This thesis deals with the development, implementation and application of statistical modeling techniques which can be employed in the analysis of credit ratings. Credit ratings are one of the most widely used measures of credit risk and are relevant for a wide array of financial market participants, from investors, as part of their investment decision process, to regulators and legislators as a means of measuring and limiting risk. The majority of credit ratings is produced by the "Big Three" credit rating agencies Standard & Poors', Moody's and Fitch. Especially in the light of the 2007-2009 financial crisis, these rating agencies have been strongly criticized for failing to assess risk accurately and for the lack of transparency in their rating methodology. However, they continue to maintain a powerful role as financial market participants and have a huge impact on the cost of funding. These points of criticism call for the development of modeling techniques that can 1) facilitate an understanding of the factors that drive the rating agencies' evaluations, 2) generate insights into the rating patterns that these agencies exhibit. This dissertation consists of three research articles. The first one focuses on variable selection and assessment of variable importance in accounting-based models of credit risk. The credit risk measure employed in the study is derived from credit ratings assigned by ratings agencies Standard & Poors' and Moody's. To deal with the lack of theoretical foundation specific to this type of models, state-of-the-art statistical methods are employed. Different models are compared based on a predictive criterion and model uncertainty is accounted for in a Bayesian setting. Parsimonious models are identified after applying the proposed techniques. The second paper proposes the class of multivariate ordinal regression models for the modeling of credit ratings. The model class is motivated by the fact that correlated ordinal data arises naturally in the context of credit ratings. From a methodological point of view, we extend existing model specifications in several directions by allowing, among others, for a flexible covariate dependent correlation structure between the continuous variables underlying the ordinal credit ratings. The estimation of the proposed models is performed using composite likelihood methods. Insights into the heterogeneity among the "Big Three" are gained when applying this model class to the multiple credit ratings dataset. A comprehensive simulation study on the performance of the estimators is provided. The third research paper deals with the implementation and application of the model class introduced in the second article. In order to make the class of multivariate ordinal regression models more accessible, the R package mvord and the complementary paper included in this dissertation have been developed. The mvord package is available on the "Comprehensive R Archive Network" (CRAN) for free download and enhances the available ready-to-use statistical software for the analysis of correlated ordinal data. In the creation of the package a strong emphasis has been put on developing a user-friendly and flexible design. The user-friendly design allows end users to estimate in an easy way sophisticated models from the implemented model class. The end users the package appeals to are practitioners and researchers who deal with correlated ordinal data in various areas of application, ranging from credit risk to medicine or psychology.

Submitted by Maria Medeiros (maria.dilva1@ufcg.edu.br) on 2018-08-29T14:12:32Z No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS - DISSERTAÇÃO (PPGF) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) / Made available in DSpace on 2018-08-29T14:12:32Z (GMT). No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS - DISSERTAÇÃO (PPGF) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) Previous issue date: 2015-04-10 / Capes / Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento. / In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.

Biological invasions are reportedly one of the major contributory factors to biodiversity loss worldwide. The impacts of invasive alien plant (IAP) species on native communities are widely documented in the scientific literature, however, there is still a lack of detailed information on their impacts within the most vulnerable habitats. Riparian habitats are highly dynamic systems and naturally disturbed, making them particularly vulnerable to invasion. Climate change, directly or indirectly, is also predicted to adversely impact river systems, which may subsequently alter invasion rates and the impacts of IAPs. However, the interactions between climate and IAPs and their combined effects on vegetation have rarely been examined. To address these knowledge gaps, this thesis investigates: (1) the role of environmental variables, such as sediment loading or climate-related changes to river flow regime, on the abundance of IAPs within riparian zones; (2) how variation in IAP abundance impacts native vegetation, relative to the effects of native dominant plant species and (3) some of the mechanisms underlying the effects of IAPs in riparian habitats. Historic and recent field survey data were used to investigate changes in riparian vegetation on British rivers during the last 20 years. Analyses indicate that IAPs had a negative but small effect on native plant diversity. Overall, changes in land use and differences in flow regime between recording periods were the most important predictors of plant community change. Specifically, IAPs had a greater probability of being present along lowland rivers that experienced increased frequency of high flow events. On a local scale across rivers in Scotland, the abundance of IAPs was constrained by greater soil moisture in summer, whilst greater abundance was associated with tree-lined banks. Both native dominant species and IAPs negatively affected subordinate species abundance to a greater extent than species richness, although this effect varied spatially with bank elevation. Artificial turf mats were used to quantify viable propagules within riverine sediment deposited over-winter along invaded riverbanks. The data indicate that there is a legacy effect of IAP abundance, with the most invaded sites being associated with higher sediment loading the following year, though, contrary to the general pattern, 12 sediment associated propagules were scarcer at invaded sites. Moreover, lower above-ground native diversity was associated with sites which had been previously invaded. Plant species composition in the propagule bank and above-ground vegetation were highly dissimilar, particularly closest to the water’s edge at highly invaded sites. This suggests that mono-specific stands of IAPs proliferate best under less disturbed environmental conditions, although fluvial disturbance events may be required to create opportunities for initial establishment. The propagule bank contributed very little to the above-ground vegetation, nor did it limit invasion, suggesting that above-ground plant composition is largely dictated by competitive interactions. The findings presented in this thesis suggest that invasion by IAPs is an additional stressor for native vegetation within riparian habitats, modifying above-ground plant communities via competition and suppressing recruitment from the propagule bank. However, native dominant species common in riparian habitats also negatively impact, subordinate species via competition, in some cases equalling the effect of IAPs. Native dominant and IAP species are differently affected by environmental factors operating in the riparian zone, which may provide future opportunities for reducing and managing invasions.

Submitted by Fernando Barbi (fcbarbi@gmail.com) on 2014-05-07T22:24:44Z No. of bitstreams: 1 TESE_FERNANDO_CARVALHAES_BARBI_204089_CDEE_FINAL.pdf: 966201 bytes, checksum: 6f481f17555ebd92319058e7f6e4c7ee (MD5) / Rejected by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br), reason: Bom dia Fernando, Conforme conversamos por telefone. Att. Suzi on 2014-05-08T12:02:11Z (GMT) / Submitted by Fernando Barbi (fcbarbi@gmail.com) on 2014-05-08T12:30:01Z No. of bitstreams: 1 TESE_FERNANDO_CARVALHAES_BARBI_204089_CDEE.pdf: 963867 bytes, checksum: 6b78db46891b72b31e89059c2a176bc9 (MD5) / Rejected by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br), reason: Fernando on 2014-05-08T12:33:32Z (GMT) / Submitted by Fernando Barbi (fcbarbi@gmail.com) on 2014-05-08T12:36:15Z No. of bitstreams: 1 TESE_FERNANDO_CARVALHAES_BARBI_204089_CDEE.pdf: 963906 bytes, checksum: 467d3c75aa7e81be984b8b5f22430c0b (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2014-05-08T12:38:09Z (GMT) No. of bitstreams: 1 TESE_FERNANDO_CARVALHAES_BARBI_204089_CDEE.pdf: 963906 bytes, checksum: 467d3c75aa7e81be984b8b5f22430c0b (MD5) / Made available in DSpace on 2014-05-08T13:28:07Z (GMT). No. of bitstreams: 1 TESE_FERNANDO_CARVALHAES_BARBI_204089_CDEE.pdf: 963906 bytes, checksum: 467d3c75aa7e81be984b8b5f22430c0b (MD5) Previous issue date: 2014-04-08 / In the first essay, 'Determinants of Credit Expansion in Brazil', analyzes the determinants of credit using an extensive bank level panel dataset. Brazilian economy has experienced a major boost in leverage in the first decade of 2000 as a result of a set factors ranging from macroeconomic stability to the abundant liquidity in international financial markets before 2008 and a set of deliberate decisions taken by President Lula's to expand credit, boost consumption and gain political support from the lower social strata. As relevant conclusions to our investigation we verify that: credit expansion relied on the reduction of the monetary policy rate, international financial markets are an important source of funds, payroll-guaranteed credit and investment grade status affected positively credit supply. We were not able to confirm the importance of financial inclusion efforts. The importance of financial sector sanity indicators of credit conditions cannot be underestimated. These results raise questions over the sustainability of this expansion process and financial stability in the future. The second essay, 'Public Credit, Monetary Policy and Financial Stability', discusses the role of public credit. The supply of public credit in Brazil has successfully served to relaunch the economy after the Lehman-Brothers demise. It was later transformed into a driver for economic growth as well as a regulation device to force private banks to reduce interest rates. We argue that the use of public funds to finance economic growth has three important drawbacks: it generates inflation, induces higher loan rates and may induce financial instability. An additional effect is the prevention of market credit solutions. This study contributes to the understanding of the costs and benefits of credit as a fiscal policy tool. The third essay, 'Bayesian Forecasting of Interest Rates: Do Priors Matter?', discusses the choice of priors when forecasting short-term interest rates. Central Banks that commit to an Inflation Target monetary regime are bound to respond to inflation expectation spikes and product hiatus widening in a clear and transparent way by abiding to a Taylor rule. There are various reports of central banks being more responsive to inflationary than to deflationary shocks rendering the monetary policy response to be indeed non-linear. Besides that there is no guarantee that coefficients remain stable during time. Central Banks may switch to a dual target regime to consider deviations from inflation and the output gap. The estimation of a Taylor rule may therefore have to consider a non-linear model with time varying parameters. This paper uses Bayesian forecasting methods to predict short-term interest rates. We take two different approaches: from a theoretic perspective we focus on an augmented version of the Taylor rule and include the Real Exchange Rate, the Credit-to-GDP and the Net Public Debt-to-GDP ratios. We also take an 'atheoretic' approach based on the Expectations Theory of the Term Structure to model short-term interest. The selection of priors is particularly relevant for predictive accuracy yet, ideally, forecasting models should require as little a priori expert insight as possible. We present recent developments in prior selection, in particular we propose the use of hierarchical hyper-g priors for better forecasting in a framework that can be easily extended to other key macroeconomic indicators. / O primeiro ensaio, "Determinantes da expansão do crédito no Brasil", analisa os determinantes do crédito usando um extenso conjunto de dados em painel sobre o sistema bancário. A economia brasileira teve um grande impulso na alavancagem na primeira década de 2000 como resultado de um conjunto de fatores que vão desde a estabilidade macroeconômica passando pela liquidez abundante nos mercados financeiros internacionais antes de 2008 até um conjunto de decisões deliberadas tomadas pelo presidente Lula para expandir o crédito, impulsionar o consumo e obter apoio político das camadas sociais mais baixas. Como conclusões verificamos que a expansão do crédito beneficiou-se da redução da taxa de juros, os mercados financeiros internacionais são uma fonte importante de recursos, o crédito garantido em folha de pagamento e o grau de investimento afetaram positivamente a oferta de crédito. Nós não fomos capazes de confirmar a importância dos esforços de inclusão financeira. A importância dos indicadores de sanidade do setor financeiro de condições de crédito não pode ser subestimada. Estes resultados levantam questões quanto à sustentabilidade desse processo de expansão e estabilidade financeira no futuro. O segundo ensaio, "Crédito Público, Política Monetária e Estabilidade Financeira", discute o papel do crédito público. A oferta de crédito público no Brasil serviu para relançar a economia após a crise desencadeada pela quebra do banco Lehman-Brothers. Mais tarde, ele foi transformado em um motor de crescimento econômico bem como num dispositivo de regulação para forçar os bancos privados a reduzir as taxas de juros. Argumenta-se que a utilização de fundos públicos para financiar o crescimento econômico tem três desvantagens importantes: ele gera inflação, induz taxas de financiamento mais elevadas e pode induzir à instabilidade financeira. Um efeito adicional é impedir o desenvolvimento de soluções de crédito de mercado. O terceiro ensaio, "Previsão Bayesiana de Taxas de Juros: as priors importam?", discute a escolha de priors para previsão das taxas de juros de curto prazo. Bancos Centrais que se comprometem com regimes de metas de inflação devem responder a variações nas expectativa de inflação e no hiato do produto de uma forma clara e transparente, respeitando a regra de Taylor. A estimativa de uma regra de Taylor pode ter que considerar um modelo não-linear com parâmetros variáveis no tempo. Este trabalho usa métodos de previsão bayesiana para as taxas de juro de curto prazo por duas abordagens diferentes. Por uma perspectiva teórica nos concentramos em uma versão aumentada da regra de Taylor. Também testamos uma abordagem baseada na teoria das expectativas da estrutura a termo cauva de juros para modelar os juros de curto prazo. A seleção dos priores é particularmente relevante para a precisão da previsão, no entanto deseja-se usar prior robustas a falta de conhecimento prévio. Apresentamos os recentes desenvolvimentos na seleção de priors, em especial, propomos o uso de priors hierárquicas da família de distribuição hiper-geométrica.

Cette thèse considère quatre systèmes physiques complexes pour lesquels il est exceptionnellement possible d’identifier des variables lentes qui contrôlent l'évolution à temps long du système complet. La séparation d'échelle de temps entre ces variables lentes et les autres variables permet d'utiliser la technique de moyennisation stochastique pour obtenir une dynamique effective pour les variables lentes. Cette thèse considère la possibilité de prédire les événements rares dans le système solaire. Nous avons étudié deux types d’événements rares. Le premier est un renversement possible de l'axe de rotation de la Terre en l'absence des effets de marée de la Lune. Le second est la désintégration de l'ensemble du système solaire interne suite à une instabilité dans l'orbite de Mercure. Pour chacun des deux problèmes, il existe des variables lentes non triviales, qui ne sont pas données par des variables physiques naturelles. La moyennisation stochastique a permis de découvrir le mécanisme physique qui conduit à ces événements rares et de donner, par une approche purement théorique, l'ordre de grandeur de la probabilité de ces phénomènes. Nous avons également montré que la déstabilisation de Mercure sur un temps inférieur à l'âge du système solaire obéit à un mécanisme d'instanton bien décrit par la théorie des grandes déviations. Le travail effectué dans cette thèse ouvre donc un nouveau champ d'action pour l'utilisation d'algorithmes de calcul d'événements rares. Nous avons utilisé pour la première fois les théorèmes de moyennisation stochastique dans le cadre de la mécanique céleste pour quantifier l'effet stochastique des astéroïdes sur la trajectoire des planètes. Enfin, une partie du travail porte sur un problème de turbulence géophysique: dans l'atmosphère de Jupiter, on peut observer des structures zonales (jets) à grande échelles évoluant beaucoup plus lentement que les tourbillons environnants. Nous montrons qu'il est pour la première fois possible d'obtenir explicitement le profil de ces jets par moyennisation des degrés de liberté turbulents rapides. / The present thesis describes four complex dynamical systems. In each system, the long-term behavior is controlled by a few number of slow variables that can be clearly identified. We show that in the limit of a large timescale separation between the slow variables and the other variables, stochastic averaging can be performed and leads to an effective dynamics for the set of slow variables. This thesis also deals with rare events predictions in the solar system. We consider two possible rare events. The first one is a very large variation of the spin axis orientation of a Moonless Earth. The second one is the disintegration of the inner solar system because of an instability in Mercury’s orbit. Both systems are controlled by non-trivial slow variables that are not given by simple physical quantities. Stochastic averaging has led to the discovery of the mechanism leading to those rare events and gives theoretical bases to compute the rare events probabilities. We also show that Mercury’s short-term destabilizations (compared to the age of the solar system) follow an instanton mechanism, and can be predicted using large deviation theory. The special algorithms devoted to the computation of rare event probabilities can thus find surprising applications in the field of celestial mechanics. We have used for the first time stochastic averaging in the field of celestial mechanics to give a relevant orders of magnitude for the long-term perturbation of planetary orbits by asteroids. A part of the work is about geophysical fluid mechanics. In Jupiter atmosphere, large scale structures (jets) can be observed, the typical time of evolution of which is much larger than that of the surrounding turbulence. We show for the first time that the mean wind velocity can be obtained explicitly by averaging the fast turbulent degrees of freedom.

Cette thèse porte sur l'étude d'algorithmes stochastiques en grande dimension ainsi qu'à leur application en statistique robuste. Dans la suite, l'expression grande dimension pourra aussi bien signifier que la taille des échantillons étudiés est grande ou encore que les variables considérées sont à valeurs dans des espaces de grande dimension (pas nécessairement finie). Afin d'analyser ce type de données, il peut être avantageux de considérer des algorithmes qui soient rapides, qui ne nécessitent pas de stocker toutes les données, et qui permettent de mettre à jour facilement les estimations. Dans de grandes masses de données en grande dimension, la détection automatique de points atypiques est souvent délicate. Cependant, ces points, même s'ils sont peu nombreux, peuvent fortement perturber des indicateurs simples tels que la moyenne ou la covariance. On va se concentrer sur des estimateurs robustes, qui ne sont pas trop sensibles aux données atypiques. Dans une première partie, on s'intéresse à l'estimation récursive de la médiane géométrique, un indicateur de position robuste, et qui peut donc être préférée à la moyenne lorsqu'une partie des données étudiées est contaminée. Pour cela, on introduit un algorithme de Robbins-Monro ainsi que sa version moyennée, avant de construire des boules de confiance non asymptotiques et d'exhiber leurs vitesses de convergence $L^{p}$ et presque sûre.La deuxième partie traite de l'estimation de la "Median Covariation Matrix" (MCM), qui est un indicateur de dispersion robuste lié à la médiane, et qui, si la variable étudiée suit une loi symétrique, a les mêmes sous-espaces propres que la matrice de variance-covariance. Ces dernières propriétés rendent l'étude de la MCM particulièrement intéressante pour l'Analyse en Composantes Principales Robuste. On va donc introduire un algorithme itératif qui permet d'estimer simultanément la médiane géométrique et la MCM ainsi que les $q$ principaux vecteurs propres de cette dernière. On donne, dans un premier temps, la forte consistance des estimateurs de la MCM avant d'exhiber les vitesses de convergence en moyenne quadratique.Dans une troisième partie, en s'inspirant du travail effectué sur les estimateurs de la médiane et de la "Median Covariation Matrix", on exhibe les vitesses de convergence presque sûre et $L^{p}$ des algorithmes de gradient stochastiques et de leur version moyennée dans des espaces de Hilbert, avec des hypothèses moins restrictives que celles présentes dans la littérature. On présente alors deux applications en statistique robuste: estimation de quantiles géométriques et régression logistique robuste.Dans la dernière partie, on cherche à ajuster une sphère sur un nuage de points répartis autour d'une sphère complète où tronquée. Plus précisément, on considère une variable aléatoire ayant une distribution sphérique tronquée, et on cherche à estimer son centre ainsi que son rayon. Pour ce faire, on introduit un algorithme de gradient stochastique projeté et son moyenné. Sous des hypothèses raisonnables, on établit leurs vitesses de convergence en moyenne quadratique ainsi que la normalité asymptotique de l'algorithme moyenné. / This thesis focus on stochastic algorithms in high dimension as well as their application in robust statistics. In what follows, the expression high dimension may be used when the the size of the studied sample is large or when the variables we consider take values in high dimensional spaces (not necessarily finite). In order to analyze these kind of data, it can be interesting to consider algorithms which are fast, which do not need to store all the data, and which allow to update easily the estimates. In large sample of high dimensional data, outliers detection is often complicated. Nevertheless, these outliers, even if they are not many, can strongly disturb simple indicators like the mean and the covariance. We will focus on robust estimates, which are not too much sensitive to outliers.In a first part, we are interested in the recursive estimation of the geometric median, which is a robust indicator of location which can so be preferred to the mean when a part of the studied data is contaminated. For this purpose, we introduce a Robbins-Monro algorithm as well as its averaged version, before building non asymptotic confidence balls for these estimates, and exhibiting their $L^{p}$ and almost sure rates of convergence.In a second part, we focus on the estimation of the Median Covariation Matrix (MCM), which is a robust dispersion indicator linked to the geometric median. Furthermore, if the studied variable has a symmetric law, this indicator has the same eigenvectors as the covariance matrix. This last property represent a real interest to study the MCM, especially for Robust Principal Component Analysis. We so introduce a recursive algorithm which enables us to estimate simultaneously the geometric median, the MCM, and its $q$ main eigenvectors. We give, in a first time, the strong consistency of the estimators of the MCM, before exhibiting their rates of convergence in quadratic mean.In a third part, in the light of the work on the estimates of the median and of the Median Covariation Matrix, we exhibit the almost sure and $L^{p}$ rates of convergence of averaged stochastic gradient algorithms in Hilbert spaces, with less restrictive assumptions than in the literature. Then, two applications in robust statistics are given: estimation of the geometric quantiles and application in robust logistic regression.In the last part, we aim to fit a sphere on a noisy points cloud spread around a complete or truncated sphere. More precisely, we consider a random variable with a truncated spherical distribution, and we want to estimate its center as well as its radius. In this aim, we introduce a projected stochastic gradient algorithm and its averaged version. We establish the strong consistency of these estimators as well as their rates of convergence in quadratic mean. Finally, the asymptotic normality of the averaged algorithm is given.

O objetivo deste trabalho é investigar e desenvolver a teoria de equações dinâmicas funcionais impulsivas em escalas temporais. Mostramos que estas equações representam um caso especial de equações diferenciais funcionais em medida impulsivas. Também, apresentamos uma relação entre estas equações e as equações diferenciais funcionais em medida e, ainda, mostramos uma relação entre elas e as equações diferenciais ordinárias generalizadas. Relacionamos, também, as equações diferenciais funcionais em medida e as equações dinâmicas funcionais em escalas temporais. Obtemos resultados sobre existência e unicidade de soluções, dependência contínua, método da média periódico e não-periódico bem como resultados de estabilidade para todos os tipos de equações descritos anteriormente. Também, provamos algumas propriedades relativas às funções regradas e aos conjuntos equiregrados em espaços de Banach, que foram essenciais para os nossos propósitos. Os resultados novos apresentados neste trabalho estão contidos em 7 artigos, dos quais dois já foram publicados e um aceito. Veja [16], [32], [34], [36], [37], [38] e [84] / The aim of this work is to investigate and develop the theory of impulsive functional dynamic equations on time scales. We prove that these equations represent a special case of impulsive measure functional differential equations. Moreover, we present a relation between these equations and measure functional differential equations and, also, a correspondence between them and generalized ordinary differential equations. Also, we clarify the relation between measure functional differential equations and functional dynamic equations on time scales. We obtain results on the existence and uniqueness of solutions, continuous dependence on parameters, non-periodic and periodic averaging principles and stability results for all these types of equations. Moreover, we prove some properties concerning regulated functions and equiregulated sets in a Banach space which were essential to our purposes. The new results presented in this work are contained in 7 papers, two of which have already been published and one accepted. See [16], [32], [34], [36], [37], [38] and [84]

Made available in DSpace on 2016-06-02T19:26:22Z (GMT). No. of bitstreams: 1 SUMIDA_Simone_Sayuri_2013.pdf: 1095632 bytes, checksum: 44723f2f9f3d3c463660010f25ea0e0d (MD5) Previous issue date: 2013-11-08 / Fragmentation, degradation of habitats, overexploitaton of species and introduction of exotic species are some of the main threats to biodiversity, as a consequence of the human consumption and expansion needs. The local preservation or preservation in situ , through the establishment of legally protected areas is one way to mitigate the expansion of these activities. Piedade municipality presents a set of favorable conditions to establish protected areas: the urbanization is relatively low, native forest remnants occupy approximately 25% of the municipal area, and there are two relevant protected areas with portions within its boundaries: the Environmental Protection Area of Itupararanga, in the northeastern part, and, the State Park of Jurupará, in the southeastern portion. The protected areas in general occupy extensive areas, with different patches, forming a landscape mosaic, and can be studied by Geospatial Technologies, specially through one of its main techniques, the Geographic Information System (GIS), which allows the aggregation of factors through different approaches. Multicriteria evaluation (MCE) is one of those approaches, which transforms and combines different factors, considering their relevance and their respective levels of influence on the production of solutions / alternatives for decision making. In this context, the purpose of this study was to define priority areas for protection, in the Piedade municipality, through the Multicriteria evaluation (MCE). The specific objective was to identify the importance and influence of the selected factors on the decision support process and to evaluate which methods of MCE is appropriated to this study: Weighted Linear Combination (WLC) or Ordered Weighted Averaging (OWA). We defined the criteria and theirs weights using the Participatory Technique. The result was one map of priority areas through WLC and two maps through OWA, with similar degrees of tradeoffs and different degrees of risk to the decision support. The methods (WLC and OWA) enable the definition of priority areas for protection, although the WLC proposes a less detailed solution, which can result in uncertainties in landscape planning. The OWA offers different solutions, considering the risk-taking and factors tradeoffs, providing a greater number of possible answers to the question of interest. The map with low risk-taking was the more appropriated to define priority areas for protection in the Piedade municipality, SP. / Fragmentação, degradação de habitats, superexploração de espécies, introdução de espécies exóticas são algumas das principais ameaças à biodiversidade, devido às necessidades de consumo e expansão humana. Uma das formas de mitigar a expansão dessas atividades e proteger a diversidade biológica, em longo prazo, é a preservação local, ou in situ, por meio do estabelecimento de áreas legalmente protegidas. O município de Piedade apresenta um conjunto de condições favoráveis à consolidação de áreas protegidas, como a urbanização relativamente baixa, a presença de valiosos remanescentes florestais que ocupam aproximadamente 25% da área do município e a existência de duas relevantes Unidades de Conservação com porções dentro de seus limites: a Área de Proteção Ambiental (APA) de Itupararanga na região nordeste do município e o Parque Estadual (PE) do Jurupará, na região sudeste. As áreas protegidas são, em geral, extensas e compostas por diferentes elementos na paisagem e podem ser estudadas por meio do Geoprocessamento, em especial, por uma de suas principais técnicas, o Sistema de Informação Geográfica (SIG), o qual permite a agregação de fatores por meio de diferentes abordagens. A Avaliação Multicriterial (AMC) é uma dessas abordagens, a qual transforma e combina diferentes fatores considerando a relevância dos mesmos e os seus respectivos níveis de influência, produzindo soluções/alternativas para a tomada de decisão. Nesse contexto, o presente trabalho teve por objetivo geral identificar áreas prioritárias à proteção, no município de Piedade, por meio da Avaliação Multicriterial (AMC). Os objetivos específicos foram identificar os fatores, e seus pesos, importantes à definição dessas áreas prioritárias, para as condições da área de estudo e avaliar qual método de AMC, se a Combinação Linear Ponderada (CLP) ou se a Média Ponderada Ordenada (MPO), é o mais apropriado ao objetivo do presente estudo. Por meio da Técnica Participatória, definiu-se os critérios e seus respectivos pesos. Obteve-se um mapa de áreas prioritárias por meio de CLP e outros dois mapas, com valores de compensação semelhantes e diferentes graus de risco para a tomada de decisão. Tanto a CLP quanto a MPO possibilitam a identificação de áreas propensas a se tornarem protegidas, porém a CLP forneceu soluções mais gerais e menos detalhadas que, se não forem bem avaliadas, podem acarretar em incertezas no planejamento da paisagem. A MPO permitiu obter distintas soluções para o processo decisório, por considerar os riscos e as compensações entre os fatores, fornecendo uma maior quantidade de possíveis respostas à questão de interesse. O mapa obtido por meio da MPO, com risco baixo de tomada de decisão, foi considerado o mais adequado para a definição de áreas prioritárias à proteção no município de Piedade, SP.

Cette thèse concerne l’étude de la propagation d’ondes acoustiques dans des structures hétérogènes. Le but essentiel de ces travaux est de confronter des résultats d’expériences numériques effectuées dans le domaine physique (espace, temps) à des prédictions analytiques pour la propagation des ondes de surface SH le long d’un demi-espace stratifié périodique produisant des spectres discontinus de dispersion pour les ondes, ainsi que pour la diffusion multiple dans des milieux aléatoires inclusionnaires (fissures, cavités). Le code numérique FDTD développé lors de cette étude a permis, en autres choses, de corroborer quantitativement les fenêtres spectrales théoriques d’existence des ondes de surface dans les demi-espaces périodiques,ainsi que de montrer des zones de validité fréquentielles des approches analytiques de diffusion multiple concernant les propriétés effectives de milieux aléatoires. / The study is concerned with acoustic waves in elastic media with a different nature of in homogeneity consisting in either periodically continuous or piece wise variation of material properties, or in random sets of defects embedded into a homogeneous matrix, with a given statistical distribution. The scope of problems is topical in non-destructive testing and other applications of ultrasound.Theoretical methods describing involved acoustic phenomena (complex dispersion features, coherent wave in random media, ensemble average techniques) often rely on certain a priori assumptions which render numerical verification especially important.The thesis presents results of analytical modelling of the propagation of surface acoustic waves along periodic half-space, for which the dispersion spectrum is rather complex (discontinuous spectrum of propagation for the surface waves). A 2nd order FDTD numerical code has been developed in order to perform numerical experiments in the space and time domains, and to corroborate the analytical predictions in the frequency domain. A good agreement of simulated results with analytical modelling demonstrates applicability and consistency of the numerical tool. Finally, the code has been used for extracting numerically the coherent wave regime (mean wave over ensemble averaging of the positions of scatterers) for the acoustic propagation in different types of populations of randomly distributed scatterers. The results indicate ranges of validity of some multiple scattering analytical techniques.

Le décrochage profond est un cas particulier du décrochage d’un avion, où l'empennage horizontal est entièrement situé dans le sillage décollé de la voilure principale. Le plan perd ainsi son efficacité, ce qui se traduit par une position d'équilibre en tangage stable, à une incidence élevée, dont il est impossible de sortir par une manœuvre simple. L’objectif de cette étude est de caractériser l’aérodynamique associée à ce phénomène et de proposer une procédure d’identification et de récupération. Il est proposé une démarche visant à déterminer la dynamique bidimensionnelle de l’écoulement autour d’une configuration aéronautique de référence. Les coefficients aérodynamiques, obtenus dans une large plage d’incidence, mettent en évidence l’effet de l’interaction entre les profils sur le décrochage, qui impacte principalement le profil aval. L’analyse des champs de vitesse fournit l’étendue et l’évolution axiale des sillages des profils. Un traitement des champs de vitesse par moyennes de phase permet de reconstruire la dynamique temporelle. À partir de ces résultats, un modèle potentiel de forçage de l’écoulement autour du profil aval permet d’expliquer la modification du coefficient de portance imposé par l’interaction. Des simulations numériques de l’écoulement, qui fournissent des champs résolus en temps, permettent de retrouver certaines évolutions expérimentales. L’ensemble des résultats est utilisé, en parallèle à des données issues d’un aéronef réel, dans un modèle de vol longitudinal afin d’analyser le comportement dynamique de l’avion. Des critères permettant d’identifier la dynamique qui conduit à cet équilibre, fournissent une détection précoce de ce dernier. / Deep stall is a specific type of airplane stall, in which the horizontal tail is inside the detached wake of the main wing. The tail loses its efficiency, leading to a stable pitching equilibrium position with a high angle-of-attack, without any easy recovery procedure. The aim of the study is to characterize the aerodynamic associated to that phenomenon in order to propose an identification and recovery procedure. The approach consists in a two-dimensional flow characterization based on an aeronautical reference configuration. Aerodynamic coefficients, obtained for a wide range of angles-of-attack, show the interaction between the airfoils on the stall of the downstream airfoil. The analysis of velocity fields gives the width and the axial development of the airfoils wakes. Phase-averages of velocity fields lead to the synthesis of flow time-development. With these results, a potential model of flow forcing on the downstream airfoil explains the lift coefficient alteration imposed by the interaction. Flow numerical simulations, giving time-resolved fields, provide good accordance with experimental developments .The whole set of results is used, concurrently with real aircraft data, inside a longitudinal flight model in order to analyze the airplane dynamical behavior. Criteria for the identification of the dynamic leading to that equilibrium provide a rapid detection of deep stall and the implementation of a recovery strategy.