This thesis focuses on two topics, computational methods for large spatial datasets and functional data ranking. Both are tackling the challenges of big and high-dimensional data. The first topic is motivated by the prohibitive computational burden in fitting Gaussian process models to large and irregularly spaced spatial datasets. Various approximation methods have been introduced to reduce the computational cost, but many rely on unrealistic assumptions about the process and retaining statistical efficiency remains an issue. We propose a new scheme to approximate the maximum likelihood estimator and the kriging predictor when the exact computation is infeasible. The proposed method provides different types of hierarchical low-rank approximations that are both computationally and statistically efficient. We explore the improvement of the approximation theoretically and investigate the performance by simulations. For real applications, we analyze a soil moisture dataset with 2 million measurements with the hierarchical low-rank approximation and apply the proposed fast kriging to fill gaps for satellite images. The second topic is motivated by rank-based outlier detection methods for functional data. Compared to magnitude outliers, it is more challenging to detect shape outliers as they are often masked among samples. We develop a new notion of functional data depth by taking the integration of a univariate depth function. Having a form of the integrated depth, it shares many desirable features. Furthermore, the novel formation leads to a useful decomposition for detecting both shape and magnitude outliers. Our simulation studies show the proposed outlier detection procedure outperforms competitors in various outlier models. We also illustrate our methodology using real datasets of curves, images, and video frames. Finally, we introduce the functional data ranking technique to spatio-temporal statistics for visualizing and assessing covariance properties, such as separability and full symmetry. We formulate test functions as functions of temporal lags for each pair of spatial locations and develop a rank-based testing procedure induced by functional data depth for assessing these properties. The method is illustrated using simulated data from widely used spatio-temporal covariance models, as well as real datasets from weather stations and climate model outputs.

This thesis investigates the choices under risk in the framework of non-expected utility theories. One of the key contributions of this thesis is providing an approach that allows for a complete characterisation of Cumulative Prospect Theory (CPT) preferences without prior knowledge of the reference point. The location of the reference point that separates gains from losses is derived endogenously, thus, without any additional assumptions on the decision maker’s risk behaviour. This is different to the convention used in the literature, according to which, the reference point is preselected. The problem arising from imposing the location of the reference point is that the underlying preference conditions might not be alligned with the predictions made by the model. Consequently, it is difficult to verify such a model or to test it empirically. The present contribution offers a set of normatively and descriptively appealing preference conditions, which enable the elicitation of the reference point from the decision maker’s behaviour. Since these conditions are derived using objective probabilities, they can also be applied to settings such as health or insurance, where the continuity of the utility function is not required. As a result, the obtained representation theorem is not only the most general foundation for CPT currently available, but it also provides further support for the use of CPT as a modelling tool in decision theory and fi…nance. Another contribution that this thesis can be credited with is an application of rank-dependent utility theory (RDU) to the problem of insurance demand in the monopoly market affected by adverse selection. The present approach extends the classical model of Stiglitz (1977) by accounting for an additional component of heterogeneity among consumers, the heterogeneity in risk perception. Speci…fically, consumers employ distinctive probability weighting functions to assess the likelihood of risky events. This aspect of consumers’' behaviour highlights the importance that the probabilistic risk attitudes within the RDU framework, such as optimism and pessimism, have for the choice of insurance contract. The analysis yields a separating equilibrium, with full insurance for a sufficiently pessimistic decision maker. An important implication of this result is that any low-risk individual who sufficiently overestimates his probability of loss will induce the uninformed insurer to o¤er him full coverage, thereby, affecting the high-risk type adversely. This outcome is consistent with the recent empirical puzzle regarding the correlation between ex-post risk and insurance coverage, according to which, agents with low exposure to risk receive a larger amount of compensation. By providing an explanation of this pattern of individual behaviour, the current work demonstrates that theory and practice of insurance demand can be reconciled to a greater extent. The paper also provides a behavioural rationale for policy intervention in the market with RDU agents, where the initial distortions in contracts due to unobservable risks are aggravated by the non-linear weighting of probability of a risky event.

Nous nous intéressons dans ce travail au problème de prévision de nouveaux liens dans des grands graphes de terrain. Nous explorons en particulier les approches topologiques dyadiques pour la prévision de liens. Différentes mesures de proximité topologique ont été étudiées dans la littérature pour prédire l’apparition de nouveaux liens. Des techniques d’apprentissage supervisé ont été aussi utilisées afin de combiner ces différentes mesures pour construire des modèles prédictifs. Le problème d’apprentissage supervisé est ici un problème difficile à cause notamment du fort déséquilibre de classes. Dans cette thèse, nous explorons différentes approches alternatives pour améliorer les performances des approches dyadiques pour la prévision de liens. Nous proposons d’abord, une approche originale de combinaison des prévisions fondée sur des techniques d’agrégation supervisée de listes triées (ou agrégation de préférences). Nous explorons aussi différentes approches pour améliorer les performances des approches supervisées pour la prévision de liens. Une première approche consiste à étendre l’ensemble des attributs décrivant un exemple (paires de noeuds) par des attributs calculés dans un réseau multiplexe qui englobe le réseau cible. Un deuxième axe consiste à évaluer l’apport destechniques de détection de communautés pour l’échantillonnage des exemples. Des expérimentations menées sur des réseaux réels extraits de la base bibliographique DBLP montrent l’intérêt des approaches proposées. / In this work, we are interested to tackle the problem of link prediction in complex networks. In particular, we explore topological dyadic approaches for link prediction. Different topological proximity measures have been studied in the scientific literature for finding the probability of appearance of new links in a complex network. Supervided learning methods have also been used to combine the predictions made or information provided by different topological measures. The create predictive models using various topological measures. The problem of supervised learning for link prediction is a difficult problem especially due to the presence of heavy class imbalance. In this thesis, we search different alternative approaches to improve the performance of different dyadic approaches for link prediction. We propose here, a new approach of link prediction based on supervised rank agregation that uses concepts from computational social choice theory. Our approach is founded on supervised techniques of aggregating sorted lists (or preference aggregation). We also explore different ways of improving supervised link prediction approaches. One approach is to extend the set of attributes describing an example (pair of nodes) by attributes calculated in a multiplex network that includes the target network. Multiplex networks have a layered structure, each layer having different kinds of links between same sets of nodes. The second way is to use community information for sampling of examples to deal with the problem of classe imabalance. Experiments conducted on real networks extracted from well known DBLP bibliographic database.

Aggression has many faces in sport. For this reason, it is a complex but fascinating field for studying the nature of aggression. All athletes have to control and channel aggression constructively into skill in their sport in order to sustain optimal performance. The purpose of this research was to study aggression in sport and determine whether aggressive energies can constructively be expressed in the rules of the game and channelled into a powerful and inspiring performance by the athlete. In sport, any type of aggression can transmute into a destructive force that can debilitate and nullify performance. Through this study, the researcher wanted to determine if the participation in Martial Arts can reduce aggression and whether progression in belt rank (beginner, intermediate and advanced) in Martial Arts could cause a gradual decrease in the aggressive behaviour of young adolescents. The researcher also wanted to determine if participation in Martial Arts, other than other types of sports activities (for example, hockey) and those 16 participants absent from any sporting activity, may serve as a deterrent to aggressiveness. A secondary aim was to determine if Martial Arts could be used as a coping strategy for young adolescents to improve their overall mental wellbeing. The core focus of this study is to determine if the participation in Martial Arts (specifically Tae Kwon Do) can reduce aggressive tendencies in young adolescents. The researcher chose Tae Kwon Do from the various Martial Arts styles, because Tae Kwon Do has a very broad combination of traditional components or elements of what any Martial Arts program consist of. It also consists of elements that are incorporated within the program that may have the desired outcome on a participant taking part in such a training program. In Martial Arts, the emphasis is on physical fitness, self-confidence and training in mental control. Most combat activities are usually thought of as providing opportunities for the display of competence and masculinity, the development of self-confidence and a release of tension with the sublimation of aggressive impulses. The term “Martial Arts” will be used throughout this study. The researcher decided on a survey method to carry out this study. Standardised questionnaires were used to determine whether progression in belt rank (beginner, intermediate and advanced) in Martial Arts (group1) could cause a gradual decrease in aggressive behaviour among young adolescents. The results of the analysis of differences between the different levels of Martial Arts showed no statistically significant differences between the levels on all the aggression sub-scales. The personal growth scores, obtained from the responses to the psychological wellbeing questionnaire, were significantly lower for the beginner group than for the other two groups (intermediate and advanced). The results on the psychological wellbeing sub-scales indicated that the personal growth and self-acceptance scores of the Martial Arts group were significantly higher than those of the other two groups (hockey and non-participation). The group that did not participated in any sporting activity, had the lowest scores. Also to be determined was whether Martial Arts could be used as a coping strategy to improve the overall mental health of these adolescents. Copyright / Dissertation (MA)--University of Pretoria, 2009. / Biokinetics, Sport and Leisure Sciences / unrestricted

As doenças cardiovasculares (DCV) representam a principal causa de mortalidade e de incapacidade, em ambos os gêneros, no Brasil e no mundo. O padrão de consumo alimentar está tanto positiva como negativamente associado aos principais fatores de risco para DCV, entre eles diabetes, hipertensão, obesidade e hipertrigliceridemia, todos componentes da síndrome metabólica. Este estudo tem como objetivos identificar os padrões alimentares em indivíduos com DCV, considerando a densidade de energia, a gordura saturada, a fibra, o sódio e o potássio consumidos, e investigar sua associação com fatores de risco de DCV e síndrome metabólica. Trata-se de um estudo transversal. Foram utilizados dados do estudo DICA Br. A amostra foi composta de indivíduos com DCV, com idade superior a 45 anos, de todas as regiões brasileiras. O consumo alimentar foi obtido por recordatório alimentar de 24h e os padrões alimentares obtidos pela regressão por posto reduzido (RPR). Para a RPR, utilizaram-se 28 grupos alimentares como preditores e como variáveis respostas componentes dietéticos. O teste de Mann Whitney foi utilizado para testar as diferenças entre as médias dos escores. Foram obtidos dados de 1.047 participantes; 95% apresentavam doença arterial coronariana; em sua maioria, eram idosos, da classe econômica C1 e C2 e estudaram até o ensino médio. A prevalência de síndrome metabólica foi de 58%. Foram extraídos dois padrões alimentares. O primeiro foi marcado pelo maior consumo de fibra alimentar e potássio, composto por arroz e feijão, frutas e sucos naturais com ou sem açúcar, legumes, carne bovina ou processada, verduras, raízes e tubérculos. O segundo padrão caracterizou-se pelo consumo de gordura saturada e maior densidade energética, representado por panificados salgados, gorduras, carne bovina e processada, doces caseiros, pizza, salgadinhos de pacote ou festa, sanduíche e alimento salgado pronto para consumo. Houve associação significativa entre o padrão alimentar 1 com medida da circunferência da cintura e nível de HDL adequados e com o padrão 2 e HDL adequado. A adoção do padrão alimentar 1 pode estar associada à proteção contra alguns dos componentes da síndrome metabólica. / Cardiovascular diseases (CVD) are the leading cause of mortality and disability in both genders in Brazil and worldwide. The dietary pattern is at the same time positive and negatively associated with the main risk factors for CVD, including diabetes, hypertension, obesity and hypertriglyceridemia, all components of the metabolic syndrome. This study aims to identify dietary patterns in individuals with CVD, considering the energy density, and the amount of saturated fatty acid, fiber, sodium and potassium of the diet, and to investigate its association with CVD risk factors and metabolic syndrome. This is a cross-sectional study, data were used from \"DICA Br\" study. The sample consisted of individuals with CVD, over 45 years old, residents from all Brazilian regions. Food consumption was obtained by one 24-hours diet recall and dietary patterns by reduced rank regression (RRR). In the RRR, 28 food groups were included as predictors and dietary components was chosen as the response variable. The Mann-Whitney test was used to test the differences between the factors scores\' means. Data of 1047 participants were analyzed. 95% have coronary artery disease, most are elderly, economical class most observed are C1 and C2. Also, most of them and studied up to high school. The prevalence of metabolic syndrome was 58%. Two dietary patterns were extracted: the first one is higher in dietary fiber and potassium, which is composed by rice, beans, fruits and natural juices with or without sugar, vegetables, beef or processed meat, roots and tubers. The second pattern is higher in saturated fatty acid and energy density, represented by breads, fats, and processed meat, homemade pastries, pizza, snacks or party package, sandwich and salty food ready for consumption. There was a significant association between dietary pattern 1 and low waist circumference and adequate high density cholesterol blood concentration. There was a significant association between dietary pattern 2 and adequate high density cholesterol blood concentration. We suggest that the adoption of the dietary pattern 1 may be associated with protection against some of the components of metabolic syndrome.

Optimierungsaufgaben unter Partiellen Differentialgleichungen (PDGLs) tauchen in verschiedensten Anwendungen der Wissenschaft und Technik auf. Wenn wir ein PDGL Problem formulieren, kann es aufgrund seiner Größe unmöglich werden, das Problem mit konventionellen Methoden zu lösen. Zusätzlich noch eine Optimierung auszuführen birgt zusätzliche Schwierigkeiten. In vielen Fällen können wir das PDGL Problem in einem kompakteren Format formulieren indem wir der zugrundeliegenden Kronecker-Produkt Struktur zwischen Raum- und Zeitdimension Aufmerksamkeit schenken. Wenn die PDGL zusätzlich mit Isogeometrischer Analysis diskretisiert wurde, können wir zusätlich eine Niedrig-Rang Approximation zwischen den einzelnen Raumdimensionen erzeugen. Diese Niedrig-Rang Approximation lässt uns die Systemmatrizen schnell und speicherschonend aufstellen. Das folgende PDGL-Problem lässt sich als Summe aus Kronecker-Produkten beschreiben, welche als eine Niedrig-Rang Tensortrain Formulierung interpretiert werden kann. Diese kann effizient im Niedrig-Rang Format gelöst werden. Wir illustrieren dies mit unterschiedlichen, anspruchsvollen Beispielproblemen.:Introduction Tensor Train Format Isogeometric Analysis PDE-constrained Optimization Bayesian Inverse Problems A low-rank tensor method for PDE-constrained optimization with Isogeometric Analysis A low-rank matrix equation method for solving PDE-constrained optimization problems A low-rank tensor method to reconstruct sparse initial states for PDEs with Isogeometric Analysis Theses and Summary Bibilography / Optimization problems governed by Partial Differential Equations (PDEs) arise in various applications of science and engineering. If we formulate a discretization of a PDE problem, it may become infeasible to treat the problem with conventional methods due to its size. Solving an optimization problem on top of the forward problem poses additional difficulties. Often, we can formulate the PDE problem in a more compact format by paying attention to the underlying Kronecker product structure between the space and time dimension of the discretization. When the PDE is discretized with Isogeometric Analysis we can additionally formulate a low-rank representation with Kronecker products between its individual spatial dimensions. This low-rank formulation gives rise to a fast and memory efficient assembly for the system matrices. The PDE problem represented as a sum of Kronecker products can then be interpreted as a low-rank tensor train formulation, which can be efficiently solved in a low-rank format. We illustrate this for several challenging PDE-constrained problems.:Introduction Tensor Train Format Isogeometric Analysis PDE-constrained Optimization Bayesian Inverse Problems A low-rank tensor method for PDE-constrained optimization with Isogeometric Analysis A low-rank matrix equation method for solving PDE-constrained optimization problems A low-rank tensor method to reconstruct sparse initial states for PDEs with Isogeometric Analysis Theses and Summary Bibilography

<div><div>In this thesis, we focus on two challenges arising in kinetic equations, high dimensions and uncertainties. To reduce the dimensions, we proposed efficient methods for linear Boltzmann and full Boltzmann equations based on dynamic low-rank frameworks. For linear Boltzmann equation, we proposed a method that is based on macro-micro decomposition of the equation; the low-rank approximation is only used for the micro part of the solution. The time and spatial discretizations are done properly so that the overall scheme is second-order accurate (in both the fully kinetic and the limit regime) and asymptotic-preserving (AP). That is, in the diffusive regime, the scheme becomes a macroscopic solver for the limiting diffusion equation that automatically captures the low-rank structure of the solution. Moreover, the method can be implemented in a fully explicit way and is thus significantly more efficient compared to the previous state of the art. We demonstrate the accuracy and efficiency of the proposed low-rank method by a number of four-dimensional (two dimensions in physical space and two dimensions in velocity space) simulations. We further study the adaptivity of low-rank methods in full Boltzmann equation. We proposed a highly efficient adaptive low- rank method in Boltzmann equation for computations of steady state solutions. The main novelties of this approach are: On one hand, to the best of our knowledge, the dynamic low- rank integrator hasn’t been applied to full Boltzmann equation till date. The full collision operator is local in spatial variable while the convection part is local in velocity variable. This separated nature is well-suited for low-rank methods. Compared with full grid method (finite difference, finite volume,...), the dynamic low-rank method can avoid the full computations of collision operators in each spatial grid/elements. Resultingly, it can achieve much better efficiency especially for some low rank flows (e.g. normal shock wave). On the other hand, our adaptive low-rank method uses a novel dynamic thresholding strategy to adaptively control the computational rank to achieve better efficiency especially for steady state solutions. We demonstrate the accuracy and efficiency of the proposed adaptive low rank method by a number of 1D/2D Maxwell molecule benchmark tests. On the other hand, for kinetic equations with uncertainties, we focus on non-intrusive sampling methods where we are able to inherit good properties (AP, positivity preserving) from existing deterministic solvers. We propose a control variate multilevel Monte Carlo method for the kinetic BGK model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carlo technique with the computation of the optimal control variate multipliers derived from local or global variance minimization prob- lems. Consistency and convergence analysis for the method equipped with a second-order positivity-preserving and asymptotic-preserving scheme in space and time is also performed. Various numerical examples confirm that the optimized multilevel Monte Carlo method outperforms the classical multilevel Monte Carlo method especially for problems with dis- continuities<br></div></div>

The focus of this diploma thesis is on methods for the subjective assessment of sound quality according to recommandations given by International Telecommunication Union ITU. The thesis is thematically divided into four parts. The first part is an interpretation of methods based on internationally accepted standards (method of small impairments, MUSHRA, general methods). The second part describes the functional blocks of application developed for this thesis in LabVIEW enviroment. Next part explains its practical application, especially its running possibilities. The last part describes a listening experiment, aim of which was to verify the application's features and to compare the results of the subjective method used in the experiment with the results of the objective method PEAQ.

Obwohl schon seit den 50er Jahren auf dem Gebiet der Automatischen Textzusammenfassung Forschung betrieben wird, wurden der Nutzen und die Notwendigkeit dieser Systeme erst mit dem Boom des Internets richtig erkannt. Das World Wide Web stellt eine täglich wachsende Menge an Informationen zu nahezu jedem Thema zur Verfügung. Um den Zeitaufwand zum Finden und auch zum Wiederfinden der richtigen Informationen zu minimieren, traten Suchmaschinen ihren Siegeszug an. Doch um einen Überblick zu einem ausgewählten Thema zu erhalten, ist eine einfache Auflistung aller in Frage kommenden Seiten nicht mehr adäquat. Zusätzliche Mechanismen wie Extraktionsalgorithmen für die automatische Generierung von Zusammenfassungen können hier helfen, Suchmaschinen oder Webkataloge zu optimieren, um so den Zeitaufwand bei der Recherche zu verringern und die Suche einfacher und komfortabler zu gestalten. In dieser Diplomarbeit wurde eine Analyse von Extraktionsalgorithmen durchgeführt, welche für die automatische Textzusammenfassung genutzt werden können. Auf Basis dieser Analyse als viel versprechend eingestufte Algorithmen wurden in Java implementiert und die mit diesen Algorithmen erstellten Zusammenfassungen in einer Evaluation verglichen.

We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations in lifted form which arise in model reduction of periodic descriptor systems. We extend the alternating direction implicit method and the Smith method to such equations. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximations to the solutions of projected periodic Lyapunov equations in lifted form with low-rank right-hand side. Moreover, we consider an application of the Lyapunov solvers to balanced truncation model reduction of periodic discrete-time descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.:1 Introduction 2 Periodic descriptor systems 3 ADI method for causal lifted Lyapunov equations 4 Smith method for noncausal lifted Lyapunov equations 5 Application to model order reduction 6 Numerical results 7 Conclusions