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Problematic weight regulation as found in obesity and Anorexia Nervosa (AN) are chronic conditions which require long-term management. In order to develop long-term strategies to manage these conditions, a clearer understanding of the factors that can contribute to the development and also recovery from these conditions are a necessity. Although obesity and AN are at the opposite end of the bodyweight spectrum, some shared psychological processes may drive these states. One factor that has been suggested to contribute to problematic weight regulation is psychosocial stress whilst positive affect systems and affect regulation processes are important for regulating stress-related experiences. Gilbert (2005) describes an affect regulation system which consists of two positive affect systems known as social rank and attachment. Whilst the latter affect system refers to the attachment bond that develops between an infant and its caregiver (which extends to adult relationships), the former is used to form relationships that allow us to compete for limited resources and maintain our status in the social environment. Affect regulation processes in the current research are self-criticism and self-reassurance. Whilst self-critical thoughts and feelings can be triggered by perceptions of being low rank, the idea that people can be self-reassuring or being able to self-reassure at times of difficulty is nested in the positive infant-caregiver attachment bond and a consequence of internalizing parental soothing (Gilbert, 2006). Hence, as stress is suggested to be an important factor in problematic weight regulation and affect systems and processes are central to the regulation of emotional responses to stress-related experiences, the current series of studies examined these factors in relation to problematic weight regulation. The current research consisted of four studies designed to examine the role of stress and affect regulation in relation to weight change, weight regain following weight loss and recovery versus symptom maintenance in AN in women. A longitudinal study (Study One) was conducted to examine the change trajectories of stress, eating pathology and bodyweight, how these changes influence each other and the role of affect regulation systems and processes on these changes in a community based sample (N = 1157). Study Two examined the role of stress and affect regulation as predictors of weight regain in those who have lost weight (N = 42) and Study Three used a measure of life events and difficulties to investigate the role of stressful life changes and affect systems on recovery and relapse following AN (N = 30). Finally, in Study four, an expressive writing task which has been demonstrated to have a positive impact on stress-related health outcomes was used to explore the role of stress, affect systems and processes on problematic weight regulation and eating at times of stress (N = 57). The findings of the research studies demonstrated that there is a concurrent link between stress and the regulation of bodyweight and eating in a community-based sample of women. However, the proposed relationship between stress, bodyweight and eating behaviours was not confirmed when examined longitudinally in a community-based sample, over a 7-month period in women who have lost weight or when examined retrospectively as contributing to symptom maintenance in women with AN. However, the main finding of the current series of studies suggested that affect systems and affect regulation processes do have important implications for regulating stress-related experiences, bodyweight and eating behaviours. Perceived low social status, greater insecurity of attachment, more self-critical and less self-reassuring thoughts and feelings were related to increases in stress levels, higher bodyweight and higher levels of dysfunctional eating patterns. In addition, whilst expressive writing did not reduce stress, influence bodyweight or improve affect regulation at times of difficulty, writing about positive experiences had a positive impact on reducing dietary restraint behaviours during a stressful period. In conclusion, these findings suggest that it may not be stress per se that contributes to unhealthy changes in bodyweight and eating behaviours but how we use our affect systems and processes to manage our emotions at times of difficulty. Consequently, these findings have important implications for practice as weight loss programmes, Eating Disorder prevention programmes and stress management interventions should address the issues of perceived low social status, self-criticism and attachment insecurities.

We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TDSE is also often posed in high dimensions, where standard methods are intractable. The sensitivity to dispersion error makes spectral methods advantageous for the TDSE. We use spectral or pseudospectral methods in all except one of the included papers. In Paper III we improve and analyse the accuracy of the Fourier pseudospectral method applied to a problem with limited regularity, and in Paper V we construct a matrix-free spectral method for problems with non-trivial boundary conditions. Due to its stiffness, the TDSE is most often solved using exponential time integration. In this thesis we use exponential operator splitting and Krylov subspace methods. We rigorously prove convergence for force-gradient operator splitting methods in Paper IV. One way of making high-dimensional problems computationally tractable is low-rank approximation. In Paper VI we prove that a splitting method for dynamical low-rank approximation is robust to singular values in the approximation approaching zero, a situation which is difficult to handle since it implies strong curvature of the approximation space. / eSSENCE

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This thesis is an ethnography of a community of professional thieves called the Kanjar-a 'caste of thieves' by practice, public perception and self-designation-in the northern Indian province of Rajasthan. It is also an argument that spells out the broader logic of rank in local society. Insofar as it offers the first ethnography of the Kanjar community- and of caste-based, professional, hereditary theft-this study is new. My analytical concern with hierarchy and rank, however, is old, engaging in the once central, and now largely out-fashioned, discussion in the sociology of South Asia. My project began with a narrow set of concerns with the place of thieving and thieves in local society. In the course of my fieldwork, however, it became apparent that the received wisdom of South Asian sociology regarding the principles of rank did not offer useful explanatory tools and that a different conception of rank was necessary to make sense of what I observed, both about the social position of Kanjars and the hierarchical social formation at large. As is so often the case, what began as a study of historically and sociologically particular circumstances became an inquiry into the pervasive regnant aspects of the local order of things.

Red deer males aggregate during the period of antler growth to bachelor groups. Social position - Rank - is unstable in these groups. Previous experiments revealed that rank modulated by agonistic behaviour influence the antler growth and antler cycle timing. Antlers are the secondary sexual characteristics of the deer family and one of the fastest growing tissue in vertebrate taxa. Their development is modulated by androgenic hormone, testosterone. In our experiment, we observed agonistic behaviour of 19 males. They were equipped with GPS collar and observation lasted for two hours in the evening an in the morning, once or twice a week from the end of May to the end of August. Deer were handled regularly for blood samples and downloading the telemetrical data from collars. Base on a statistical analysis we found that in our bachelor group 13 stags kept similar interindividual distances which did not exceed the 22 metres level. These stags - the closest associates - differed in the sum of agonistic interactions. Those who reached 8 or less interactions were called Friends, while subgroup of the others reaching much more interactions were classified as Rivals. We found that number of interactions depended on average distance among males in groups (Friends and Rivals). Rivals with increasing distance...

In this thesis we study the computation of the greatest common divisor of two polynomials. Firstly, properties of Sylvester matrices are considered as well as their role in computation. We then note, that this approach can be naturally generalized for several polynomials. In the penultimate section, Bézout matrices are studied as an analogy to the Sylvester ones, providing necessary comparison. Extension for more than polynomials is presented here as well. Algorithms corresponding to the individual approaches are presented as well. Finally, the algorithms are implemented in MATLAB and are compared in numerical experiments. Powered by TCPDF (www.tcpdf.org)

En apprentissage automatique on a pour but d'apprendre un modèle, à partir de données, qui soit capable de faire des prédictions sur des nouvelles données (pas explorées auparavant). Pour obtenir un modèle qui puisse se généraliser sur les nouvelles données, et éviter le sur-apprentissage, nous devons restreindre le modèle. Ces restrictions sont généralement une connaissance a priori de la structure du modèle. Les premières approches considérées dans la littérature sont la régularisation de Tikhonov et plus tard le Lasso pour induire de la parcimonie dans la solution. La parcimonie fait partie d'un concept fondamental en apprentissage automatique. Les modèles parcimonieux sont attrayants car ils offrent plus d'interprétabilité et une meilleure généralisation (en évitant le sur-apprentissage) en induisant un nombre réduit de paramètres dans le modèle. Au-delà de la parcimonie générale et dans de nombreux cas, les modèles sont structurellement contraints et ont une représentation simple de certains éléments fondamentaux, comme par exemple une collection de vecteurs, matrices ou tenseurs spécifiques. Ces éléments fondamentaux sont appelés atomes. Dans ce contexte, les normes atomiques fournissent un cadre général pour estimer ce type de modèles. périodes de modèles. Le but de cette thèse est d'utiliser le cadre de parcimonie convexe fourni par les normes atomiques pour étudier une forme de parcimonie matricielle. Tout d'abord, nous développons un algorithme efficace basé sur les méthodes de Frank-Wolfe et qui est particulièrement adapté pour résoudre des problèmes convexes régularisés par une norme atomique. Nous nous concentrons ensuite sur l'estimation de la structure des modèles graphiques gaussiens, où la structure du modèle est encodée dans la matrice de précision et nous étudions le cas avec des variables manquantes. Nous proposons une formulation convexe avec une approche algorithmique et fournissons un résultat théorique qui énonce les conditions nécessaires pour récupérer la structure souhaitée. Enfin, nous considérons le problème de démixage d'un signal en deux composantes ou plus via la minimisation d’une somme de normes ou de jauges, encodant chacune la structure a priori des composants à récupérer. En particulier, nous fournissons une garantie de récupération exacte dans le cadre sans bruit, basée sur des mesures d'incohérence / The goal of machine learning is to learn a model from some data that will make accurate predictions on data that it has not seen before. In order to obtain a model that will generalize on new data, and avoid overfitting, we need to restrain the model. These restrictions are usually some a priori knowledge of the structure of the model. First considered approaches included a regularization, first ridge regression and later Lasso regularization for inducing sparsity in the solution. Sparsity, also known as parsimony, has emerged as a fundamental concept in machine learning. Parsimonious models are appealing since they provide more interpretability and better generalization (avoid overfitting) through the reduced number of parameters. Beyond general sparsity and in many cases, models are constrained structurally so they have a simple representation in terms of some fundamental elements, consisting for example of a collection of specific vectors, matrices or tensors. These fundamental elements are called atoms. In this context, atomic norms provide a general framework for estimating these sorts of models. The goal of this thesis is to use the framework of convex sparsity provided by atomic norms to study a form of matrix sparsity. First, we develop an efficient algorithm based on Frank-Wolfe methods that is particularly adapted to solve problems with an atomic norm regularization. Then, we focus on the structure estimation of Gaussian graphical models, where the structure of the graph is encoded in the precision matrix and study the case with unobserved variables. We propose a convex formulation with an algorithmic approach and provide a theoretical result that states necessary conditions for recovering the desired structure. Finally, we consider the problem of signal demixing into two or more components via the minimization of a sum of norms or gauges, encoding each a structural prior on the corresponding components to recover. In particular, we provide general exact recovery guarantees in the noiseless setting based on incoherence measures

Depuis 1960 et le résultat fondateur de Karatsuba, on sait que la complexité de la multiplication (d’entiers ou de polynômes) est sous-quadratique : étant donné un anneau R quelconque, le produit sur R[X] des polynômes a_0 + a_1 X et b_0 + b_1 X, pour tous a_0, a_1, b_0 et b_1 dans R, peut être calculé en seulement trois et non pas quatre multiplications sur R : (a_0 + a_1 X)(b_0 + b_1 X) = m_0 + (m_2 - m_0 - m_1)X + m_1 X^2, avec les trois produits m_0 = a_0b_0, m_1 = a_1b_1 et m_2 = (a_0 + a_1)(b_0 + b_1). De la même manière, l’algorithme de Strassen permet de multiplier deux matrices 2nx2n en seulement sept produits de matrices nxn. Les deux exemples précédents tombent dans la catégorie des applications bilinéaires : des fonctions de la forme Phi : K^m x K^n -> K^l, pour un corps donné K, linéaires en chacune des deux variables. Parmi les applications bilinéaires les plus classiques, on trouve ainsi la multiplication de polynômes, de matrices, ou encore d’éléments d’extensions algébriques de corps finis. Étant donnée une application bilinéaire Phi, calculer le nombre minimal de multiplications nécessaires au calcul de cette application est un problème NP-difficile. L'objectif de cette thèse est de proposer des algorithmes minimisant ce nombre de multiplications. Deux angles d'attaques ont été suivis. Un premier aspect de cette thèse est l'étude du problème du calcul de la complexité bilinéaire sous l'angle de la reformulation de ce problème en termes de recherche de sous-espaces vectoriels de matrices de rang donné. Ce travail a donné lieu à un algorithme tenant compte de propriétés intrinsèques aux produits considérés tels que les produits matriciels ou polynomiaux sur des corps finis. Cet algorithme a permis de trouver toutes les décompositions possibles, sur F_2, pour le produit de polynômes modulo X^5 et le produit de matrices 3x2 par 2x3. Un autre aspect de ma thèse est celui du développement d’algorithmes asymptotiquement rapides pour la multiplication entière. Une famille particulière d'algorithmes récents ont été proposés suite à un article de Fürer publié en 2007, qui proposait un premier algorithme, reposant sur la transformée de Fourier rapide (FFT) permettant de multiplier des entiers de n bits en O(n log n 2^{O(log^* n)}), où log^* est la fonction logarithme itéré. Dans cette thèse, un algorithme dont la complexité dépend d'une conjecture de théorie des nombres est proposé, reposant sur la FFT et l'utilisation de premiers généralisés de Fermat. Une analyse de complexité permet d'obtenir une estimation en O(n log n 4^{log^* n}) / Since 1960 and the result of Karatsuba, we know that the complexity of the multiplication (of integers or polynomials) is sub-quadratic: given a ring R, the product in R[X] of polynomials a_0 + a_1 X and b_0 + b_1 X, for any a_0, a_1, b_0 and b_1 in R, can be computed with three and not four multiplications over R: (a_0 + a_1X)(b_0 + b_1X) = m_0 + (m_2 - m_0 - m_1)X + m_1X^2, with the three multiplications m_0 = a_0b_0, m_1 = a_1b_1 et m_2 = (a_0 + a_1)(b_0 + b_1). In the same manner, Strassen's algorithm allows one to multiply two matrices 2nx2n with only seven products of matrices nxn. The two previous examples fall in the category of bilinear maps: these are functions of the form Phi : K^m x K^n -> K^l, given a field K, linear in each variable. Among the most classical bilinear maps, we have the multiplication of polynomials, matrices, or even elements of algebraic extension of finite fields. Given a bilinear map Phi, computing the minimal number of multiplications necessary to the evaluation of this map is a NP-hard problem. The purpose of this thesis is to propose algorithms minimizing this number of multiplications. Two angles of attack have been studied. The first aspect of this thesis is to study the problem of the computation of the bilinear complexity under the angle of the reformulation of this problem in terms of research of matrix subspaces of a given rank. This work led to an algorithm taking into account intrinsic properties of the considered products such as matrix or polynomial products over finite fields. This algorithm allows one to find all the possible decompositions, over F_2, for the product of polynomials modulo X^5 and the product of matrices 3x2 by 2x3. Another aspect of this thesis was the development of fast asymptotic methods for the integer multiplication. There is a particular family of algorithms that has been proposed after an article by Fürer published in 2007. This article proposed a first algorithm, relying on fast Fourier transform (FFT), allowing one to multiply n-bit integers in O(n log n 2^{O(log^* n)}), where log^* is the iterated logarithm function. In this thesis, an algorithm, relying on a number theoretical conjecture, has been proposed, involving the use of FFT and generalized Fermat primes. With a careful complexity analysis of this algorithm, we obtain a complexity in O(nlog n 4^{log^* n})

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.