Cette thèse est consacrée à l’étude du problème de transport de Monge pour le coût quadratique en géométrie sous-Riemannienne et des conditions essentielles à l’obtention des résultats d’existence et et d’unicité de solutions. Ces travaux consistent à étendre ces résultats au cas des structures sous-Riemanniennes admettant des géodésiques minimisantes singulières. Dans une première partie, on développe des techniques inspirées de travaux de Cavalletti et Huesmann pour d’obtenir des résultats significatifs pour des structures de rang 2 en dimension 4. Dans une deuxième partie, on étudie des outils analytiques de la h-semiconcavité de la distance sousriemannienne et on montre comment ce type de régularité peut aboutit à l’obtention d’existence et d’unicité de solutions dans un cas général. / This thesis is devoted to the study of the Monge transport problem for the quadratic cost in sub-Riemannian geometry and the essential conditions to obtain existence and uniqueness of solutions. These works consist in extending these results to the case of sub-Riemannian structures admitting singular minimizing geodesics. In a first part, we develop techniques inspired by works by Cavalletti and Huesmann in order to obtain significant results for structures of rank 2 in dimension 4. In a second part, we study analytical tools of the h-semiconcavity of the sub-Riemannian distance and we show how this type of regularity can lead to the well-posedness of the Monge problem in general cases.

No description available.

Building an accurate and reliable model for prediction for different application domains, is one of the most significant challenges in knowledge discovery and data mining. This thesis focuses on building and enhancing a generic predictive model for estimating a future value by extracting association rules (knowledge) from a quantitative database. This model is applied to several data sets obtained from different benchmark problems, and the results are evaluated through extensive experimental tests. The thesis presents an incremental development process for the prediction model with three stages. Firstly, a Knowledge Discovery (KD) model is proposed by integrating Fuzzy C-Means (FCM) with Apriori approach to extract Fuzzy Association Rules (FARs) from a database for building a Knowledge Base (KB) to predict a future value. The KD model has been tested with two road-traffic data sets. Secondly, the initial model has been further developed by including a diversification method in order to improve a reliable FARs to find out the best and representative rules. The resulting Diverse Fuzzy Rule Base (DFRB) maintains high quality and diverse FARs offering a more reliable and generic model. The model uses FCM to transform quantitative data into fuzzy ones, while a Multiple Support Apriori (MSapriori) algorithm is adapted to extract the FARs from fuzzy data. The correlation values for these FARs are calculated, and an efficient orientation for filtering FARs is performed as a post-processing method. The FARs diversity is maintained through the clustering of FARs, based on the concept of the sharing function technique used in multi-objectives optimization. The best and the most diverse FARs are obtained as the DFRB to utilise within the Fuzzy Inference System (FIS) for prediction. The third stage of development proposes a hybrid prediction model called Fuzzy Associative Classification Rule Mining (FACRM) model. This model integrates the ii improved Gustafson-Kessel (G-K) algorithm, the proposed Fuzzy Associative Classification Rules (FACR) algorithm and the proposed diversification method. The improved G-K algorithm transforms quantitative data into fuzzy data, while the FACR generate significant rules (Fuzzy Classification Association Rules (FCARs)) by employing the improved multiple support threshold, associative classification and vertical scanning format approaches. These FCARs are then filtered by calculating the correlation value and the distance between them. The advantage of the proposed FACRM model is to build a generalized prediction model, able to deal with different application domains. The validation of the FACRM model is conducted using different benchmark data sets from the University of California, Irvine (UCI) of machine learning and KEEL (Knowledge Extraction based on Evolutionary Learning) repositories, and the results of the proposed FACRM are also compared with other existing prediction models. The experimental results show that the error rate and generalization performance of the proposed model is better in the majority of data sets with respect to the commonly used models. A new method for feature selection entitled Weighting Feature Selection (WFS) is also proposed. The WFS method aims to improve the performance of FACRM model. The prediction performance is improved by minimizing the prediction error and reducing the number of generated rules. The prediction results of FACRM by employing WFS have been compared with that of FACRM and Stepwise Regression (SR) models for different data sets. The performance analysis and comparative study show that the proposed prediction model provides an effective approach that can be used within a decision support system.

O gerenciamento de uma escola-fazenda é atividade complexa, exigindo profissionais qualificados e ferramentas de apoio para tomada de decisão. O desafio é selecionar atividades agropecuárias que otimizem os recursos disponíveis. Nesse contexto, o objetivo deste estudo é desenvolver um modelo matemático para uma escola-fazenda aplicando a técnica de Programação Linear para identificar a combinação ótima de atividades agrícolas, pecuárias e agroindustriais de modo a atender a um mínimo custo - a demanda de alimentos da população que reside no local e possibilitar a realização de práticas pedagógicas. O modelo tem aplicação na Escola de Canuanã da Fundação Bradesco, localizada em uma área de 2.549,07 hectares, no município de Formoso do Araguaia, Tocantins. Na comunidade residem 1.173 pessoas, sendo 909 alunos que estudam em regime de internato. Os alunos do Ensino Médio fazem o Curso Técnico em Agropecuária de forma concomitante e para isso a escola-fazenda precisa proporcionar um ambiente de aprendizagem com diversidade de culturas vegetais, criação de animais e produção agroindustrial. A estruturação do modelo foi realizada paralelamente a um programa de formação técnica pedagógica para gestores e professores com encontros presenciais e videoconferências. A equipe escolar auxiliou na coleta de dados, acompanhou a modelagem e interpretação de resultados para utilizar a ferramenta com os alunos e validou o modelo em encontro presencial na Escola de Canuanã. O modelo matemático proposto é composto por uma função objetivo e cinco conjuntos de restrições que se referem à produção animal, vegetal e agroindustrial, refeições e disponibilidade de recursos. Destaca-se que foram necessárias restrições pedagógicas para garantir um mínimo de animais, culturas e produtos agroindustriais como recursos para as aulas práticas. Os resultados indicaram uma solução ótima com redução do número de algumas espécies animais e alterações nas áreas de produção vegetal, destacando-se maior investimento na horticultura. Ao comparar o custo médio atual da escola-fazenda com aquele indicado pelo modelo de otimização, nota-se que poderia haver redução de 54,2%, resultado de uma realocação dos recursos produtivos, sem comprometer o abastecimento da comunidade e a realização de práticas pedagógicas. Transformar sistemas reais de produção agropecuária em um conjunto de equações envolve habilidades do domínio cognitivo e afetivo. A elaboração do modelo proporciona mobilização de conhecimentos, troca de informações, estabelecimento de relações entre as atividades, avaliação dos dados para gerar parâmetros e criação de equações matemáticas, estimulando postura reflexiva. Esses processos são inerentes do ensino e aprendizagem, o que valida o emprego desta ferramenta na área pedagógica. Destaca-se ainda, que a modelagem propicia a multidisciplinaridade e identifica áreas que demandam pesquisas. Conclui-se que o modelo proposto é uma ferramenta de apoio à decisão com potencial para contribuir na gestão organizacional, na formação de técnicos e docentes em modelagem matemática e na elaboração de métodos para as práticas pedagógicas contribuindo com o processo de ensino-aprendizagem. / Management of farm-school is a complex activity requiring skilled professionals and support tools for decision making. The challenge lies in selecting agricultural activities to optimize available resources. In this context, the objective of this study is to develop a mathematical model for a farm-school using Linear Programming to identify the optimal combination of agricultural, livestock and food processing activities to provide food for the local population and to allow practical lessons. The model has application at the Canuanã School of Bradesco Foundation in area of 2,549.07 in Formoso do Araguaia, Tocantins state. There are 1173 inhabitants, of which 909 are studying in a boarding. The high school students are studying Agricultural Technician and the farmschool must provide a learning environment with a diversity of crops, livestock and food processing production. The model formulation was performed alongside a technical training program for managers and teachers with meetings and videoconferences. The school staff assisted in data collection followed the modeling and interpretation of results for using the tool with students and validated the model in meeting in Canuanã. The mathematical model consists of an objective function and five sets of constraints that refer to animal production, agricultural and food processing, food supply and resource availability. It is noteworthy that restrictions were necessary to ensure a minimum of animals, crops and agro-industrial products to practical lessons with students. The results indicated an optimal solution by reducing the number of some animal species and some changes in the agricultural, emphasizing greater investment in horticulture. When comparing the current average cost of farm-school with that indicated by the optimization model, we note that there could be a reduction of 54.2%, as a result of productive resources reallocation without compromising the food supply to the community and the realization of pedagogical practices. Transforming real systems of agricultural production in a set of equations involves skills of cognitive and affective domain. The model provides mobilization of knowledge, exchange of information, establishing relationships between activities, evaluating data to generate parameters and creating mathematical equations, encouraging reflective posture. These processes are inherent in teaching and learning, which validates the use of this tool. Note also, that modeling provides a multidisciplinary and identifies areas that require research. It is concluded that the proposed model is a decision support tool with the potential to contribute in organizational management, training of technicians and teachers in mathematical modeling and developing methods for teaching practices contributing to the process of teaching and learning.

Preocupados com aspectos ambientais relacionados com a recuperação de solventes e, também, com os riscos envolvidos em experimentos trivialmente executados em disciplinas de Química Orgânica Experimental, utilizamos critérios numéricos para avaliá-los e determinar a viabilidade de se adotarem práticas alternativas, em ambas as frentes. Neste contexto, comparamos, do ponto de vista ambiental, a viabilidade de recuperação de alguns solventes, por destilação, no Setor de Tratamento de Resíduos e Solventes (STRES), com a incineração completa dos mesmos materiais, em incinerador industrial. Para isto, procedemos à separação, por destilação, dos componentes de algumas misturas de solventes. Após determinação das composições dos destilados, por cromatografia em fase gasosa, inserimos os dados obtidos no software ECOSOLVENT para comparamos os impactos ambientais (considerando o EI99 como indicador da Avaliação do Ciclo de Vida) destas destilações com os das incinerações das misturas brutas. Para a maior parte dos casos, foi constatado um menor impacto ambiental para os processos de destilação, justificando-se a continuidade dos trabalhos do STRES. Quanto aos experimentos de Química Orgânica Experimental, combinamos a pontuação de riscos sugerida pela National Fire Protection Association-USA, com o critério de Economia Atômica, tanto para os processos tradicionais como para as modificações sugeridas. Estas últimas levaram, numericamente, a riscos menores, sem alteração das Economias Atômicas. / Concerned with environmental issues related to the recovery of solvents and also to the risks involved in trivial Experimental Organic Chemistry practices, we used numerical criteria to evaluate the feasibility of adopting alternative practices on both fronts. In this context, we compared, from the environmental point of view, the recovery feasibility of some solvents, by distillation, at the Setor de Tratamento de Resíduos e Solventes (STRES), with their complete incineration in an industrial incinerator. Therefore, we proceed to the separation, by distillation, of the components of some mixtures of solvents. After determining the composition of the distillates, by gas chromatography, we input the obtained data into the ECOSOLVENT software in order to compare the environmental impacts (considering the EI99 indicator for the Life Cycle Assessment calculations), arising from these distillations, with those from direct incineration of the crude mixtures of solvents. For most cases, distillation impacts were found to be smaller than those for incineration, thus justifiyng the existence of STRES. As for the Experimental Organic Chemistry practices, we cobined the American National Fire Protection Association`s risks score with the Atom Economy concept for the current, and for some suggested modified procedures. These latter ones led to numerical smaller risks without changing the Atomic Economies.

Preocupados com aspectos ambientais relacionados com a recuperação de solventes e, também, com os riscos envolvidos em experimentos trivialmente executados em disciplinas de Química Orgânica Experimental, utilizamos critérios numéricos para avaliá-los e determinar a viabilidade de se adotarem práticas alternativas, em ambas as frentes. Neste contexto, comparamos, do ponto de vista ambiental, a viabilidade de recuperação de alguns solventes, por destilação, no Setor de Tratamento de Resíduos e Solventes (STRES), com a incineração completa dos mesmos materiais, em incinerador industrial. Para isto, procedemos à separação, por destilação, dos componentes de algumas misturas de solventes. Após determinação das composições dos destilados, por cromatografia em fase gasosa, inserimos os dados obtidos no software ECOSOLVENT para comparamos os impactos ambientais (considerando o EI99 como indicador da Avaliação do Ciclo de Vida) destas destilações com os das incinerações das misturas brutas. Para a maior parte dos casos, foi constatado um menor impacto ambiental para os processos de destilação, justificando-se a continuidade dos trabalhos do STRES. Quanto aos experimentos de Química Orgânica Experimental, combinamos a pontuação de riscos sugerida pela National Fire Protection Association-USA, com o critério de Economia Atômica, tanto para os processos tradicionais como para as modificações sugeridas. Estas últimas levaram, numericamente, a riscos menores, sem alteração das Economias Atômicas. / Concerned with environmental issues related to the recovery of solvents and also to the risks involved in trivial Experimental Organic Chemistry practices, we used numerical criteria to evaluate the feasibility of adopting alternative practices on both fronts. In this context, we compared, from the environmental point of view, the recovery feasibility of some solvents, by distillation, at the Setor de Tratamento de Resíduos e Solventes (STRES), with their complete incineration in an industrial incinerator. Therefore, we proceed to the separation, by distillation, of the components of some mixtures of solvents. After determining the composition of the distillates, by gas chromatography, we input the obtained data into the ECOSOLVENT software in order to compare the environmental impacts (considering the EI99 indicator for the Life Cycle Assessment calculations), arising from these distillations, with those from direct incineration of the crude mixtures of solvents. For most cases, distillation impacts were found to be smaller than those for incineration, thus justifiyng the existence of STRES. As for the Experimental Organic Chemistry practices, we cobined the American National Fire Protection Association`s risks score with the Atom Economy concept for the current, and for some suggested modified procedures. These latter ones led to numerical smaller risks without changing the Atomic Economies.

<p>Using the finite element software FEMLAB® solutions are computed to Dirichlet problems for the Infinity-Laplace equation ∆∞(<i>u</i>) ≡ <i>u</i>²_x<i>u</i>_xx+ 2<i>u</i>_x<i>u</i>_y<i>u</i>_xy+<i>u</i>²_y<i>u</i>_yy= 0. For numerical reasons ∆<i>q</i>(<i>u</i>) = div (|▼<i>u</i>|<i>q</i>▼<i>u</i>)<i> = </i>0, which (formally) approaches as ∆∞(<i>u</i>) = 0 as <i>q</i> → ∞, is used in computation. A parametric nonlinear solver is used, which employs a variant of the damped Newton-Gauss method. The analysis of the experiments is done using the known theory of solutions to Dirichlet problems for ∆∞(<i>u</i>) = 0, which includes AMLEs (Absolutely Minimizing Lipschitz Extensions), sets of uniqueness, critical segments and lines of singularity. From the experiments one main conjecture is formulated: For Dirichlet problems, which have a non-constant boundary function, it is possible to predict the structure of the lines of singularity in solutions in the Infinity-Laplace case by examining the corresponding Laplace case.</p>

Using the finite element software FEMLAB® solutions are computed to Dirichlet problems for the Infinity-Laplace equation ∆∞(u) ≡ u2xuxx + 2uxuyuxy + u2yuyy = 0. For numerical reasons ∆q(u) = div (|▼u|q▼u) = 0, which (formally) approaches as ∆∞(u) = 0 as q → ∞, is used in computation. A parametric nonlinear solver is used, which employs a variant of the damped Newton-Gauss method. The analysis of the experiments is done using the known theory of solutions to Dirichlet problems for ∆∞(u) = 0, which includes AMLEs (Absolutely Minimizing Lipschitz Extensions), sets of uniqueness, critical segments and lines of singularity. From the experiments one main conjecture is formulated: For Dirichlet problems, which have a non-constant boundary function, it is possible to predict the structure of the lines of singularity in solutions in the Infinity-Laplace case by examining the corresponding Laplace case.

The made-up software let to construct the cylindrical shell with composition in laminate by chosen test (reinforcement’s corner, number of shells), also it offer to simulate a reliability of construction and to optimise it by chosen in statistic parameters. Shell’s parameters can be evaluated like episodic variables, which are modulated with Monte - Carlo method. There is given opportunity to evaluate construction’s reliability: of the supposition that distribution of strain at shell is known, construction can be optimised when we are minimizing mass. If we want to show construction’s distribution of limitary state in dotted chart, we have to model strain’s value in every Monte – Carlo step. It is computed factors, which have influence for shell’s strain in construction’s stability. In such succession of operations is controlled the reliability of model’s evaluation. There are analysed parameters, which have the biggest influence for strain at shell. Studied the minimal shell’s mass fluctuation in dependence with dispersion and also parameter’s, of construction strain, overtop probability.

Dois modelos mecânicos, o pêndulo-invertido e o massa-mola, explicam como os mecanismos pendular e elástico minimizam o dispêndio energético advindo dos músculos durante caminhada e corrida humana. A presente tese testa dois efeitos que, para nosso conhecimento, todavia não possuem respostas conclusivas da literatura, nomeadamente o processo de envelhecimento na mecânica da corrida humana e o efeito da inclinação do terreno na velocidade ótima da caminhada. Para estudar o primeiro efeito, as forças de reação do solo provenientes de uma plataforma de força (4m x 0,50m), foram usadas para a posterior comparação de: i) trabalho mecânico, ii) parâmetros do sistema massa-mola e, iii) assimetrias contatodespregue entre jovens e idosos. Os idosos produzem menos força durante a fase de trabalho mecânico positivo com uma menor oscilação vertical total e oscilação durante a fase aérea. Conseqüentemente a capacidade de armazenar e re-utilizar energia elástica dos tendões é prejudicada contribuindo para o maior dispêndio energético neste grupo quando comparado com jovens.Para o modelo do custo eletromiográfico (EMG) da caminhada humana criou-se duas abordagens: experimental e teórica. Em ambas as abordagens, informações da atividade EMG de dezesseis músculos, sendo 8 posturais e 8 propulsores foram coletadas e analisadas a partir da integral EMG. A abordagem teórica parece ter uma melhor relação com as evidências experimentais sobre a energética da caminhada humana em inclinações. Os principais mecanismos envolvidos na nova hipótese são i) músculos posturais que não realizam trabalho muscular, exercem uma função importante na determinação do dispêndio energético total e ii) a presente hipótese leva em consideração a co-contração de músculos antagonistas no dispêndioenergético total. Mais experimentos são necessários para confirmar o modelo apresentado neste estudo. Além disso, através de estratégias de otimização e predição linear, um modelo teórico foi delineado a fim de determinar parâmetros mecânicos (comprimento de passada e velocidade de progressão) e energéticos da locomoção terrestre em situações onde as informações disponíveis são apenas a massa e uma curva força de reação vertical versus tempo. Os resultados advindos do modelamento correspondem aos parâmetros determinados experimentalmente. Laboratórios que detenham apenas uma plataforma de força, ou nas áreas onde as informações de entrada do atual modelo sejam as únicas informações (e.g. paleontologia, biomecânica forênsica, etc), a predição de variáveis primárias da locomoção podem ser preditas com razoável acurácia. / Two mechanical models, the inverted pendulum and spring-mass, explain how do the pendular and elastic mechanisms minimizing energy expenditure from muscles during human walking and running. Here, we test two effects that, to our knowledge, do not have yet conclusive responses from literature, specifically the ageing effects on mechanics of human running, and the effect of gradient on walking optimal speed. In order to check the former effect, the ground reaction forces came from a force platform (4m x 0.5m) were used for a later comparison: i) mechanical work, ii) spring-mass parameters and, iii) landing-takeoff asymmetries. The old subjects produce less force during positive work resulting in a smaller overall and aerial vertical oscillation of the centre of mass. Consequently, the potential for restore elastic energy from tendons is reduced contributing to greater energy expenditure than in young subjects. In relation to Electromyographical (EMG) Cost of human walking we created two approaches: experimental and theoretical. In both approaches, information from EMG activity of sixteen muscles, eight postural and eight propulsor were collected and analysed. The theoretical approach seems to fit better with the energy expenditure during gradient walking. The main mechanisms involved in this new hypothesis are i) postural muscles that do not perform muscular work, play an important role in the total energy expenditure and ii) the present hypothesis take the co-contraction into account of the antagonist muscles in the total energy expenditure. Further experiments are necessary to confirm this hypothesis. Besides, using optimization and linear prediction procedures, a theoretical model was designed to estimate mechanical parameters (stride length and velocity of progression) and energetic variables of terrestrial locomotion when available information consists only of mass and one vertical ground reaction force versus time.The results from this modelling are similar to experimentally obtained data. Laboratories with just one force platform, or in areas where the present model’s input information be the unique accessible data (e.g. palaeontology, forensic biomechanics, etc) the prime variables of locomotion may be estimated with reasonable accuracy.