Contexte: L’importance écologique des fourmis dans les écosystèmes terrestres justifie qu’elles soient considérées comme groupe cible pour des actions de conservation. De plus, de par leur abondance, leur facilité de récolte et leur réponse à des perturbations, elles présentent un potentiel intéressant comme groupe indicateur précoce de l’état de santé des écosystèmes. Par contre, pour le choix d’aires à protéger, leur utilité comme intégrateur des conditions de milieu par rapport à des indicateurs classiques tels que les assemblages de plantes n’est pas clairement établie. En d’autres termes, répondent-elles plus finement que les plantes à différentes conditions de milieu et dans ce cas doit-on s’attendre à trouver au sein de formations végétales comparables plusieurs types d’assemblages de foumis? Si tel est le cas, la méthode utilisant les assemblages de végétaux pour sélectionner les sites à protéger peut ne pas permettre une conservation efficace de la diversité des fourmis. Ce type de problématique s’aborde bien le long de gradients environnementaux. Pour faciliter l’interprétation des résultats en terme de réponse aux facteurs abiotiques il est préférable de limiter le nombre de facteurs qui varient en même temps. Dans ce sens, le Chaco sec paraguayen représente un système très favorable: faible déclivité, faibles variations de températures moyennes mais gamme très étendue de conditions de pluviométrie (350mm à 1000mm de précipitations moyennes annuelles) et des sols variables (texture limoneuse à sableuse). L’aridité est l’un des principaux facteurs pouvant limiter la diversité des fourmis soit directement en exerçant un stress physiologique sur les espèces, soit indirectement en limitant la productivité primaire de l’habitat. Les conditions édaphiques peuvent également avoir une influence en affectant par exemple la survie des colonies qui nidifient dans le sol. Objectifs: Les principaux buts de la thèse sont (1) de déterminer l’influence de l’aridité et des conditions édaphiques sur la distribution et la structure des assemblages de fourmis terricoles du sol en forêts tropicales sèches, (2) mettre en évidence les mécanismes qui facilitent la coexistence des espèces de fourmis à l’échelle locale, (3) déterminer si à l’échelle régionale les fourmis et les plantes répondent de façon similaire aux conditions du milieu. Méthode: Onze localités ont été échantillonnées le long d’un transect régional long de 400km. Au niveau de chaque localité, trois transects élémentaires longs de 200m et séparés les uns des autres par 200m ont été effectués. La myrmécofaune a été échantillonnée à l’aide de 20 pièges à fosse et de 20 Winkler par transect élémentaire. La végétation de chaque site a été caractérisée sur base de l’abondance de 45 espèces d’arbres ou d’arbustes caractéristiques de la flore chaquéenne. Les propriétés physico-chimiques du sol ont également été mesurées. A fine échelle, l’organisation spatio-temporelle d’un assemblage a été étudié dans une localité de référence. Résultats: Au total, plus de 50.000 spécimens correspondant à 206 espèces de fourmis ont été collectés avec en moyenne (± SD) 62 ± 10 espèces par localité. Pour un même effort d’échantillonnage, le nombre d’espèces de fourmis récoltées à l’aide des pièges à fosse augmente avec l’aridité et une tendance inverse est observée pour les Winkler. Puisque les Winkler peuvent entraîner une sévère sous-estimation de la diversité des fourmis d’un habitat, seules les données des pièges à fosse sont utilisées pour la suite des analyses. La diversité locale  des assemblages de fourmis n’apparaît corrélée ni à l’aridité, ni aux conditions édaphiques. En revanche, ces facteurs, et spécialement la texture du sol, influencent la composition des assemblages. Trois complexes myrmécofauniques sont mis en évidence: le premier dans la localité la plus sèche (350mm) et la plus sableuse (>90% de sable dans la fraction minérale du sol), le second dans la localité la plus humide (1000mm, sol argilo-limoneux) et le dernier dans des localités présentant de larges conditions de pluviométrie (350-850mm) et de sol (limoneux à sablo-limoneux). Les plantes répondent encore plus finement à ces facteurs abiotiques. A l’échelle locale, l’établissement d’une ségrégation spatio-temporelle fine des espèces de fourmis lors de l’exploitation des ressources alimentaires facilite la coexistence interspécifique. Cette ségrégation est engendrée par l’existence de deux compromis: l’un entre les capacités des espèces à dominer et à découvrir les ressources et l’autre entre la capacité de dominance et la tolérance aux températures élevées. Conclusions: Nos résultats contredisent l’hypothèse selon laquelle les fourmis répondent plus finement que les plantes aux conditions du milieu. A l’échelle du gradient étudié, une augmentation de l’aridité n’affecte pas la diversité des fourmis. La productivité de l’habitat ne semble pas déterminer la richesse des assemblages et la tolérance à l’aridité semble répandue au sein des Formicidae. La texture du sol apparaît être le facteur le plus déterminant des distributions spatiales observées. Dans le Chaco sec paraguayen, une sélection des sites à protéger sur base des assemblages végétaux est susceptible de maximiser la conservation de la diversité biologique des fourmis. Notre étude de la distribution de la myrmécofaune, basée sur la plus large gamme de pluviométrie envisagée à ce jour, pourra constituer le point de départ d'un suivi des assemblages de fourmis dominantes du Chaco sec paraguayen dans le but d'investiguer l'impact des changements climatiques globaux sur ces organismes.

This thesis studies the trading of the Chinese American Depositories Receipts (ADRs) and their respective underlying H shares issued in Hong Kong. The primary intention of this work is to investigate the arbitrage opportunity between the Chinese ADRs and their underlying H shares. This intention is motivated by the market observation that hedge funds are often in the top 10 shareholders of these Chinese ADRs. We start our study from the origin place of the Chinese ADRs, China’s stock market. We pay particular attention to the ownership structure of the Chinese listed firms, because part of the Chinese ADRs also listed A shares (exclusively owned by the Chinese citizens) in Shanghai. We also pay attention to the market microstructures and trading costs of the three China-related stock exchanges. We then proceed to empirical study on the Chinese ADRs arbitrage possibility by comparing the return distribution of two securities; we find these two securities are different in their return distributions, and which is due to the inequality in the higher moments, such as skewness, and kurtosis. Based on the law of one price and the weak-form efficient markets, the prices of identical securities that are traded in different markets should be similar, as any deviation in their prices will be arbitraged away. Given the intrinsic property of the ADRs that a convenient transferable mechanism exists between the ADRs and their underlying shares which makes arbitrage easy; the different return distributions of the ADRs and the underlying shares address the question that if arbitrage is costly that the equilibrium price of the security achieved in each market is affected mainly by its local market where the Chinese ADRs/the underlying Hong Kong shares are traded, such as the demand for and the supply of the stock in each market, the different market microstructures and market mechanisms which produce different trading costs in each market, and different noise trading arose from asymmetric information across multi-markets. And because of these trading costs, noise trading risk, and liquidity risk, the arbitrage opportunity between the two markets would not be exploited promptly. This concern then leads to the second intention of this work that how noise trading and trading cost comes into playing the role of determining asset prices, which makes us to empirically investigate the comovement effect, as well as liquidity risk. With regards to these issues, we progress into two strands, firstly, we test the relationship between the price differentials of the Chinese ADRs and the market return of the US and Hong Kong market. This test is to examine the comovement effect which is caused by asynchronous noise trading. We find the US market impact dominant over Hong Kong market impact, though both markets display significant impact on the ADRs’ price differentials. Secondly, we analyze the liquidity effect on the Chinese ADRs and their underlying Hong Kong shares by using two proxies to measure illiquidity cost and liquidity risk. We find significant positive relation between return and trading volume which is used to capture liquidity risk. This finding leads to a deeper study on the relationship between trading volume and return volatility from market microstructure perspective. In order to verify a proper model to describe return volatility, we carry out test to examine the heteroscedasticity condition, and proceed to use two asymmetric GARCH models to capture leverage effect. We find the Chinese ADRs and their underlying Hong Kong shares have different patterns in the leverage effect as modeled by these two asymmetric GARCH models, and this finding from another angle explains why these two securities are unequal in the higher moments of their return distribution. We then test two opposite hypotheses about volume-volatility relation. The Mixture of Distributions Hypothesis suggests a positive relation between contemporaneous volume and volatility, while the Sequential Information Arrival Hypothesis indicates a causality relationship between lead-lag volume and volatility. We find supportive evidence for the Sequential Information Arrival Hypothesis but not for the Mixture of Distributions Hypothesis.

Ce mémoire présente l’étude de la faisabilité de la planification de traitements pour la curiethérapie interstitielle du sein en utilisant l’imagerie par résonance magnétique (IRM) seule au lieu de l’imagerie par tomodensitométrie (CT). L'imagerie CT étant la référence, la mesure des différences observables sur la distribution de doses provenant des deux types d’imagerie a été effectuée. Des fantômes de seins ont été fabriqués et utilisés, ainsi que l’imagerie de patients. La taille des fantômes en fonction du positionnement dans l’appareil d’IRM et la longueur reconstruite des cathéters ont été analysées. Les différences dans les distributions de doses de fantômes et de patients ont été calculées en s’assurant que la reconstruction des cathéters provenant des images CT et IRM est la seule variable. La différence dans les critères de doses à respecter est plus grande lorsque la taille du fantôme et/ou un déplacement latéral dans l’IRM sont plus grands. La longueur reconstruite des cathéters est comparable entre les deux techniques d’imagerie. Pour le petit fantôme des différences <2% ont été observées pour tous les critères de dose. Pour le grand fantôme et pour les patients, une valeur maximale de 5% est observée pour les critères sur la cible, mais peut atteindre 19% pour le critère Externe V150%/V100% pour le grand fantôme et 33% pour les patients. Par contre, le seuil clinique de ce critére est toujours respecté. Ceci nous indique que pour la plupart des patients, la zone à traiter serait bien couverte en utilisant les images IRM uniquement pour planifier. / This dissertation presents the study of the feasibility of planning for interstitial breast brachytherapy treatments using only magnetic resonance imaging (MRI) instead of computed tomography (CT) imaging. CT imaging being the reference, the measurement of observable differences on dose distributions from the two types of imaging has been done. Breast phantoms has been fabricated and used, as imaging of patients. Size of the phantoms according to the positioning inside the MRI device and catheters reconstructed length has been analysed. Differences in dose distributions of phantoms and patients have been calculated by ensuring that catheters reconstruction from CT and MRI images is the only variable. The difference in respecting the dose’s criteria is bigger when the size and/or the lateral shift into the MRI are bigger. The catheters’ reconstructed length is similar between the two imaging techniques. For the small phantom, differences <2% has been observed for all dose criteria. For the large phantom and for patients, a maximum value of 5% is observed for targets criteria, but can reach 19% for External V150/V100 criterion for the large phantom and 33% for patients. However, clinical threshold for this criterion is still respected. This tells us that for most patients, the treatment region would be covered by using MRI images only for planning.

This thesis concentrates on different approaches of solving decision making problems with an aspect of randomness. The basic methodologies of converting stochastic optimization problems to deterministic optimization problems are described. The proximity of solution of a problem and its empirical counterpart is shown. The empirical counterpart is used when we don't know the distribution of the random elements of the former problem. The distribution with heavy tails, stable distribution and their relationship is described. The stochastic dominance and the possibility of defining problems with stochastic dominance is introduced. The proximity of solution of problem with second order stochastic dominance and the solution of its empirical counterpart is proven. A portfolio management problem with second order stochastic dominance is solved by solving the equivalent empirical problem. Powered by TCPDF (www.tcpdf.org)

We propose Bayesian methods for selecting and estimating different types of mixture models which are widely used inGenetics and MolecularBiology. We specifically propose data-driven selection and estimation methods for a generalized mixture model, which accommodates the usual (independent) and the first-order (dependent) models in one framework, and QTL (quantitativetrait locus) mapping models for independent and pedigree data. For clustering genes through a mixture model, we propose three nonparametric Bayesian methods: a marginal nested Dirichlet process (NDP), which is able to cluster distributions and, a predictive recursion clustering scheme (PRC) and a subset nonparametric Bayesian (SNOB) clustering algorithm for clustering bigdata. We analyze and compare the performance of the proposed methods and traditional procedures of selection, estimation and clustering in simulated and real datasets. The proposed methods are more flexible, improve the convergence of the algorithms and provide more accurate estimates in many situations. In addition, we propose methods for estimating non observable QTLs genotypes and missing parents and improve the Mendelian probability of inheritance of nonfounder genotype using conditional independence structures.We also suggest applying diagnostic measures to check the goodness of fit of QTLmappingmodels. / Nos propomos métodos Bayesianos para selecionar e estimar diferentes tipos de modelos de mistura que são amplamente utilizados em Genética e Biologia Molecular. Especificamente, propomos métodos direcionados pelos dados para selecionar e estimar um modelo de mistura generalizado, que descreve o modelo de mistura usual (independente) e o de primeira ordem numa mesma estrutura, e modelos de mapeamento de QTL com dados independentes e familiares. Para agrupar genes através de modelos de mistura, nos propomos três métodos Bayesianos não-paramétricos: o processo de Dirichlet aninhado que possibilita agrupamento de distribuições e, um algoritmo preditivo recursivo e outro Bayesiano não- paramétrico exato para agrupar dados de alta dimensão. Analisamos e comparamos o desempenho dos métodos propostos e dos procedimentos tradicionais de seleção e estimação de modelos e agrupamento de dados em conjuntos de dados simulados e reais. Os métodos propostos são mais flexíveis, aprimoram a convergência dos algoritmos e apresentam estimativas mais precisas em muitas situações. Além disso, nos propomos procedimentos para estimar o genótipo não observável dos QTL se de pais faltantes e melhorar a probabilidade Mendeliana de herança genética do genótipo dos descendentes através da estrutura condicional de independência entre as variáveis. Também sugerimos aplicar medidas de diagnóstico para verificar a qualidade do ajuste dos modelos de mapeamento de QTLs.

Budongo Forest Reserve (BFR) is a flagship reserve for primate conservation due to its abundant chimpanzee (Pan troglodytes) population, and its current management policy for multiple economic, conservation and environmental benefits. The identification and better understanding of the structure and dynamics of the forest/plant community types, patterns of species distribution and quantitative properties of their diversity is important to the conservation and sustainable management of tropical rainforests. This study seeks to contribute to a better understanding of the BFR forest community types, species diversity patterns and environmental correlates, as well as natural regeneration processes (i.e. seedling establishment and sprouting). Data on vegetation and environmental variables were collected using rectangular 50 x 100m (0.5 ha) plots, sub-divided into five equal contiguous (20 x 50 m) 0.1 ha sub-plots. Data on land-use/cover changes, and relevant associated socio-economic parameters were collected through the analysis of multi-temporal satellite imagery and field observations, as well as interviews of local households and key informants. The study revealed significant land-use/cover changes, with the area under sugarcane cultivation increasing over 17-fold, from 690 ha in 1988 to 12729 ha in 2002, with a concomitant loss of about 4680 ha (8.2% loss) of forest/woodland, mainly in the southern part of BFR. These changes are attributed to agricultural expansion, a rapidly increasing human population, exacerbated by large influxes of refugees, lack of alternative sources of income, conflicts of interest and political interference in the management of BFR, and an unclear land tenure system. The need for more land for agricultural expansion and the loss of woodlands (a source of building materials and fuelwood for the local communities) is leading to the invasion of and encroachment on BFR, which threatens plant and wild animal conservation. The study revealed that the vegetation of BFR is formed by a mosaic of plant communities, with the major forest types being; Pseudospondias microcarpa Swamp Forest, Funtumia elastica - Pouteria altissima, Lasiodiscus mildbraedi - Khaya anthotheca and Cynometra alexandri - Rinorea ilicifolia forest communities. Canonical correspondence analysis (CCA) indicated that soil nutrients (Si, Ca, N, Fe and Li) and anthropogenic disturbances are the main factors controlling forest community patterns. The variances explained as a proportion of total inertia were relatively high (0.53 and 0.56 for basal area and abundance, respectively), showing how well the measured variables explained species composition. These plant communities differed significantly in terms of woody species diversity and richness; being highest in the Pseudospondias microcarpa swamp and lowest in the Cynometra alexandri-Rinorea ilicifolia forest. However, about 48 species were shared between the forest community types. A total of 269 species representing 171 genera and 51 families was recorded. Fisher’s alpha-diversity ranged 4.45-30.59 and 3.07-29.7 for stem diameters ≥2.0 cm and ≥10 cm, respectively, being significantly higher for stem diameters ≥2.0 cm. The use of stem diameters ≥2.0 cm unveiled 53 more species (19.7%), with only 216 species recorded for the standard ≥10 cm dbh minimum size usually applied in tropical forests. A SHE analysis also showed greater richness (ln(S)) and H diversity for the >2.0 cm than the ≥10cm stem diameters. Hence, the study reaffirmed that the use of 10 cm as a minimum dbh in woody plant diversity studies in forests, where many tree species rarely exceed 10 cm stem diameter, is highly likely to underestimate diversity and richness, potentially biasing the understanding of diversity patterns. The most speciose families were Euphorbiaceae, Fabaceae, Rubiaceae, Moraceae, Meliaceae, Rutaceae, Annonaceae, and Flacourtiaceae, accounting for 147 species. Families with the highest Familial Importance values (FIV) were; Fabaceae (17.5), followed by Euphorbiaceae (16.3), and Ulmaceae (8.35). The BFR exhibits characteristics intermediate between log-normal and log-series species-abundance distributions, indicating a community with a small number of abundant species and a relatively large proportion of rare species. Both Whittaker’s (βw) and the Morisita-Horn Index measures of β-diversity consistently showed higher β-diversity for logged and arboricide treated areas, followed by logged only, and then nature reserve historical management practice types. β-diversity was relatively high at the total forest community scale, but lower for stem diameter ≥2.0 cm than ≥10.0 cm data. Environmental variables significantly explained 66.5% and 61.9% of the variance in species composition for stem diameter ≥2.0 cm and ≥10.0 cm data, respectively. Hence, the variation in species composition of BFR is characterised by significant spatial patterns, and the patterns in β-diversity are to a great extent associated with environmental heterogeneity (i.e. soil nutrients, topographic and light gradients) and anthropogenic disturbances. Investigation of natural regeneration showed that sprouting is generally common among the woody species, with both canopy and sub-canopy trees sprouting prolifically. Of the 122 species affected by ii harvesting, and tree and branch fall disturbances, 199 (97.5%) from 31 families sprouted from the cut stumps, with only Caloncoba crepiniana (De Wild. & Th.Dur.) Gilg exhibiting both stem and root sprouting. Stump basal diameter, height, bark-thickness, and height of stump above the ground at which the first sprout emerged, were significant predictors of sprouting ability among individuals. Number of sprouts/stump differed significantly among families, species, and stump size-classes. Of the 241 seedling species, representing 46 families, about 30.3% were rare (only 2-10 individuals); while 12% were very rare (only 1 individual each). Cynometra alexandri C.H. Wright and Lasiodiscus mildbraedii Engl. were the most abundant seedlings and also among the most widely distributed species in the forest. Analysis of similarity (ANOSIM) revealed significant differences in seedling composition between transects, but not between topographic positions or historical management practice types. Canonical Correspondence Analysis (CCA) showed that the measured environmental variables significantly explained 59.4% of the variance in seedling species distributions, with the three most important variables being organic matter, titanium and leaf area index (LAI; an indicator of light availability below the canopy). Hence, the important mechanisms influencing regeneration via seedlings in BFR operate through the soil system, and the ground and canopy vegetation characteristics. Nine of the 15 intensively studied multiple-use species, namely L. mildbraedii, Celtis Mildbraedii Engl., Pouteria altissima (A. Chiev.) Aubrev. & Pellegr., Chrysophyllum albidum G. Don., C. alexandri, Diospyros abyssinica (Hiern) F. White, Funtumia elastica (Preuss) Stapf., Chrysophyllum perpulchrum Hutch. & Dalz, and Antiaris toxicaria (Pers.) Lesch. had highly negative size-class distribution (SCD) slopes and substantial seedling regeneration. While Alstonia boonei De Wild. and Cordia millenii Bak. had weakly negative SCD slopes and pulsed or sporadic regeneration patterns. The wide distribution of seedlings for a variety of species, and with most of the intensively studied species having population structures showing healthy regeneration patterns, suggests that BFR is currently experiencing a continuous regeneration phase. In conclusion, the gradients in the vegetation of BFR are a reflection not only of site conditions as shown by the edaphic and abiotic factors, but also the history of human interventions.

O objetivo do mapeamento de QTL (Quantitative Trait Loci ) e identificar sua posição no genoma, isto e, identificar em qual cromossomo esta e qual sua localização nesse cromossomo, bem como estimar seus efeitos genéticos. Uma vez que as localizações dos QTL não são conhecidas a priori, marcadores são usados frequentemente para auxiliar no seu mapeamento. Alguns marcadores podem estar altamente ligados a um ou mais QTL e, dessa forma eles podem mostrar uma alta associação com a característica fenotípica. O efeito genético do QTL e os valores fenotípicos de uma característica quantitativa são normalmente descritos por um modelo linear. Uma vez que as localizações dos QTL não são conhecidas a priori, marcadores são utilizados para representá-los. Em geral, e utilizado um numero grande de marcadores. Esses marcadores são utilizados no modelo linear para proceder ao processo de associação; dessa forma o modelo especificado contem um numero elevado de parâmetros a serem estimados. No entanto, e esperado que muitos destes parâmetros sejam não significativos, necessitando de um tratamento especial. Na estimação bayesiana esse problema e tratado por meio da estrutura de distribuições a priori utilizada. Um parâmetro que e esperado assumir o valor zero (não significativo) e naturalmente especificado por meio de uma distribuição que coloque um peso maior no zero, encolhimento bayesiano. Neste trabalho e proposta a utilização de dois modelos que utilizam distribuições a priori de encolhimento. Um dos modelos esta relacionado com o uso da distribuição a priori Laplace (Lasso bayesiano) e o outro com a Horseshoe (Estimador Horseshoe). Para avaliar o desempenho dos modelos na determinação da associação entre marcadores e QTL, realizou-se um estudo de simulação. Foi analisada a associação entre marcadores e QTL utilizando três características fenotípicas: produção de grãos, altura da espiga e altura da planta. Comparou-se os resultados obtidos neste trabalho com analises feitas na literatura na detecção dos marcadores associados a essas características. A implementação computacional dos algoritmos foi feita utilizando a linguagem C e executada no pacote estatístico R. O programa implementado na linguagem C e apresentado e disponibilizado. Devido a interação entre as linguagens de programação C e R, foi possível executar o programa no ambiente R. / The objective of the mapping of quantitative trait loci (QTL) is to identify its position in the genome, ie, identify which chromosome is and what is its location in the chromosome, as well as to estimate their genetic eects. Since the location of QTL are not known a priori, markers are often used to assist in it mapping. Some markers may be closely linked to one or more QTL, and thus they may show a strong association with the phenotypic trait. The genetic eect of QTL and the phenotypic values of a quantitative trait are usually described by a linear model. Since the QTL locations are not known a priori, markers are used to represent them. Generally is used a large number of markers. These markers are used in the linear model to make the process of association and thus the model specied contains a large number of parameters to be estimated. However, it is expected that many of these parameters are not signicant, requiring a special treatment. In Bayesian estimation this problem is treated through structure priori distribution used. A parameter that is expected to assume the value zero (not signicant) is naturally specied by means of a distribution that put more weight at zero, bayesian shrinkage. This paper proposes the use of two models using priori distributions to shrinkage. One of the models is related to the use of priori distribution Laplace (bayesian Lasso) and the other with Horseshoe (Horseshoe Estimator). To evaluate the performance of the models to determine the association between markers and QTL, we performed a simulation study. We analyzed the association between markers and QTL using three phenotypic traits: grain yield, ear height and plant height. We compared the results obtained in this study with analyzes in the literature on the detection of markers associated with these characteristics. The computational implementation of the algorithms was done using the C language and executed the statistical package R. The program is implemented in C languages presented and made available. Due to the interaction between the programming languages C and R, it was possible execute the program in the environment R.

Esta pesquisa tem como finalidade discutir os impactos da variabilidade espacial e temporal de precipitações intensas nas vazões de cursos d\'água em bacias urbanizadas mediante a análise de dados históricos da pluviometria obtidos durante eventos críticos. A bacia hidrográfica do rio Tietê, em sua porção mais urbanizada, é a área objeto deste estudo. Após uma revisão sobre o tema na literatura específica, foram desenvolvidas chuvas de projeto com os padrões observados e com padrões teóricos, frequentemente utilizados na geração das tormentas sintéticas. O volume total precipitado foi associado ao período de retorno (TR) de 100 anos, a partir da análise estatística de chuvas pontuais e pela aplicação de fatores de redução de área (FRA) observados na área em estudo e de outras regiões, que vêm sendo utilizados em projetos de drenagem, sem qualquer estudo de validação; o intuito foi o de demonstrar a importância da definição de FRA específicos, a fim de evitar superdimensionamentos e otimizar as soluções. As chuvas de projeto foram aplicadas num modelo matemático de transformação chuva-vazão, devidamente calibrado, para obtenção das vazões de projeto resultantes no limite de jusante da bacia hidrográfica, frente aos diferentes padrões de solicitações hidrológicas. Para auxiliar a calibração do modelo estavam disponíveis dados dos postos telemétricos do Sistema de Alerta a Inundações de São Paulo - SAISP, curvas-chave e, para melhor representação dos eventos de precipitação observados, pode-se contar com as imagens do radar de Ponte Nova, em complementação às informações da rede de superfície. A comparação dos resultados obtidos no modelo hidrológico mostrou que os efeitos dos parâmetros variáveis (volume, distribuição espacial e temporal) são expressivos na composição dos hidrogramas de projeto. Dos testes realizados, identificaram-se as situações mais e menos críticas para a bacia, em termos de distribuição espacial e temporal e duração da chuva de projeto, além de estabelecer as diferenças no dimensionamento do sistema de drenagem pela adoção de FRA específico. Concluiu-se que, pela metodologia proposta, é possível chegar a vazões máximas de projeto apenas pela simulação de tormentas sintéticas, com diferenças de 10% a 20% das tormentas observadas maximizadas. Há, no entanto, a necessidade de realização de estudos adicionais, tanto para definição dos valores de FRA específicos, quanto de simulação de quantidade maior de padrões críticos observados, para a aplicação prática das indicações desse estudo com maior confiabilidade. / This research aims to discuss the impact of the spatial and temporal variability of heavy rainfall in the river flows in urbanized catchments by the historical rainfall data analysis obtained during critical events. The Tiete River catchment, in its most urbanized portion, is the subject of study of this research. After a review of the subject in the specific literature, design rainfall was developed along with the observed and theoretical patterns, often used in the generation of synthetic storms. The total volume precipitated was associated with the 100 years return period (RP), from the statistical analysis of point rainfall and for the application of areal reduction factors (ARF) observed in the study area and in other regions, which have been used in drainage projects without any validation study; the intention was to demonstrate the importance of the definition of specific ARF, in order to avoid oversizing and optimizing solutions. The design precipitation was applied on rainfall-runoff mathematical model, properly calibrated, so as to obtain the resulting design flow at the downstream boundary of the catchment, facing the different patterns of hydrological solicitations. In order to assist the calibration of the model, available data has been used from telemetric stations of the Sistema de Alerta a Inundações de São Paulo (São Paulo Flooding Alert System) - SAISP, discharge curves, and for better representation of the observed precipitation events, can be counted on the images taken from the Ponte Nova radar, as a complement to the information from the surface network. The comparison of the results of the hydrological model has shown that the effects of the variable parameters (volume, spatial and temporal distributions) are significant in the composition of the design hydrograph. Out of the performed tests, the most and the least critical situations were identified concerning the catchment in terms of both spatial and temporal distribution as well as the duration of the design storm. Also, the differences in the dimensions of the of the drainage system design were established by the adoption of specific ARF. Thus, it has been concluded, according to the proposed methodology, that it is possible to reach maximum design flow just by simulating synthetic storms, with differences ranging from 10% to 20% of the observed storms maximized. However, there is a need for additional studies, either to set up setting specific values of ARF or to simulate a larger quantity of critical patterns observed, in order to apply the indications of this study with higher reliability.

Dans cette thèse, nous proposons une nouvelle méthode d'estimation non-paramétrique de la densité de probabi lité. Cette méthode d'estimation imprécise combine la théorie de distribution de Schwartz et la théorie de possibilité. La méthode d'estimation que nous proposons est une extension de la méthode d'estimation à noyau. Cette extension est basée sur une nouvelle méthode de représentation de la notion de voisinage sur laquelle s'appuie l'estimation à noyau. Cette représentation porte le nom de noyau maxitif. L'estimation produite est de nature intervalliste. Elle est une enveloppe convexe d'un ensemble d'estimation de Parzen-Rosenblatt obtenus avec un ensemble de noyaux contenus dans une famille particulière. Nous étudions un certain nombre des propriétés théoriques liées à cette nouvelle méthode d'estimation. Parmi ces propriétés, nous montrons un certain type de convergence de cet estimateur. Nous montrons aussi une aptitude particulière de ce type d'estimation à quantifier l'erreur d'estimation liée à l'aspect aléatoire de la distribution des observations. Nous proposons un certain nombre d'algorithmes de faible complexité permettant de programmer facilement les méthodes que nous proposons / This manuscript, proposes a new nonparametric method for estimating the probability density function. This estimation method combines the Schwartz distribution theory and the possibility theory. It is an extension of the kernel density estimator that leads to imprecise estimation. It is based on a new method for modeling neighborhood. The interval valued estimate it produces is a convex envelope of the Parzen-Rosenblatt estimates obtained with kernels belonging to a coherent convex family. We propose some theoretical properties of this new method. Among these properties, we have shown a kind of convergence of this estimator. We also shown a particular aptitude of this estimator to quantify the error due to random variation in observation. We also propose very low complexity algorithms to compute the proposed methods.

No estudo dos raios cósmicos de ultra alta energia utilizando detectores de superfície a energia da partícula primária é estimada pela distribuição lateral (LDF - Lateral Distribution Function), que descreve a amplitude do sinal das estações em função da distância ao centro do chuveiro. Entretanto, com exceção da estimativa do centro do chuveiro, não se utiliza a LDF para obter mais nenhuma informação sobre o chuveiro, talvez porque ela não possua uma parametrização que a descreva completamente, especialmente para os chuveiros com energias mais altas. As primeiras interações dos raios cósmicos com a atmosfera são determinantes para o desenvolvimento dos chuveiros atmosféricos extensos. Tais interações dependem, entre outras coisas, da composição química dos raios cósmicos. Diferenças nessas interações podem causar alterações nas flutuações da distribuição lateral. Através de simulações dos chuveiros com diferentes partículas primárias pode ser possível estimar a composição dos raios cósmicos de ultra alta energia, comparando as flutuações das distribuições laterais de eventos reais com as de eventos simulados. Uma das grandezas relevantes para a flutuação da LDF é a incerteza do sinal das estações. O framework de análise do Observatório Pierre Auger aplica uma correção parametrizada empiricamente à incerteza do sinal das estações. Neste trabalho foi apresentada uma justificativa estatística para esta correção, que está relacionada à distribuição do sinal não ser uma Poisson, mas uma composição de processos com diferentes distribuições. Para a realização deste trabalho foi gerada uma biblioteca de chuveiros produzidos por dois simuladores de chuveiros atmosféricos, AIRES e CORSIKA, sendo que o AIRES utilizou o SIBYLL como modelo de interação hadrônica enquanto o CORSIKA utilizou o EPOS. Foram produzidos chuveiros iniciados por prótons e núcleos de ferro com os dois simuladores, e suas distribuições angulares foram consideradas isotrópicas. A distribuição de energia desses eventos segue uma lei de potência e varia entre 1 e 200 EeV. Utilizando a função de Nishimura, Kamata e Greisen (NKG) como parametrização para a LDF se observa resíduos sistematicamente positivos nas estações mais distantes do centro do chuveiro, que também têm o sinal mais próximo do trigger. Uma das hipóteses levantadas em outros trabalhos para esse comportamento é que ele estaria relacionado à influência das estações silenciosas, mas este trabalho mostra que o uso dessas estações tem pouca influência na flutuação da LDF. Na verdade esse efeito é causado porque as parametrizações da LDF no Offline não consideram que os sinais das estações possuem um corte devido o trigger, isto é, que a função de densidade de probabilidade que descreve o sinal real não é a mesma que descreve o sinal que é observado. Neste trabalho é proposta uma correção para as parametrizações da LDF que é implementada no Offline. Como resultado desta correção é observada uma redução significativa dos resíduos que eram sistematicamente positivos e que, após a correção, passam a ser compatíveis com zero. Neste trabalho foram realizadas três análises independentes para comparar os eventos reais com os simulados, das quais duas não dependem diretamente do ajuste da LDF e também não são sensíveis à energia. Elas permitem uma comparação entre os sinais supondo uma relação simples entre eles. No primeiro caso supõe-se que a diferença no sinal é devido à componente muônica do chuveiro e no segundo supõe-se que os dois conjuntos de eventos comparados são bem descritos por funções NKG mas com parâmetros S1000 diferentes. A terceira análise utiliza os resíduos dos ajustes da LDF e permite observar a composição em função da energia da partícula primária. Essa última análise foi realizada utilizando a função NKG com e sem correção do efeito do trigger. As diferentes análises utilizadas para estimar a composição dos raios cósmicos apresentaram resultados consistentes entre si, apesar das limitações encontradas em algumas delas. Todos esses indicadores de composição da partícula primária obtidos pelo detector de superfície são consistentes com os resultados obtidos pelas análises de Xmax do detector de fluorescência, reforçando a tese de que a composição dos raios cósmicos é predominantemente de próton entre 1 e 10 EeV e entre próton e ferro para energias acima de aproximadamente 10 EeV. / The energy of ultra high energy cosmic rays can be estimated from the lateral distribution function (LDF) of the shower as measured by surface detectors. The LDF describes the particle density as a function of the distance from the shower center. However, with the exception of the position of the shower center, no other information is extracted from it, may because it does not have a parametrization or an analytic function that describes it completely. The first interactions of cosmic rays with the atmosphere are decisive for the development of the extensive air showers. Such interactions, among other things, depend on the chemical composition of comic rays. Differences in these interactions can cause changes in the fluctuation shape of lateral distribution. Through simulations of showers with different primary particles it may be possible to estimate the composition of ultra high energy cosmic rays comparing the fluctuation shape of the lateral distributions of real events with those from simulated ones. One of the quantities relevant to the fluctuation of the LDF signal is the uncertainty of the stations. The analysis framework of the Pierre Auger Observatory applies a correction to the signal uncertainty of the signal. The parameterization of this correction is obtained empirically. In this work a statistical justification for this correction is proposed and is related to distribution of the signal which is not Poisson, but a composition of processes with different distributions. For this work a library of showers using two simulators of air showers, AIRES and CORSIKA, was produced. The showers simulated with the AIRES used SIBYLL as a hadronic interaction model while COSIKA used EPOS. Showers initiated by protons and iron nuclei with the two simulators were produced, and their angular distribution was considered isotropic. The energy distribution of these events follows a power law and ranges from 1 to 200 EeV. Using the Nishimura, Kamata and Greisen (NKG) function as a parameterization for the LDF, one obtains residues that are systematically positive at stations further from the center of the shower. These stations have a signalclose to the trigger level. One of the hypothesis raised in other works for this behavior is that it is related to the influence of the silent stations, but this work shows that their use has little impact on the fluctuation shape of the LDF. In fact, this effect is caused because the parametrizations of LDF in the Offline ignore that the signals of the stations have a cut due to the trigger, ie, the probability density function that describes the real signal is not the same that describes the observed signal. This work proposes a correction to the parameterizations of the LDF and implements it in the Offline. As a result of this correction, the residues, which were always positive, are significantly reduced and compatible with zero. In this study three independent analysis were performed to compare real and simulated events, two of them not dependent directly of the LDF fit and also not sensitive to the primary particle energy. They allow a comparison between the signals assuming a simple relationship between them. The first case assumes that the difference in signal is due to the muonic component of the shower and the second assumes that the two compared sets of events are well described by NKG functions but with different S1000. The third analysis uses the residues of the LDF fits and is able to observe the composition of as a function of primary particle energy. This last analysis was performed using the NKG function with and without correction of the trigger effect. The different analysis used to estimate the composition of cosmic rays showed results consistent, despite the limitations found in some of them. The primary particle composition obtained from the surface detectors in this work is consistent with the results derived from the elongation rate measured by the fluorescence detectors, supporting the hypotesis that the composition of cosmic rays is predominantly proton becoming heavier for energies above 10 EeV.