 9 JF - Journal of Combinatorial Designs TI - Existence of small ordered orthogonal arrays VL - 31 ER - TY - THES AB - Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases. AU - Weiß, Charlene ID - 50300 TI - Linear programming bounds in classical association schemes ER - TY - GEN AB - A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space over $\mathbb{F}_p$ equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-$(n,k,\lambda)$ design in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $k$-spaces such that each totally isotropic $t$-space is contained in exactly $\lambda$ members of $Y$. Nontrivial examples are currently only known for $t\leq 2$. We show that $t$-$(n,k,\lambda)$ designs in polar spaces exist for all $t$ and $p$ provided that $k>\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a probabilistic method by Kuperberg, Lovett, and Peled, and it is thus nonconstructive. AU - Weiß, Charlene ID - 50299 T2 - arXiv:2311.08288 TI - Nontrivial $t$-designs in polar spaces exist for all $t$ ER - TY - JOUR AU - Häsel-Weide, Uta AU - Schmidt, R. AU - Büker, Petra ID - 48596 IS - 1 JF - Zeitschrift für Schul- Und Professionsentwicklung. (PFLB) TI - „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung VL - 5 ER - TY - CONF AU - Graf, Lara Marie AU - Häsel-Weide, Uta AU - Höveler, K. AU - Nührenbörger, M. ED - Drijvers, P. ED - Csapodi, C. ED - Palmér, H. ED - Gosztonyi, K. ED - Kónya, E. ID - 51131 T2 - Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) TI - Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics ER - TY - JOUR AB - Given a geometrically finite hyperbolic surface of infinite volume it is a classical result of Patterson that the positive Laplace-Beltrami operator has no $L^2$-eigenvalues $\geq 1/4$. In this article we prove a generalization of this result for the joint $L^2$-eigenvalues of the algebra of commuting differential operators on Riemannian locally symmetric spaces $\Gamma\backslash G/K$ of higher rank. We derive dynamical assumptions on the $\Gamma$-action on the geodesic and the Satake compactifications which imply the absence of the corresponding principal eigenvalues. A large class of examples fulfilling these assumptions are the non-compact quotients by Anosov subgroups. AU - Weich, Tobias AU - Wolf, Lasse Lennart ID - 31189 JF - Communications in Mathematical Physics TI - Absence of principal eigenvalues for higher rank locally symmetric spaces VL - 403 ER - TY - JOUR AB - In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems. AU - Schütte, Philipp AU - Weich, Tobias AU - Barkhofen, Sonja ID - 31059 JF - Communications in Mathematical Physics TI - Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems VL - 398 ER - TY - GEN AB - We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of meromorphically continued weighted zeta functions established by the authors together with Barkhofen (2021). To make this applicable for numerics we express the weighted zeta as the logarithmic derivative of a suitable parameter dependent Fredholm determinant similar to Borthwick (2014). As an additional difficulty our transfer operator has to include a contracting direction which we account for with techniques developed by Rugh (1992). We achieve a further improvement in convergence speed for our algorithm in the case of surfaces with additional symmetries by proving and applying a symmetry reduction of weighted zeta functions. AU - Schütte, Philipp AU - Weich, Tobias ID - 51206 T2 - arXiv:2308.13463 TI - Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions ER - TY - GEN AB - Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the asymptotic growth of $\Gamma$ in the two direction defined by the two factors. We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of $\Gamma$. AU - Weich, Tobias AU - Wolf, Lasse Lennart ID - 51207 T2 - arXiv:2304.09573 TI - Temperedness of locally symmetric spaces: The product case ER - TY - JOUR AU - Steffen, Eckhard AU - Wolf, Isaak Hieronymus ID - 51351 JF - Discrete Applied Mathematics KW - Applied Mathematics KW - Discrete Mathematics and Combinatorics SN - 0166-218X TI - Bounds for the chromatic index of signed multigraphs VL - 337 ER - TY - CHAP AU - Cappello, Chiara AU - Steffen, Eckhard ID - 45190 SN - 9783031261039 T2 - The Digital Twin of Humans TI - Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks ER - TY - JOUR AU - Steffen, Eckhard AU - Wolf, Isaak Hieronymus ID - 51357 JF - Discrete Mathematics KW - Discrete Mathematics and Combinatorics KW - Theoretical Computer Science SN - 0012-365X TI - Rotation r-graphs ER - TY - GEN AB - We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\'e 21.11 (2020)]. We provide a Lieb-Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb-Robinson bounds. AU - Hinrichs, Benjamin AU - Lemm, Marius AU - Siebert, Oliver ID - 51375 T2 - arXiv:2310.17736 TI - On Lieb-Robinson bounds for a class of continuum fermions ER - TY - GEN AB - In the Bogoliubov-Fr\"ohlich model, we prove that an impurity immersed in a Bose-Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions. AU - Hinrichs, Benjamin AU - Lampart, Jonas ID - 51376 T2 - arXiv:2311.05361 TI - A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate ER - TY - JOUR AB - For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle-Taylor resonances and establish a spectral gap which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e. a 1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on $G/K$. AU - Hilgert, Joachim AU - Weich, Tobias AU - Wolf, Lasse Lennart ID - 31190 IS - 10 JF - Analysis & PDE TI - Higher rank quantum-classical correspondence VL - 16 ER - TY - GEN AB - We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on vector spaces associated with the set of non backtracking paths in the graphs. The second kind of operators are averaging operators acting on vector spaces associated with the space of vertices of the graph. The choice of vector spaces reflects regularity properties. Our main results are correspondences between classical and quantum spectral objects as well as some automatic regularity properties for eigenfunctions of transfer operators. AU - Bux, Kai-Uwe AU - Hilgert, Joachim AU - Weich, Tobias ID - 51205 T2 - arXiv:2307.10876 TI - Spectral correspondences for finite graphs without dead ends ER - TY - JOUR AB - In this paper we complete the program of relating the Laplace spectrum for rank one compact locally symmetric spaces with the first band Ruelle-Pollicott resonances of the geodesic flow on its sphere bundle. This program was started by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for general rank one spaces. Except for the case of hyperbolic surfaces a countable set of exceptional spectral parameters always left untreated since the corresponding Poisson transforms are neither injective nor surjective. We use vector valued Poisson transforms to treat also the exceptional spectral parameters. For surfaces the exceptional spectral parameters lead to discrete series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the situation is more complicated, but can be described completely. AU - Arends, Christian AU - Hilgert, Joachim ID - 31210 JF - Journal de l’École polytechnique — Mathématiques KW - Ruelle resonances KW - Poisson transforms KW - locally symmetric spaces KW - principal series representations SN - 2429-7100 TI - Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters VL - 10 ER - TY - JOUR AU - Hilgert, Joachim AU - Arends, C. ID - 51383 JF - J. de l'École polytechnique — Mathématiques TI - Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters VL - 10 ER - TY - JOUR AU - Hilgert, Joachim AU - Glöckner, H. ID - 51384 JF - J. Diff. Equations TI - Aspects of control theory on infinite-dimensional Lie groups and G-manifolds VL - 343 ER - TY - GEN AU - Hilgert, Joachim AU - Arends, C. AU - Frahm, J. ID - 51499 TI - A pairing formula for resonant states on finite regular graphs ER - TY - GEN AU - Hilgert, Joachim AU - Arends, C. AU - Frahm, J. ID - 51500 TI - Edge Laplacians and vector valued Poisson transforms for graphs ER - TY - GEN AU - Hilgert, Joachim AU - Baier, T. AU - Kaya, O. AU - Mourao, J. AU - Nunes, J. ID - 51502 TI - Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem ER - TY - GEN AU - Hilgert, Joachim AU - Guedes Bonthonneau, Y. AU - Guillarmou, C. AU - Weich, Tobias ID - 51521 TI - Ruelle-Taylor resonances of Anosov actions ER - TY - GEN AB - We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order O(t−2) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization. AU - Sonntag, Konstantin AU - Peitz, Sebastian ID - 32447 T2 - arXiv:2307.00975 TI - Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping ER - TY - GEN AB - 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". AU - Bernreuther, Marco AU - Dellnitz, Michael AU - Gebken, Bennet AU - Müller, Georg AU - Peitz, Sebastian AU - Sonntag, Konstantin AU - Volkwein, Stefan ID - 46578 T2 - arXiv:2308.01113 TI - Multiobjective Optimization of Non-Smooth PDE-Constrained Problems ER - TY - JOUR AU - Celledoni, Elena AU - Glöckner, Helge AU - Riseth, Jørgen AU - Schmeding, Alexander ID - 34803 JF - BIT Numerical Mathematics TI - Deep neural networks on diffeomorphism groups for optimal shape reparametrization VL - 63 ER - TY - JOUR AU - Glöckner, Helge AU - Hilgert, Joachim ID - 34793 JF - Journal of Differential Equations KW - 22E65 KW - 28B05 KW - 34A12 KW - 34H05 KW - 46E30 KW - 46E40 SN - 0022-0396 TI - Aspects of control theory on infinite-dimensional Lie groups and G-manifolds VL - 343 ER - TY - JOUR AB - 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. AU - Glöckner, Helge ID - 34805 IS - 1 JF - Journal of Convex Analysis TI - Diffeomorphism groups of convex polytopes VL - 30 ER - TY - JOUR AU - Glöckner, Helge AU - Tárrega, Luis ID - 34801 IS - 1 JF - Journal of Lie Theory TI - Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups VL - 33 ER - TY - BOOK ED - Gräßler, Iris ED - Maier, Günter W. ED - Steffen, Eckhard ED - Roesmann, Daniel ID - 45191 SN - 9783031261039 TI - The Digital Twin of Humans ER - TY - JOUR AU - Gilbert, H. AU - Schürmann, M. AU - Liebendörfer, M. AU - Lawson, D. AU - Hodds, M. ID - 52806 JF - International Journal of Mathematical Education in Science and Technology KW - Applied Mathematics KW - Education KW - Mathematics (miscellaneous) SN - 0020-739X TI - Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland ER - TY - CHAP AU - Biehler, Rolf AU - Guntermann, Dominik AU - Liebendörfer, Michael AU - Krämer, Sandra AU - Schlüter, Sarah ED - Goethe-Universität Frankfur, IDMI-Primar ID - 52811 SN - 978-3-95987-208-9 T2 - Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik TI - Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos VL - 1 ER - TY - CHAP AU - Göller, Robin AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Besser, Michael ED - Härterich, Jörg ED - Kallweit, Michael ED - Rolka, Katrin ED - Skill, Thomas ID - 52810 SN - 978-3-95987-264-5 T2 - Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum TI - Erfassung und Vergleich (mathematischer) Eingangsvoraussetzungen angehender Studierender verschiedener mathematikhaltiger Studiengänge ER - TY - CHAP AU - Kempen, Leander AU - Liebendörfer, Michael ED - Härterich, Jörg ED - Kallweit, Michael ED - Rolka, Katrin ED - Skill, Thomas ID - 52809 SN - 978-3-95987-264-5 T2 - Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum TI - Zu digital - zu viel - zu schwer? Qualitative Einsichten in das Erleben und Handeln von Erstsemester-Studierenden der Mathematik während der Corona-Pandemie ER - TY - CHAP AU - Schlüter, Sarah AU - Liebendörfer, Michael ED - Goethe-Universität Frankfur, IDMI-Primar ID - 52813 SN - 978-3-95987-208-9 T2 - Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik TI - Bearbeitungsmuster von Studierenden im Umgang mit formalen Definitionen im Kontext konstanter Folgen VL - 2 ER - TY - CHAP AU - Krämer, Sandra AU - Liebendörfer, Michael ED - Goethe-Universität Frankfur, IDMI-Primar ID - 52812 SN - 978-3-95987-208-9 T2 - Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik TI - Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben VL - 2 ER - TY - JOUR AB - 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. ID - 52807 TI - Preservice teachers’ mathematics-related values and expectancy in the transition from school to university ER - TY - CHAP AB - 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. AU - Banholzer, Stefan AU - Gebken, Bennet AU - Dellnitz, Michael AU - Peitz, Sebastian AU - Volkwein, Stefan ED - Michael, Hintermüller ED - Roland, Herzog ED - Christian, Kanzow ED - Michael, Ulbrich ED - Stefan, Ulbrich ID - 16296 SN - 978-3-030-79392-0 T2 - Non-Smooth and Complementarity-Based Distributed Parameter Systems TI - ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation ER - TY - CHAP AB - 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. AU - Peitz, Sebastian AU - Dellnitz, Michael AU - Bannenberg, Sebastian ED - Bock, H. G. ED - Küfer, K.-H. ED - Maas, P. ED - Milde, A. ED - Schulz, V. ID - 30294 SN - 1612-3956 T2 - German Success Stories in Industrial Mathematics TI - Efficient Virtual Design and Testing of Autonomous Vehicles VL - 35 ER - TY - JOUR AU - Cresson, Jacky AU - Jiménez, Fernando AU - Ober-Blöbaum, Sina ID - 30490 JF - AIMS TI - Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations VL - 14(1) ER - TY - JOUR AB - 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. AU - Caillau, Jean-Baptiste AU - Djema, Walid AU - Gouzé, Jean-Luc AU - Maslovskaya, Sofya AU - Pomet, Jean-Baptiste ID - 30861 JF - Journal of Optimization Theory and Applications KW - Applied Mathematics KW - Management Science and Operations Research KW - Control and Optimization SN - 0022-3239 TI - Turnpike Property in Optimal Microbial Metabolite Production ER - TY - JOUR AB - 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 . AU - Cekić, Mihajlo AU - Delarue, Benjamin AU - Dyatlov, Semyon AU - Paternain, Gabriel P. ID - 31982 IS - 1 JF - Inventiones mathematicae KW - General Mathematics SN - 0020-9910 TI - The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds VL - 229 ER - TY - CHAP AU - Häsel-Weide, Uta AU - Wallner, Melina AU - Hattermann, M. ED - Gutzmann, M. ED - Carle, U. ID - 32233 T2 - Anfangsunterricht für alle Kinder - Willkommen in der Schule! TI - Symmetrieverständnis von Anfang an ER - TY - CHAP AU - Häsel-Weide, Uta AU - Seitz, S. AU - Wallner, Melina AU - Wilke, Y. ED - Lutz, D. ED - Becker, J. ED - Buchhaupt, F. ED - Katzenbach, D. ED - Strecker, A. ED - Urban, M. ID - 32339 T2 - Qualifizierung für Inklusion. Sekundarstufe TI - Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe ER - TY - JOUR AU - Hähn, K. AU - Häsel-Weide, Uta AU - Scherer, P. ID - 32338 IS - 2 JF - QfI - Qualifizierung für Inklusion TI - Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. VL - 3 ER - TY - JOUR AB - 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. AU - Klus, Stefan AU - Nüske, Feliks AU - Peitz, Sebastian ID - 29673 IS - 31 JF - Journal of Physics A: Mathematical and Theoretical TI - Koopman analysis of quantum systems VL - 55 ER - TY - GEN AB - 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. AU - Gebken, Bennet ID - 34618 T2 - arXiv:2210.04579 TI - Using second-order information in gradient sampling methods for nonsmooth optimization ER - TY - JOUR AU - Glöckner, Helge ID - 34792 IS - 2 JF - p-Adic Numbers, Ultrametric Analysis, and Applications KW - 20Exx KW - 22Exx KW - 32Cxx SN - 2070-0466 TI - Non-Lie subgroups in Lie groups over local fields of positive characteristic VL - 14 ER - TY - JOUR AU - Glöckner, Helge AU - Schmeding, Alexander ID - 34791 IS - 2 JF - Annals of Global Analysis and Geometry KW - 58D15 KW - 22E65 KW - 26E15 KW - 26E20 KW - 46E40 KW - 46T20 KW - 58A05 SN - 0232-704X TI - Manifolds of mappings on Cartesian products VL - 61 ER - TY - JOUR AB - 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. AU - Glöckner, Helge ID - 34796 IS - 5 JF - Axioms SN - 2075-1680 TI - Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces VL - 11 ER - TY - GEN AB - 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. AU - Glöckner, Helge ID - 34804 T2 - arXiv:2206.11711 TI - Birkhoff decompositions for loop groups with coefficient algebras ER - TY - THES AB - 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. AU - Gebken, Bennet ID - 31556 TI - Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization ER - TY - GEN AB - 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. AU - Berkemeier, Manuel Bastian AU - Peitz, Sebastian ID - 33150 T2 - arXiv:2208.12094 TI - Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients ER - TY - JOUR AB - 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. AU - Bieker, Katharina AU - Gebken, Bennet AU - Peitz, Sebastian ID - 20731 IS - 11 JF - IEEE Transactions on Pattern Analysis and Machine Intelligence TI - On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation VL - 44 ER - TY - JOUR AB - 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. AU - Kolb, Martin AU - Weich, Tobias AU - Wolf, Lasse Lennart ID - 31193 IS - 4 JF - Annales Henri Poincaré KW - Mathematical Physics KW - Nuclear and High Energy Physics KW - Statistical and Nonlinear Physics SN - 1424-0637 TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature VL - 23 ER - TY - JOUR AU - Guedes Bonthonneau, Yannick AU - Weich, Tobias ID - 35306 IS - 3 JF - Journal of the European Mathematical Society KW - Applied Mathematics KW - General Mathematics SN - 1435-9855 TI - Ruelle–Pollicott resonances for manifolds with hyperbolic cusps VL - 24 ER - TY - JOUR AU - Hesse, Kerstin AU - Le Gia, Quoc Thong ID - 34633 JF - Journal of Computational and Applied Mathematics KW - Applied Mathematics KW - Computational Mathematics SN - 0377-0427 TI - L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data VL - 408 ER - TY - JOUR AU - Hanusch, Maximilian ID - 34817 IS - 1 JF - Communications in Analysis and Geometry KW - regularity of Lie groups SN - 1019-8385 TI - Regularity of Lie groups VL - 30 ER - TY - GEN AU - Hanusch, Maximilian ID - 34856 TI - Analysis 1 und 2 Skript/Buch ER - TY - JOUR AU - Kolb, Martin AU - Klump, Alexander ID - 35644 IS - 4 JF - Theory of Probability and its Applications TI - Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary VL - 67 ER - TY - JOUR AB - 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. AU - Kolb, Martin AU - Liesenfeld, Matthias ID - 35649 IS - 27 JF - Electronic Journal of Probability TI - On non-extinction in a Fleming-Viot-type particle model with Bessel drift ER - TY - JOUR AB - 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. AU - Denisov, Denis AU - Hinrichs, Günter AU - Kolb, Martin AU - Wachtel, Vitali ID - 35650 JF - Electronic Journal of Probability TI - Persistence of autoregressive sequences with logarithmic tails VL - 27 ER - TY - JOUR AU - Liebendörfer, Michael AU - Göller, Robin AU - Gildehaus, Lara AU - Kortemeyer, Jörg AU - Biehler, Rolf AU - Hochmuth, Reinhard AU - Ostsieker, Laura AU - Rode, Jana AU - Schaper, Niclas ID - 35685 IS - 5 JF - International Journal of Mathematical Education in Science and Technology KW - Applied Mathematics KW - Education KW - Mathematics (miscellaneous) SN - 0020-739X TI - The role of learning strategies for performance in mathematics courses for engineers VL - 53 ER - TY - JOUR AU - Biehler, Rolf AU - Langlotz, Hubert AU - Zappe, Wilfried ID - 35718 IS - 232 JF - mathematik lehren TI - Alles normal?! Daten auf Normalverteilung prüfen–mit schulischen Mitteln VL - 2022 ER - TY - CHAP AB - 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. AU - Nieszporek, Ralf AU - Griese, Birgit AU - Biehler, Rolf ED - Peters, S. A. ED - Zapata-Cardona, L. ED - Bonafini, F. ED - Fan, A. ID - 35696 T2 - Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics TI - Facilitators’ Orientations Towards Learning Goals, Perceived Challenges, and Teaching Resources for a PD Course on Conditional Probability ER - TY - CONF AB - 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. AU - Biehler, Rolf ED - Peters, S. A. ED - Zapata-Cardona, L. ED - Bonafini, F. ED - Fan, A. ID - 34919 T2 - Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics TI - Revisiting Fundamental Ideas for Statistics Education From the Perspective of Machine Learning and Its Applications ER - TY - JOUR AB - 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. AU - Biehler, Rolf AU - De Veaux, Richard AU - Engel, Joachim AU - Kazak, Sibel AU - Frischemeier, Daniel ID - 34920 IS - 2 JF - Statistics Education Research Journal KW - Education KW - Statistics and Probability SN - 1570-1824 TI - Editorial: Research on Data Science Education VL - 21 ER - TY - JOUR AU - Biehler, Rolf AU - Griese, Birgit ID - 35926 IS - 232 JF - mathematik lehren TI - Modellieren im Stochastikunterricht: Annahmen hinterfragen, Ergebnisse validieren VL - 2022 ER - TY - CONF AU - Hoffmann, Max AU - Biehler, Rolf ED - Halverscheid, Stefan ED - Kersten, Ina ED - Schmidt-Thieme, Barbara ID - 31367 T2 - Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen TI - Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie. ER - TY - CONF AU - Biehler, Rolf AU - Hoffmann, Max ED - Isaev, Viktor ED - Eichler, Andreas ED - Loose, Frank ID - 31365 SN - 2197-8751 T2 - Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik TI - Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium ER - TY - DATA AU - Schürmann, Mirko AU - Büdenbender-Kuklinski, C. AU - Lankeit, Elisa AU - Liebendörfer, Michael AU - Hochmuth, R. AU - Biehler, Rolf AU - Schaper, N. ID - 35698 TI - Dokumentation der Erhebungsinstrumente des Projekts WiGeMath ER - TY - JOUR AB - 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. AU - Liebendörfer, Michael AU - Kempen, Leander AU - Schukajlow, Stanislaw ID - 37470 JF - ZDM – Mathematics Education KW - General Mathematics KW - Education SN - 1863-9690 TI - First-year university students' self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study ER - TY - JOUR AB - 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. AU - Büdenbender-Kuklinski, Christiane AU - Hochmuth, Reinhard AU - Liebendörfer, Michael ID - 37472 JF - International Journal of Research in Undergraduate Mathematics Education KW - Education KW - Mathematics (miscellaneous) SN - 2198-9745 TI - Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students ER - TY - JOUR AU - Winkler, Michael ID - 35577 JF - Calculus of Variations and Partial Differential Equations TI - Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar. VL - 61 ER - TY - JOUR AU - Winkler, Michael ID - 35599 JF - Advanced Nonlinear Studies TI - Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings. VL - 22 ER - TY - JOUR AU - Winkler, Michael ID - 35597 JF - Nonlinear Analysis: Real World Applications TI - Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in a nutrient-poor environments. VL - 63 ER - TY - JOUR AU - Winkler, Michael ID - 35598 JF - Mathematische Nachrichten TI - A unifying approach toward boundedness in Keller-Segel type cross-diffusion systems via conditional $L^\infty$ estimates for taxis gradients. VL - 295 ER - TY - JOUR AU - Winkler, Michael ID - 35600 JF - Partial Differential Equations and Applications TI - Oscillatory decay in a degenerate parabolic equation. VL - 3 ER - TY - JOUR AU - Winkler, Michael ID - 35582 JF - Indiana University Mathematics Journal TI - A critical blow-up exponent for flux limitation in a Keller-Segel system VL - 7 ER - TY - JOUR AU - Winkler, Michael ID - 35590 JF - Journal of Differential Equations TI - Unlimited growth in logarithmic Keller-Segel systems VL - 309 ER - TY - JOUR AU - Lankeit, Johannes AU - Winkler, Michael ID - 35528 JF - Nonlinearity TI - Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary VL - 35 ER - TY - JOUR AU - Winkler, Michael ID - 35568 JF - Communications in Mathematical Physics TI - Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction. VL - 389 ER - TY - JOUR AU - Winkler, Michael ID - 35574 JF - Proceedings of the London Mathematical Society TI - A family of mass-critical Keller-Segel systems. VL - 124 ER - TY - JOUR AB - An initial-boundary value problem for a coupled chemotaxis-Navier–Stokes model with porous medium type diffusion is considered. Previous related literature has provided profound knowledge in cases when the system is augmented with no-flux/no-flux/no-slip boundary conditions for the density of cells, the chemical concentration and the fluid velocity field, respectively; in particular, available qualitative results strongly indicate that only trivial solution behavior can be expected on large time scales. In line with refined modeling approaches to oxygen evolution near fluid-air interfaces, this study now focuses on situations involving a fixed chemoattractant concentration on the boundary. Despite an apparent loss of mathematically favorable energy structures thereby induced, by means of an alternative variational approach a basic theory of global existence is developed in a natural framework of weak solvability. Beyond this, some additional qualitative information on the large time behavior of these solutions is derived by identifying a certain global relaxation property. Specifically, a second result asserts, within a suitable topological setting, the existence of a bounded set which eventually absorbs each individual of the obtained trajectories, and the diameter of which is bounded only by the physically relevant quantities of total population size and prescribed boundary concentration of the chemical signal. AU - Black, Tobias AU - Winkler, Michael ID - 34676 IS - 01 JF - Mathematical Models and Methods in Applied Sciences KW - Applied Mathematics KW - Modeling and Simulation SN - 0218-2025 TI - Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary VL - 32 ER - TY - CONF AU - Liebendörfer, Michael AU - Profeta, Angelo AU - Krämer, Sandra AU - Schlüter, Sarah AU - Becher, Silvia AU - Biehler, Rolf AU - Mai, Tobias AU - Schmitz, Angela ID - 39062 TI - Enriching videos with interactive questions to enhance students’ cognitive activity: concept and implementation ER - TY - CONF AU - Griese, Birgit AU - Nieszporek, Ralf AU - Biehler, Rolf ID - 39058 TI - Facilitators’ views on content goals, learning obstacles, and teaching resources in reference to conditional probability ER - TY - CONF AU - Podworny, Susanne AU - Fleischer, Yannik AU - Stroop, Dietlinde AU - Biehler, Rolf ID - 39064 TI - An example of rich, real and multivariate survey data for use in school ER - TY - JOUR AU - Kang, Kyungkeun AU - Lee, Jihoon AU - Winkler, Michael ID - 35483 JF - Discrete and Continuous Dynamical Systems TI - Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$. VL - 42 ER - TY - JOUR AB - We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$ and a varying constant $κ\in\,[0,\infty[$. Using elementary symmetric functions, we present polynomials which are simultaneous eigenfunctions of the $L_k$ for all $κ\in\,]0,\infty[$. This leads to martingales associated with the Heckman-Opdam diffusions $ (X_{t,1},\ldots,X_{t,N})_{t\ge0}$. As our results extend to the freezing case $κ=\infty$ with a deterministic limit after some renormalization, we find formulas for the expectations $\mathbb E(\prod_{j=1}^N(y-X_{t,j})),$ $y\in\mathbb C$. AU - Rösler, Margit AU - Voit, Michael ID - 38039 IS - 780 JF - Contemporary Mathematics TI - Elementary symmetric polynomials and martingales for Heckman-Opdam processes ER - TY - CONF AU - Häsel-Weide, Uta AU - Nührenbörger, M. ED - Hodgen, J. ED - Geraniou, E. ED - Bolondi, G. ED - Ferretti, F. ID - 40312 T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Inclusive math practices in primary school. Twelfth Congress of the European Society for Research in Mathematics Education ER - TY - CONF AB - We report on our work with students in our data science courses, focusing on the analysis of students’ results. This study represents an in-depth analysis of students’ creation and documentation of machine learning models. The students were supported by educationally designed Jupyter Notebooks, which are used as worked examples. Using the worked example, students document their results in a so-called computational essay. We examine which aspects of creating computational essays are difficult for students to find out how worked examples should be designed to support students without being too prescriptive. We analyze the computational essays produced by students and draw consequences for redesigning our worked example. AU - Fleischer, Yannik AU - Hüsing, Sven AU - Biehler, Rolf AU - Podworny, Susanne AU - Schulte, Carsten ED - Peters, S. A. ED - Zapata-Cardona, L. ED - Bonafini, F. ED - Fan, A. ID - 35674 T2 - Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics TI - Jupyter Notebooks for Teaching, Learning, and Doing Data Science ER - TY - JOUR AB - This study examines modelling with machine learning. In the context of a yearlong data science course, the study explores how upper secondary students apply machine learning with Jupyter Notebooks and document the modelling process as a computational essay incorporating the different steps of the CRISP-DM cycle. The students’ work is based on a teaching module about decision trees in machine learning and a worked example of such a modelling process. The study outlines the students’ performance in carrying out the machine learning technically and reasoning about bias in the data, different data preparation steps, the application context, and the resulting decision model. Furthermore, the context of the study and the theoretical backgrounds are presented. AU - Fleischer, Yannik AU - Biehler, Rolf AU - Schulte, Carsten ID - 35672 IS - 2 JF - Statistics Education Research Journal KW - Education KW - Statistics and Probability SN - 1570-1824 TI - Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks VL - 21 ER - TY - JOUR AU - Bellomo, Nicolas AU - Outada, Nisrine AU - Soler, Juan AU - Tao, Youshan AU - Winkler, Michael ID - 35479 JF - Mathematical Models & Methods in Applied Sciences TI - Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. VL - 32 ER - TY - JOUR AU - Lankeit, Johannes AU - Winkler, Michael ID - 35530 JF - Journal of Evolution Equations TI - Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptiva effects. VL - 22 ER -