TY - JOUR
AB - In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized
partial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19941
IS - 3
JF - Journal of Geometric Mechanics
TI - Backward error analysis for variational discretisations of partial differential equations
VL - 14
ER -
TY - JOUR
AB - Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes.
AU - Offen, Christian
AU - Ober-Blöbaum, Sina
ID - 23382
JF - Chaos: An Interdisciplinary Journal of Nonlinear Science
TI - Symplectic integration of learned Hamiltonian systems
VL - 32(1)
ER -
TY - CONF
AU - Dröse, Jennifer
ID - 40613
T2 - Beiträge zum Mathematikunterricht
TI - Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen
ER -
TY - CONF
AU - Graf, Lara Marie
AU - Häsel-Weide, Uta
AU - Nührenbörger, Marcus
AU - Höveler, Karina
ID - 47520
T2 - Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik
TI - Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen
ER -
TY - CONF
AU - Schwerin, Imke
ID - 47519
T2 - Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik
TI - Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis
ER -
TY - CHAP
AU - Dellori, Anna
AU - Wessel, Lena
ED - Karunakaran, S.S.
ED - Higgins, A.
ID - 48407
T2 - Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education
TI - Pre-service Teachers' Professional Development: Relating Abstract Algebra and School Algebra
ER -
TY - JOUR
AU - Wessel, Lena
AU - Dröse, Jennifer
ID - 48408
JF - mathematik lehren
TI - Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten
VL - 233
ER -
TY - CHAP
AU - Wessel, Lena
AU - Leuders, Timo
ED - Biehler, Rolf
ED - Liebendörfer, Michael
ED - Gueudet, G.
ED - Rasmussen, C.
ED - Winslow, C.
ID - 46160
SN - 1869-4918
T2 - Practice-Oriented Research in Tertiary Mathematics Education
TI - Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory
ER -
TY - JOUR
AU - Dellori, Anna
AU - Wessel, Lena
ID - 48325
JF - Beiträge zum Mathematikunterricht 2022
TI - Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra
ER -
TY - CHAP
AU - Dröse, Jennifer
AU - Neugebauer, P.
AU - Delucchi Danhier, R.
AU - Mertins, B.
ED - Kleine, P.
ED - Graulich, N.
ED - Kuhn, J.
ED - Schindler, M.
ID - 45373
T2 - Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis
TI - Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen
ER -
TY - JOUR
AU - Prediger, S.
AU - Dröse, Jennifer
AU - Stahnke, R.
AU - Ademmer, C.
ID - 45374
JF - Journal of Mathematics Teacher Education
TI - Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth
ER -
TY - CONF
AU - Dröse, Jennifer
AU - Griese, B.
AU - Wessel, Lena
ID - 45379
T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)
TI - Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities
ER -
TY - CONF
AB - Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example.
AU - Vertovec, Nikolaus
AU - Ober-Blöbaum, Sina
AU - Margellos, Kostas
ID - 30733
TI - Verification of safety critical control policies using kernel methods
ER -
TY - CHAP
AU - Dellori, Anna
AU - Wessel, Lena
ED - Trigueros, M.
ED - Barquero, B.
ED - Hochmuth, R.
ED - Peters, J.
ID - 48385
T2 - Proceedings of INDRUM2022
TI - Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra
ER -
TY - JOUR
AB - AbstractTeachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles (N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves.
AU - Dröse, Jennifer
AU - Prediger, Susanne
ID - 40607
JF - Journal für Mathematik-Didaktik
KW - Education
KW - General Mathematics
SN - 0173-5322
TI - Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements
ER -
TY - CONF
AU - Dröse, Jennifer
AU - Griese, Birgit
AU - Wessel, Lena
ID - 48389
T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)
TI - Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities
ER -
TY - CONF
AU - Dröse, Jennifer
AU - Wessel, Lena
ED - Fernandez, C.
ED - Llinares, S.
ED - Gutiérrez, A.
ED - Planas, N.
ID - 45378
T2 - Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME
TI - Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task
ER -
TY - JOUR
AB - In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.
AU - Barkhofen, Sonja
AU - Schütte, Philipp
AU - Weich, Tobias
ID - 31057
IS - 24
JF - Journal of Physics A: Mathematical and Theoretical
TI - Semiclassical formulae For Wigner distributions
VL - 55
ER -
TY - THES
AB - Vorgestellt wird ein Entwicklungsforschungsprojekt zur Konzeption und Durchführung einer Veranstaltung "Geometrie für Lehramtsstudierende". Die Schwerpunkte des Projekts sind zum einen die inhaltliche Gestaltung der Veranstaltung und zum anderen die Umsetzung von Professionsorientierung. Bezogen auf den inhaltlichen Aufbau wird das auf metrischen Räumen aufbauende Axiomensystem der "Saccheri-Ebene" vorgestellt und mit alternativen axiomatischen Zugängen zur ebenen Geometrie verglichen. Die Frage nach der Umsetzung von Professionsorientierung in Fachveranstaltungen ist eng mit der Problematik der zweiten Diskontinuität verbunden. In der Arbeit wird dieses Problem auf Grundlage der Synthese von theoretischen Hintergründen zur Bedeutung von mathematischem Wissen und Können für professionelle Handlungskompetenz von Mathematiklehrkräften diskutiert und darauf aufbauend werden theoriebasierte Entwurfsprinzipien für professionsorientierte Fachveranstaltungen entworfen. Zentrale Elemente der methodischen Gestaltung sind die sogenannten "Schnittstellenwochen" zu den Themen Kongruenz und Symmetrie sowie das begleitende Schnittstellen-ePortfolio. Das zentrale Ergebnis der Arbeit ist ein theoretisch fundiertes und empirisch evaluiertes ganzheitliches Veranstaltungskonzept für eine professionsorientierte Geometrie-Veranstaltung für Lehramtsstudierende, dessen Konzeption auf andere Fachveranstaltungen übertragbar ist. Darüber hinaus ergeben sich im Rahmen der durchgeführten Entwicklungsforschung verschiedene neue Beiträge zur Geometriedidaktik in Schule- und Hochschule.
AU - Hoffmann, Max
ID - 31363
TI - Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende
ER -
TY - JOUR
AU - Bux, Kai-Uwe
AU - Hilgert, Joachim
AU - Weich, Tobias
ID - 35322
IS - 2
JF - Journal of Spectral Theory
KW - Geometry and Topology
KW - Mathematical Physics
KW - Statistical and Nonlinear Physics
SN - 1664-039X
TI - Poisson transforms for trees of bounded degree
VL - 12
ER -
TY - JOUR
AU - Hilgert, Joachim
AU - Weich, Tobias
AU - Bux, K.-U.
ID - 51385
JF - J. of Spectral Theory
TI - Poisson transforms for trees of bounded degree
VL - 12
ER -
TY - GEN
AU - Hilgert, Joachim
ID - 51554
T2 - Mathematische Semesterberichte
TI - Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021
VL - 69
ER -
TY - CONF
AU - Werth, Gerda
ID - 52574
T2 - Beiträge zum Mathematikunterricht
TI - Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings
ER -
TY - JOUR
AU - Nüske, Feliks
AU - Gelß, Patrick
AU - Klus, Stefan
AU - Clementi, Cecilia
ID - 24169
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
TI - Tensor-based computation of metastable and coherent sets
ER -
TY - JOUR
AU - Klus, Stefan
AU - Gelß, Patrick
AU - Nüske, Feliks
AU - Noé, Frank
ID - 24170
JF - Machine Learning: Science and Technology
SN - 2632-2153
TI - Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry
ER -
TY - JOUR
AU - Goelz, Christian
AU - Mora, Karin
AU - Stroehlein, Julia Kristin
AU - Haase, Franziska Katharina
AU - Dellnitz, Michael
AU - Reinsberger, Claus
AU - Vieluf, Solveig
ID - 21195
JF - Cognitive Neurodynamics
TI - Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults
ER -
TY - JOUR
AB - We present a flexible trust region descend algorithm for unconstrained and
convexly constrained multiobjective optimization problems. It is targeted at
heterogeneous and expensive problems, i.e., problems that have at least one
objective function that is computationally expensive. The method is
derivative-free in the sense that neither need derivative information be
available for the expensive objectives nor are gradients approximated using
repeated function evaluations as is the case in finite-difference methods.
Instead, a multiobjective trust region approach is used that works similarly to
its well-known scalar pendants. Local surrogate models constructed from
evaluation data of the true objective functions are employed to compute
possible descent directions. In contrast to existing multiobjective trust
region algorithms, these surrogates are not polynomial but carefully
constructed radial basis function networks. This has the important advantage
that the number of data points scales linearly with the parameter space
dimension. The local models qualify as fully linear and the corresponding
general scalar framework is adapted for problems with multiple objectives.
Convergence to Pareto critical points is proven and numerical examples
illustrate our findings.
AU - Berkemeier, Manuel Bastian
AU - Peitz, Sebastian
ID - 21337
IS - 2
JF - Mathematical and Computational Applications
TI - Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
VL - 26
ER -
TY - JOUR
AB - The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.
AU - Nüske, Feliks
AU - Koltai, Péter
AU - Boninsegna, Lorenzo
AU - Clementi, Cecilia
ID - 21820
JF - Entropy
SN - 1099-4300
TI - Spectral Properties of Effective Dynamics from Conditional Expectations
ER -
TY - JOUR
AB - In this article, we present an efficient descent method for locally Lipschitz
continuous multiobjective optimization problems (MOPs). The method is realized
by combining a theoretical result regarding the computation of descent
directions for nonsmooth MOPs with a practical method to approximate the
subdifferentials of the objective functions. We show convergence to points
which satisfy a necessary condition for Pareto optimality. Using a set of test
problems, we compare our method to the multiobjective proximal bundle method by
M\"akel\"a. The results indicate that our method is competitive while being
easier to implement. While the number of objective function evaluations is
larger, the overall number of subgradient evaluations is lower. Finally, we
show that our method can be combined with a subdivision algorithm to compute
entire Pareto sets of nonsmooth MOPs.
AU - Gebken, Bennet
AU - Peitz, Sebastian
ID - 16867
JF - Journal of Optimization Theory and Applications
TI - An efficient descent method for locally Lipschitz multiobjective optimization problems
VL - 188
ER -
TY - JOUR
AB - It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs.
AU - Gebken, Bennet
AU - Peitz, Sebastian
ID - 16295
JF - Journal of Global Optimization
TI - Inverse multiobjective optimization: Inferring decision criteria from data
VL - 80
ER -
TY - THES
AB - Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung.
AU - Gerlach, Raphael
ID - 32057
TI - The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems
ER -
TY - JOUR
AU - Delarue, Benjamin
AU - Ramacher, Pablo
ID - 32016
IS - 6
JF - Journal of Symplectic Geometry
TI - Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions
VL - 19
ER -
TY - JOUR
AU - Li, Jiaao
AU - Ma, Yulai
AU - Miao, Zhengke
AU - Shi, Yongtang
AU - Wang, Weifan
AU - Zhang, Cun-Quan
ID - 34042
JF - Journal of Combinatorial Theory, Series B
KW - Computational Theory and Mathematics
KW - Discrete Mathematics and Combinatorics
KW - Theoretical Computer Science
SN - 0095-8956
TI - Nowhere-zero 3-flows in toroidal graphs
VL - 153
ER -
TY - JOUR
AB - A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.
AU - Glöckner, Helge
AU - Willis, George A.
ID - 34786
JF - Journal of Algebra
KW - Contraction group
KW - Torsion group
KW - Extension
KW - Cocycle
KW - Section
KW - Equivariant cohomology
KW - Abelian group
KW - Nilpotent group
KW - Isomorphism types
SN - 0021-8693
TI - Decompositions of locally compact contraction groups, series and extensions
VL - 570
ER -
TY - JOUR
AU - Glöckner, Helge
AU - Willis, George A.
ID - 34790
JF - J. Reine Angew. Math.
KW - 22D05
KW - 22A05
KW - 20E18
SN - 0075-4102
TI - Locally pro-p contraction groups are nilpotent
VL - 781
ER -
TY - JOUR
AU - Glöckner, Helge
ID - 34795
IS - 1
JF - Mathematische Nachrichten
SN - 0025-584X
TI - Direct limits of regular Lie groups
VL - 294
ER -
TY - GEN
AB - Let $G$ be a Lie group over a totally disconnected local field and $\alpha$
be an analytic endomorphism of $G$. The contraction group of $\alpha$ ist the
set of all $x\in G$ such that $\alpha^n(x)\to e$ as $n\to\infty$. Call sequence
$(x_{-n})_{n\geq 0}$ in $G$ an $\alpha$-regressive trajectory for $x\in G$ if
$\alpha(x_{-n})=x_{-n+1}$ for all $n\geq 1$ and $x_0=x$. The anti-contraction
group of $\alpha$ is the set of all $x\in G$ admitting an $\alpha$-regressive
trajectory $(x_{-n})_{n\geq 0}$ such that $x_{-n}\to e$ as $n\to\infty$. The
Levi subgroup is the set of all $x\in G$ whose $\alpha$-orbit is relatively
compact, and such that $x$ admits an $\alpha$-regressive trajectory
$(x_{-n})_{n\geq 0}$ such that $\{x_{-n}\colon n\geq 0\}$ is relatively
compact. The big cell associated to $\alpha$ is the set $\Omega$ of all all
products $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and
$z$ in the anti-contraction group. Let $\pi$ be the mapping from the cartesian
product of the contraction group, Levi subgroup and anti-contraction group to
$\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\Omega$ is open in $G$ and
$\pi$ is \'{e}tale for suitable immersed Lie subgroup structures on the three
subgroups just mentioned. Moreover, we study group-theoretic properties of
contraction groups and anti-contraction groups.
AU - Glöckner, Helge
ID - 34806
T2 - arXiv:2101.02981
TI - Contraction groups and the big cell for endomorphisms of Lie groups over local fields
ER -
TY - CONF
AU - Ober-Blöbaum, Sina
AU - Vermeeren, M.
ID - 29421
T2 - 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC
TI - Superconvergence of galerkin variational integrators
VL - 54(19)
ER -
TY - JOUR
AB - Model predictive control is a prominent approach to construct a feedback
control loop for dynamical systems. Due to real-time constraints, the major
challenge in MPC is to solve model-based optimal control problems in a very
short amount of time. For linear-quadratic problems, Bemporad et al. have
proposed an explicit formulation where the underlying optimization problems are
solved a priori in an offline phase. In this article, we present an extension
of this concept in two significant ways. We consider nonlinear problems and -
more importantly - problems with multiple conflicting objective functions. In
the offline phase, we build a library of Pareto optimal solutions from which we
then obtain a valid compromise solution in the online phase according to a
decision maker's preference. Since the standard multi-parametric programming
approach is no longer valid in this situation, we instead use interpolation
between different entries of the library. To reduce the number of problems that
have to be solved in the offline phase, we exploit symmetries in the dynamical
system and the corresponding multiobjective optimal control problem. The
results are verified using two different examples from autonomous driving.
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
ID - 16294
JF - International Journal of Robust and Nonlinear Control
TI - Explicit multiobjective model predictive control for nonlinear systems with symmetries
VL - 31(2)
ER -
TY - JOUR
AU - Djema, Walid
AU - Giraldi, Laetitia
AU - Maslovskaya, Sofya
AU - Bernard, Olivier
ID - 29543
JF - Automatica
KW - Electrical and Electronic Engineering
KW - Control and Systems Engineering
SN - 0005-1098
TI - Turnpike features in optimal selection of species represented by quota models
VL - 132
ER -
TY - GEN
AB - We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.
AU - Schütte, Philipp
AU - Weich, Tobias
AU - Delarue, Benjamin
ID - 31058
TI - Resonances and weighted zeta functions for obstacle scattering via smooth models
ER -
TY - GEN
AU - Hoffmann, Max
ID - 31385
T2 - Mathematische Semesterberichte
TI - Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie
VL - 68
ER -
TY - CHAP
AU - Hoffmann, Max
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 31364
SN - 2197-8751
T2 - Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert
TI - Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn
ER -
TY - JOUR
AB - Abstract
For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.
AU - Küster, Benjamin
AU - Weich, Tobias
ID - 31261
IS - 11
JF - International Mathematics Research Notices
KW - General Mathematics
SN - 1073-7928
TI - Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
VL - 2021
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Nührenbürger, Marcus
ID - 31576
IS - 14
JF - Zeitschrift für Grundschulforschung (ZfG)
TI - Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Schöttler, Christian
ID - 31577
IS - 2
JF - Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)
SN - 2701-9012
TI - Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen
ER -
TY - JOUR
AU - Li, Jiaao
AU - Ma, Yulai
AU - Shi, Yongtang
AU - Wang, Weifan
AU - Wu, Yezhou
ID - 32810
JF - European Journal of Combinatorics
KW - Discrete Mathematics and Combinatorics
SN - 0195-6698
TI - On 3-flow-critical graphs
VL - 100
ER -
TY - JOUR
AB - The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-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
ID - 33278
IS - 4
JF - Annales Henri Poincaré
TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
VL - 23
ER -
TY - GEN
AU - Weich, Tobias
AU - Budde, Julia
ID - 32099
T2 - arXiv:2103.02968v1
TI - Wave Front Sets of Nilpotent Lie Group Representations
ER -
TY - JOUR
AB - While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.
AU - Richthammer, Thomas
AU - Fiedler, Michael
ID - 33481
JF - Stochastic Processes and their Applications
TI - A lower bound on the displacement of particles in 2D Gibbsian particle systems
VL - 132
ER -