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The present work considers the normal approximation of the binomial distribution and yields estimations of the supremum distance of the distribution functions of the binomial- and the corresponding standardized normal distribution. The type of the estimations correspond to the classical Berry-Esseen theorem, in the special case that all random variables are identically Bernoulli distributed. In this case we state the optimal constant for the Berry-Esseen theorem. In the proof of these estimations several inequalities regarding the density as well as the distribution function of the binomial distribution are presented. Furthermore in the estimations mentioned above the distribution function is replaced by the probability of arbitrary, not only unlimited intervals and in this new situation we also present an upper bound.
The equity premium (Mehra and Prescott, 1985) is still a puzzle in the sense that there are still no convincing explanations for the size of the equity premium. In this dissertation, we study this long-standing puzzle and several possible behavioral explanations. First, we apply the IRR methodology proposed by Fama and French (1999) to achieve large firm level data on the equity premia for N = 28,256 companies in 54 countries around the world. Second, by using preferences data from the INTRA study (Rieger et. al., 2014), we could test the relevant risk factors together with time cognition to explain the equity premium. We document the failure of the Myopic Loss Aversion hypothesis by Benartzi and Thaler (1995) but provides rigorous empirical evidence to support the behavioral theory of ambiguity aversion to account for the equity premium. The observations shed some light on the new approach of integrating risk and ambiguity (together with time preferences) into a more general model of uncertainty, in which both risk premium and ambiguity premium play roles in asset pricing models.
Cognitive performance is contingent upon multiple factors. Beyond the impact of en-vironmental circumstances, the bodily state may hinder or promote cognitive processing. Af-ferent transmission from the viscera, for instance, is crucial not only for the genesis of affect and emotion, but further exerts significant influences on memory and attention. In particular, afferent cardiovascular feedback from baroreceptors demonstrated subcortical and cortical inhibition. Consequences for human cognition and behavior are the impairment of simple perception and sensorimotor functioning. Four studies are presented that investigate the mod-ulatory impact of baro-afferent feedback on selective attention. The first study demonstrates that the modulation of sensory processing by baroreceptor activity applies to the processing of complex stimulus configurations. By the use of a visual masking task in which a target had to be selected against a visual mask, perceptual interference was reduced when target and mask were presented during the ventricular systole compared to the diastole. In study two, selection efficiency was systematically manipulated in a visual selection task in which a target letter was flanked by distracting stimuli. By comparing participants" performance under homogene-ous and heterogeneous stimulus conditions, selection efficiency was assessed as a function of the cardiac cycle phase in which the targets and distractors were presented. The susceptibility of selection performance to the stimulus condition at hand was less pronounced during the ventricular systole compared to the diastole. Study one and two therefore indicate that inter-ference from irrelevant sensory input, resulting from temporally overlapping processing traces or from the simultaneous presentation of distractor stimuli, is reduced during phases of in-creased baro-afferent feedback. Study three experimentally manipulated baroreceptor activity by systematically varying the participant- body position while a sequential distractor priming task was completed. In this study, negative priming and distractor-response binding effects were obtained as indices of controlled and automatic distractor processing, respectively. It was found that only controlled distractor processing was affected by tonic increases in baro-receptor activity. In line with study one and two these results indicate that controlled selection processes are more efficient during enhanced baro-afferent feedback, observable in dimin-ished aftereffects of controlled distractor processing. Due to previous findings that indicated baro-afferent transmission to affect central, rather than response-related processing stages, study four measured lateralized-readiness potentials (LRPs) and reaction times (RTs), while participants, again, had to selectively respond to target stimuli that were surrounded by dis-tractors. The impact of distractor inhibition on stimulus-related, but not on response-related LRPs suggests that in a sequential distractor priming task, the sensory representations of dis-tractors, rather than motor responses are targeted by inhibition. Together with the results from studies one through three and the finding of baroreceptor-mediated behavioral inhibition tar-geting central processing stages, study four corroborates the presumption of baro-afferent signal transmission to modulate controlled processes involved in selective attention. In sum, the work presented shows that visual selective attention benefits from in-creased baro-afferent feedback as its effects are not confined to simple perception, but may facilitate the active suppression of neural activity related to sensory input from distractors. Hence, due to noise reduction, baroreceptor-mediated inhibition may promote effective selec-tion in vision.
The efficacy and effectiveness of psychotherapeutic interventions have been proven time and again. We therefore know that, in general, evidence-based treatments work for the average patient. However, it has also repeatedly been shown that some patients do not profit from or even deteriorate during treatment. Patient-focused psychotherapy research takes these differences between patients into account by focusing on the individual patient. The aim of this research approach is to analyze individual treatment courses in order to evaluate when and under which circumstances a generally effective treatment works for an individual patient. The goal is to identify evidence based clinical decision rules for the adaptation of treatment to prevent treatment failure. Patient-focused research has illustrated how different intake indicators and early change patterns predict the individual course of treatment, but they leave a lot of variance unexplained. The thesis at hand analyzed whether Ecological Momentary Assessment (EMA) strategies could be integrated into patient-focused psychotherapy research in order to improve treatment response prediction models. EMA is an electronically supported diary approach, in which multiple real-time assessments are conducted in participants" everyday lives. We applied EMA over a two-week period before treatment onset in a mixed sample of patients seeking outpatient treatment. The four daily measurements in the patients" everyday environment focused on assessing momentary affect and levels of rumination, perceived self-efficacy, social support and positive or negative life events since the previous assessment. The aim of this thesis project was threefold: First, to test the feasibility of EMA in a routine care outpatient setting. Second, to analyze the interrelation of different psychological processes within patients" everyday lives. Third and last, to test whether individual indicators of psychological processes during everyday life, which were assessed before treatment onset, could be used to improve prediction models of early treatment response. Results from Study I indicate good feasibility of EMA application during the waiting period for outpatient treatment. High average compliance rates over the entire assessment period and low average burdens perceived by the patients support good applicability. Technical challenges and the results of in-depth missing analyses are reported to guide future EMA applications in outpatient settings. Results from Study II shed further light on the rumination-affect link. We replicated results from earlier studies, which identified a negative association between state rumination and affect on a within-person level and additionally showed a) that this finding holds for the majority but not every individual in a diverse patient sample with mixed Axis-I disorders, b) that rumination is linked to negative but also to positive affect and c) that dispositional rumination significantly affects the state rumination-affect association. The results provide exploratory evidence that rumination might be considered a transdiagnostic mechanism of psychological functioning and well-being. Results from Study III finally suggest that the integration of indicators derived from EMA applications before treatment onset can improve prediction models of early treatment response. Positive-negative affect ratios as well as fluctuations in negative affect measured during patients" daily lives allow the prediction of early treatment response. Our results indicate that the combination of commonly applied intake predictors and EMA indicators of individual patients" daily experiences can improve treatment response predictions models. We therefore conclude that EMA can successfully be integrated into patient-focused research approaches in routine care settings to ameliorate or optimize individual care.
Matching problems with additional resource constraints are generalizations of the classical matching problem. The focus of this work is on matching problems with two types of additional resource constraints: The couple constrained matching problem and the level constrained matching problem. The first one is a matching problem which has imposed a set of additional equality constraints. Each constraint demands that for a given pair of edges either both edges are in the matching or none of them is in the matching. The second one is a matching problem which has imposed a single equality constraint. This constraint demands that an exact number of edges in the matching are so-called on-level edges. In a bipartite graph with fixed indices of the nodes, these are the edges with end-nodes that have the same index. As a central result concerning the couple constrained matching problem we prove that this problem is NP-hard, even on bipartite cycle graphs. Concerning the complexity of the level constrained perfect matching problem we show that it is polynomially equivalent to three other combinatorial optimization problems from the literature. For different combinations of fixed and variable parameters of one of these problems, the restricted perfect matching problem, we investigate their effect on the complexity of the problem. Further, the complexity of the assignment problem with an additional equality constraint is investigated. In a central part of this work we bring couple constraints into connection with a level constraint. We introduce the couple and level constrained matching problem with on-level couples, which is a matching problem with a special case of couple constraints together with a level constraint imposed on it. We prove that the decision version of this problem is NP-complete. This shows that the level constraint can be sufficient for making a polynomially solvable problem NP-hard when being imposed on that problem. This work also deals with the polyhedral structure of resource constrained matching problems. For the polytope corresponding to the relaxation of the level constrained perfect matching problem we develop a characterization of its non-integral vertices. We prove that for any given non-integral vertex of the polytope a corresponding inequality which separates this vertex from the convex hull of integral points can be found in polynomial time. Regarding the calculation of solutions of resource constrained matching problems, two new algorithms are presented. We develop a polynomial approximation algorithm for the level constrained matching problem on level graphs, which returns solutions whose size is at most one less than the size of an optimal solution. We then describe the Objective Branching Algorithm, a new algorithm for exactly solving the perfect matching problem with an additional equality constraint. The algorithm makes use of the fact that the weighted perfect matching problem without an additional side constraint is polynomially solvable. In the Appendix, experimental results of an implementation of the Objective Branching Algorithm are listed.
Globalization and the emergence of global value chains have not only changed the way we live, but also the way economists study international economics. These changes are visible in various areas and dimension. This dissertation deals " mostly empirically " with some of these issues related to global value chains. It starts by critically examining the political economy forces determining the occurrence and the extent of trade liberalization conditions in World Bank lending agreements. The focal point is whether these are affected by the World Bank- most influential member countries. Afterwards, the thesis moves on to describe trade of the European Union member countries at each stage of the value chain. The description is based on a new classification of goods into parts, components and final products as well as a newly developed measure describing the average level of development of a countries trading partners. This descriptive exercise is followed by critically examining discrepancies between gross trade and trade in value added with respect to comparative advantage. A gravity model is employed to contrast results when studying the institutional determinants of comparative advantage. Finally, the thesis deals with determinants of regional location choices for foreign direct investment. The analysis is based on a theoretical new economic geography model and employs a newly developed index that accounts for the presence of potentially all suppliers and buyers at all stages of the value chain.
Floods are hydrological extremes that have enormous environmental, social and economic consequences.The objective of this thesis was a contribution to the implementation of a processing chain that integrates remote sensing information into hydraulic models. Specifically, the aim was to improve water elevation and discharge simulations by assimilating microwave remote sensing-derived flood information into hydraulic models. The first component of the proposed processing chain is represented by a fully automated flood mapping algorithm that enables the automated, objective, and reliable flood extent extraction from Synthetic Aperture Radar images, providing accurate results in both rural and urban regions. The method operates with minimum data requirements and is efficient in terms of computational time. The map obtained with the developed algorithm is still subject to uncertainties, both introduced by the flood mapping algorithm and inherent in the image itself. In this work, particular attention was given to image uncertainty deriving from speckle. By bootstrapping the original satellite image pixels, several synthetic images were generated and provided as input to the developed flood mapping algorithm. From the analysis performed on the mapping products, speckle uncertainty can be considered as a negligible component of the total uncertainty. In the final step of the proposed processing chain real event water elevations, obtained from satellite observations, were assimilated in a hydraulic model with an adapted version of the Particle Filter, modified to work with non-Gaussian distribution of observations. To deal with model structure error and possibly biased observations, a global and a local weight variant of the Particle Filter were tested. The variant to be preferred depends on the level of confidence that is attributed to the observations or to the model. This study also highlighted the complementarity of remote sensing derived and in-situ data sets. An accurate binary flood map represents an invaluable product for different end users. However, deriving from this binary map additional hydraulic information, such as water elevations, is a way of enhancing the value of the product itself. The derived data can be assimilated into hydraulic models that will fill the gaps where, for technical reasons, Earth Observation data cannot provide information, also enabling a more accurate and reliable prediction of flooded areas.
In the first part of this work we generalize a method of building optimal confidence bounds provided in Buehler (1957) by specializing an exhaustive class of confidence regions inspired by Sterne (1954). The resulting confidence regions, also called Buehlerizations, are valid in general models and depend on a designated statistic'' that can be chosen according to some desired monotonicity behaviour of the confidence region. For a fixed designated statistic, the thus obtained family of confidence regions indexed by their confidence level is nested. Buehlerizations have furthermore the optimality property of being the smallest (w.r.t. set inclusion) confidence regions that are increasing in their designated statistic. The theory is eventually applied to normal, binomial, and exponential samples. The second part deals with the statistical comparison of pairs of diagnostic tests and establishes relations 1. between the sets of lower confidence bounds, 2. between the sets of pairs of comparable lower confidence bounds, and 3. between the sets of admissible lower confidence bounds in various models for diverse parameters of interest.
1.The Discursive Construction of Black Masculinity: Intersections of Race, Gender, and Sexuality
1.1.The Plight of Black Men: A History of Lynchings and Castrations
1.2.The Discursive Construction of the Black Man as Otherrn
1.3.Black Corporeality and the Scopic Regime of Racism
2. Ralph Ellison's 'Invisible man'
2.1.Invisible Black Men: Between Emasculation and Hypermasculinityrn
2.2.Transcending Invisibility
In recent years, the study of dynamical systems has developed into a central research area in mathematics. Actually, in combination with keywords such as "chaos" or "butterfly effect", parts of this theory have been incorporated in other scientific fields, e.g. in physics, biology, meteorology and economics. In general, a discrete dynamical system is given by a set X and a self-map f of X. The set X can be interpreted as the state space of the system and the function f describes the temporal development of the system. If the system is in state x ∈ X at time zero, its state at time n ∈ N is denoted by f^n(x), where f^n stands for the n-th iterate of the map f. Typically, one is interested in the long-time behaviour of the dynamical system, i.e. in the behaviour of the sequence (f^n(x)) for an arbitrary initial state x ∈ X as the time n increases. On the one hand, it is possible that there exist certain states x ∈ X such that the system behaves stably, which means that f^n(x) approaches a state of equilibrium for n→∞. On the other hand, it might be the case that the system runs unstably for some initial states x ∈ X so that the sequence (f^n(x)) somehow shows chaotic behaviour. In case of a non-linear entire function f, the complex plane always decomposes into two disjoint parts, the Fatou set F_f of f and the Julia set J_f of f. These two sets are defined in such a way that the sequence of iterates (f^n) behaves quite "wildly" or "chaotically" on J_f whereas, on the other hand, the behaviour of (f^n) on F_f is rather "nice" and well-understood. However, this nice behaviour of the iterates on the Fatou set can "change dramatically" if we compose the iterates from the left with just one other suitable holomorphic function, i.e. if we consider sequences of the form (g∘f^n) on D, where D is an open subset of F_f with f(D)⊂ D and g is holomorphic on D. The general aim of this work is to study the long-time behaviour of such modified sequences. In particular, we will prove the existence of holomorphic functions g on D having the property that the behaviour of the sequence of compositions (g∘f^n) on the set D becomes quite similarly chaotic as the behaviour of the sequence (f^n) on the Julia set of f. With this approach, we immerse ourselves into the theory of universal families and hypercyclic operators, which itself has developed into an own branch of research. In general, for topological spaces X, Y and a family {T_i: i ∈ I} of continuous functions T_i:X→Y, an element x ∈ X is called universal for the family {T_i: i ∈ I} if the set {T_i(x): i ∈ I} is dense in Y. In case that X is a topological vector space and T is a continuous linear operator on X, a vector x ∈ X is called hypercyclic for T if it is universal for the family {T^n: n ∈ N}. Thus, roughly speaking, universality and hypercyclicity can be described via the following two aspects: There exists a single object which allows us, via simple analytical operations, to approximate every element of a whole class of objects. In the above situation, i.e. for a non-linear entire function f and an open subset D of F_f with f(D)⊂ D, we endow the space H(D) of holomorphic functions on D with the topology of locally uniform convergence and we consider the map C_f:H(D)→H(D), C_f(g):=g∘f|_D, which is called the composition operator with symbol f. The transform C_f is a continuous linear operator on the Fréchet space H(D). In order to show that the above-mentioned "nice" behaviour of the sequence of iterates (f^n) on the set D ⊂ F_f can "change dramatically" if we compose the iterates from the left with another suitable holomorphic function, our aim consists in finding functions g ∈ H(D) which are hypercyclic for C_f. Indeed, for each hypercyclic function g for C_f, the set of compositions {g∘f^n|_D: n ∈ N} is dense in H(D) so that the sequence of compositions (g∘f^n|_D) is kind of "maximally divergent" " meaning that each function in H(D) can be approximated locally uniformly on D via subsequences of (g∘f^n|_D). This kind of behaviour stands in sharp contrast to the fact that the sequence of iterates (f^n) itself converges, behaves like a rotation or shows some "wandering behaviour" on each component of F_f. To put it in a nutshell, this work combines the theory of non-linear complex dynamics in the complex plane with the theory of dynamics of continuous linear operators on spaces of holomorphic functions. As far as the author knows, this approach has not been investigated before.