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Variational inequality problems constitute a common basis to investigate the theory and algorithms for many problems in mathematical physics, in economy as well as in natural and technical sciences. They appear in a variety of mathematical applications like convex programming, game theory and economic equilibrium problems, but also in fluid mechanics, physics of solid bodies and others. Many variational inequalities arising from applications are ill-posed. This means, for example, that the solution is not unique, or that small deviations in the data can cause large deviations in the solution. In such a situation, standard solution methods converge very slowly or even fail. In this case, so-called regularization methods are the methods of choice. They have the advantage that an ill-posed original problem is replaced by a sequence of well-posed auxiliary problems, which have better properties (like, e.g., a unique solution and a better conditionality). Moreover, a suitable choice of the regularization term can lead to unconstrained auxiliary problems that are even equivalent to optimization problems. The development and improvement of such methods are a focus of current research, in which we take part with this thesis. We suggest and investigate a logarithmic-quadratic proximal auxiliary problem (LQPAP) method that combines the advantages of the well-known proximal-point algorithm and the so-called auxiliary problem principle. Its exploration and convergence analysis is one of the main results in this work. The LQPAP method continues the recent developments of regularization methods. It includes different techniques presented in literature to improve the numerical stability: The logarithmic-quadratic distance function constitutes an interior point effect which allows to treat the auxiliary problems as unconstrained ones. Furthermore, outer operator approximations are considered. This simplifies the numerical solution of variational inequalities with multi-valued operators since, for example, bundle-techniques can be applied. With respect to the numerical practicability, inexact solutions of the auxiliary problems are allowed using a summable-error criterion that is easy to implement. As a further advantage of the logarithmic-quadratic distance we verify that it is self-concordant (in the sense of Nesterov/Nemirovskii). This motivates to apply the Newton method for the solution of the auxiliary problems. In the numerical part of the thesis the LQPAP method is applied to linearly constrained, differentiable and nondifferentiable convex optimization problems, as well as to nonsymmetric variational inequalities with co-coercive operators. It can often be observed that the sequence of iterates reaches the boundary of the feasible set before being close to an optimal solution. Against this background, we present the strategy of under-relaxation, which robustifies the LQPAP method. Furthermore, we compare the results with an appropriate method based on Bregman distances (BrPAP method). For differentiable, convex optimization problems we describe the implementation of the Newton method to solve the auxiliary problems and carry out different numerical experiments. For example, an adaptive choice of the initial regularization parameter and a combination of an Armijo and a self-concordance step size are evaluated. Test examples for nonsymmetric variational inequalities are hardly available in literature. Therefore, we present a geometric and an analytic approach to generate test examples with known solution(s). To solve the auxiliary problems in the case of nondifferentiable, convex optimization problems we apply the well-known bundle technique. The implementation is described in detail and the involved functions and sequences of parameters are discussed. As far as possible, our analysis is substantiated by new theoretical results. Furthermore, it is explained in detail how the bundle auxiliary problems are solved with a primal-dual interior point method. Such investigations have by now only been published for Bregman distances. The LQPAP bundle method is again applied to several test examples from literature. Thus, this thesis builds a bridge between theoretical and numerical investigations of solution methods for variational inequalities.
The role of cortisol and cortisol dynamics in patients after aneurysmal subarachnoid hemorrhage
(2011)
Spontaneous aneurysmal subarachnoid hemorrhage (SAH) is a form of stroke which constitutes a severe trauma to the brain and often leads to serious long-term medical and psychosocial sequels which persist for years after the acute event. Recently, adrenocorticotrophic hormone deficiency has been identified as one possible consequence of the bleeding and is assumed to occur in around 20% of all survivors. Additionally, a number of studies report a high prevalence of post-SAH symptoms such as lack of initiative, fatigue, loss of concentration, impaired quality of life and psychiatric symptoms such as depression. The overlap of these symptoms and those of patients with untreated partial or complete hypopituitarism lead to the suggestion that neuroendocrine dysregulations may contribute to the psychosocial sequels of SAH. Therefore, one of the aims of this work is to gain insights into the role of neuroendocrine dysfunction on quality of life and the prevalence of psychiatric sequels in SAH-patients. Additionally, as data on cortisol dynamics after SAH are scarce, diurnal cortisol profiles are investigated in patients in the acute and chronic phase, as well as the cortisol awakening response and feedback sensitivity in the chronic phase after SAH. As a result, it can be shown that some SAH patients exhibit lower serum cortisol levels but at the same time a higher cortisol awakening response in saliva than healthy controls. Also, patients in the chronic phase after SAH do have a stable diurnal cortisol rhythm while there are disturbances in around 50% of all patients in the acute phase, leading to the conclusion that a single baseline measurement of cortisol is of no substantial use for diagnosing cortisol dysregulations in the acute phase after SAH. It is assumed that in SAH patients endocrine changes occur over time and that a combination of adrenal exhaustion and a subsequent downregulation of corticosteroid binding globulin may be the most probable causes for the dissociation of serum cortisol concentrations and salivary cortisol profiles in the investigated SAH patients. These changes may be an emergency response after SAH and, as elevated free cortisol levels are connected to a better psychosocial outcome in patients in the chronic phase after SAH, this reaction may even be adaptive.
The demand for reliable statistics has been growing over the past decades, because more and more political and economic decisions are based on statistics, e.g. regional planning, allocation of funds or business decisions. Therefore, it has become increasingly important to develop and to obtain precise regional indicators as well as disaggregated values in order to compare regions or specific groups. In general, surveys provide the information for these indicators only for larger areas like countries or administrative divisions. However, in practice, it is more interesting to obtain indicators for specific subdivisions like on NUTS 2 or NUTS 3 levels. The Nomenclature of Units for Territorial Statistics (NUTS) is a hierarchical system of the European Union used in statistics to refer to subdivisions of countries. In many cases, the sample information on such detailed levels is not available. Thus, there are projects such as the European Census, which have the goal to provide precise numbers on NUTS 3 or even community level. The European Census is conducted amongst others in Germany and Switzerland in 2011. Most of the participating countries use sample and register information in a combined form for the estimation process. The classical estimation methods of small areas or subgroups, such as the Horvitz-Thompson (HT) estimator or the generalized regression (GREG) estimator, suffer from small area-specific sample sizes which cause high variances of the estimates. The application of small area methods, for instance the empirical best linear unbiased predictor (EBLUP), reduces the variance of the estimates by including auxiliary information to increase the effective sample size. These estimation methods lead to higher accuracy of the variables of interest. Small area estimation is also used in the context of business data. For example during the estimation of the revenues of specific subgroups like on NACE 3 or NACE 4 levels, small sample sizes can occur. The Nomenclature statistique des activités économiques dans la Communauté européenne (NACE) is a system of the European Union which defines an industry standard classification. Besides small sample sizes, business data have further special characteristics. The main challenge is that business data have skewed distributions with a few large companies and many small businesses. For instance, in the automotive industry in Germany, there are many small suppliers but only few large original equipment manufacturers (OEM). Altogether, highly influential units and outliers can be observed in business statistics. These extreme values in connection with small sample sizes cause severe problems when standard small area models are applied. These models are generally based on the normality assumption, which does not hold in the case of outliers. One way to solve these peculiarities is to apply outlier robust small area methods. The availability of adequate covariates is important for the accuracy of the above described small area methods. However, in business data, the auxiliary variables are hardly available on population level. One of several reasons for that is the fact that in Germany a lot of enterprises are not reflected in business registers due to truncation limits. Furthermore, only listed enterprises or companies which trespass specific thresholds are obligated to publish their results. This limits the number of potential auxiliary variables for the estimation. Even though there are issues with available covariates, business data often include spatial dependencies which can be used to enhance small area methods. Next to spatial information based on geographic characteristics, group-specific similarities like related industries based on NACE codes can be used. For instance, enterprises from the same NACE 2 level, e.g. sector 47 retail trade, behave more similar than two companies from different NACE 2 levels, e.g. sector 05 mining of coal and sector 64 financial services. This spatial correlation can be incorporated by extending the general linear mixed model trough the integration of spatially correlated random effects. In business data, outliers as well as geographic or content-wise spatial dependencies between areas or domains are closely linked. The coincidence of these two factors and the resulting consequences have not been fully covered in the relevant literature. The only approach that combines robust small area methods with spatial dependencies is the M-quantile geographically weighted regression model. In the context of EBLUP-based small area models, the combination of robust and spatial methods has not been considered yet. Therefore, this thesis provides a theoretical approach to this scientific and practical problem and shows its relevance in an empirical study.
Edition und Kommentar von 27 Texten auf Papyrus aus den französisch-italienischen Grabungen in Tebtynis (Umm el-Breigât), Ägypten. Alle Texte stammen aus römischer Zeit und sind in Tebtynis gefunden worden. Sie werden hier erstmals mit Abschrift, Übersetzung und Kommentar herausgegeben und beleuchten diverse Aspekte des täglichen Lebens, so auf Verwaltung, Wirtschaft, Rechtsangelegenheiten, Bevölkerung, Religion, Steuerwesen, Arbeitsalltag, Vertragswesen, geschäftliche und erbrechtliche Angelegenheiten. Es handelt sich somit um Quellenmaterial für alle altertumswissenschaftlichen Nachbarsdisziplinen. Folgende Texte sind enthalten: 1. Rundschreiben des Praefectus Aegypti; 2. Monatsbericht der Sitologen von Kerkesis; 3. κατ'ἄνδρα-Bericht der Sitologen von Kerkesis (Verso von Nr. 2); 4. Fragment eines Amtlichen Schreibens; 5. Verhandlungsprotokoll; 6. Liste von Dörfern und Geldsummen; 7. Liturgie-Vorschlagsliste (?); 8. Personenliste; 9. Aufstellung über Naturalien; 10. Tempelabrechnung; 11. Zensusdeklaration; 12. Schluß einer Eingabe mit Namenliste; 13. Eingabe der Thenherakleia?; 14. Quittungsbogen für verschiedene Steuern; 15. Quittungen für Dammsteuer; 16. Fragment einer Lohnquittung für Arbeiten auf einem Kleros (?); 17. Fragment einer Lohnquittung; 18. Liste von Zahlungen in Weizen; 19. Abrechnung von Außenständen in Naturalien und Geld; 20. Agoranomischer Vertrag über ein Geld- und Getreidedarlehen; 21. Donatio mortis causa; 22. Geschäftsbrief: Heron an Heron; 23. Geschäftsbrief: Heron an Heron; 24. Geschäftsbrief: Heron an Sabinos; 25. Brief; 26. Brief; 27. Fragment mit Erwähnung von Dörfern und Immobilien (descr.)
The complicated human alternative GR promoter region plays a pivotal role in the regulation of GR levels. In this thesis, both genomic and environmental factors linked with GR expression are covered. This research showed that GR promoters were susceptible to silencing by methylation and the activity of the individual promoters was also modulated by SNPs. E2F1 is a major element to drive the expression of GR 1F transcripts and single CpG dinucleotide methylation cannot mediate the inhibition of transcription in vitro. Also, the distribution of GR first exons and 3" splice variants (GRα and GR-P) is expressed throughout the human brain with no region-specific alternative first exon usage. These data mirrored the consistently low levels of methylation in the brain, and the observed homogeneity throughout the studied regions. Taken together, the research presented in this thesis explored several layers of complexity in GR transcriptional regulation.
There is a lot of evidence for the impact of acute glucocorticoid treatment on hippocampus-dependent explicit learning and memory (memory for facts and events). But there have been few studies, investigating the effect of glucocorticoids on implicit learning and memory. We conducted three studies with different methodology to investigate the effect of glucocorticoids on different forms of implicit learning. In Study 1, we investigated the effect of cortisol depletion on short-term habituation in 49 healthy subjects. 25 participants received oral metyrapone (1500 mg) to suppress endogenous cortisol production, while 24 controls received oral placebo. Eye blink electromyogram (EMG) responses to 105 dB acoustic startle stimuli were assessed. Effective endogenous cortisol suppression had no effect on short-term habituation of the startle reflex, but startle eye blink responses were significantly increased in the metyrapone group. The latter findings are in line with previous human studies, which have shown that excess cortisol, sufficient to fully occupy central nervous system (CNS) corticosteroid receptors, may reduce startle eye blink. This effect may be mediated by CNS mechanisms controlling cortisol feedback. In Study 2, we investigated delay or trace eyeblink conditioning in a patient group with a relative hypocortisolism (30 patients with fibromyaligia syndrome/FMS) compared to 20 healthy control subjects. Conditioned eyeblink response probability was assessed by EMG. Morning cortisol levels, ratings of depression, anxiety and psychosomatic complaints as well as general symptomatology and psychological distress were assessed. As compared to healthy controls FMS patients showed lower morning cortisol levels, and trace eyeblink conditioning was facilitated whereas delay eyeblink conditioning was reduced. Cortisol measures correlate significantly only with trace eyeblink conditioning. Our results are in line with studies of pharmacologically induced hyper- and hypocortisolism, which affected trace eyeblink conditioning. We suggest that endocrine mechanisms affecting hippocampus-mediated forms of associative learning may play a role in the generation of symptoms in these patients.rnIn Study 3, we investigated the effect of excess cortisol on implicit sequence learning in healthy subjects. Oral cortisol (30 mg) was given to 29 participants, whereas 31 control subjects received placebo. All volunteers performed a 5-choice serial reaction time task (SRTT). The reaction speed of every button-press was determined and difference-scores were calculated as a proof of learning. Compared to the control group, we found a delayed learning in the cortisol group at the very beginning of the task. This study is the first human investigation, indicating impaired implicit memory function after exogenous administration of the stress hormone cortisol. Our findings support a previous neuroimaging study, which suggested that the medial temporal lobe (including the hippocampus) is also active in implicit sequence learning, but our results may also depend on the engagement of other brain structures.
This work is concerned with two kinds of objects: regular expressions and finite automata. These formalisms describe regular languages, i.e., sets of strings that share a comparatively simple structure. Such languages - and, in turn, expressions and automata - are used in the description of textual patterns, workflow and dependence modeling, or formal verification. Testing words for membership in any given such language can be implemented using a fixed - i.e., finite - amount of memory, which is conveyed by the phrasing finite-automaton. In this aspect they differ from more general classes, which require potentially unbound memory, but have the potential to model less regular, i.e., more involved, objects. Other than expressions and automata, there are several further formalisms to describe regular languages. These formalisms are all equivalent and conversions among them are well-known.However, expressions and automata are arguably the notions which are used most frequently: regular expressions come natural to humans in order to express patterns, while finite automata translate immediately to efficient data structures. This raises the interest in methods to translate among the two notions efficiently. In particular,the direction from expressions to automata, or from human input to machine representation, is of great practical relevance. Probably the most frequent application that involves regular expressions and finite automata is pattern matching in static text and streaming data. Common tools to locate instances of a pattern in a text are the grep application or its (many) derivatives, as well as awk, sed and lex. Notice that these programs accept slightly more general patterns, namely ''POSIX expressions''. Concerning streaming data, regular expressions are nowadays used to specify filter rules in routing hardware.These applications have in common that an input pattern is specified in form a regular expression while the execution applies a regular automaton. As it turns out, the effort that is necessary to describe a regular language, i.e., the size of the descriptor,varies with the chosen representation. For example, in the case of regular expressions and finite automata, it is rather easy to see that any regular expression can be converted to a finite automaton whose size is linear in that of the expression. For the converse direction, however, it is known that there are regular languages for which the size of the smallest describing expression is exponential in the size of the smallest describing automaton.This brings us to the subject at the core of the present work: we investigate conversions between expressions and automata and take a closer look at the properties that exert an influence on the relative sizes of these objects.We refer to the aspects involved with these consideration under the titular term of Relative Descriptional Complexity.
Durch Bodendegradation werden jedes Jahr weltweit große Schäden verursacht. Die beiden Hauptverursacher für die globale Bodendegradation sind die Wind- und die Wassererosion. Für die Planung von effizienten Schutzmaßnahmen oder regionalen Managementplänen ist es deshalb wichtig zu verstehen, dass die beiden Prozesse nicht nur als abgekoppelte Phänomene auftreten. Auch wenn seit einiger Zeit das Bewusstsein hierfür zugenommen hat und eine steigende Anzahl von Bodenerosionsstudien auf diesen Sachverhalt eingehen, so bestehen vor allem bei der Abschätzung der relativen Bedeutung und dem Verständnis der vorhandenen Interaktionen zwischen der Wind- und Wassererosion noch substantielle Wissenslücken. Da indirekte Messverfahren, wie beispielsweise die Luftbildauswertung oder die Fernerkundung, für mikro-skalige Prozessstudien ungeeignet sind, beschränken sich die Studien zur Erfassung der Interaktion beider Prozesse zumeist auf die direkten und/oder experimentellen Messungen. Ein Vergleich der Abtragsraten und eine Untersuchung der Interaktionen zwischen der Wind- und der Wassererosion ist jedoch sehr schwierig, da es bislang kein Messinstrument gibt, dass einfach und schnell, die durch Wind, Wasser oder deren Zusammenwirken verursachten Erosionsraten auf natürlichen Oberflächen bestimmen kann. Aus diesem Grund wurde im Rahmen dieses Dissertationsprojekts erstmals, ein mobiler Windkanal mit integrierter Beregnungsanlage konzipiert und umgesetzt. Seine simulierten Wind- und Niederschlagseigenschaften wurden in Labormessungen mit einem Laserdistrometer, Niederschlagssammlern, Anemometern und Nebelversuchen bestimmt. Die beim Einsatz der Anlage in unterschiedlichen Messkampagnen gewonnenen Erkenntnisse zu seinem Aufbau flossen stetig in die Weiterentwicklung des Kanals ein. Die Qualität der simulierten Bedingungen im Kanal können nach den Modifikationen und unter Einbeziehung der Anforderungen an einen geländefähigen Kanal mit guter Mobilität, als sehr gut bezeichnet werden. Insbesondere die Reproduzierbarkeit der simulierten Bedingungen treten hier positiv hervor. Die angestrebten Ziele dieser Arbeit konnten weitestgehend erfüllt werden. Mit dem mobilen Windkanal mit integrierter Beregnungsanlage steht in Zukunft eine Anlage zur Verfügung, mit der die Abtragsraten der Wind- und Wassererosion im Gelände, getrennt und in ihrer gemeinsamen Wirkung, gemessen werden können. Durch den Einsatz der Anlage ist es möglich, einige der noch offenen wissenschaftlichen Fragen zur relativen Bedeutung und Interaktion der beiden Prozesse zukünftig zu untersuchen, um weitere Erkenntnisse über Ihren Einfluss auf die Bodendegradation, in Abhängigkeit von Landnutzungsänderungen und dem Klimawandel, zu erhalten.
By rodent studies it has been shown that the mineralocorticoid receptor (MR) is a candidate gene for the investigation of cognitive functions comparable to human executive function. The present work addresses the question if polymorphisms in the MR gene can act as a "probe" to explain a part of the interindividual variance of human executive functions. For this purpose, 72 healthy young participants were assigned to four equally sized groups, concerning their particular MR genotype for two common MR polymorphisms. They were investigated in an electroencephalogram (EEG) test session, accomplishing two cognitive tests while delivering saliva samples for subsequent cortisol measures. The two tests chosen for the assessment of executive functions were the Attention Network Task (ANT) and a modified version of the Wisconsin Card Sorting Test (WCST).Chapter 1 of the present work reports of the rational bases for the empirical approach, which were built up on a broad theoretical background presented in Chapter 2. In the third chapter, the investigation and results of the statistical analysis for behavioral data (i.e. reaction times, accuracy/error rates) are presented. No association with MR polymorphisms was found for the reaction times of both tests. For the accuracy rate, differences between genotype groups were found for ANT and WCST, indicating an association of MR polymorphisms and accuracy in the Alertness and Executive Control network of the ANT and during the detection of an intradimensional shift in the WCST. Data acquisition and the results for EEG data analyses are presented in Chapter 4. The results show that groups differing for MR genotype show different activity over prefrontal motor areas during the process of answering to the ANT. Those group differences again were prominent for the Alertness and Executive Control network. A tendency for further significant group differences was found for activity on frontopolar positions in extradimensional rule switching. Chapter 5 summarizes the findings for the analysis of salivary free cortisol, showing a tendency for an association between MR polymorphisms and a mildly stimulated Hypothalamus-pituitary-adrenal (HPA) axis during the test situation. The results of the different measures are integrated and discussed in Chapter 6 within the scope of novel findings in investigating the functionality of the chosen MR polymorphisms. Finally, Chapter 7 gives an outlook on the methodology and constraints of future research strategies to further describe the role of the MR in human cognitive function.