Avec l'émergence des nouvelles technologies, les communications sans fil n'ont cessé de croître afin de permettre aux utilisateurs un accès à l'information et aux services électroniques, et ceci indépendamment de leur position géographique. Les réseaux sans fil ont aussi trouvé leur place pour des applications spécifiques telles que les transmissions radio utilisées pour l'interconnexion de capteurs. Ce type de réseau peut être considéré comme un sous-ensemble des réseaux ad hoc. Des contraintes spécifiques s'appliquent alors aux utilisateurs de ces réseaux, telles que la difficulté d'accès pour la maintenance, les problèmes liés à la miniaturisation et au nombre élevé de capteurs. L'objectif de cette thèse est d'étudier les contraintes énergétiques liées à l'utilisation des batteries à capacité limitée pour l'alimentation des capteurs. Pour atteindre cet objectif, nous avons proposé de représenter les réseaux de capteurs à travers une image à échelle de gris : les zones claires correspondant aux zones riches en énergie, alors que les zones sombres représentent des régions avec une capacité énergétique faible. Des filtres issus du monde de traitement d'image sont alors appliqués à cette image représentant l'énergie. Ainsi, nous proposons des filtres de convolution de type Sobel ou de type filtre moyen pour nos algorithmes de routage et nous construisons une matrice énergétique pour chaque capteur. Cette matrice est alors utilisée avec le produit de convolution pour guider le routage. Les différents algorithmes proposés font ensuite l'objet de simulations avec le simulateur de réseaux OMNeT++.

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In this thesis, we use martingales to show that the dilation of a sequence of monotone convolutions $D_\frac{1}{b_n} (\mu_1 \triangleright \mu_2 \triangleright \cdots \triangleright \mu_n)$ is stable, where $\mu_j$ are probability distributions with the condition $\sum \limits_{n=1}^\infty \frac{1}{b_n} \text{var}(\mu_n) < \infty$. This proves a law of large numbers for monotonically independent random variables.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

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En utilisant des méthodes fonctionnelles et numériques, on localise le spectre d'un opérateur différentiel et on construit des solutions approchées pour des classes d'équations de Fredholm de seconde espèce, dont deux sont à noyau faiblement singulier. Dans le premier chapitre, on étudie le conditionnement pseudospectral pour un opérateur de convection-diffusion non autoadjoint défini sur un ouvert non borné. A partir du résultat de conditionnement pseudospectral, on localise le spectre de l'opérateur. Dans le deuxième chapitre, on régularise le noyau d'un opérateur intégral en utilisant un produit de convolution, puis on approche le noyau ainsi obtenu par son développement en série de Fourier tronqué. On obtient un opérateur intégral de rang fini, ce qui nous permet de construire une solution approchée / Using functional and numerical methods, we localize the spectrum of a differential operator and we build approximate solutions for classes of Fredholm equations of the second kind, two of which have a weakly singular kernel. In the first chapter, we study the pseudospectral stability of a convection-diffusion nonselfadjoint operator defined on an open unbounded set. From the result of pseudospectral stability, we localize the spectrum of the operator. In the second chapter, we regularize the kernel of an integral operator using a convolution product, then we approach the new kernel by its truncated Fourier series. We obtain an integral operator of finite rank, which allows us to compute an approximate solution numerically

In this project two machine learning methods, Support Vector Machine, SVM, and Convolutional Neural Network, CNN, are studied to determine which method performs best on a labeled data set containing time series of light intensity from extrasolar stars. The main difficulty is that in the data set there are a lot more non exoplanet stars than there are stars with orbiting exoplanets. This is causing a so called imbalanced data set which in this case is improved by i.e. mirroring the curves of stars with an orbiting exoplanet and adding them to the set. Trying to improve the results further, some preprocessing is done before implementing the methods on the data set. For the SVM, feature extraction and fourier transform of the time-series are important measures but further preprocessing alternatives are investigated. For the CNN-method the time-series are both detrended and smoothed, giving two inputs for the same light curve. All code is implemented in python. Of all the validation parameters recall is considered the main priority since it is more important to find all exoplanets than finding all non exoplanets. CNN turned out to be the best performing method for the chosen configurations with 1.000 in recall which exceeds SVM’s recall 0.800. Considering the second validation parameter precision CNN is also the best performing method with a precision of 0.769 over SVM's 0.571.

Finding disparity maps between stereo images is a well studied topic within computer vision. While both classical and machine learning approaches exist in the literature, they frequently struggle to correctly solve the disparity in regions with low texture, sharp edges or occlusions. Finding approximate solutions to these problem areas is frequently referred to as disparity refinement, and is usually carried out separately after an initial disparity map has been generated. In the recent literature, the use of Normalized Convolution in Convolutional Neural Networks have shown remarkable results when applied to the task of stereo depth completion. This thesis investigates how well this approach performs in the case of disparity refinement. Specifically, we investigate how well such a method can improve the initial disparity maps generated by the stereo matching algorithm developed at Saab Dynamics using a rectified stereo rig. To this end, a dataset of ground truth disparity maps was created using equipment at Saab, namely a setup for structured light and the stereo rig cameras. Because the end goal is a dataset fit for training networks, we investigate an approach that allows for efficient creation of significant quantities of dense ground truth disparities. The method for generating ground truth disparities generates several disparity maps for every scene measured by using several stereo pairs. A densified disparity map is generated by merging the disparity maps from the neighbouring stereo pairs. This resulted in a dataset of 26 scenes and 104 dense and accurate disparity maps. Our evaluation results show that the chosen Normalized Convolution Network based method can be adapted for disparity map refinement, but is dependent on the quality of the input disparity map.

This thesis is devoted to an investigation of boundedness of a general convolution operator between certain weighted Lorentz-type spaces with the aim of proving analogues of the Young convolution inequality for these spaces. Necessary and sufficient conditions on the kernel function are given, for which the convolution operator with the fixed kernel is bounded between a certain domain space and the weighted Lorentz space of type Gamma. The considered domain spaces are the weighted Lorentz-type spaces defined in terms of the nondecreasing rearrangement of a function, the maximal function or the difference of these two quantities. In each case of the domain space, the corresponding Young-type convolution inequality is proved and the optimality of involved rearrangement-invariant spaces in shown. Furthermore, covering of the previously existing results is also discussed and some properties of the new rearrangement-invariant function spaces obtained during the process are studied. / <p>Paper II was a manuscript at the time of the defense.</p>

O processo de pasteurização tem como objetivo garantir a segurança e qualidade nutricional do alimento e aumentar sua vida de prateleira. O conhecimento da distribuição do tempo de residência (DTR) do alimento em cada etapa do processo contínuo é importante para uma avaliação adequada do processo e das alterações que causa no alimento. Este trabalho tem como objetivo estudar a DTR em um processo de pasteurização contínuo assistido por micro-ondas aplicado a alimentos líquidos e propor modelos de escoamento para representá-la. Para isso, foram realizados experimentos de estímulo-resposta com alimentação tipo pulso por técnica condutimétrica utilizando uma solução saturada de NaCl como traçador. Com isso, foram obtidas as curvas de DTR do sistema completo, dos trocadores de calor das seções de pré-aquecimento e resfriamento, de seis tubos de retenção com diferentes diâmetros e comprimentos (volumes entre 40 e 125 mL) e do sistema de aquisição de dados de condutividade elétrica. Os experimentos foram realizados em quatro vazões volumétricas (0,5, 0,7, 0,9 e 1,1 L/min), a temperatura ambiente (19 a 26 °C) e como fluido de trabalho foi utilizada uma corrente de alimentação de água com concentração 0,5 g/L de NaCl para estabilizar a leitura de condutividade elétrica. Foram realizadas três repetições por vazão para o processo completo, trocadores de calor e tubos de retenção, e cinco repetições por vazão para o sistema de aquisição de dados, dada a maior sensibilidade. Observou-se a necessidade de realizar o procedimento de convolução numérica para avaliar a distorção na curva de DTR do processo causada pelo escoamento na célula do sistema de aquisição de dados. Foram testados cinco modelos de escoamento: dispersão axial, compartimentado PFR+CSTR, tanques em série, convecção generalizada e y-laminar. O critério de ajuste dos modelos foi a minimização do erro quadrático entre valores experimentais e calculados da curva E(t). Os modelos de dispersão axial e y-laminar foram o que apresentaram melhor ajuste para os tubos de retenção e o modelo de convecção generalizada apresentou melhor ajuste para os trocadores de calor. O regime de escoamento durante os experimentos variou entre laminar e de transição (valores de Reynolds entre 1259 e 4238). Os resultados para o sistema completo e trocadores de calor foram satisfatórios, para os tubos de retenção foi observada uma grande incerteza nos valores dos parâmetros e foi observada a importância da convolução numérica em sistemas de pequeno volume. / Pasteurization process aims to ensure the safety and nutritional quality of the food and increase its shelf life. The knowledge of residence time distribution (RTD) of the food in each step of continuous processes is important to evaluate the process and changes that it causes in foods. This work aims to study the RTD in a continuous pasteurization process assisted by microwave applied to liquid foods and propose flow models to represent it. For this reason, stimulus-response experiments by pulse injection were conducted by conductimetric technique using a saturated solution of NaCl as a tracer. Thus, it was obtained the RTD of the complete process, heat exchangers of preheating section and cooling section, six retention tubes with different diameters and lengths (volumes between 40 and 125 mL) and of the electrical conductivity data acquisition system. The experiments were carried out at four volumetric flow rates (0.5, 0.7, 0.9 and 1.1 L/min), at room temperature (19 to 26 °C) and water with 0.5 g/L of NaCl was used as the work fluid to stabilize the electrical conductivity reading. Three repetitions per volumetric flow rate were performed for the complete process, heat exchangers and holding tubes, and five repetitions per volumetric flow rate were performed for the data acquisition system, given the higher sensibility. It was observed the need to apply the numerical convolution procedure to evaluate the distortion in the RTD curve of the process caused by the flow through the data acquisition system. Five flow models were tested: axial dispersion, PFR+CSTR association, tanks in series, generalized convection and y-laminar. The adjustment criterion of the parameters was the minimization of the quadratic error between experimental and calculated E(t) values. The axial dispersion and y-laminar models provided the best adjustments for the holding tubes and the generalized convection model provided the best adjustment for the heat exchangers. The flow regime during the experiments varied between laminar and transition (Reynolds values between 1259 and 4238). The results for the complete system and heat exchangers were satisfactory, for the holding tubes was observed a great uncertainty in the parameters values and was observed the importance of numerical convolution in small volume systems.