<p>A faithful depiction of the tropical atmosphere requires three-dimensional sets of observations. Despite the increasing amount of observations presently available, these will hardly ever encompass the entire atmosphere and, in addition, observations have errors. Additional (background) information will always be required to complete the picture. Valuable added information comes from the physical laws governing the flow, usually mediated via a numerical weather prediction (NWP) model. These models are, however, never going to be error-free, why a reliable estimate of their errors poses a real challenge since the whole truth will never be within our grasp. </p><p>The present thesis addresses the question of improving the analysis procedures for NWP in the tropics. Improvements are sought by addressing the following issues:</p><p>- the efficiency of the internal model adjustment, </p><p>- the potential of the reliable background-error information, as compared to observations,</p><p>- the impact of a new, space-borne line-of-sight wind measurements, and</p><p>- the usefulness of multivariate relationships for data assimilation in the tropics.</p><p>Most NWP assimilation schemes are effectively univariate near the equator. In this thesis, a multivariate formulation of the variational data assimilation in the tropics has been developed. The proposed background-error model supports the mass-wind coupling based on convectively-coupled equatorial waves. The resulting assimilation model produces balanced analysis increments and hereby increases the efficiency of all types of observations.</p><p>Idealized adjustment and multivariate analysis experiments highlight the importance of direct wind measurements in the tropics. In particular, the presented results confirm the superiority of wind observations compared to mass data, in spite of the exact multivariate relationships available from the background information. The internal model adjustment is also more efficient for wind observations than for mass data. </p><p>In accordance with these findings, new satellite wind observations are expected to contribute towards the improvement of NWP and climate modeling in the tropics. Although incomplete, the new wind-field information has the potential to reduce uncertainties in the tropical dynamical fields, if used together with the existing satellite mass-field measurements.</p><p>The results obtained by applying the new background-error representation to the tropical short-range forecast errors of a state-of-art NWP model suggest that achieving useful tropical multivariate relationships may be feasible within an operational NWP environment.</p>

In the last decades, the explosion of data from quantitative techniques has revolutionised our understanding of biological processes. In this scenario, advanced statistical methods and algorithms are becoming fundamental to decipher the dynamics of biochemical mechanisms such those involved in the regulation of gene expression. Here we develop mechanistic models and approximate inference techniques to reverse engineer the dynamics of gene regulation, from mRNA and/or protein time series data. We start from an existent variational framework for statistical inference in transcriptional networks. The framework is based on a continuous-time description of the mRNA dynamics in terms of stochastic differential equations, which are governed by latent switching variables representing the on/off activity of regulating transcription factors. The main contributions of this work are the following. We speeded-up the variational inference algorithm by developing a method to compute a posterior approximate distribution over the latent variables using a constrained optimisation algorithm. In addition to computational benefits, this method enabled the extension to statistical inference in networks with a combinatorial model of regulation. A limitation of this framework is the fact that inference is possible only in transcriptional networks with a single-layer architecture (where a single or couples of transcription factors regulate directly an arbitrary number of target genes). The second main contribution in this work is the extension of the inference framework to hierarchical structures, such as feed-forward loop. In the last contribution we define a general structure for transcription-translation networks. This work is important since it provides a general statistical framework to model complex dynamics in gene regulatory networks. The framework is modular and scalable to realistically large systems with general architecture, thus representing a valuable alternative to traditional differential equation models. All models are embedded in a Bayesian framework; inference is performed using a variational approach and compared to exact inference where possible. We apply the models to the study of different biological systems, from the metabolism in E. coli to the circadian clock in the picoalga O. tauri.

In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established. / FUSION

Topic models allow the probabilistic modeling of term frequency occurrences in documents. The fitted model can be used to estimate the similarity between documents as well as between a set of specified keywords using an additional layer of latent variables which are referred to as topics. The R package topicmodels provides basic infrastructure for fitting topic models based on data structures from the text mining package tm. The package includes interfaces to two algorithms for fitting topic models: the variational expectation-maximization algorithm provided by David M. Blei and co-authors and an algorithm using Gibbs sampling by Xuan-Hieu Phan and co-authors.

No description available.

Due to restricted budgets of relief organizations, costs of hiring transportation service providers steer distribution decisions and limit the impact of disaster relief. To improve the success of future humanitarian operations, it is of paramount importance to understand this relationship in detail and to identify mitigation actions, always considering the interdependencies between multiple independent actors in humanitarian logistics. In this paper, we develop a game-theoretic model in order to investigate the influence of transportation costs on distribution decisions in long-term relief operations and to evaluate measures for improving the fulfillment of beneficiary needs. The equilibrium of the model is a Generalized Nash Equilibrium, which has had few applications in the supply chain context to date. We formulate it, utilizing the construct of a Variational Equilibrium, as a Variational Inequality and perform numerical simulations in order to study the effects of three interventions: an increase in carrier competition, a reduction of transportation costs and an extension of framework agreements. The results yield important implications for policy makers and humanitarian organizations (HOs). Increasing the number of preselected carriers strengthens the bargaining power of HOs and improves impact up to a certain limit. The limit is reached when carriers set framework rates equal to transportation unit costs. Reductions of transportation costs have a consistently positive, but decreasing marginal benefit without any upper bound. They provide the highest benefit when the bargaining power of HOs is weak. On the contrary, extending framework agreements enables most improvements when the bargaining power of HOs is strong.

Estendemos para a teria de campos o método variacional de Kleinert. Este método foi primeiramente usado na mecânica quântica e fornece uma expansão em cumulantes convergente. Sua extensão para a teoria de campos não é trivial devido às divergências ultravioletas que aparecem quando a dimensão do espaço é maior que 2. Devido a estas divergências, a teoria deve ser regularizada e normalizada. Além das dificuldades usuais associadas com a renormalização, devemos decidir se calculamos o valor ótimo do parâmetro variacional antes ou depois da renormalização. Nesta tese abordamos o problema da renormalização do potencial efetivo variacional. Primeiramente, mostramos que o potencial efetivo variacional em temperatura zero coincide com o \"potencial efetivo pós-gaussiano\" introduzido por Stancu e Stevenson. Em seguida, apresentamos um esquema de renormalização que permite que renormalizemos a teoria antes de calcular o parâmetro variacional ótimo. Usando este esquema mostramos que o potencial efetivo usual, calculado em ordem 1-loop, pode ser obtido a partir do esquema variacional de Kleinert inteirando uma única vez a equação que determina o parâmetro variacional. Para o potencial efetivo em ordem 2-loops esta aproximação não é tão boa. A renormalização da teoria antes do cálculo do parâmetro variacional permite que estudemos o potencial efetivo variacional numericamente e de forma não-perturbativa, como foi feito por Kleinert para a mecânica quântica. / We have extended the Kleinert variational technique to field theory. This method was first used in quantum mechanics and provides a convergent cumulate expansion that is extremely accurate. Its extension to field theory is non-trivial because of the ultraviolet divergences that appear when the space dimension is greater than 2. Due to these divergences the theory has to be regularized and renormalized. In addition to the usual difficulties associated with renormalization, one has to decide whether one calculates the optimum value of the variational parameter before or after renormalization. In this thesis we deal with the renormalization of the variational effective potential. Firstly, we show that the zero temperature regularized variational potential coincides with the post-Gaussian effective potential introduced by Stancu and Stenvenson. Secondly, we present a renormalization scheme that enables one to renormalize the theory before calculating the optimum variational parameter. Using this scheme we show that the usual 1-loop effective potential can be obtained from the Kleinert variational scheme by interacting only once the equation that determines the variational parameter. In this sense, the 1-loop expansion is contained within the variational scheme. For the 2-loop effective potential the same approximation is not so good. The renormalization of the theory before the calculation of the variational parameter allows one to study the variational effective potential numerically and in a non-pertubative way, as it was done in quantum mechanics by Kleinert.

Orientador: Bruto Max Pimentel Escobar / Co-orientador: / Banca:Andrey Yuryevich Mikhaylov / Banca: Edmundo Capelas de Oliveira / Resumo: A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para finalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo / Abstract: The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism / Mestre

Esta dissertação busca aproveitar os métodos de penalidades exatas diferenciáveis de programação não-linear para resolver problemas de desigualdades variacionais. Problemas desse tipo têm recebido grande atenção na literatura recentemente e possuem aplicações em diversas áreas como Engenharia, Física e Economia. Métodos de penalidades exatas diferenciáveis foram desenvolvidos nos anos 70 e 80 para resolver problemas de otimização com restrições por meio da solução de problemas irrestritos. Esses problemas são tais que, com uma escolha apropriada do parâmetro de penalização, uma solução do problema original é recuperada após a resolução de um único problema irrestrito. A função a ser minimizada é semelhante a um lagrangiano aumentado clássico, porém uma estimativa do multiplicador é automaticamente calculada a partir do ponto primal. Nesse trabalho, mostramos como acoplar a estimativa de multiplicadores sugerida por Glad e Polak [27] ao lagrangiano aumentado clássico para desigualdades variacionais sugerido por Auslender e Teboulle. Obtivemos assim uma penalidade exata para problemas de desigualdades variacionais. Os resultados mais finos de exatidão foram obtidos no caso de problemas de complementaridade não-linear. Uma característica importante da penalidade proposta é que ela não envolve informações de segunda ordem das funções que definem a desigualdade variacional. Além desses resultados, que formam o núcleo da dissertação, apresentamos uma breve revisão de penalidades não-exatas diferenciáveis , exatas não-diferenciáveis e exatas diferenciáveis em otimização. / This work intends to build upon differentiable exact penalty methods for nonlinear programming, using them to solve variational inequality problems. Such problems have been given a lot of attention in the literature lately and have applications to diverse areas of knowledge such as Engineering, Physics and Economics. Differentiable exact penalty methods were developed during the 70s and 80s to solve constrained optimization problems by means of the solution of unconstrained problems. Those problems are such that, with an appropriate choice of the penalty parameter, one finds a solution of the original constrained problem by solving only one unconstrained problem. The function which is minimized is similar to the classic augmented lagrangian, but an estimate of the multiplier is automatically calculated from the primal point. In this thesis we show how to couple Glad and Polak?s multiplier estimate, with the classic augmented lagrangian of a variational inequality developed by Auslender and Teboulle. This allowed us to obtain an exact penalty function for variational inequality problems. The best exactness results were obtained in the particular case of nonlinear complementarity problems. An important characteristic of the proposed penalty is that it doesn?t involve second order information of any of the functions which compose the variational inequality. In addition to those results, which are the core of this work, we also present a brief review of inexact differentiable penalties, exact nondifferentiable penalties and differentiable exact penalties in optimization.

Esta dissertação busca aproveitar os métodos de penalidades exatas diferenciáveis de programação não-linear para resolver problemas de desigualdades variacionais. Problemas desse tipo têm recebido grande atenção na literatura recentemente e possuem aplicações em diversas áreas como Engenharia, Física e Economia. Métodos de penalidades exatas diferenciáveis foram desenvolvidos nos anos 70 e 80 para resolver problemas de otimização com restrições por meio da solução de problemas irrestritos. Esses problemas são tais que, com uma escolha apropriada do parâmetro de penalização, uma solução do problema original é recuperada após a resolução de um único problema irrestrito. A função a ser minimizada é semelhante a um lagrangiano aumentado clássico, porém uma estimativa do multiplicador é automaticamente calculada a partir do ponto primal. Nesse trabalho, mostramos como acoplar a estimativa de multiplicadores sugerida por Glad e Polak [27] ao lagrangiano aumentado clássico para desigualdades variacionais sugerido por Auslender e Teboulle. Obtivemos assim uma penalidade exata para problemas de desigualdades variacionais. Os resultados mais finos de exatidão foram obtidos no caso de problemas de complementaridade não-linear. Uma característica importante da penalidade proposta é que ela não envolve informações de segunda ordem das funções que definem a desigualdade variacional. Além desses resultados, que formam o núcleo da dissertação, apresentamos uma breve revisão de penalidades não-exatas diferenciáveis , exatas não-diferenciáveis e exatas diferenciáveis em otimização. / This work intends to build upon differentiable exact penalty methods for nonlinear programming, using them to solve variational inequality problems. Such problems have been given a lot of attention in the literature lately and have applications to diverse areas of knowledge such as Engineering, Physics and Economics. Differentiable exact penalty methods were developed during the 70s and 80s to solve constrained optimization problems by means of the solution of unconstrained problems. Those problems are such that, with an appropriate choice of the penalty parameter, one finds a solution of the original constrained problem by solving only one unconstrained problem. The function which is minimized is similar to the classic augmented lagrangian, but an estimate of the multiplier is automatically calculated from the primal point. In this thesis we show how to couple Glad and Polak?s multiplier estimate, with the classic augmented lagrangian of a variational inequality developed by Auslender and Teboulle. This allowed us to obtain an exact penalty function for variational inequality problems. The best exactness results were obtained in the particular case of nonlinear complementarity problems. An important characteristic of the proposed penalty is that it doesn?t involve second order information of any of the functions which compose the variational inequality. In addition to those results, which are the core of this work, we also present a brief review of inexact differentiable penalties, exact nondifferentiable penalties and differentiable exact penalties in optimization.