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Institut
- Fachbereich 4 (13)
- Raum- und Umweltwissenschaften (6)
- Fachbereich 1 (4)
- Fachbereich 6 (4)
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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.
When do anorexic patients perceive their body as too fat? Aggravating and ameliorating factors
(2019)
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.
Finding behavioral parameterization for a 1-D water balance model by multi-criteria evaluation
(2019)
Evapotranspiration is often estimated by numerical simulation. However, to produce accurate simulations, these models usually require on-site measurements for parameterization or calibration. We have to make sure that the model realistically reproduces both, the temporal patterns of soil moisture and evapotranspiration. In this study, we combine three sources of information: (i) measurements of sap velocities; (ii) soil moisture; and (iii) expert knowledge on local runoff generation and water balance to define constraints for a “behavioral” forest stand water balance model. Aiming for a behavioral model, we adjusted soil moisture at saturation, bulk resistance parameters and the parameters of the water retention curve (WRC). We found that the shape of the WRC influences substantially the behavior of the simulation model. Here, only one model realization could be referred to as “behavioral”. All other realizations failed for a least one of our evaluation criteria: Not only transpiration and soil moisture are simulated consistently with our observations, but also total water balance and runoff generation processes. The introduction of a multi-criteria evaluation scheme for the detection of unrealistic outputs made it possible to identify a well performing parameter set. Our findings indicate that measurement of different fluxes and state variables instead of just one and expert knowledge concerning runoff generation facilitate the parameterization of a hydrological model.
This doctoral thesis includes five studies that deal with the topics work, well-being, and family formation, as well as their interaction. The studies aim to find answers to the following questions: Do workers’ personality traits determine whether they sort into jobs with performance appraisals? Does job insecurity result in lower quality and quantity of sleep? Do public smoking bans affect subjective well-being by changing individuals’ use of leisure time? Can risk preferences help to explain non-traditional family forms? And finally, are differences in out-of-partnership birth rates between East and West Germany driven by cultural characteristics that have evolved in the two separate politico-economic systems? To answer these questions, the following chapters use basic economic subjects such as working conditions, income, and time use, but also employ a range of sociological and psychological concepts such as personality traits and satisfaction measures. Furthermore, all five studies use data from the German Socio-Economic Panel (SOEP), a representative longitudinal panel of private households in Germany, and apply state-of-the-art microeconometric methods. The findings of this doctoral thesis are important for individuals, employers, and policymakers. Workers and employers benefit from knowing the determinants of occupational sorting, as vacancies can be filled more accurately. Moreover, knowing which job-related problems lead to lower well-being and potentially higher sickness absence likely increases efficiency in the workplace. The research on smoking bans and family formation in chapters 4, 5, and 6 is particularly interesting for policymakers. The results on the effects of smoking bans on subjective well-being presented in chapter 4 suggest that the impacts of tobacco control policies could be weighed more carefully. Additionally, understanding why women are willing to take the risks associated with single motherhood can help to improve policies targeting single mothers.
Background: Increasing exposure to engineered inorganic nanoparticles takes actually place in both terrestric and aquatic ecosystems worldwide. Although we already know harmful effects of AgNP on the soil bacterial community, information about the impact of the factors functionalization, concentration, exposure time, and soil texture on the AgNP effect expression are still rare. Hence, in this study, three soils of different grain size were exposed for up to 90 days to bare and functionalized AgNP in concentrations ranging from 0.01 to 1.00 mg/kg soil dry weight. Effects on soil microbial community were quantified by various biological parameters, including 16S rRNA gene, photometric, and fluorescence analyses.
Results: Multivariate data analysis revealed significant effects of AgNP exposure for all factors and factor combinations investigated. Analysis of individual factors (silver species, concentration, exposure time, soil texture) in the unifactorial ANOVA explained the largest part of the variance compared to the error variance. In depth analysis of factor combinations revealed even better explanation of variance. For the biological parameters assessed in this study, the matching of soil texture and silver species, and the matching of soil texture and exposure time were the two most relevant factor combinations. The factor AgNP concentration contributed to a lower extent to the effect expression compared to silver species, exposure time and physico–chemical composition of soil.
Conclusions: The factors functionalization, concentration, exposure time, and soil texture significantly impacted the effect expression of AgNP on the soil microbial community. Especially long-term exposure scenarios are strongly needed for the reliable environmental impact assessment of AgNP exposure in various soil types.
Entrepreneurial ventures are associated with economic growth, job creation, and innovation. Most entrepreneurial ventures need external funding to succeed. However, they often find it difficult to access traditional forms of financing, such as bank loans. To overcome this hurdle and to provide entrepreneurial ventures with badly-needed external capital, many types of entrepreneurial finance have emerged over the past decades and continue to emerge today. Inspired by these dynamics, this postdoctoral thesis contains five empirical studies that address novel questions regarding established (e.g., venture capital, business angels) and new types of entrepreneurial finance (i.e., initial coin offerings).
Because EU water quality policy can result in infrastructure creation or adaptation at the local level across member states, compliance cases are worth examining critically from a sustainable spatial planning perspective. In this study, the 2000 EU Water Framework Directive’s (WFD) reach to local implementation efforts in average towns and cities is shown through the case study of nonconforming household wastewater infrastructure in the German state of Rhineland Palatinate. Seeing wastewater as a socio-technical infrastructure, we ask how the WFD implementation can be understood in the context of local infrastructure development, sustainability, and spatial planning concepts. In particular, this study examines what compliance meant for the centralization or decentralization of local wastewater infrastructure systems—and the sustainability implications for cities
from those choices.
Abstract: Thermal infrared (TIR) multi-/hyperspectral and sun-induced fluorescence (SIF) approaches together with classic solar-reflective (visible, near-, and shortwave infrared reflectance (VNIR)/SWIR) hyperspectral remote sensing form the latest state-of-the-art techniques for the detection of crop water stress. Each of these three domains requires dedicated sensor technology currently in place for ground and airborne applications and either have satellite concepts under development (e.g., HySPIRI/SBG (Surface Biology and Geology), Sentinel-8, HiTeSEM in the TIR) or are subject to satellite missions recently launched or scheduled within the next years (i.e., EnMAP and PRISMA (PRecursore IperSpettrale della Missione Applicativa, launched on March 2019) in the VNIR/SWIR, Fluorescence Explorer (FLEX) in the SIF). Identification of plant water stress or drought is of utmost importance to guarantee global water and food supply. Therefore, knowledge of crop water status over large farmland areas bears large potential for optimizing agricultural water use. As plant responses to water stress are numerous and complex, their physiological consequences affect the electromagnetic signal in different spectral domains. This review paper summarizes the importance of water stress-related applications and the plant responses to water stress, followed by a concise review of water-stress detection through remote sensing, focusing on TIR without neglecting the comparison to other spectral domains (i.e., VNIR/SWIR and SIF) and multi-sensor approaches. Current and planned sensors at ground, airborne, and satellite level for the TIR as well as a selection of commonly used indices and approaches for water-stress detection using the main multi-/hyperspectral remote sensing imaging techniques are reviewed. Several important challenges are discussed that occur when using spectral emissivity, temperature-based indices, and physically-based approaches for water-stress detection in the TIR spectral domain. Furthermore, challenges with data processing and the perspectives for future satellite missions in the TIR are critically examined. In conclusion, information from multi-/hyperspectral TIR together with those from VNIR/SWIR and SIF sensors within a multi-sensor approach can provide profound insights to actual plant (water) status and the rationale of physiological and biochemical changes. Synergistic sensor use will open new avenues for scientists to study plant functioning and the response to environmental stress in a wide range of ecosystems.
In order to discuss potential sustainability issues of expanding silage maize cultivation in Rhineland-Palatinate, spatially explicit monitoring is necessary. Publicly available statistical records are often not a sufficient basis for extensive research, especially on soil health, where risk factors like erosion and compaction depend on variables that are specific to every site, and hard to generalize for larger administrative aggregates. The focus of this study is to apply established classification algorithms to estimate maize abundance for each independent pixel, while at the same time accounting for their spatial relationship. Therefore, two ways to incorporate spatial autocorrelation of neighboring pixels are combined with three different classification models. The performance of each of these modeling approaches is analyzed and discussed. Finally, one prediction approach is applied to the imagery, and the overall predicted acreage is compared to publicly available data. We were able to show that Support Vector Machine (SVM) classification and Random Forests (RF) were able to distinguish maize pixels reliably, with kappa values well above 0.9 in most cases. The Generalized Linear Model (GLM) performed substantially worse. Furthermore, Regression Kriging (RK) as an approach to integrate spatial autocorrelation into the prediction model is not suitable in use cases with millions of sparsely clustered training pixels. Gaussian Blur is able to improve predictions slightly in these cases, but it is possible that this is only because it smoothes out impurities of the reference data. The overall prediction with RF classification combined with Gaussian Blur performed well, with out of bag error rates of 0.5% in 2009 and 1.3% in 2016. Despite the low error rates, there is a discrepancy between the predicted acreage and the official records, which is 20% in 2009 and 27% in 2016.
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.
With two-thirds to three-quarters of all companies, family firms are the most common firm type worldwide and employ around 60 percent of all employees, making them of considerable importance for almost all economies. Despite this high practical relevance, academic research took notice of family firms as intriguing research subjects comparatively late. However, the field of family business research has grown eminently over the past two decades and has established itself as a mature research field with a broad thematic scope. In addition to questions relating to corporate governance, family firm succession and the consideration of entrepreneurial families themselves, researchers mainly focused on the impact of family involvement in firms on their financial performance and firm strategy. This dissertation examines the financial performance and capital structure of family firms in various meta-analytical studies. Meta-analysis is a suitable method for summarizing existing empirical findings of a research field as well as identifying relevant moderators of a relationship of interest.
First, the dissertation examines the question whether family firms show better financial performance than non-family firms. A replication and extension of the study by O’Boyle et al. (2012) based on 1,095 primary studies reveals a slightly better performance of family firms compared to non-family firms. Investigating the moderating impact of methodological choices in primary studies, the results show that outperformance holds mainly for large and publicly listed firms and with regard to accounting-based performance measures. Concerning country culture, family firms show better performance in individualistic countries and countries with a low power distance.
Furthermore, this dissertation investigates the sensitivity of family firm performance with regard to business cycle fluctuations. Family firms show a pro-cyclical performance pattern, i.e. their relative financial performance compared to non-family firms is better in economically good times. This effect is particularly pronounced in Anglo-American countries and emerging markets.
In the next step, a meta-analytic structural equation model (MASEM) is used to examine the market valuation of public family firms. In this model, profitability and firm strategic choices are used as mediators. On the one hand, family firm status itself does not have an impact on firms‘ market value. On the other hand, this study finds a positive indirect effect via higher profitability levels and a negative indirect effect via lower R&D intensity. A split consideration of family ownership and management shows that these two effects are mainly driven by family ownership, while family management results in less diversification and internationalization.
Finally, the dissertation examines the capital structure of public family firms. Univariate meta-analyses indicate on average lower leverage ratios in family firms compared to non-family firms. However, there is significant heterogeneity in mean effect sizes across the 45 countries included in the study. The results of a meta-regression reveal that family firms use leverage strategically to secure their controlling position in the firm. While strong creditor protection leads to lower leverage ratios in family firms, strong shareholder protection has the opposite effect.
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.
A satellite-based climatology of wind-induced surface temperature anomalies for the Antarctic
(2019)
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.
Understanding the mechanisms that shape access to the fisheries ecosystem service in Tsokomey, Accra
(2019)
Questions of access to ecosystem services remain largely unaddressed. Yet, in the coming decades, addressing access to services and securing them for livelihoods and well-being of people will likely gain importance, especially to guide according policies at the local scale. Through a qualitative approach, this paper addresses the mechanisms that shape access to the fisheries eco- system service in Accra, Ghana. The analysis uses a framework that focuses on access to land, tools and technology, knowledge and information, capital and credit, as well as labor. This research reveals how access is organized across the different categories of this framework and how people’s well-being is shaped. Moreover, it helps to further our understanding of what regulates the access to ecosystem services and how to address future shocks and capacity in terms of production of ecosystem services.
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.
Die vorgelegte Dissertation trägt den Titel Regularization Methods for Statistical Modelling in Small Area Estimation. In ihr wird die Verwendung regularisierter Regressionstechniken zur geographisch oder kontextuell hochauflösenden Schätzung aggregatspezifischer Kennzahlen auf Basis kleiner Stichproben studiert. Letzteres wird in der Fachliteratur häufig unter dem Begriff Small Area Estimation betrachtet. Der Kern der Arbeit besteht darin die Effekte von regularisierter Parameterschätzung in Regressionsmodellen, welche gängiger Weise für Small Area Estimation verwendet werden, zu analysieren. Dabei erfolgt die Analyse primär auf theoretischer Ebene, indem die statistischen Eigenschaften dieser Schätzverfahren mathematisch charakterisiert und bewiesen werden. Darüber hinaus werden die Ergebnisse durch numerische Simulationen veranschaulicht, und vor dem Hintergrund empirischer Anwendungen kritisch verortet. Die Dissertation ist in drei Bereiche gegliedert. Jeder Bereich behandelt ein individuelles methodisches Problem im Kontext von Small Area Estimation, welches durch die Verwendung regularisierter Schätzverfahren gelöst werden kann. Im Folgenden wird jedes Problem kurz vorgestellt und im Zuge dessen der Nutzen von Regularisierung erläutert.
Das erste Problem ist Small Area Estimation in der Gegenwart unbeobachteter Messfehler. In Regressionsmodellen werden typischerweise endogene Variablen auf Basis statistisch verwandter exogener Variablen beschrieben. Für eine solche Beschreibung wird ein funktionaler Zusammenhang zwischen den Variablen postuliert, welcher durch ein Set von Modellparametern charakterisiert ist. Dieses Set muss auf Basis von beobachteten Realisationen der jeweiligen Variablen geschätzt werden. Sind die Beobachtungen jedoch durch Messfehler verfälscht, dann liefert der Schätzprozess verzerrte Ergebnisse. Wird anschließend Small Area Estimation betrieben, so sind die geschätzten Kennzahlen nicht verlässlich. In der Fachliteratur existieren hierfür methodische Anpassungen, welche in der Regel aber restriktive Annahmen hinsichtlich der Messfehlerverteilung benötigen. Im Rahmen der Dissertation wird bewiesen, dass Regularisierung in diesem Kontext einer gegen Messfehler robusten Schätzung entspricht - und zwar ungeachtet der Messfehlerverteilung. Diese Äquivalenz wird anschließend verwendet, um robuste Varianten bekannter Small Area Modelle herzuleiten. Für jedes Modell wird ein Algorithmus zur robusten Parameterschätzung konstruiert. Darüber hinaus wird ein neuer Ansatz entwickelt, welcher die Unsicherheit von Small Area Schätzwerten in der Gegenwart unbeobachteter Messfehler quantifiziert. Es wird zusätzlich gezeigt, dass diese Form der robusten Schätzung die wünschenswerte Eigenschaft der statistischen Konsistenz aufweist.
Das zweite Problem ist Small Area Estimation anhand von Datensätzen, welche Hilfsvariablen mit unterschiedlicher Auflösung enthalten. Regressionsmodelle für Small Area Estimation werden normalerweise entweder für personenbezogene Beobachtungen (Unit-Level), oder für aggregatsbezogene Beobachtungen (Area-Level) spezifiziert. Doch vor dem Hintergrund der stetig wachsenden Datenverfügbarkeit gibt es immer häufiger Situationen, in welchen Daten auf beiden Ebenen vorliegen. Dies beinhaltet ein großes Potenzial für Small Area Estimation, da somit neue Multi-Level Modelle mit großem Erklärungsgehalt konstruiert werden können. Allerdings ist die Verbindung der Ebenen aus methodischer Sicht kompliziert. Zentrale Schritte des Inferenzschlusses, wie etwa Variablenselektion und Parameterschätzung, müssen auf beiden Levels gleichzeitig durchgeführt werden. Hierfür existieren in der Fachliteratur kaum allgemein anwendbare Methoden. In der Dissertation wird gezeigt, dass die Verwendung ebenenspezifischer Regularisierungsterme in der Modellierung diese Probleme löst. Es wird ein neuer Algorithmus für stochastischen Gradientenabstieg zur Parameterschätzung entwickelt, welcher die Informationen von allen Ebenen effizient unter adaptiver Regularisierung nutzt. Darüber hinaus werden parametrische Verfahren zur Abschätzung der Unsicherheit für Schätzwerte vorgestellt, welche durch dieses Verfahren erzeugt wurden. Daran anknüpfend wird bewiesen, dass der entwickelte Ansatz bei adäquatem Regularisierungsterm sowohl in der Schätzung als auch in der Variablenselektion konsistent ist.
Das dritte Problem ist Small Area Estimation von Anteilswerten unter starken verteilungsbezogenen Abhängigkeiten innerhalb der Kovariaten. Solche Abhängigkeiten liegen vor, wenn eine exogene Variable durch eine lineare Transformation einer anderen exogenen Variablen darstellbar ist (Multikollinearität). In der Fachliteratur werden hierunter aber auch Situationen verstanden, in welchen mehrere Kovariate stark korreliert sind (Quasi-Multikollinearität). Wird auf einer solchen Datenbasis ein Regressionsmodell spezifiziert, dann können die individuellen Beiträge der exogenen Variablen zur funktionalen Beschreibung der endogenen Variablen nicht identifiziert werden. Die Parameterschätzung ist demnach mit großer Unsicherheit verbunden und resultierende Small Area Schätzwerte sind ungenau. Der Effekt ist besonders stark, wenn die zu modellierende Größe nicht-linear ist, wie etwa ein Anteilswert. Dies rührt daher, dass die zugrundeliegende Likelihood-Funktion nicht mehr geschlossen darstellbar ist und approximiert werden muss. Im Rahmen der Dissertation wird gezeigt, dass die Verwendung einer L2-Regularisierung den Schätzprozess in diesem Kontext signifikant stabilisiert. Am Beispiel von zwei nicht-linearen Small Area Modellen wird ein neuer Algorithmus entwickelt, welche den bereits bekannten Quasi-Likelihood Ansatz (basierend auf der Laplace-Approximation) durch Regularisierung erweitert und verbessert. Zusätzlich werden parametrische Verfahren zur Unsicherheitsmessung für auf diese Weise erhaltene Schätzwerte beschrieben.
Vor dem Hintergrund der theoretischen und numerischen Ergebnisse wird in der Dissertation demonstriert, dass Regularisierungsmethoden eine wertvolle Ergänzung der Fachliteratur für Small Area Estimation darstellen. Die hier entwickelten Verfahren sind robust und vielseitig einsetzbar, was sie zu hilfreichen Werkzeugen der empirischen Datenanalyse macht.
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.
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.
Hypothalamic-pituitary-adrenal (HPA) axis-related genetic variants influence the stress response
(2019)
The physiological stress system includes the hypothalamic-pituitary-adrenal (HPA) axis and the sympathetic-adrenal-medullary system (SAM). Parameters representing these systems such as cortisol, blood pressure or heart rate define the physiological reaction in response to a stressor. The main objective of the studies described in this thesis was to understand the role of the HPA-related genetic factors in these two systems. Genetic factors represent one of the components causing individual variations in physiological stress parameters. Five genes involved in the functioning of the HPA axis regarding stress responses are examined in this thesis. They are: corticotropin-releasing hormone (CRH), the glucocorticoid receptor (GR), the mineralocorticoid receptor (MR), the 5-hydroxytryptamine-transporter-linked polymorphic region (5-HTTLPR) in the serotonin transporter (5-HTT) and the brain-derived neurotrophic factor (BDNF) gene. Two hundred thirty-two healthy participants were genotyped. The influence of genetic factors on physiological parameters, such as post-awakening cortisol and blood pressure was assessed, as well as the influence of genetic factors on stress reactivity in response to a socially evaluated cold pressor test (SeCPT). Three studies tested the HPA-related genes each on three different levels. The first study examined the influences of genotypes and haplotypes of these five genes on physiological as well as psychological stress indicators (Chapter 2). The second study examined the effects of GR variants (genotypes and haplotypes) and promoter methylation level on both the SAM system and the HPA axis stress reactivity (Chapter 3). The third study comprised the characterization of CRH promoter haplotypes in an in-vitro study and the association of the CRH promoter with stress indicators in vivo (Chapter 4).
Computer simulation has become established in a two-fold way: As a tool for planning, analyzing, and optimizing complex systems but also as a method for the scientific instigation of theories and thus for the generation of knowledge. Generated results often serve as a basis for investment decisions, e.g., road construction and factory planning, or provide evidence for scientific theory-building processes. To ensure the generation of credible and reproducible results, it is indispensable to conduct systematic and methodologically sound simulation studies. A variety of procedure models exist that structure and predetermine the process of a study. As a result, experimenters are often required to repetitively but thoroughly carry out a large number of experiments. Moreover, the process is not sufficiently specified and many important design decisions still have to be made by the experimenter, which might result in an unintentional bias of the results.
To facilitate the conducting of simulation studies and to improve both replicability and reproducibility of the generated results, this thesis proposes a procedure model for carrying out Hypothesis-Driven Simulation Studies, an approach that assists the experimenter during the design, execution, and analysis of simulation experiments. In contrast to existing approaches, a formally specified hypothesis becomes the key element of the study so that each step of the study can be adapted and executed to directly contribute to the verification of the hypothesis. To this end, the FITS language is presented, which enables the specification of hypotheses as assumptions regarding the influence specific input values have on the observable behavior of the model. The proposed procedure model systematically designs relevant simulation experiments, runs, and iterations that must be executed to provide evidence for the verification of the hypothesis. Generated outputs are then aggregated for each defined performance measure to allow for the application of statistical hypothesis testing approaches. Hence, the proposed assistance only requires the experimenter to provide an executable simulation model and a corresponding hypothesis to conduct a sound simulation study. With respect to the implementation of the proposed assistance system, this thesis presents an abstract architecture and provides formal specifications of all required services.
To evaluate the concept of Hypothesis-Driven Simulation Studies, two case studies are presented from the manufacturing domain. The introduced approach is applied to a NetLogo simulation model of a four-tiered supply chain. Two scenarios as well as corresponding assumptions about the model behavior are presented to investigate conditions for the occurrence of the bullwhip effect. Starting from the formal specification of the hypothesis, each step of a Hypothesis-Driven Simulation Study is presented in detail, with specific design decisions outlined, and generated inter- mediate data as well as final results illustrated. With respect to the comparability of the results, a conventional simulation study is conducted which serves as reference data. The approach that is proposed in this thesis is beneficial for both practitioners and scientists. The presented assistance system allows for a more effortless and simplified execution of simulation experiments while the efficient generation of credible results is ensured.