@inproceedings{43097,
  author       = {{Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde and Zandieh, Michelle and Martínez-Planell, Rafael}},
  booktitle    = {{Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}},
  editor       = {{Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}},
  title        = {{{Innovations in university teaching based on mathematic education research}}},
  year         = {{2023}},
}

@article{43105,
  author       = {{Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}},
  issn         = {{1468-1218}},
  journal      = {{Nonlinear Analysis: Real World Applications}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}},
  publisher    = {{Elsevier BV}},
  title        = {{{Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}}},
  doi          = {{10.1016/j.nonrwa.2023.103868}},
  volume       = {{73}},
  year         = {{2023}},
}

@inbook{43227,
  author       = {{Vitt, Vivian and Häsel-Weide, Uta}},
  booktitle    = {{Mathematica Didactica, 46}},
  title        = {{{Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}}},
  doi          = {{https://doi.org/10.18716/ojs/md/2023.1671}},
  year         = {{2023}},
}

@article{34832,
  author       = {{Hanusch, Maximilian}},
  journal      = {{Annals of Global Analysis and Geometry}},
  keywords     = {{Lax equation, generalized Baker-Campbell-Dynkin-Hausdorff formula, regularity of Lie groups}},
  number       = {{21}},
  title        = {{{The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}}},
  doi          = {{10.1007/s10455-023-09888-y}},
  volume       = {{63}},
  year         = {{2023}},
}

@article{44857,
  abstract     = {{Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives.}},
  author       = {{Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}},
  issn         = {{0399-0559}},
  journal      = {{RAIRO - Operations Research}},
  keywords     = {{Management Science and Operations Research, Computer Science Applications, Theoretical Computer Science}},
  number       = {{3}},
  pages        = {{1045--1058}},
  publisher    = {{EDP Sciences}},
  title        = {{{Algorithms for the genome median under a restricted measure of rearrangement}}},
  doi          = {{10.1051/ro/2023052}},
  volume       = {{57}},
  year         = {{2023}},
}

@unpublished{44859,
  author       = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}},
  booktitle    = {{arXiv:2305.08619}},
  title        = {{{Sets of r-graphs that color all r-graphs}}},
  year         = {{2023}},
}

@article{34833,
  author       = {{Hanusch, Maximilian}},
  journal      = {{Indagationes Mathematicae.}},
  keywords     = {{Lie group actions and analytic 1-submanifolds}},
  number       = {{4}},
  pages        = {{752--811}},
  title        = {{{Decompositions of Analytic 1-Manifolds}}},
  doi          = {{10.1016/j.indag.2023.02.003}},
  volume       = {{34}},
  year         = {{2023}},
}

@unpublished{45498,
  abstract     = {{We present a novel method for high-order phase reduction in networks of
weakly coupled oscillators and, more generally, perturbations of reducible
normally hyperbolic (quasi-)periodic tori. Our method works by computing an
asymptotic expansion for an embedding of the perturbed invariant torus, as well
as for the reduced phase dynamics in local coordinates. Both can be determined
to arbitrary degrees of accuracy, and we show that the phase dynamics may
directly be obtained in normal form. We apply the method to predict remote
synchronisation in a chain of coupled Stuart-Landau oscillators.}},
  author       = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}},
  booktitle    = {{arXiv:2306.03320}},
  pages        = {{29}},
  title        = {{{A parametrisation method for high-order phase reduction in coupled  oscillator networks}}},
  year         = {{2023}},
}

@article{45712,
  author       = {{Häsel-Weide, Uta}},
  journal      = {{Die Grundschulzeitschrift}},
  number       = {{339}},
  pages        = {{6--11}},
  publisher    = {{Friedrich Verlag}},
  title        = {{{ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen}}},
  year         = {{2023}},
}

@article{45713,
  author       = {{Graf, Lara Marie and Wienhues, Inga and Häsel-Weide, Uta}},
  journal      = {{Die Grundschulzeitschrift}},
  number       = {{339}},
  pages        = {{20--23}},
  publisher    = {{Friedrich Verlag}},
  title        = {{{Addition und Subtraktion verstehen}}},
  year         = {{2023}},
}

@unpublished{46117,
  abstract     = {{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
$\Gamma$.}},
  author       = {{Weich, Tobias and Wolf, Lasse L.}},
  booktitle    = {{arXiv:2304.09573}},
  title        = {{{Temperedness of locally symmetric spaces: The product case}}},
  year         = {{2023}},
}

@article{46256,
  author       = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}},
  issn         = {{0895-4801}},
  journal      = {{SIAM Journal on Discrete Mathematics}},
  keywords     = {{General Mathematics}},
  number       = {{3}},
  pages        = {{1548--1565}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}}},
  doi          = {{10.1137/22m1500654}},
  volume       = {{37}},
  year         = {{2023}},
}

@article{29240,
  abstract     = {{The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,
we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.}},
  author       = {{Ober-Blöbaum, Sina and Offen, Christian}},
  issn         = {{0377-0427}},
  journal      = {{Journal of Computational and Applied Mathematics}},
  keywords     = {{Lagrangian learning, variational backward error analysis, modified Lagrangian, variational integrators, physics informed learning}},
  pages        = {{114780}},
  publisher    = {{Elsevier}},
  title        = {{{Variational Learning of Euler–Lagrange Dynamics from Data}}},
  doi          = {{10.1016/j.cam.2022.114780}},
  volume       = {{421}},
  year         = {{2023}},
}

@article{29236,
  abstract     = {{The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.}},
  author       = {{McLachlan, Robert and Offen, Christian}},
  journal      = {{Journal of Geometric Mechanics}},
  keywords     = {{variational integrators, backward error analysis, Euler--Lagrange equations, multistep methods, conjugate symplectic methods}},
  number       = {{1}},
  pages        = {{98--115}},
  publisher    = {{AIMS Press}},
  title        = {{{Backward error analysis for conjugate symplectic methods}}},
  doi          = {{10.3934/jgm.2023005}},
  volume       = {{15}},
  year         = {{2023}},
}

@article{37654,
  abstract     = {{Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when
learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite
the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we
enhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach
allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,
a pendulum on a cart and a two-body problem from astrodynamics are considered.}},
  author       = {{Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}},
  issn         = {{1054-1500}},
  journal      = {{Chaos}},
  number       = {{6}},
  publisher    = {{AIP Publishing}},
  title        = {{{Hamiltonian Neural Networks with Automatic Symmetry Detection}}},
  doi          = {{10.1063/5.0142969}},
  volume       = {{33}},
  year         = {{2023}},
}

@article{23428,
  abstract     = {{The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.
samples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the
best of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.}},
  author       = {{Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}},
  journal      = {{Journal of Nonlinear Science}},
  title        = {{{Finite-data error bounds for Koopman-based prediction and control}}},
  doi          = {{10.1007/s00332-022-09862-1}},
  volume       = {{33}},
  year         = {{2023}},
}

@article{21600,
  abstract     = {{Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.}},
  author       = {{Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}},
  journal      = {{SIAM Journal on Scientific Computing}},
  number       = {{2}},
  pages        = {{A579--A595}},
  title        = {{{Efficient time stepping for numerical integration using reinforcement  learning}}},
  doi          = {{10.1137/21M1412682}},
  volume       = {{45}},
  year         = {{2023}},
}

@inproceedings{46757,
  author       = {{Schwerin, Imke and Häsel-Weide, Uta}},
  booktitle    = {{International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}},
  editor       = {{Novotna, J. and Moraova, H.}},
  location     = {{Prag}},
  pages        = {{297--305}},
  publisher    = {{Charles University}},
  title        = {{{Second grader´s understanding of doubling and halfing in various representations}}},
  year         = {{2023}},
}

@inbook{46758,
  author       = {{Schmidt, Rebekka and Tenberge, Claudia and Häsel-Weide, Uta}},
  booktitle    = {{Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre}},
  editor       = {{Vöing, N. and Schmidt, R. and Neiske, I.}},
  pages        = {{297--318}},
  publisher    = {{Visual Ink Publishing}},
  title        = {{{Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern}}},
  year         = {{2023}},
}

@article{56200,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “<jats:italic>interface ePortfolio</jats:italic>” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of <jats:italic>profession orientation</jats:italic>. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers.</jats:p>}},
  author       = {{Hoffmann, Max and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  number       = {{4}},
  pages        = {{737--751}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}}},
  doi          = {{10.1007/s11858-023-01505-3}},
  volume       = {{55}},
  year         = {{2023}},
}