We consider a linear regression model for which we assume that some of the observed variables are irrelevant for the prediction. Including the wrong variables in the statistical model can either lead to the problem of having too little information to properly estimate the statistic of interest, or having too much information and consequently describing fictitious connections. This thesis considers discrete optimization to conduct a variable selection. In light of this, the subset selection regression method is analyzed. The approach gained a lot of interest in recent years due to its promising predictive performance. A major challenge associated with the subset selection regression is the computational difficulty. In this thesis, we propose several improvements for the efficiency of the method. Novel bounds on the coefficients of the subset selection regression are developed, which help to tighten the relaxation of the associated mixed-integer program, which relies on a Big-M formulation. Moreover, a novel mixed-integer linear formulation for the subset selection regression based on a bilevel optimization reformulation is proposed. Finally, it is shown that the perspective formulation of the subset selection regression is equivalent to a state-of-the-art binary formulation. We use this insight to develop novel bounds for the subset selection regression problem, which show to be highly effective in combination with the proposed linear formulation. In the second part of this thesis, we examine the statistical conception of the subset selection regression and conclude that it is misaligned with its intention. The subset selection regression uses the training error to decide on which variables to select. The approach conducts the validation on the training data, which oftentimes is not a good estimate of the prediction error. Hence, it requires a predetermined cardinality bound. Instead, we propose to select variables with respect to the cross-validation value. The process is formulated as a mixed-integer program with the sparsity becoming subject of the optimization. Usually, a cross-validation is used to select the best model out of a few options. With the proposed program the best model out of all possible models is selected. Since the cross-validation is a much better estimate of the prediction error, the model can select the best sparsity itself. The thesis is concluded with an extensive simulation study which provides evidence that discrete optimization can be used to produce highly valuable predictive models with the cross-validation subset selection regression almost always producing the best results.

It is well-known that katabatic winds can be detected as warm signatures in the surface temperature over the slopes of the Antarctic ice sheets. For appropriate synoptic forcing and/or topographic channeling, katabatic surges occur, which result in warm signatures also over adjacent ice shelves. Moderate Resolution Imaging Spectroradiometer (MODIS) ice surface temperature (IST) data are used to detect warm signatures over the Antarctic for the winter periods 2002–2017. In addition, high-resolution (5 km) regional climate model data is used for the years of 2002 to 2016. We present a case study and a climatology of wind-induced IST anomalies for the Ross Ice Shelf and the eastern Weddell Sea. The IST anomaly distributions show maxima around 10–15K for the slopes, but values of more than 25K are also found. Katabatic surges represent a strong climatological signal with a mean warm anomaly of more than 5K on more than 120 days per winter for the Byrd Glacier and the Nimrod Glacier on the Ross Ice Shelf. The mean anomaly for the Brunt Ice Shelf is weaker, and exceeds 5K on about 70 days per winter. Model simulations of the IST are compared to the MODIS IST, and show a very good agreement. The model data show that the near-surface stability is a better measure for the response to the wind than the IST itself.

Background In light of the current biodiversity crisis, DNA barcoding is developing into an essential tool to quantify state shifts in global ecosystems. Current barcoding protocols often rely on short amplicon sequences, which yield accurate identification of biological entities in a community but provide limited phylogenetic resolution across broad taxonomic scales. However, the phylogenetic structure of communities is an essential component of biodiversity. Consequently, a barcoding approach is required that unites robust taxonomic assignment power and high phylogenetic utility. A possible solution is offered by sequencing long ribosomal DNA (rDNA) amplicons on the MinION platform (Oxford Nanopore Technologies). Findings Using a dataset of various animal and plant species, with a focus on arthropods, we assemble a pipeline for long rDNA barcode analysis and introduce a new software (MiniBar) to demultiplex dual indexed Nanopore reads. We find excellent phylogenetic and taxonomic resolution offered by long rDNA sequences across broad taxonomic scales. We highlight the simplicity of our approach by field barcoding with a miniaturized, mobile laboratory in a remote rainforest. We also test the utility of long rDNA amplicons for analysis of community diversity through metabarcoding and find that they recover highly skewed diversity estimates. Conclusions Sequencing dual indexed, long rDNA amplicons on the MinION platform is a straightforward, cost-effective, portable, and universal approach for eukaryote DNA barcoding. Although bulk community analyses using long-amplicon approaches may introduce biases, the long rDNA amplicons approach signifies a powerful tool for enabling the accurate recovery of taxonomic and phylogenetic diversity across biological communities.

Cet article analyse les pratiques quotidiennes des habitants de Sarre, de Lorraine, du Luxembourg, de Rhénanie-Palatinat et de Wallonie effectuées dans les régions voisines. L’hypothèse est l’existence d’une réalité de vie transfrontalière dans la Grande Région à partir des pratiques transfrontalières de ses habitants. Dans une telle perspective socio-constructiviste, on ne demande pas ce qu'est la Grande Région SaarLorLux, mais comment elle est constituée ou comment elle se manifeste dans la vie quotidienne de ses habitants. Pour donner des éléments de réponse, seront analysées les pratiques transfrontalières les plus courantes, notamment le fait de faire des achats et du shopping, se détendre dans la nature/faire du tourisme, fréquenter des manifestations culturelles et rendre visite à des amis et à la famille. Les considérations se basent sur trois études empiriques récentes dans l’espace d'analyse, qui sont mises en rapport et contextualisées socio-culturellement et socio-économiquement dans le but de relever l'organisation spatiale, les motivations ainsi que d'autres facteurs contextuels des pratiques transfrontalières dans la Grande Région SaarLorLux. Dans cette approche, les flux de mobilité et les préférences spatiales sont reconstruits à partir des pratiques quotidiennes qui donnent un aperçu des réalités de vie transfrontalière dans la Grande Région SaarLorLux.

Dans les écoles secondaires, le conseil de coopération offre aussi aux élèves un espace pour exprimer leurs demandes et explorer, dans un processus démocratique, les potentiels d’amélioration pour la classe et l’école. Les supports ci-dessous vous aideront à préparer et à mener les réunions de manière autonome.

Avant de mettre en place le conseil de coopération dans une classe, il faut en préparer l’organisation, le contenu et la méthode. Cet article fournit des indications sur sa mise en place et propose des méthodes concrètes pour le mener à bien.

C’est la participation des citoyen(ne)s engagé(e)s qui fait vivre la démocratie. À cette fin, il est nécessaire de familiariser le plus tôt possible les enfants et les adolescents aux méthodes démocratiques. Le conseil de coopération est un outil d’éducation à la démocratie qui offre aux élèves de nombreuses possibilités pour expérimenter la participation et renforcer leurs compétences démocratiques.

A huge number of clinical studies and meta-analyses have shown that psychotherapy is effective on average. However, not every patient profits from psychotherapy and some patients even deteriorate in treatment. Due to this result and the restricted generalization of clinical studies to clinical practice, a more patient-focused research strategy has emerged. The question whether a particular treatment works for an individual case is the focus of this paradigm. The use of repeated assessments and the feedback of this information to therapists is a major ingredient of patient-focused research. Improving patient outcomes and reducing dropout rates by the use of psychometric feedback seems to be a promising path. Therapists seem to differ in the degree to which they make use of and profit from such feedback systems. This dissertation aims to better understand therapist differences in the context of patient-focused research and the impact of therapists on psychotherapy. Three different studies are included, which focus on different aspects within the field: Study I (Chapter 5) investigated how therapists use psychometric feedback in their work with patients and how much therapists differ in their usage. Data from 72 therapists treating 648 patients were analyzed. It could be shown that therapists used the psychometric feedback for most of their patients. Substantial variance in the use of feedback (between 27% and 52%) was attributable to therapists. Therapists were more likely to use feedback when they reported being satisfied with the graphical information they received. The results therefore indicated that not only patient characteristics or treatment progress affected the use of feedback. Study II (Chapter 6) picked up on the idea of analyzing systematic differences in therapists and applied it to the criterion of premature treatment termination (dropout). To answer the question whether therapist effects occur in terms of patients’ dropout rates, data from 707 patients treated by 66 therapists were investigated. It was shown that approximately six percent of variance in dropout rates could be attributed to therapists, even when initial impairment was controlled for. Other predictors of dropout were initial impairment, sex, education, personality styles, and treatment expectations. Study III (Chapter 7) extends the dissertation by investigating the impact of a transfer from one therapist to another within ongoing treatments. Data from 124 patients who agreed to and experienced a transfer during their treatment were analyzed. A significant drop in patient-rated as well as therapist-rated alliance levels could be observed after a transfer. On average, there seemed to be no difficulties establishing a good therapeutic alliance with the new therapist, although differences between patients were observed. There was no increase in symptom severity due to therapy transfer. Various predictors of alliance and symptom development after transfer were investigated. Impacts on clinical practice were discussed. Results of the three studies are discussed and general conclusions are drawn. Implications for future research as well as their utility for clinical practice and decision-making are presented.

Die Praxishefte Demokratische Schulkultur erscheinen halbjährlich und bieten Schulleitungen und Schulpersonal theoretische Grundlagen und praxisorientierte Anleitungen zur demokratiepädagogischen Schulentwicklung. Jedes Themenheft ist jeweils einer demokratiepädagogischen Bauform oder strategischen Frage der Schulentwicklung gewidmet. Die Praxishefte werden allen Luxemburger Schulen als Printausgabe zur Verfügung gestellt und online mit zusätzlichen Materialien und in französischer Fassung vorgehalten.

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.