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 -