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This thesis considers the general task of computing a partition of a set of given objects such that each set of the partition has a cardinality of at least a fixed number k. Among such kinds of partitions, which we call k-clusters, the objective is to find the k-cluster which minimises a certain cost derived from a given pairwise difference between objects which end up the same set. As a first step, this thesis introduces a general problem, denoted by (||.||,f)-k-cluster, which models the task to find a k-cluster of minimum cost given by an objective function computed with respect to specific choices for the cost functions f and ||.||. In particular this thesis considers three different choices for f and also three different choices for ||.|| which results in a total of nine different variants of the general problem. Especially with the idea to use the concept of parameterised approximation, we first investigate the role of the lower bound on the cluster cardinalities and find that k is not a suitable parameter, due to remaining NP-hardness even for the restriction to the constant 3. The reductions presented to show this hardness yield the even stronger result which states that polynomial time approximations with some constant performance ratio for any of the nine variants of (||.||,f)-k-cluster require a restriction to instances for which the pairwise distance on the objects satisfies the triangle inequality. For this restriction to what we informally refer to as metric instances, constant-factor approximation algorithms for eight of the nine variants of (||.||,f)-k-cluster are presented. While two of these algorithms yield the provably best approximation ratio (assuming P!=NP), others can only guarantee a performance which depends on the lower bound k. With the positive effect of the triangle inequality and applications to facility location in mind, we discuss the further restriction to the setting where the given objects are points in the Euclidean metric space. Considering the effect of computational hardness caused by high dimensionality of the input for other related problems (curse of dimensionality) we check if this is also the source of intractability for (||.||,f)-k-cluster. Remaining NP-hardness for restriction to small constant dimensionality however disproves this theory. We then use parameterisation to develop approximation algorithms for (||.||,f)-k-cluster without restriction to metric instances. In particular, we discuss structural parameters which reflect how much the given input differs from a metric. This idea results in parameterised approximation algorithms with parameters such as the number of conflicts (our name for pairs of objects for which the triangle inequality is violated) or the number of conflict vertices (objects involved in a conflict). The performance ratios of these parameterised approximations are in most cases identical to those of the approximations for metric instances. This shows that for most variants of (||.||,f)-k-cluster efficient and reasonable solutions are also possible for non-metric instances.
Die Dissertation untersucht vergleichend deutsch-japanische fotografische Kriegspropaganda des Zweiten Weltkrieges anhand der zu jener Zeit auflagenstärksten illustrierten Zeitschriften "Illustrierter Beobachter" auf deutscher und "Shashin Shūhō" (Fotografische Wochenzeitung) auf japanischer Seite. Unter Rückgriff auf die ikonographisch-ikonologische Methode des Kunsthistorikers Erwin Panofsky bei gleichzeitiger Bezugnahme auf das Bildverständnis Charles Sanders Peirces werden Muster der bildlichen Darstellung von Kindern und Jugendlichen analysiert, um hierdurch Rückschlüsse zu ziehen auf Gemeinsamkeiten und Unterschiede in der Ausgestaltung der Bildpropaganda beider Länder unmittelbar vor und im Zweiten Weltkrieg (1939-1945), auf allgemeine Tendenzen in der Gestaltung von Propaganda im selben Zeitraum, auf die Organisation und Funktion von Propaganda in radikalnationalistischen Staaten. Gleichzeitig wird durch Einbeziehung der Rezipientensicht die Frage nach Mehrdeutigkeit und, hiermit einhergehend, Wirkungsweise und Wirkungsgrad der Propaganda gestellt. Schwerpunkt der Untersuchung bilden sämtliche publizierten Ausgaben der zweiten Jahreshälften 1938 und 1943.
At any given moment, our senses are assaulted with a flood of information from the environment around us. We need to pick our way through all this information in order to be able to effectively respond to that what is relevant to us. In most cases we are usually able to select information relevant to our intentions from what is not relevant. However, what happens to the information that is not relevant to us? Is this irrelevant information completely ignored so that it does not affect our actions? The literature suggests that even though we mayrnignore an irrelevant stimulus, it may still interfere with our actions. One of the ways in which irrelevant stimuli can affect actions is by retrieving a response with which it was associated. An irrelevant stimulus that is presented in close temporal contiguity with a relevant stimulus can be associated with the response made to the relevant stimulus " an observation termed distractor-response binding (Rothermund, Wentura, & De Houwer, 2005). The studies presented in this work take a closer look at such distractor-response bindings, and therncircumstances in which they occur. Specifically, the study reported in chapter 6 examined whether only an exact repetition of the distractor can retrieve the response with which it was associated, or whether even similar distractors may cause retrieval. The results suggested that even repeating a similar distractor caused retrieval, albeit less than an exact repetition. In chapter 7, the existence of bindings between a distractor and a response were tested beyond arnperceptual level, to see whether they exist at an (abstract) conceptual level. Similar to perceptual repetition, distractor-based retrieval of the response was observed for the repetition of concepts. The study reported in chapter 8 of this work examined the influence of attention on the feature-response binding of irrelevant features. The results pointed towards a stronger binding effects when attention was directed towards the irrelevant feature compared to whenrnit was not. The study in chapter 9 presented here looked at the processes underlying distractor-based retrieval and distractor inhibition. The data suggest that motor processes underlie distractor-based retrieval and cognitive process underlie distractor inhibition. Finally, the findings of all four studies are also discussed in the context of learning.
We will consider discrete dynamical systems (X,T) which consist of a state space X and a linear operator T acting on X. Given a state x in X at time zero, its state at time n is determined by the n-th iteration T^n(x). We are interested in the long-term behaviour of this system, that means we want to know how the sequence (T^n (x))_(n in N) behaves for increasing n and x in X. In the first chapter, we will sum up the relevant definitions and results of linear dynamics. In particular, in topological dynamics the notions of hypercyclic, frequently hypercyclic and mixing operators will be presented. In the setting of measurable dynamics, the most important definitions will be those of weakly and strongly mixing operators. If U is an open set in the (extended) complex plane containing 0, we can define the Taylor shift operator on the space H(U) of functions f holomorphic in U as Tf(z) = (f(z)- f(0))/z if z is not equal to 0 and otherwise Tf(0) = f'(0). In the second chapter, we will start examining the Taylor shift on H(U) endowed with the topology of locally uniform convergence. Depending on the choice of U, we will study whether or not the Taylor shift is weakly or strongly mixing in the Gaussian sense. Next, we will consider Banach spaces of functions holomorphic on the unit disc D. The first section of this chapter will sum up the basic properties of Bergman and Hardy spaces in order to analyse the dynamical behaviour of the Taylor shift on these Banach spaces in the next part. In the third section, we study the space of Cauchy transforms of complex Borel measures on the unit circle first endowed with the quotient norm of the total variation and then with a weak-* topology. While the Taylor shift is not even hypercyclic in the first case, we show that it is mixing for the latter case. In Chapter 4, we will first introduce Bergman spaces A^p(U) for general open sets and provide approximation results which will be needed in the next chapter where we examine the Taylor shift on these spaces on its dynamical properties. In particular, for 1<=p<2 we will find sufficient conditions for the Taylor shift to be weakly mixing or strongly mixing in the Gaussian sense. For p>=2, we consider specific Cauchy transforms in order to determine open sets U such that the Taylor shift is mixing on A^p(U). In both sections, we will illustrate the results with appropriate examples. Finally, we apply our results to universal Taylor series. The results of Chapter 5 about the Taylor shift allow us to consider the behaviour of the partial sums of the Taylor expansion of functions in general Bergman spaces outside its disc of convergence.
The implicit power motive is one of the most researched motives in motivational psychology—at least in adults. Children have rarely been subject to investigation and there are virtually no results on behavioral and affective correlates of the implicit power motive in children. As behavior and affect are important components of conceptual validation, the empirical data in this dissertation focused on identifying three correlates, namely resource control behavior (study 1), power stress (study 2), and persuasive behavior (study 3). In each study, the implicit power motive was measured via the Picture Story Exercise, using an adapted version for children. Children across samples were between 4 and 11 years old.
Results from study 1 and 2 showed that children’s power-related behavior corresponded with evidence from adult samples: children with a high implicit power motive secure attractive resources and show negative reactions to a thwarted attempt to exert influence. Study 3 contradicted existing evidence with adults in that children’s persuasive behavior was not associated with nonverbal, but with verbal strategies of persuasion. Despite this inconsistency, these results are, together with the validation of a child-friendly Picture Story Exercise version, an important step into further investigating and confirming the concept of the implicit power motive and how to measure it in children.
Fostering positive and realistic self-concepts of individuals is a major goal in education worldwide (Trautwein & Möller, 2016). Individuals spend most of their childhood and adolescence in school. Thus, schools are important contexts for individuals to develop positive self-perceptions such as self-concepts. In order to enhance positive self-concepts in educational settings and in general, it is indispensable to have a comprehensive knowledge about the development and structure of self-concepts and their determinants. To date, extensive empirical and theoretical work on antecedents and change processes of self-concept has been conducted. However, several research gaps still exist, and several of these are the focus of the present dissertation. Specifically, these research gaps encompass (a) the development of multiple self-concepts from multiple perspectives regarding stability and change, (b) the direction of longitudinal interplay between self-concept facets over the entire time period from childhood to late adolescence, and (c) the evidence that a recently developed structural model of academic self-concept (nested Marsh/Shavelson model [Brunner et al., 2010]) fits the data in elementary school students, (d) the investigation of structural changes in academic self-concept profile formation within this model, (e) the investigation of dimensional comparison processes as determinants of academic self-concept profile formation in elementary school students within the internal/external frame of reference model (I/E model; Marsh, 1986), (f) the test of moderating variables for dimensional comparison processes in elementary school, (g) the test of the key assumptions of the I/E model that effects of dimensional comparisons depend to a large degree on the existence of achievement differences between subjects, and (h) the generalizability of the findings regarding the I/E model over different statistical analytic methods. Thus, the aim of the present dissertation is to contribute to close these gaps with three studies. Thereby, data from German students enrolled in elementary school to secondary school education were gathered in three projects comprising the developmental time span from childhood to adolescence (ages 6 to 20). Three vital self-concept areas in childhood and adolescence were in-vestigated: general self-concept (i.e., self-esteem), academic self-concepts (general, math, reading, writing, native language), and social self-concepts (of acceptance and assertion). In all studies, data were analyzed within a latent variable framework. Findings are discussed with respect to the research aims of acquiring more comprehensive knowledge on the structure and development of significant self-concept in childhood and adolescence and their determinants. In addition, theoretical and practical implications derived from the findings of the present studies are outlined. Strengths and limitations of the present dissertation are discussed. Finally, an outlook for future research on self-concepts is given.
Background and rationale: Changing working conditions demand adaptation, resulting in higher stress levels in employees. In consequence, decreased productivity, increasing rates of sick leave, and cases of early retirement result in higher direct, indirect, and intangible costs. Aims of the Research Project: The aim of the study was to test the usefulness of a novel translational diagnostic tool, Neuropattern, for early detection, prevention, and personalized treatment of stress-related disorders. The trial was designed as a pilot study with a wait list control group. Materials and Methods: In this study, 70 employees of the Forestry Department Rhineland-Palatinate, Germany, were enrolled. Subjects were block-randomized according to the functional group of their career field, and either underwent Neuropattern diagnostics immediately, or after a waiting period of three months. After the diagnostic assessment, their physicians received the Neuropattern Medical Report, including the diagnostic results and treatment recommendations. Participants were informed by the Neuropattern Patient Report, and were eligible to an individualized Neuropattern Online Counseling account. Results: The application of Neuropattern diagnostics significantly improved mental health and health-related behavior, reduced perceived stress, emotional exhaustion, overcommitment and possibly, presenteeism. Additionally, Neuropattern sensitively detected functional changes in stress physiology at an early stage, thus allowing timely personalized interventions to prevent and treat stress pathology. Conclusion: The present study encouraged the application of Neuropattern diagnostics to early intervention in non-clinical populations. However, further research is required to determine the best operating conditions.
The economic growth theory analyses which factors affect economic growth and tries to analyze how it can last. A popular neoclassical growth model is the Ramsey-Cass-Koopmans model, which aims to determine how much of its income a nation or an economy should save in order to maximize its welfare. In this thesis, we present and analyze an extended capital accumulation equation of a spatial version of the Ramsey model, balancing diffusive and agglomerative effects. We model the capital mobility in space via a nonlocal diffusion operator which allows for jumps of the capital stock from one location to an other. Moreover, this operator smooths out heterogeneities in the factor distributions slower, which generated a more realistic behavior of capital flows. In addition to that, we introduce an endogenous productivity-production operator which depends on time and on the capital distribution in space. This operator models the technological progress of the economy. The resulting mathematical model is an optimal control problem under a semilinear parabolic integro-differential equation with initial and volume constraints, which are a nonlocal analog to local boundary conditions, and box-constraints on the state and the control variables. In this thesis, we consider this problem on a bounded and unbounded spatial domain, in both cases with a finite time horizon. We derive existence results of weak solutions for the capital accumulation equations in both settings and we proof the existence of a Ramsey equilibrium in the unbounded case. Moreover, we solve the optimal control problem numerically and discuss the results in the economic context.
Quadratische Optimierungsprobleme (QP) haben ein breites Anwendungsgebiet, wie beispielsweise kombinatorische Probleme einschließlich des maximalen Cliquenroblems. Motzkin und Straus [25] zeigten die Äquivalenz zwischen dem maximalen Cliquenproblem und dem standard quadratischen Problem. Auch mathematische Statistik ist ein weiteres Anwendungsgebiet von (QP), sowie eine Vielzahl von ökonomischen Modellen basieren auf (QP), z.B. das quadratische Rucksackproblem. In [5] Bomze et al. haben das standard quadratische Optimierungsproblem (StQP) in ein Copositive-Problem umformuliert. Im Folgenden wurden Algorithmen zur Lösung dieses copositiviten Problems von Bomze und de Klerk in [6] und Dür und Bundfuss in [9] entwickelt. Während die Implementierung dieser Algorithmen einige vielversprechende numerische Ergebnisse hervorbrachten, konnten die Autoren nur die copositive Neuformulierung des (StQP)s lösen. In [11] präsentierte Burer eine vollständig positive Umformulierung für allgemeine (QP)s, sogar mit binären Nebenbedingungen. Leider konnte er keine Methode zur Lösung für ein solches vollständig positives Problem präsentieren, noch wurde eine copositive Formulierung vorgeschlagen, auf die man die oben erwähnten Algorithmen modifizieren und anwenden könnte, um diese zu lösen. Diese Arbeit wird einen neuen endlichen Algorithmus zur Lösung eines standard quadratischen Optimierungsproblems aufstellen. Desweiteren werden in dieser Thesis copositve Darstellungen für ungleichungsbeschränkte sowie gleichungsbeschränkte quadratische Optimierungsprobleme vorgestellt. Für den ersten Ansatz wurde eine vollständig positive Umformulierung des (QP) entwickelt. Die copositive Umformulierung konnte durch Betrachtung des dualen Problems des vollständig positiven Problems erhalten werden. Ein direkterer Ansatz wurde gemacht, indem das Lagrange-Duale eines äquivalenten quadratischen Optimierungsproblems betrachtet wurde, das durch eine semidefinite quadratische Nebenbedingung beschränkt wurde. In diesem Zusammenhang werden Bedingungen für starke Dualität vorgeschlagen.
Theoretischer Hintergrund: Essstörungen sind schwere psychische Störungen, welche aufgrund ihrer Komplexität, der hohen Mortalitätsrate sowie häufiger Chronifizierungen zu den Herausforderungen für Therapie und Forschung zählen. Die Herzratenvariabilität, als Indikator autonomer Regulation, scheint insbesondere bei Anorexie-Patientinnen zu Gunsten einer höheren parasympathischen Aktivität verschoben. Dieser Befund lässt sich anhand des Model Of Neurovisceral Integration erklären: Gemäß dieses Modells stellt eine erhöhte Herzratenvariabilität einen Hinweis für erfolgreiche Selbstregulation dar. Letztere scheint für restriktives Essverhalten essentiell, während sie bei impulsiven Verhaltensweisen wie Essanfälle und Erb-rechen reduziert sein sollte. Die bisherige Studienlage zur Herzratenvariabilität bei Essstörungen ist aufgrund der begrenzten Anzahl der Studien, der geringen Stichprobengrößen und Nicht- Berücksichtigung sinnvoller Drittvariablen jedoch noch inkonsistent und oftmals widersprüchlich. Neben der physiologischen Komponente werden in der Essstörungssymptomatik Veränderungen im kognitiven und emotionalen Erleben beschrieben. Zur Untersuchung beider Konstrukte erweisen sich Methoden des Ecological Momentary Assessment als aufschlussreich, da hierbei das Verhalten im Alltag der Patienten erhoben wird. Die bisherige Literatur zeigte bislang eine gute Anwendbarkeit der Methodik bei Essstörungspatienten, wobei die Anzahl der Studien gering ist. So fehlen bislang Studien, welche Emotionen und Kognitionen in Bezug zu Mahlzeiten und Sättigungsempfindungen setzen, obgleich solche Zusammenhänge in der kognitiven Verhaltenstherapie als zentral angesehen werden. Methode: Zu Beginn einer stationären psychosomatischen Behandlung wurden bei N=51 Probandinnen (Anorexia Nervosa: 19, Bulimia Nervosa: 15, gesunde Kontrollgruppe: 17) zeit- und frequenzanalytische Parameter der Herzratenvariabilität unter Berücksichtigung des Alters und des BMI in einer standardisierten fünfminütigen Laboruntersuchung untersucht. Am selben Tag fand außerdem eine stündliche Erhebung von Essverhalten, essstörungsspezifischen Kognitionen und negativen Emotionen mittels Smartphone statt. Am Ende der Behandlung wurde die Untersuchung wiederholt. Allgemein lineare Modelle wurden ebenso wie Mehrebenenmodelle zur statistischen Überprüfung der Hypothesen eingesetzt. Ergebnisse: Anorexie-Patientinnen zeigten tendenziell eine höhere parasympathische Aktivität als gesunde Probandinnen. Im Vergleich zu den beiden anderen Gruppen wiesen Bulimie-Patientinnen die niedrigste HRV auf. Antidepressiva führten zu einer Verringerung der HRV, genauso wie bei Anorexie-Patientinnen die Krankheitsdauer. Zusammenhänge mit erlebten Essanfällen konnten nicht festgestellt werden. Im Therapieverlauf zeigte sich, dass sich bei Anorexie-Patientinnen die HRV nach erfolgreicher Gewichtszunahme signifikant verringerte. Des Weiteren zeigten Essstörungspatientinnen höhere Ausprägungen in essstörungsspezifischen Kognitionen und negativen Emotionen während des Messtages. Mahlzeiten führten zu einer Verschlechterung der Stimmung, insbesondere bei restriktiven Anorexie-Patientinnen. Das Sättigungsempfinden einer Mahlzeit hatte einen signifikanten Einfluss auf die Bewertung dieser bei der klinischen Stichprobe, nicht jedoch bei gesunden Probandinnen. Am Ende der psychosomatischen Behandlung zeigte sich eine deutliche Verbesserung der essstörungsspezifischen Kognitionen und Mahlzeit-Bewertungen. Mahlzeiten hatten überdies einen geringeren Einfluss auf die Stimmung als zu Behandlungsbeginn. Diskussion: Die Auffälligkeiten im psychischen und physiologischen Bereich bei Essstörungspatientinnen sind Ausdruck eines vielschichtigen Krankheitsbildes, welches jedoch durch intensive Therapieangebote veränderbar ist. Das Hinzuziehen sinnvoller Drittvariablen erscheint bei Untersuchungen zur Herzratenvariabilität bei Essstörungspatienten essentiell. Darüber hin-aus zeigt die vorliegende Studie erstmals Zusammenhänge zwischen Mahlzeiten, Sättigungsempfinden und Essstörungssymptomatik mittels Ecological Momentary Assessment. Diese Methodik bietet einen inkrementellen Nutzen in der Erhebung verhaltensnaher Therapieerfolge. Resultierende Therapieansätze und Implikationen der Studie werden aufgezeigt.