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Modern decision making in the digital age is highly driven by the massive amount of
data collected from different technologies and thus affects both individuals as well as
economic businesses. The benefit of using these data and turning them into knowledge
requires appropriate statistical models that describe the underlying observations well.
Imposing a certain parametric statistical model goes along with the need of finding
optimal parameters such that the model describes the data best. This often results in
challenging mathematical optimization problems with respect to the model’s parameters
which potentially involve covariance matrices. Positive definiteness of covariance matrices
is required for many advanced statistical models and these constraints must be imposed
for standard Euclidean nonlinear optimization methods which often results in a high
computational effort. As Riemannian optimization techniques proved efficient to handle
difficult matrix-valued geometric constraints, we consider optimization over the manifold
of positive definite matrices to estimate parameters of statistical models. The statistical
models treated in this thesis assume that the underlying data sets used for parameter
fitting have a clustering structure which results in complex optimization problems. This
motivates to use the intrinsic geometric structure of the parameter space. In this thesis,
we analyze the appropriateness of Riemannian optimization over the manifold of positive
definite matrices on two advanced statistical models. We establish important problem-
specific Riemannian characteristics of the two problems and demonstrate the importance
of exploiting the Riemannian geometry of covariance matrices based on numerical studies.
Even though proper research on Cauchy transforms has been done, there are still a lot of open questions. For example, in the case of representation theorems, i.e. the question when a function can be represented as a Cauchy transform, there is 'still no completely satisfactory answer' ([9], p. 84). There are characterizations for measures on the circle as presented in the monograph [7] and for general compactly supported measures on the complex plane as presented in [27]. However, there seems to exist no systematic treatise of the Cauchy transform as an operator on $L_p$ spaces and weighted $L_p$ spaces on the real axis.
This is the point where this thesis draws on and we are interested in developing several characterizations for the representability of a function by Cauchy transforms of $L_p$ functions. Moreover, we will attack the issue of integrability of Cauchy transforms of functions and measures, a topic which is only partly explored (see [43]). We will develop different approaches involving Fourier transforms and potential theory and investigate into sufficient conditions and characterizations.
For our purposes, we shall need some notation and the concept of Hardy spaces which will be part of the preliminary Chapter 1. Moreover, we introduce Fourier transforms and their complex analogue, namely Fourier-Laplace transforms. This will be of extraordinary usage due to the close connection of Cauchy and Fourier(-Laplace) transforms.
In the second chapter we shall begin our research with a discussion of the Cauchy transformation on the classical (unweighted) $L_p$ spaces. Therefore, we start with the boundary behavior of Cauchy transforms including an adapted version of the Sokhotski-Plemelj formula. This result will turn out helpful for the determination of the image of the Cauchy transformation under $L_p(\R)$ for $p\in(1,\infty).$ The cases $p=1$ and $p=\infty$ are playing special roles here which justifies a treatise in separate sections. For $p=1$ we will involve the real Hardy space $H_{1}(\R)$ whereas the case $p=\infty$ shall be attacked by an approach incorporating intersections of Hardy spaces and certain subspaces of $L_{\infty}(\R).$
The third chapter prepares ourselves for the study of the Cauchy transformation on subspaces of $L_{p}(\R).$ We shall give a short overview of the basic facts about Cauchy transforms of measures and then proceed to Cauchy transforms of functions with support in a closed set $X\subset\R.$ Our goal is to build up the main theory on which we can fall back in the subsequent chapters.
The fourth chapter deals with Cauchy transforms of functions and measures supported by an unbounded interval which is not the entire real axis. For convenience we restrict ourselves to the interval $[0,\infty).$ Bringing once again the Fourier-Laplace transform into play, we deduce complex characterizations for the Cauchy transforms of functions in $L_{2}(0,\infty).$ Moreover, we analyze the behavior of Cauchy transform on several half-planes and shall use these results for a fairly general geometric characterization. In the second section of this chapter, we focus on Cauchy transforms of measures with support in $[0,\infty).$ In this context, we shall derive a reconstruction formula for these Cauchy transforms holding under pretty general conditions as well as results on the behaviur on the left half-plane. We close this chapter by rather technical real-type conditions and characterizations for Cauchy transforms of functions in $L_p(0,\infty)$ basing on an approach in [82].
The most common case of Cauchy transforms, those of compactly supported functions or measures, is the subject of Chapter 5. After complex and geometric characterizations originating from similar ideas as in the fourth chapter, we adapt a functional-analytic approach in [27] to special measures, namely those with densities to a given complex measure $\mu.$ The chapter is closed with a study of the Cauchy transformation on weighted $L_p$ spaces. Here, we choose an ansatz through the finite Hilbert transform on $(-1,1).$
The sixth chapter is devoted to the issue of integrability of Cauchy transforms. Since this topic has no comprehensive treatise in literature yet, we start with an introduction of weighted Bergman spaces and general results on the interaction of the Cauchy transformation in these spaces. Afterwards, we combine the theory of Zen spaces with Cauchy transforms by using once again their connection with Fourier transforms. Here, we shall encounter general Paley-Wiener theorems of the recent past. Lastly, we attack the issue of integrability of Cauchy transforms by means of potential theory. Therefore, we derive a Fourier integral formula for the logarithmic energy in one and multiple dimensions and give applications to Fourier and hence Cauchy transforms.
Two appendices are annexed to this thesis. The first one covers important definitions and results from measure theory with a special focus on complex measures. The second appendix contains Cauchy transforms of frequently used measures and functions with detailed calculations.
The COVID-19 pandemic has affected schooling worldwide. In many places, schools closed for weeks or months, only part of the student body could be educated at any one time, or students were taught online. Previous research discloses the relevance of schooling for the development of cognitive abilities. We therefore compared the intelligence test performance of 424 German secondary school students in Grades 7 to 9 (42% female) tested after the first six months of the COVID-19 pandemic (i.e., 2020 sample) to the results of two highly comparable student samples tested in 2002 (n = 1506) and 2012 (n = 197). The results revealed substantially and significantly lower intelligence test scores in the 2020 sample than in both the 2002 and 2012 samples. We retested the 2020 sample after another full school year of COVID-19-affected schooling in 2021. We found mean-level changes of typical magnitude, with no signs of catching up to previous cohorts or further declines in cognitive performance. Perceived stress during the pandemic did not affect changes in intelligence test results between the two measurements.
COVID-19 was a harsh reminder that diseases are an aspect of human existence and mortality. It was also a live experiment in the formation and alteration of disease-related attitudes. Not only are these attitudes relevant to an individual’s self-protective behavior, but they also seem to be associated with social and political attitudes more broadly. One of these attitudes is Social Darwinism, which holds that a pandemic benefits society by enabling nature “to weed out the weak”. In two countries (N = 300, N = 533), we introduce and provide evidence for the reliability, validity, and usefulness of the Disease-Related Social Darwinism (DRSD) Short Scale measuring this concept. Results indicate that DRSD is meaningful related to other central political attitudes like Social Dominance Orientation, Authoritarianism and neoliberalism. Importantly, the scale significantly predicted people’s protective behavior during the Pandemic over and above general social Darwinism. Moreover, it significantly predicted conservative attitudes, even after controlling for Social Dominance Orientation.
Die Dissertation beschäftigt sich mit einer neuartigen Art von Branch-and-Bound Algorithmen, deren Unterschied zu klassischen Branch-and-Bound Algorithmen darin besteht, dass
das Branching durch die Addition von nicht-negativen Straftermen zur Zielfunktion erfolgt
anstatt durch das Hinzufügen weiterer Nebenbedingungen. Die Arbeit zeigt die theoretische Korrektheit des Algorithmusprinzips für verschiedene allgemeine Klassen von Problemen und evaluiert die Methode für verschiedene konkrete Problemklassen. Für diese Problemklassen, genauer Monotone und Nicht-Monotone Gemischtganzzahlige Lineare Komplementaritätsprobleme und Gemischtganzzahlige Lineare Probleme, präsentiert die Arbeit
verschiedene problemspezifische Verbesserungsmöglichkeiten und evaluiert diese numerisch.
Weiterhin vergleicht die Arbeit die neue Methode mit verschiedenen Benchmark-Methoden
mit größtenteils guten Ergebnissen und gibt einen Ausblick auf weitere Anwendungsgebiete
und zu beantwortende Forschungsfragen.
The forensic application of phonetics relies on individuality in speech. In the forensic domain, individual patterns of verbal and paraverbal behavior are of interest which are readily available, measurable, consistent, and robust to disguise and to telephone transmission. This contribution is written from the perspective of the forensic phonetic practitioner and seeks to establish a more comprehensive concept of disfluency than previous studies have. A taxonomy of possible variables forming part of what can be termed disfluency behavior is outlined. It includes the “classical” fillers, but extends well beyond these, covering, among others, additional types of fillers as well as prolongations, but also the way in which fillers are combined with pauses. In the empirical section, the materials collected for an earlier study are re-examined and subjected to two different statistical procedures in an attempt to approach the issue of individuality. Recordings consist of several minutes of spontaneous speech by eight speakers on three different occasions. Beyond the established set of hesitation markers, additional aspects of disfluency behavior which fulfill the criteria outlined above are included in the analysis. The proportion of various types of disfluency markers is determined. Both statistical approaches suggest that these speakers can be distinguished at a level far above chance using the disfluency data. At the same time, the results show that it is difficult to pin down a single measure which characterizes the disfluency behavior of an individual speaker. The forensic implications of these findings are discussed.
Redox-driven biogeochemical cycling of iron plays an integral role in the complex process network of ecosystems, such as carbon cycling, the fate of nutrients and greenhouse gas emissions. We investigate Fe-(hydr)oxide (trans)formation pathways from rhyolitic tephra in acidic topsoils of South Patagonian Andosols to evaluate the ecological relevance of terrestrial iron cycling for this sensitive fjord ecosystem. Using bulk geochemical analyses combined with micrometer-scale-measurements on individual soil aggregates and tephra pumice, we document biotic and abiotic pathways of Fe released from the glassy tephra matrix and titanomagnetite phenocrysts. During successive redox cycles that are controlled by frequent hydrological perturbations under hyper-humid climate, (trans)formations of ferrihydrite-organic matter coprecipitates, maghemite and hematite are closely linked to tephra weathering and organic matter turnover. These Fe-(hydr)oxides nucleate after glass dissolution and complexation with organic ligands, through maghemitization or dissolution-(re)crystallization processes from metastable precursors. Ultimately, hematite represents the most thermodynamically stable Fe-(hydr)oxide formed under these conditions and physically accumulates at redox interfaces, whereas the ferrihydrite coprecipitates represent a so far underappreciated terrestrial source of bio-available iron for fjord bioproductivity. The insights into Fe-(hydr)oxide (trans)formation in Andosols have implications for a better understanding of biogeochemical cycling of iron in this unique Patagonian fjord ecosystem.
We use a novel sea-ice lead climatology for the winters of 2002/03 to 2020/21 based on satellite observations with 1 km2 spatial resolution to identify predominant patterns in Arctic wintertime sea-ice leads. The causes for the observed spatial and temporal variabilities are investigated using ocean surface current velocities and eddy kinetic energies from an ocean model (Finite Element Sea Ice–Ice-Shelf–Ocean Model, FESOM) and winds from a regional climate model (CCLM) and ERA5 reanalysis, respectively. The presented investigation provides evidence for an influence of ocean bathymetry and associated currents on the mechanic weakening of sea ice and the accompanying occurrence of sea-ice leads with their characteristic spatial patterns. While the driving mechanisms for this observation are not yet understood in detail, the presented results can contribute to opening new hypotheses on ocean–sea-ice interactions. The individual contribution of ocean and atmosphere to regional lead dynamics is complex, and a deeper insight requires detailed mechanistic investigations in combination with considerations of coastal geometries. While the ocean influence on lead dynamics seems to act on a rather long-term scale (seasonal to interannual), the influence of wind appears to trigger sea-ice lead dynamics on shorter timescales of weeks to months and is largely controlled by individual events causing increased divergence. No significant pan-Arctic trends in wintertime leads can be observed.
Regional climate models are a valuable tool for the study of the climate processes and climate change in polar regions, but the performance of the models has to be evaluated using experimental data. The regional climate model CCLM was used for simulations for the MOSAiC period with a horizontal resolution of 14 km (whole Arctic). CCLM was used in a forecast mode (nested in ERA5) and used a thermodynamic sea ice model. Sea ice concentration was taken from AMSR2 data (C15 run) and from a high-resolution data set (1 km) derived from MODIS data (C15MOD0 run). The model was evaluated using radiosonde data and data of different profiling systems with a focus on the winter period (November–April). The comparison with radiosonde data showed very good agreement for temperature, humidity, and wind. A cold bias was present in the ABL for November and December, which was smaller for the C15MOD0 run. In contrast, there was a warm bias for lower levels in March and April, which was smaller for the C15 run. The effects of different sea ice parameterizations were limited to heights below 300 m. High-resolution lidar and radar wind profiles as well as temperature and integrated water vapor (IWV) data from microwave radiometers were used for the comparison with CCLM for case studies, which included low-level jets. LIDAR wind profiles have many gaps, but represent a valuable data set for model evaluation. Comparisons with IWV and temperature data of microwave radiometers show very good agreement.
The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win
(2023)
Power motivation is considered a key component of successful leadership. Based on its dualistic nature, the need for power (nPower) can be expressed in a dominant or a prosocial manner. Whereas dominant motivation is associated with antisocial behaviors, prosocial motivation is characterized by more benevolent actions (e.g., helping, guiding). Prosocial enactment of the power motive has been linked to a wide range of beneficial outcomes, yet less has been investigated what determines a prosocial enactment of the power motive. According to Personality Systems Interactions (PSI) theory, action orientation (i.e., the ability to self-regulate affect) promotes prosocial enactment of the implicit power motive and initial findings within student samples verify this assumption. In the present study, we verified the role of action orientation as an antecedent for prosocial power enactment in a leadership sample (N = 383). Additionally, we found that leaders personally benefited from a prosocial enactment strategy. Results show that action orientation through prosocial power motivation leads to reduced power-related anxiety and, in turn, to greater leader well-being. The integration of motivation and self-regulation research reveals why leaders enact their power motive in a certain way and helps to understand how to establish a win-win situation for both followers and leaders.