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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.
This dissertation deals with consistent estimates in household surveys. Household surveys are often drawn via cluster sampling, with households sampled at the first stage and persons selected at the second stage. The collected data provide information for estimation at both the person and the household level. However, consistent estimates are desirable in the sense that the estimated household-level totals should coincide with the estimated totals obtained at the person-level. Current practice in statistical offices is to use integrated weighting. In this approach consistent estimates are guaranteed by equal weights for all persons within a household and the household itself. However, due to the forced equality of weights, the individual patterns of persons are lost and the heterogeneity within households is not taken into account. In order to avoid the negative consequences of integrated weighting, we propose alternative weighting methods in the first part of this dissertation that ensure both consistent estimates and individual person weights within a household. The underlying idea is to limit the consistency conditions to variables that emerge in both the personal and household data sets. These common variables are included in the person- and household-level estimator as additional auxiliary variables. This achieves consistency more directly and only for the relevant variables, rather than indirectly by forcing equal weights on all persons within a household. Further decisive advantages of the proposed alternative weighting methods are that original individual rather than the constructed aggregated auxiliaries are utilized and that the variable selection process is more flexible because different auxiliary variables can be incorporated in the person-level estimator than in the household-level estimator.
In the second part of this dissertation, the variances of a person-level GREG estimator and an integrated estimator are compared in order to quantify the effects of the consistency requirements in the integrated weighting approach. One of the challenges is that the estimators to be compared are of different dimensions. The proposed solution is to decompose the variance of the integrated estimator into the variance of a reduced GREG estimator, whose underlying model is of the same dimensions as the person-level GREG estimator, and add a constructed term that captures the effects disregarded by the reduced model. Subsequently, further fields of application for the derived decomposition are proposed such as the variable selection process in the field of econometrics or survey statistics.
Nonlocal operators are used in a wide variety of models and applications due to many natural phenomena being driven by nonlocal dynamics. Nonlocal operators are integral operators allowing for interactions between two distinct points in space. The nonlocal models investigated in this thesis involve kernels that are assumed to have a finite range of nonlocal interactions. Kernels of this type are used in nonlocal elasticity and convection-diffusion models as well as finance and image analysis. Also within the mathematical theory they arouse great interest, as they are asymptotically related to fractional and classical differential equations.
The results in this thesis can be grouped according to the following three aspects: modeling and analysis, discretization and optimization.
Mathematical models demonstrate their true usefulness when put into numerical practice. For computational purposes, it is important that the support of the kernel is clearly determined. Therefore nonlocal interactions are typically assumed to occur within an Euclidean ball of finite radius. In this thesis we consider more general interaction sets including norm induced balls as special cases and extend established results about well-posedness and asymptotic limits.
The discretization of integral equations is a challenging endeavor. Especially kernels which are truncated by Euclidean balls require carefully designed quadrature rules for the implementation of efficient finite element codes. In this thesis we investigate the computational benefits of polyhedral interaction sets as well as geometrically approximated interaction sets. In addition to that we outline the computational advantages of sufficiently structured problem settings.
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive the shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.
Der vorliegende Sammelband geht auf die UniGR-Fachtagung Edu.GR - Europa leben lernen / Edu.GR - Apprendre à vivre l’Europe zurück, die am 20. September 2018 an der Universität Trier stattfand. Die Beiträge befassen sich aus unterschiedlichen Perspektiven – so aus Sicht der Bildungswissenschaften, der Fachdidaktiken, der Sozialwissenschaften und der Bildungspraxis – mit der Frage der Gestaltung Europas am Beispiel der Großregion. Vorgestellt und diskutiert werden neben Konzepten transnationaler Bildung auch empirische Analysen des Denkens und Handelns der Beteiligten in grenzregionalen (Aus-)Bildungskontexten sowie ausgewählte Beispiele transnationaler Bildungspraxis.
Petits pays ayant d’importants besoins de main-d’œuvre, le Luxembourg et la Suisse attirent tous deux un grand nombre de travailleurs frontaliers. C’est dans une perspective comparative que les 19 auteurs impliqués dans ce Cahier Thématique analysent la situation des travailleurs frontaliers dans les principaux pôles d’emploi transfrontaliers (Luxembourg, Bâle, Genève), mais également au Tessin. En tenant compte des éléments contextuels et méthodologiques, géographes, économistes, sociologues et politologues se focalisent sur les questions d’emploi, le quotidien transfrontalier et les perceptions des frontaliers par la société. Cette approche collective et pluridisciplinaire est résumée par les éditeurs en identifiant des enjeux communs pour le Luxembourg et la Suisse.
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.
Rückkehrprozesse aus Genderperspektive: remigrierte (Spät-)Aussiedler-Ehepaare in Westsibirien
(2019)
Die Studie untersucht die Rückkehrprozesse von (Spät-)Aussiedler-Ehepaaren aus Deutschland nach Westsibirien. Ein besonderes Augenmerk wird auf die Sichtweisen der Frauen und Männer hinsichtlich ihrer gemachten Erfahrung der Remigration gelegt. Darüber hinaus analysiert die Studie einerseits die Gemeinsamkeiten und Unterschiede beider Geschlechter im Hinblick auf die Rückkehrmotive, die Zufriedenheit mit der Wiederanpassung in Russland sowie die Einstellung hinsichtlich einer erneuten Migration nach Deutschland. Andererseits fokussiert die Arbeit auf die Geschlechterverhältnisse unter den Ehegatten im Prozess der Entscheidungsfindung zur Remigration. Die Studie folgt einem qualitativen methodischen Ansatz und verbindet verschiedene Forschungsrichtungen, genauer (Re)Migrations-, Familien-, (Spät-)AussiedlerInnen- und Geschlechterforschung.
Heimatfabrik Lokalmuseum bietet einen neuen Blick auf lokal verankerte Museen. Anhand von ausgewählten Fallbeispielen, die durch eine quantitative Untersuchung von etwa 370 Museen im Großherzogtum Luxemburg und in der belgischen Region Wallonien ergänzt werden, analysiert die Autorin, welche Identifikationsangebote bäuerliche Alltagsmuseen, Stadtmuseen, Industriemuseen, Kriegsmuseen und Auswanderermuseen ihren Besuchern bieten. Wen schließen die Museumsverantwortlichen durch ihre Erzählweisen ein und wen grenzen sie aus? Wie gehen sie mit sprachlichen, konfessionellen, kulturellen, sexuellen und soziale Minderheiten um?
Das Buch beginnt mit der Klärung der Frage, wie sich das Heimatverständnis in Luxemburg in Luxemburg und im angrenzenden Wallonien im Spannungsfeld zwischen dem klassischen Heimatbegriff des deutschsprachigen Raums und der Inwertsetzung der Landschaft durch die französischen Humangeographen seit der Mitte des 19. Jahrhunderts entwickelt hat. Aus diesem unterschiedlichen Zugang zu dem was als enger Kreis des gesellschaftlichen Zusammenhalts empfunden wird, ergeben sich verschiedene Typen von lokalhistorischen Museen, die die Autorin in historischer Perspektive vorstellt.
Indem sie Dinge des Alltags durch die Aufnahme in ihre Sammlungen zu symbolischen Zeichenträgern einer Gesellschaft erheben sind Museen privilegierte Orte für die Schaffung von Heritage. Mit den Ausstellungen erzeugen die Museumsträger eine subjektiv empfundene gesellschaftliche Einheit, die von manchen Besucher als Heimat angenommen oder abgelehnt wird, andere wiederum gleichgültig lässt. Vor diesem Hintergrund dieser Feststellung beschäftigt sich die Autorin mit dem, was unter lokalem heritage zu verstehen ist und welcher gestalterischen Mittel sich die Verantwortlichen von lokalhistorischen Museen bedienen um ihre Vorstellung von Heimat zu konstruieren. Anhand der Themenbereiche bäuerlicher Alltag, Natur, Ein- und Auswanderung, Krieg sowie Industrie geht das Buch der Frage nach, wie interne und externe Museumsstakeholder das vom Museum vermittelte Heimatbild und damit verbunden auch die nationale Geschichtskultur mitbestimmen.
Das Buch möchte dazu beitragen, den Blick einer interessierten Öffentlichkeit für lokales Kulturerbe zu schulen sowie Historiker auf das Potenzial von lokalhistorischen Museen hinzuweisen. In diesem Sinne ist die Untersuchung auch ein Plädoyer für die Anerkennung der Besonderheit von außerakademischer historischer Aufarbeitung und für die Verstärkung der Zusammenarbeit zwischen universitärer und außeruniversitärer Forschung.
The World's second oldest system of judicial review of national legislation emerged through court practice from the very first years after the adoption of the Constitution of Norway in 1814. The review is exercised by the ordinary courts at all levels with the single Supreme Court as the last instance. No specialized constitutional court has been established. The independence of the judiciary is generally recognized as high. But what degree of legitimacy should judges appointed in order to ensure ordinary judicial business enjoy when exercising a basically political function like reviewing and possibly setting aside acts of Parliament?