La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés. / We propose a method for analysing count or Poisson data based on the procedure called Poisson Regression Interactive Multilevel Modeling (PRIMM) introduced by Christiansen and Morris (1997). The Poisson regression in the PRIMM method has fixed effects only, whereas our model incorporates random effects. As well as Christiansen and Morris (1997), the model studied aims at doing inference based on adequate analytical approximations of posterior distributions of the parameters. This avoids the use of computationally expensive methods such as Markov chain Monte Carlo (MCMC) methods. The approximations are based on the Laplace's method and asymptotic theory. Estimates of Poisson mixed effects regression parameters are obtained through the maximization of their joint posterior density via the Newton-Raphson algorithm. This study also provides the first two posterior moments of the Poisson parameters involved. The posterior distributon of these parameters is approximated by a gamma distribution. Applications to two datasets show that our model can be somehow considered as a generalization of the PRIMM method since it also allows clustered count data. Finally, the model is applied to data involving many types of adverse events recorded by the participants of a drug clinical trial which involved a quadrivalent vaccine containing measles, mumps, rubella and varicella. The Poisson regression incorporates the fixed effect corresponding to the covariate treatment/control as well as a random effect associated with the biological system of the body affected by the adverse events.

Nonrigid deformation modeling and estimation from images is a technically challenging task due to its nonlinear, nonconvex and high-dimensional nature. Traditional optimization procedures often rely on good initializations and give locally optimal solutions. On the other hand, learning-based methods that directly model the relationship between deformed images and their parameters either cannot handle complicated forms of mapping, or suffer from the Nyquist Limit and the curse of dimensionality due to high degrees of freedom in the deformation space. In particular, to achieve a worst-case guarantee of ∈ error for a deformation with d degrees of freedom, the sample complexity required is O(1/∈d). In this thesis, a generative model for deformation is established and analyzed using a unified theoretical framework. Based on the framework, three algorithms, Data-Driven Descent, Top-down and Bottom-up Hierarchical Models, are designed and constructed to solve the generative model. Under Lipschitz conditions that rule out unsolvable cases (e.g., deformation of a blank image), all algorithms achieve globally optimal solutions to the specific generative model. The sample complexity of these methods is substantially lower than that of learning-based approaches, which are agnostic to deformation modeling. To achieve global optimality guarantees with lower sample complexity, the structureembedded in the deformation model is exploited. In particular, Data-driven Descentrelates two deformed images that are far away in the parameter space by compositionalstructures of deformation and reduce the sample complexity to O(Cd log 1/∈).Top-down Hierarchical Model factorizes the local deformation into patches once theglobal deformation has been estimated approximately and further reduce the samplecomplexity to O(Cd/1+C2 log 1/∈). Finally, the Bottom-up Hierarchical Model buildsrepresentations that are invariant to local deformation. With the representations, theglobal deformation can be estimated independently of local deformation, reducingthe sample complexity to O((C/∈)d0) (d0 ≪ d). From the analysis, this thesis showsthe connections between approaches that are traditionally considered to be of verydifferent nature. New theoretical conjectures on approaches like Deep Learning, arealso provided. practice, broad applications of the proposed approaches have also been demonstrated to estimate water distortion, air turbulence, cloth deformation and human pose with state-of-the-art results. Some approaches even achieve near real-time performance. Finally, application-dependent physics-based models are built with good performance in document rectification and scene depth recovery in turbulent media.

The ability to learn is essential for robots to function and perform services within a dynamic human environment. Robot programming by demonstration facilitates learning through a human teacher without the need to develop new code for each task that the robot performs. In order for learning to be generalizable, the robot needs to be able to grasp the underlying structure of the task being learned. This requires appropriate knowledge abstraction and representation. The goal of this thesis is to develop a learning by imitation system that abstracts knowledge of human demonstrations of a task and represents the abstracted knowledge in a hierarchical framework. The learning by imitation system is capable of performing both action and object recognition based on video stream data at the lower level of the hierarchy, while the sequence of actions and object states observed is reconstructed at the higher level of the hierarchy in order to form a coherent representation of the task. Furthermore, error recovery capabilities are included in the learning by imitation system to improve robustness to unexpected situations during task execution. The first part of the thesis focuses on motion learning to allow the robot to both recognize the actions for task representation at the higher level of the hierarchy and to perform the actions to imitate the task. In order to efficiently learn actions, the actions are segmented into meaningful atomic units called motion primitives. These motion primitives are then modeled using dynamic movement primitives (DMPs), a dynamical system model that can robustly generate motion trajectories to arbitrary goal positions while maintaining the overall shape of the demonstrated motion trajectory. The DMPs also contain weight parameters that are reflective of the shape of the motion trajectory. These weight parameters are clustered using affinity propagation (AP), an efficient exemplar clustering algorithm, in order to determine groups of similar motion primitives and thus, performing motion recognition. The approach of DMPs combined with APs was experimentally verified on two separate motion data sets for its ability to recognize and generate motion primitives. The second part of the thesis outlines how the task representation is created and used for imitating observed tasks. This includes object and object state recognition using simple computer vision techniques as well as the automatic construction of a Petri net (PN) model to describe an observed task. Tasks are composed of a sequence of actions that have specific pre-conditions, i.e. object states required before the action can be performed, and post-conditions, i.e. object states that result from the action. The PNs inherently encode pre-conditions and post-conditions of a particular event, i.e. action, and can model tasks as a coherent sequence of actions and object states. In addition, PNs are very flexible in modeling a variety of tasks including tasks that involve both sequential and parallel components. The automatic PN creation process has been tested on both a sequential two block stacking task and a three block stacking task involving both sequential and parallel components. The PN provides a meaningful representation of the observed tasks that can be used by a robot to imitate the tasks. Lastly, error recovery capabilities are added to the learning by imitation system in order to allow the robot to readjust the sequence of actions needed during task execution. The error recovery component is able to deal with two types of errors: unexpected, but known situations and unexpected, unknown situations. In the case of unexpected, but known situations, the learning system is able to search through the PN to identify the known situation and the actions needed to complete the task. This ability is useful not only for error recovery from known situations, but also for human robot collaboration, where the human unexpectedly helps to complete part of the task. In the case of situations that are both unexpected and unknown, the robot will prompt the human demonstrator to teach how to recover from the error to a known state. By observing the error recovery procedure and automatically extending the PN with the error recovery information, the situation encountered becomes part of the known situations and the robot is able to autonomously recover from the error in the future. This error recovery approach was tested successfully on errors encountered during the three block stacking task.

In the thesis "On Boundaries of Statistical Models" problems related to a description of probability distributions with zeros, lying in the boundary of a statistical model, are treated. The distributions considered are joint distributions of finite collections of finite discrete random variables. Owing to this restriction, statistical models are subsets of finite dimensional real vector spaces. The support set problem for exponential families, the main class of models considered in the thesis, is to characterize the possible supports of distributions in the boundaries of these statistical models. It is shown that this problem is equivalent to a characterization of the face lattice of a convex polytope, called the convex support. The main tool for treating questions related to the boundary are implicit representations. Exponential families are shown to be sets of solutions of binomial equations, connected to an underlying combinatorial structure, called oriented matroid. Under an additional assumption these equations are polynomial and one is placed in the setting of commutative algebra and algebraic geometry. In this case one recovers results from algebraic statistics. The combinatorial theory of exponential families using oriented matroids makes the established connection between an exponential family and its convex support completely natural: Both are derived from the same oriented matroid. The second part of the thesis deals with hierarchical models, which are a special class of exponential families constructed from simplicial complexes. The main technical tool for their treatment in this thesis are so called elementary circuits. After their introduction, they are used to derive properties of the implicit representations of hierarchical models. Each elementary circuit gives an equation holding on the hierarchical model, and these equations are shown to be the "simplest", in the sense that the smallest degree among the equations corresponding to elementary circuits gives a lower bound on the degree of all equations characterizing the model. Translating this result back to polyhedral geometry yields a neighborliness property of marginal polytopes, the convex supports of hierarchical models. Elementary circuits of small support are related to independence statements holding between the random variables whose joint distributions the hierarchical model describes. Models for which the complete set of circuits consists of elementary circuits are shown to be described by totally unimodular matrices. The thesis also contains an analysis of the case of binary random variables. In this special situation, marginal polytopes can be represented as the convex hulls of linear codes. Among the results here is a classification of full-dimensional linear code polytopes in terms of their subgroups. If represented by polynomial equations, exponential families are the varieties of binomial prime ideals. The third part of the thesis describes tools to treat models defined by not necessarily prime binomial ideals. It follows from Eisenbud and Sturmfels' results on binomial ideals that these models are unions of exponential families, and apart from solving the support set problem for each of these, one is faced with finding the decomposition. The thesis discusses algorithms for specialized treatment of binomial ideals, exploiting their combinatorial nature. The provided software package Binomials.m2 is shown to be able to compute very large primary decompositions, yielding a counterexample to a recent conjecture in algebraic statistics.

We considered a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a high dimension spatial field. The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provides a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. Karhunen-Lo'eve expansion and Discrete Cosine transform were used for dimension reduction of the random spatial field. Furthermore, we used a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we have shown that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. The need for multiple evaluations of the forward model on a high dimension spatial field (e.g. in the context of MCMC) together with the high dimensionality of the posterior, results in many computation challenges. We developed two-stage reversible jump MCMC method which has the ability to screen the bad proposals in the first inexpensive stage. Channelized spatial fields were represented by facies boundaries and variogram-based spatial fields within each facies. Using level-set based approach, the shape of the channel boundaries was updated with dynamic data using a Bayesian hierarchical model where the number of points representing the channel boundaries is assumed to be unknown. Statistical emulators on a large scale spatial field were introduced to avoid the expensive likelihood calculation, which contains the forward simulator, at each iteration of the MCMC step. To build the emulator, the original spatial field was represented by a low dimensional parameterization using Discrete Cosine Transform (DCT), then the Bayesian approach to multivariate adaptive regression spline (BMARS) was used to emulate the simulator. Various numerical results were presented by analyzing simulated as well as real data.

A observação de gradientes latitudinais em aspectos da história de vida de aves tem motivado o estudo da evolução e variabilidade das histórias de vida nestes organismos. Um exemplo bem documentado é a variação no tamanho da ninhada, onde aves de latitudes menores tendem a ter ninhadas menores do que os seus homólogos de latitudes altas. Uma hipótese que visa explicar esta variação propõe que a sobrevivência em latitudes tropicais é maior para compensar o tamanho da ninhada menor e evitar a extinção das populações. Esta explicação tem tido grande aceitação e apoio por parte de alguns estudos, mas tem sido questionada por outros que não encontraram taxas de sobrevivência mais elevadas em aves tropicais. De modo implícito, todos estes estudos basearam seus resultados na sobrevivência de indivíduos adultos. As populações com o tamanho da ninhada menor não poderiam crescer da mesma maneira que as populações com ninhadas maiores; portanto, se justifica acreditar que algo deve mudar com a latitude para manter o balanço em tamanho populacional. Na busca por explicações alternativas para a persistência das populações de aves tropicais com relativamente pequenos tamanhos de ninhada, surge outra hipótese que propõe que, se não houver diferenças na sobrevivência de indivíduos adultos entre latitudes, o aspecto fundamental que varia é a sobrevivência juvenil, com sobrevivência maior para os juvenis das zonas tropicais em comparação com os juvenis das zonas temperadas. No entanto, atualmente há pouca evidência que suporta esta conclusão. Os resultados contrastantes desses estudos sugerem a falta de um consenso geral sobre a hipótese de que as aves tropicais têm taxas de sobrevivência mais elevadas do que as aves de regiões temperadas, motivando a formulação de hipóteses alternativas e convidando novos testes de hipótese. Neste estudo, pretendemos a) avaliar o efeito da idade sobre a sobrevivência em aves tropicais, estimando as probabilidades anuais de sobrevivência aparentes idade-específicas para um conjunto de aves passeriformes de sub-bosque na Amazônia central brasileira; e b) contribuir para o debate sobre o gradiente latitudinal na sobrevivência de adultos, comparando nossas estimativas com estimativas de outras latitudes. Para estimar a sobrevivência idade-específica ajustamos aos nossos dados um modelo Cormack-Jolly-Seber (CJS) hierárquico para n espécies, que trata os parâmetros espécie-específicos como efeitos aleatórios, que são estimados e que descrevem todo o conjunto de espécies; para comparação de métodos, ajustamos uma versão de efeitos fixos do modelo. Para a determinação da idade das aves usamos o sistema WRP. Apresentamos uma nova variante do modelo CJS com um parâmetro de mistura para a sobrevivência de aves de idade incerta no momento da primeira captura. Encontramos efeito forte da idade na sobrevivência, com probabilidades de sobrevivência menor para os jovens do que para os adultos; evidência de efeito latitude sobre a sobrevivência, que suporta a hipótese amplamente aceita de variação na sobrevivência com a latitude; e discutimos diferenças metodológicas interessantes entre modelo de efeitos aleatórios e fixos relacionados com a precisão das estimativas e o âmbito de inferência, que nos levam a concluir que os modelos de efeitos aleatórios são os mais adequados para a nossa análise. Concluímos que não é necessário invocar uma hipótese alternativa de maior sobrevivência juvenil nos trópicos a fim de explicar o gradiente latitudinal no tamanho da ninhada. / The observation of latitudinal gradients in bird life history traits has motivated the study of avian life history evolution and variability. A well-documented example is the variation in clutch size, where lower latitude birds tend to have smaller clutches than their higher latitude counterparts. A hypothesis that explains this variation proposes that survival in tropical latitudes is higher to compensate for smaller clutch size and prevent population extinctions. This explanation has had a wide acceptance and support by some studies, but has been questioned by others who have not found such higher survival rates in tropical birds. In an implicit manner, all these studies have based their results on adult survival. Populations with smaller clutch size would not be able to grow as well as populations with larger clutches; therefore one is justified to believe that something else must change with latitude. In the search for alternative explanations to the persistence of tropical bird populations with relatively small clutch sizes it has also been proposed that, if there were no differences in adult survival among latitudes, the fundamental trait that varies is juvenile survival, with higher survival rates for tropical juveniles birds than for temperate ones. However, currently there is little evidence that supports this conclusion. The contrasting results of those studies suggest a lack of a general consensus about the hypothesis that tropical birds have higher survival rates than birds of temperate regions, motivating the formulation of alternative hypotheses, and inviting further tests of the hypothesis. In our study we aim to a) assess the effect of age on survival in a tropical bird community, estimating age-specific annual apparent survival probabilities for a set of passerine understory birds from the central Brazilian Amazon; and b) contribute to the debate about the latitudinal gradient in adult survival by comparing our adult survival estimates to estimates of temperate-zone adult survival probabilities. To estimate the age-specific survival we fit to our data a hierarchical multispecies Cormack-Jolly-Seber (CJS) model for n species, that treats species-specific parameters as random effects that are estimated and that describe the whole assemblage of species; for comparison of methods, we also fit a fixed-effects version of the model. To age birds we use the cycle-based WRP system. We introduce a novel variant of CJS model with a mixture component for the survival of birds of uncertain age at the time of banding. We found strong effect of age on survival, with juveniles surviving less than adults; evidence of latitude effect on survival, that supports the widely accepted hypothesis of variation on survival with latitude; and methodological differences between random and fixed effects model related to precision of estimates and scope of inference, that lead us to conclude that random-effects models are more appropriate for our analysis. We conclude that there is no reason for an alternative latitudinal trend in juvenile survival to account for the general trend in clutch size.

A observação de gradientes latitudinais em aspectos da história de vida de aves tem motivado o estudo da evolução e variabilidade das histórias de vida nestes organismos. Um exemplo bem documentado é a variação no tamanho da ninhada, onde aves de latitudes menores tendem a ter ninhadas menores do que os seus homólogos de latitudes altas. Uma hipótese que visa explicar esta variação propõe que a sobrevivência em latitudes tropicais é maior para compensar o tamanho da ninhada menor e evitar a extinção das populações. Esta explicação tem tido grande aceitação e apoio por parte de alguns estudos, mas tem sido questionada por outros que não encontraram taxas de sobrevivência mais elevadas em aves tropicais. De modo implícito, todos estes estudos basearam seus resultados na sobrevivência de indivíduos adultos. As populações com o tamanho da ninhada menor não poderiam crescer da mesma maneira que as populações com ninhadas maiores; portanto, se justifica acreditar que algo deve mudar com a latitude para manter o balanço em tamanho populacional. Na busca por explicações alternativas para a persistência das populações de aves tropicais com relativamente pequenos tamanhos de ninhada, surge outra hipótese que propõe que, se não houver diferenças na sobrevivência de indivíduos adultos entre latitudes, o aspecto fundamental que varia é a sobrevivência juvenil, com sobrevivência maior para os juvenis das zonas tropicais em comparação com os juvenis das zonas temperadas. No entanto, atualmente há pouca evidência que suporta esta conclusão. Os resultados contrastantes desses estudos sugerem a falta de um consenso geral sobre a hipótese de que as aves tropicais têm taxas de sobrevivência mais elevadas do que as aves de regiões temperadas, motivando a formulação de hipóteses alternativas e convidando novos testes de hipótese. Neste estudo, pretendemos a) avaliar o efeito da idade sobre a sobrevivência em aves tropicais, estimando as probabilidades anuais de sobrevivência aparentes idade-específicas para um conjunto de aves passeriformes de sub-bosque na Amazônia central brasileira; e b) contribuir para o debate sobre o gradiente latitudinal na sobrevivência de adultos, comparando nossas estimativas com estimativas de outras latitudes. Para estimar a sobrevivência idade-específica ajustamos aos nossos dados um modelo Cormack-Jolly-Seber (CJS) hierárquico para n espécies, que trata os parâmetros espécie-específicos como efeitos aleatórios, que são estimados e que descrevem todo o conjunto de espécies; para comparação de métodos, ajustamos uma versão de efeitos fixos do modelo. Para a determinação da idade das aves usamos o sistema WRP. Apresentamos uma nova variante do modelo CJS com um parâmetro de mistura para a sobrevivência de aves de idade incerta no momento da primeira captura. Encontramos efeito forte da idade na sobrevivência, com probabilidades de sobrevivência menor para os jovens do que para os adultos; evidência de efeito latitude sobre a sobrevivência, que suporta a hipótese amplamente aceita de variação na sobrevivência com a latitude; e discutimos diferenças metodológicas interessantes entre modelo de efeitos aleatórios e fixos relacionados com a precisão das estimativas e o âmbito de inferência, que nos levam a concluir que os modelos de efeitos aleatórios são os mais adequados para a nossa análise. Concluímos que não é necessário invocar uma hipótese alternativa de maior sobrevivência juvenil nos trópicos a fim de explicar o gradiente latitudinal no tamanho da ninhada. / The observation of latitudinal gradients in bird life history traits has motivated the study of avian life history evolution and variability. A well-documented example is the variation in clutch size, where lower latitude birds tend to have smaller clutches than their higher latitude counterparts. A hypothesis that explains this variation proposes that survival in tropical latitudes is higher to compensate for smaller clutch size and prevent population extinctions. This explanation has had a wide acceptance and support by some studies, but has been questioned by others who have not found such higher survival rates in tropical birds. In an implicit manner, all these studies have based their results on adult survival. Populations with smaller clutch size would not be able to grow as well as populations with larger clutches; therefore one is justified to believe that something else must change with latitude. In the search for alternative explanations to the persistence of tropical bird populations with relatively small clutch sizes it has also been proposed that, if there were no differences in adult survival among latitudes, the fundamental trait that varies is juvenile survival, with higher survival rates for tropical juveniles birds than for temperate ones. However, currently there is little evidence that supports this conclusion. The contrasting results of those studies suggest a lack of a general consensus about the hypothesis that tropical birds have higher survival rates than birds of temperate regions, motivating the formulation of alternative hypotheses, and inviting further tests of the hypothesis. In our study we aim to a) assess the effect of age on survival in a tropical bird community, estimating age-specific annual apparent survival probabilities for a set of passerine understory birds from the central Brazilian Amazon; and b) contribute to the debate about the latitudinal gradient in adult survival by comparing our adult survival estimates to estimates of temperate-zone adult survival probabilities. To estimate the age-specific survival we fit to our data a hierarchical multispecies Cormack-Jolly-Seber (CJS) model for n species, that treats species-specific parameters as random effects that are estimated and that describe the whole assemblage of species; for comparison of methods, we also fit a fixed-effects version of the model. To age birds we use the cycle-based WRP system. We introduce a novel variant of CJS model with a mixture component for the survival of birds of uncertain age at the time of banding. We found strong effect of age on survival, with juveniles surviving less than adults; evidence of latitude effect on survival, that supports the widely accepted hypothesis of variation on survival with latitude; and methodological differences between random and fixed effects model related to precision of estimates and scope of inference, that lead us to conclude that random-effects models are more appropriate for our analysis. We conclude that there is no reason for an alternative latitudinal trend in juvenile survival to account for the general trend in clutch size.

Made available in DSpace on 2017-07-10T19:23:48Z (GMT). No. of bitstreams: 1 Sergio_ Bazilio.pdf: 3134289 bytes, checksum: 8461a5a239e9c7674bb3db224824dc63 (MD5) Previous issue date: 2015-02-12 / Benthic macroinvertebrate community is very important to streams, since they make part of the energy flow and are also an important food source for adjacent and upper trophic levels. They form a very diversified fauna and their structure may be influenced by several environmental factors, which vary in time, space and in an analyzed scale. Samples were taken from benthic macroinvertebrates and environmental descriptors during winter, spring and summer of 2012 and autumn of 2013 in ten sampling points in Lontra river watershed (Paraná, Brazil). Thus, this study aimed at: a) characterizing the watershed morphometry in Lontra river with data from the Shuttle Radar Topography Mission (SRTM); b) analyzing the structure of benthic macroinvertebrate community according to their taxonomic family level and functional groups; c) investigating seasonal variation (during the four seasons) and spatial variation of this community structure due to spatial differences in morphological and physiographic characteristics of the sampled sections; d) identifying the community variability of benthic macroinvertebrates at three spatial scales (river, river segment and mesohabitat) emphasizing spatial scales, which best explain the community structure in this watershed; e) investigating which measured environmental descriptors influence on the community structure and f) which variability percentage in organisms richness can be explained by the measured local environmental descriptors. / Os macroinvertebrados bentônicos constituem uma importante comunidade em riachos, pois participam do fluxo de energia, logo são um importante recurso alimentar para níveis tróficos adjacentes e superiores. Formam uma fauna bastante diversificada e a estrutura dessa comunidade pode ser influenciada por diversos fatores ambientais, os quais variam no tempo, no espaço e na escala analisada. Realizaram-se amostragens de macroinvertebrados bentônicos e descritores ambientais nos períodos de inverno, primavera e verão de 2012 e outono de 2013 em dez pontos amostrais na bacia do Rio Lontra (PR, Brasil). O presente estudo objetivou: a) caracterizar morfometricamente a microbacia do Rio Lontra com dados do projeto da Missão do Radar Transportado Espacial (SRTM). b) analisar a estrutura da comunidade de macroinvertebrados bentônicos em nível taxonômico de família e de grupos funcionais; c) investigar a variação sazonal (nas quatro estações do ano) e a variação espacial da estrutura da comunidade em função de diferenças espaciais nas características morfofisiográficas dos trechos amostrados; d) identificar a variabilidade da comunidade de macroinvertebrados bentônicos em três escalas espaciais (rio, segmento de rio e mesohabitat) com ênfase nas escalas espaciais que melhor explicam a estrutura da comunidade nesta bacia; e) investigar quais descritores ambientais mensurados influenciam a estrutura da comunidade e f) qual porcentagem da variabilidade na riqueza de organismos pode ser explicada pelos descritores ambientais locais mensurados.

Consideramos dois tópicos distintos relacionados a modelos clássicos da mecânica estatísticas de equilíbrio. O primeiro constitui-se na análise de equação parabólicas semi-lineares associadas à transformação de grupo de renormalização para o gás de Coulomb hierárquico bidimensional e o gás dipolos hierárquicos em dimensão d>1 após tomarmos um limite apropriado (limite L 1 do tamanho do bloco). O outro tópico estudado foi a construção de uma função majorante (, z) para a pressão termodinâmica de um gás formado por partículas interagentes com atividade z e temperatura -1, cuja interação entre dois corpos pode ser decomposta em escalas como um potencial estável. Somos capazes de demonstrar que o problema de valor inicial dado pela equação do gás de Coulomb está bem definido (existência, unicidade e dependência contínua das soluções) em um espaço funcional adequado e a solução converge assintoticamente para uma das infinitas contáveis soluções de equilíbrio. Quanto ao gás de dipolos, embora não tenhamos conseguido provar a existência e unicidade das soluções, garantimos que a única solução estacionária limitada inferiormente é a trivial nula, que é uma solução estável. Ao menos no caso dos modelos hierárquicos, os resultados obtidos permitem dar uma resposta definitiva à conjectura de Gallavotti e Nicolò sobre uma sequência infinita de transições de fase. A função majorante é construída como a solução de uma equação diferencial parcial quase-linear de primeira ordem. Através da do método das características relacionamos a solução (majorante) à função W de Lambert cuja expansão em série possui uma singularidade originada pelo corte que a função W possui no plano complexo. A descrição da função majorante como uma função W possui no plano complexo. A descrição da função majorante como uma função W permite uma melhora nas estimativas de raio de convergência para série de Mayer para pressão. / We have considered in this thesis two distinct topics related to classic models in equilibrium statistical mechanics. The first one is the analysis of semilinear parabolic partial differential equations given by a suitable limit (size of block L 1) in the renormalization group for the dipole gas in any dimension d>1. The other topic is the construction of a majorant function (, z) for the thermodynamic -1 whose potential admits a scale decomposition in terms of some stable potential. We are capable to demonstrate the well-posedness (existence, uniqueness and continuous dependence of solutions) for Coulomb gas equations and the global asymptotic convergence of the flow to one of its countably many equilibrium solutions. The dipole gas equations are technically more difficult and lack the results weve achieved in Coulomb gas but, despite its difficulties, we can establish the uniqueness of the trivial solution as a equilibrium ane and its stabilish. At least for hierarchical models, the established results give a definite answer to Gallovotti and Niclolòs conjecture of na infinite of phase transitions. The majorant function is constructed as the solution of a first order quase-linear partial differential equation. By means of the characteristics method we are able to relate its solution (the majorant) to Lamberts W-function whose series expansion possess a singularity given by W-function allows better estimates for Mayer series convergence.

Investigated in this thesis are the possibilities and effects of reducing CAN data collected from forklifts. The purpose of reducing the data was to create the possibility of exporting and managing data for multiple forklifts and a relatively long period of time. For doing that was an autoregressive filter implemented for filtering and decimating data. Connected to the decimation was also the aim of generating a data set that could be used for analyzing lift sequences and in particular the usage of fork adjustment functions during lift sequences. The findings in the report are that an AR (18) model works well for filtering and decimating the data. Information losses are unavoidable but kept at a relatively low level, and the size of data becomes manageable. Each row in the decimated data is labeled as belonging to a lift sequence or as not belonging to a lift sequence given a manually specified definition of the lift sequence event. From the lift sequences is information about the lift like number of usages of each fork adjustment function, load weight and fork height gathered. The analysis of the lift sequences gave that the lift/lower function on average is used 4.75 times per lift sequence and the reach function 3.23 times on average. For the side shift the mean is 0.35 per lift sequence and for the tilt the mean is 0.10. Moreover, it was also found that the struggling time on average is about 17 % of the total lift sequence time. The proportion of the lift that is struggling time was also shown to differ between drivers, with the lowest mean proportion being 7 % and the highest 30 %.