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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.
Harvesting of silage maize in late autumn on waterlogged soils may result in several ecological problems such as soil compaction and may subsequently be a major threat to soil fertility in Europe. It was hypothesized that perennial energy crops might reduce the vulnerability for soil compaction through earlier harvest dates and improved soil stability. However, the performance of such crops to be grown on soil that are periodically waterlogged and implications for soil chemical and microbial properties are currently an open issue. Within the framework of a two-year pot experiment we investigated the potential of the cup plant (Silphium perfoliatum L.), Jerusalem artichoke (Helianthus tuberosus), giant knotweed (Fallopia japonicum X bohemica), tall wheatgrass (Agropyron elongatum), and reed canary grass (Phalaris arundinacea) for cultivation under periodically waterlogged soil conditions during the winter half year and implications for soil chemical and biological properties. Examined perennial energy crops coped with periodical waterlogging and showed yields 50% to 150% higher than in the control which was never faced with waterlogging. Root formation was similar in waterlogged and non-waterlogged soil layers. Soil chemical and microbial properties clearly responded to different soil moisture treatments. For example, dehydrogenase activity was two to four times higher in the periodically waterlogged treatment compared to the control. Despite waterlogging, aerobic microbial activity was significantly elevated indicating morphological and metabolic adaptation of the perennial crops to withstand waterlogged conditions. Thus, our results reveal first evidence of a site-adapted biomass production on periodical waterlogged soils through the cultivation of perennial energy crops and for intense plant microbe interactions.
Partizipativer Unterricht, der nicht nur aus punktuell erlebter Teilnahme besteht, ist — wie Charlotte Keuler es im Leitartikel des vorliegenden Heftes formuliert — durch die Herausforderungen, vor die uns unsere globalisierte Welt stellt, in vielerlei Hinsicht unabdingbar geworden. Kommunikationsfähigkeit, interkulturelle Kompetenz, Wissensmanagement und andere oft zitierte „soft skills“ sind Schlüsselkompetenzen des 21. Jahrhunderts.
In der Vorrede zur ersten Auflage von Die Welt als Wille und Vorstellung legt Arthur Schopenhauer dem Leser seines Werkes seine Absicht nahe, welche in der Mitteilung eines „einzigen Gedankens“ besteht. Doch dieser mitzuteilende Gedanke wird an keiner Stelle des Werkes explizit und direkt als solchen von Schopenhauer ausgesprochen und genannt. Dies gibt bis heute in der Schopenhauer-Forschung Anlass zu kontroversen Auseinandersetzungen: Wie lautet Schopenhauers „einziger Gedanke“? Wo befindet er sich konkret? Und ist er überhaupt mitteilbar?
Trotz zahlreicher Forschungsarbeiten zur Thematik des „einzigen Gedankens“ wurde bisher der Einfluss der indischen Philosophie, genauer des Oupnek’hat, vernachlässigt, obwohl genauestens nachgewiesen und nachgezeichnet werden kann, mit welchen Quellen sich Schopenhauer zum Zeitpunkt der Entstehung seiner Philosophie intensiv beschäftigt hat. Auch verweist er selbst immer wieder auf bestimmte Stellen aus dem Oupnek’hat und zitiert Passagen an ganz wesentlichen Stellen in seinem Werk.
Um den „einzigen Gedanken“ im Werk Schopenhauers erfassen zu können, reicht es nicht aus, nur vom Hauptwerk selbst auszugehen, sondern es müssen ebenfalls die Jahre und Schriften während der Entstehung seiner Philosophie bis zum Hauptwerk berücksichtigt werden, und damit verbunden auch die Quellen, die Schopenhauer beeinflusst haben, wozu insbesondere das Oupnek’hat samt seinen eigenen Randnotizen gehört.
Our goal is to approximate energy forms on suitable fractals by discrete graph energies and certain metric measure spaces, using the notion of quasi-unitary equivalence. Quasi-unitary equivalence generalises the two concepts of unitary equivalence and norm resolvent convergence to the case of operators and energy forms defined in varying Hilbert spaces.
More precisely, we prove that the canonical sequence of discrete graph energies (associated with the fractal energy form) converges to the energy form (induced by a resistance form) on a finitely ramified fractal in the sense of quasi-unitary equivalence. Moreover, we allow a perturbation by magnetic potentials and we specify the corresponding errors.
This aforementioned approach is an approximation of the fractal from within (by an increasing sequence of finitely many points). The natural step that follows this realisation is the question whether one can also approximate fractals from outside, i.e., by a suitable sequence of shrinking supersets. We partly answer this question by restricting ourselves to a very specific structure of the approximating sets, namely so-called graph-like manifolds that respect the structure of the fractals resp. the underlying discrete graphs. Again, we show that the canonical (properly rescaled) energy forms on such a sequence of graph-like manifolds converge to the fractal energy form (in the sense of quasi-unitary equivalence).
From the quasi-unitary equivalence of energy forms, we conclude the convergence of the associated linear operators, convergence of the spectra and convergence of functions of the operators – thus essentially the same as in the case of the usual norm resolvent convergence.
Ziel der hier bereitgestellten Anforderungskataloge ist es, einen Überblick über die Anforderungen zu geben, welche an FDM-Services in den Geisteswissenschaften und in der Psychologie gestellt werden. Dies soll Hochschulen und außeruniversitären Forschungseinrichtungen die Möglichkeit geben, ihre eigenen Servicekataloge um FDM-Services zu erweitern, welche auf die spezifischen Bedarfe der Forschenden in diesen Disziplinen abgestimmt sind. Zudem sollen diese Anforderungskataloge als Vorlage für die Entwicklung weiterer Anforderungskataloge dienen, welche die fachspezifischen FDM-Services in anderen Fachdisziplinen spezifizieren.
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.
For grape canopy pixels captured by an unmanned aerial vehicle (UAV) tilt-mounted RedEdge-M multispectral sensor in a sloped vineyard, an in situ Walthall model can be established with purely image-based methods. This was derived from RedEdge-M directional reflectance and a vineyard 3D surface model generated from the same imagery. The model was used to correct the angular effects in the reflectance images to form normalized difference vegetation index (NDVI)orthomosaics of different view angles. The results showed that the effect could be corrected to a certain scope, but not completely. There are three drawbacks that might restrict a successful angular model construction and correction: (1) the observable micro shadow variation on the canopy enabled by the high resolution; (2) the complexity of vine canopies that causes an inconsistency between reflectance and canopy geometry, including effects such as micro shadows and near-infrared (NIR) additive effects; and (3) the resolution limit of a 3D model to represent the accurate real-world optical geometry. The conclusion is that grape canopies might be too inhomogeneous for the tested method to perform the angular correction in high quality.
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.