Die Implementierung eines Klassenrats ist mit der Hoffnung verbunden, die demokratischen Kompetenzen von Schüler*innen zu stärken. Welche Kompetenzen die Teilnehmer*innen mithilfe dieser demokratiepädagogischen Methode tatsächlich erwerben und wie sich der Klassenrat auf die Klassengemeinschaft auswirkt, hat eine empirische Studie1 am Lycée Nic Biever in Dudelange untersucht.

An Grundschulen bietet der Klassenrat eine Möglichkeit für Schüler*innen, erste Schritte demokratischen Umgangs zu erlernen oder auch zu vertiefen. Hier lernen sie in einem geschützten Raum sich zu verschiedensten Themen zu äußern, Konflikte lösungsorientiert zu verarbeiten und Verantwortung zu übernehmen. Die hier vorgestellten Materialien sollen bei der Einführung und Durchführung des Klassenrats helfen.

Sollten Plastikverpackungen verboten werden? Was spricht gegen eine Wahlberechtigung ab 14 Jahren? Wie sollte die EU mit möglichen Auswirkungen des Brexits umgehen? – Auch solche Fragen haben im Klassenrat ihre Berechtigung, denn ihre Diskussion bietet besondere Chancen für demokratische Lernprozesse.

In this thesis, we consider the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Due to the exponentially increasing computational complexity in the number of dimensions—the so-called curse of dimensionality—they present a considerable computational challenge and become infeasible even for moderate problem sizes. Multilinear algebra and tensor numerical methods have a wide range of applications in the fields of data science and scientific computing. Due to the typically large problem sizes in practical settings, efficient methods, which exploit low-rank structures, are essential. In this thesis, we consider an application each in both of these fields. Tensor completion, or imputation of unknown values in partially known multiway data is an important problem, which appears in statistics, mathematical imaging science and data science. Under the assumption of redundancy in the underlying data, this is a well-defined problem and methods of mathematical optimization can be applied to it. Due to the fact that tensors of fixed rank form a Riemannian submanifold of the ambient high-dimensional tensor space, Riemannian optimization is a natural framework for these problems, which is both mathematically rigorous and computationally efficient. We present a novel Riemannian trust-region scheme, which compares favourably with the state of the art on selected application cases and outperforms known methods on some test problems. Optimization problems governed by partial differential equations form an area of scientific computing which has applications in a variety of areas, ranging from physics to financial mathematics. Due to the inherent high dimensionality of optimization problems arising from discretized differential equations, these problems present computational challenges, especially in the case of three or more dimensions. An even more challenging class of optimization problems has operators of integral instead of differential type in the constraint. These operators are nonlocal, and therefore lead to large, dense discrete systems of equations. We present a novel solution method, based on separation of spatial dimensions and provably low-rank approximation of the nonlocal operator. Our approach allows the solution of multidimensional problems with a complexity which is only slightly larger than linear in the univariate grid size; this improves the state of the art for a particular test problem problem by at least two orders of magnitude.

Objective Our study investigated body image representations in female patients with anorexia nervosa and healthy controls using a size estimation with pictures of their own body. We also explored a method to reduce body image distortions through right hemispheric activation. Method Pictures of participants’ own bodies were shown on the left or right visual fields for 130 ms after presentation of neutral, positive, or negative word primes, which could be self-relevant or not, with the task of classifying the picture as “thinner than”, “equal to”, or “fatter than” one’s own body. Subsequently, activation of the left- or right hemispheric through right- or left-hand muscle contractions for 3 min., respectively. Finally, participants completed the size estimation task again. Results The distorted “fatter than” body image was found only in patients and only when a picture of their own body appeared on the right visual field (left hemisphere) and was preceded by negative self-relevant words. This distorted perception of the patients’ body image was reduced after left-hand muscle contractions (right hemispheric activation). Discussion To reduce body image distortions it is advisable to find methods that help anorexia nervosa patients to increase their self-esteem. The body image distortions were ameliorated after right hemispheric activation. A related method to prevent distorted body-image representations in these patients may be Eye Movement Desensitization and Reprocessing (EMDR) therapy.

Many combinatorial optimization problems on finite graphs can be formulated as conic convex programs, e.g. the stable set problem, the maximum clique problem or the maximum cut problem. Especially NP-hard problems can be written as copositive programs. In this case the complexity is moved entirely into the copositivity constraint. Copositive programming is a quite new topic in optimization. It deals with optimization over the so-called copositive cone, a superset of the positive semidefinite cone, where the quadratic form x^T Ax has to be nonnegative for only the nonnegative vectors x. Its dual cone is the cone of completely positive matrices, which includes all matrices that can be decomposed as a sum of nonnegative symmetric vector-vector-products. The related optimization problems are linear programs with matrix variables and cone constraints. However, some optimization problems can be formulated as combinatorial problems on infinite graphs. For example, the kissing number problem can be formulated as a stable set problem on a circle. In this thesis we will discuss how the theory of copositive optimization can be lifted up to infinite dimension. For some special cases we will give applications in combinatorial optimization.

Die forschungsprozessspezifische Kompetenzmatrix stellt einen Baustein im Rahmen des durch das BMBF geförderten Forschungsprojektes „Prozessorientierte Entwicklung von Managementinstrumenten für Forschungsdaten im Lebenszyklus“ (PODMAN) dar. Im Rahmen des PODMAN-Projektes soll ein Referenzmodell und ein zugehöriges prozessorientiertes Benchmarking-Verfahren zur Implementierung des Forschungsdatenmanagements an Hochschulen und außeruniversitären Forschungseinrichtungen entwickelt werden. Darüber soll den Hochschulen und außeruniversitären Forschungseinrichtungen ein Orientierungsrahmen bereitgestellt werden, den sie flexibel zur Umsetzung eigener Datenmanagementstrategien nutzen können. In diesem Zusammenhang sollen Instrumente entwickelt werden, welche eine erfolgreiche Organisation der Zusammenarbeit und Kommunikation sowie der Qualifizierung aller am Forschungsdatenmanagementprozess beteiligten Akteure erlauben. Die forschungsprozessspezifische Kompetenzmatrix hat als eines dieser Instrumente zwei Funktionen: Erstens definiert sie die zur Implementierung eines umfassenden institutionellen FDM-Konzeptes notwendigen Aufgaben und zweitens die damit verbundenen Kompetenzen der ausführenden Akteure.