In this Ph. D. thesis we discuss four different problems in analysis: (a) sharp inequalities related to the restriction phenomena for the Fourier transform, with emphasis on some Strichartz-type estimates; (b) extremal approximations of exponential type for the Gaussian and for a class of even functions, with applications to analytic number theory; (c) radial symmetrization approach to convolution-like inequalities for the Boltzmann collision operator; (d) regularity of maximal operators with respect to weak derivatives and weak continuity. / text

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Smoothing filters have been extensively used for noise removal and image restoration. Directional filters are widely used in computer vision and image processing tasks such as motion analysis, edge detection, line parameter estimation and texture analysis. It is practically impossible to tune the filters to all possible positions and orientations in real time due to huge computation requirement. The efficient way is to design a few basis filters, and express the output of a directional filter as a weighted sum of the basis filter outputs. Directional filters having these properties are called "Steerable Filters." This thesis work emphasis is on the implementation of proposed computationally efficient separable and steerable Gaussian smoothers on a Xilinx VirtexII Pro FPGA platform. FPGAs are Field Programmable Gate Arrays which consist of a collection of logic blocks including lookup tables, flip flops and some amount of Random Access Memory. All blocks are wired together using an array of interconnects. The proposed technique [2] is implemented on a FPGA hardware taking the advantage of parallelism and pipelining.

Falling in indoor home setting can be dangerous for elderly population (in USA and globally), causing hospitalization, long term reduced mobility, disability or even death. Prevention of fall by monitoring different human activities or identifying the aftermath of fall has greater significance for elderly population. This is possible due to the availability and emergence of miniaturized sensors with advanced electronics and data analytics tools. This thesis aims at developing machine learning models to classify fall activities and non-fall activities. In this thesis, two types of neural networks with different parameters were tested for their capability in dealing with such tasks. A publicly available dataset was used to conduct the experiments. The two types of neural network models, convolution and recurrent neural network, were developed and evaluated. Convolution neural network achieved an accuracy of over 95% for classifying fall and non-fall activities. Recurrent neural network provided an accuracy of over 97% accuracy in predicting fall, non-fall and a third category activity (defined in this study as “pre/postcondition”). Both neural network models show high potential for being used in fall prevention and management activity. Moreover, two theoretical designs of fall detection systems were proposed in this thesis based on the developed convolution and recurrent neural networks.

Medidas de correlação angular perturbada diferencial no tempo - TDPAC - foram efetuadas com um sistema de detetores de HPGe com o objetivo de ampliar o conjunto de nuclídeos utilizáveis como sondas de prova de campo magnético e de gradiente de campo elétrico na matéria. A análise dos espectros obtidos considera a convolução angular de ordem superior a dois, o que está fora do escopo do procedimento convencional quando se utiliza o arranjo experimental padrão. O algoritmo é baseado no método dos mínimos quadrados e considera rigorosamente as incertezas estatísticas dos dados. O programa de cálculo implementado é orientado a objetos, que representam as estruturas matemáticas envolvidas na redução dos dados pelo método dos mínimos quadrados e os sistemas físicos característicos do experimento. Os detetores semicondutores mostraram-se inadequados ao estudo de materiais por TDPAC nas condições experimentais disponíveis. O método de análise proposto aqui foi aplicado à redução dos espectros obtidos em outros laboratórios, que utilizam cintiladores rápidos, resultando na determinação de parâmetros associados à estrutura cristalina para os quais a análise convencional não é sensível, em particulas dos coeficientes de atenuação temporal da correlação para cada uma das freqüências de oscilação. Esta metodologia permite calcular corretamente as incertezas nos parâmetros, notadamente nas frações de ocupação de diferentes sítios pela sonda de prova. / Time dependent perturbed angular correlation TDPAC measurements were performed with a HPGe detector array aiming to increase the set of nuclides usable as magnetic field and electric field gradient probes in matter. The analysis of the obtained spectra takes into account the convolution of the perturbation function with the detector time response and angular correlation coefficients of order greater than two, which is not in scope of the conventional procedure. The algorithm is based on the least-squares method and considers rigorously the data statistical uncertainties. The implanted computer code is built on objects representing the mathematical entities used in data reduction by the least-squares method and the physical components of the experiment. The semiconductor detectors were found unsuitable for material study through TDPAC in the available experimental conditions. The analysis method proposed here was applied to the reduction of spectra obtained by other Laboratories that use fast scintillators, giving crystalline structure related parameters which cannot be determined in the conventional analysis, particularly correlation time attenuation parameters for each oscillation frequency. The uncertainties in the fitted parameters are correctly calculated by this method notably in the site probe occupation fractions.

La robotique autonome est employée avec succès dans des environnements industriels contrôlés, où les instructions suivent des plans d’action prédéterminés.La robotique domestique est le challenge des années à venir et comporte un certain nombre de nouvelles difficultés : il faut passer de l'hypothèse d'un monde fermé borné à un monde ouvert. Un robot ne peut plus compter seulement sur ses données capteurs brutes qui ne font qu'indiquer la présence ou l'absence d'objets. Il lui faut aussi comprendre les relations implicites entre les objets de son environnement ainsi que le sens des tâches qu'on lui assigne. Il devra également pouvoir interagir avec des humains et donc partager leur conceptualisation à travers le langage. En effet, chaque langue est une représentation abstraite et compacte du monde qui relie entre eux une multitude de concepts concrets et purement abstraits. Malheureusement, les observations réelles sont plus complexes que nos représentations sémantiques simplifiées. Elles peuvent donc rentrer en contradiction, prix à payer d'une représentation finie d'un monde "infini". Pour répondre à ces difficultés, nous proposons dans cette thèse une architecture globale combinant différentes modalités de représentation d'environnement. Elle permet d'interpréter une représentation physique en la rattachant aux concepts abstraits exprimés en langage naturel. Le système est à double entrée : les données capteurs vont alimenter la modalité de perception tandis que les données textuelles et les interactions avec l'humain seront reliées à la modalité sémantique. La nouveauté de notre approche se situe dans l'introduction d'une modalité intermédiaire basée sur la notion d'instance (réalisation physique de concepts sémantiques). Cela permet notamment de connecter indirectement et sans contradiction les données perceptuelles aux connaissances en langage naturel.Nous présentons dans ce cadre une méthode originale de création d'ontologie orientée vers la description d'objets physiques. Du côté de la perception, nous analysons certaines propriétés des descripteurs image génériques extraits de couches intermédiaires de réseaux de neurones convolués. En particulier, nous montrons leur adéquation à la représentation d'instances ainsi que leur usage dans l'estimation de transformation de similarité. Nous proposons aussi une méthode de rattachement d'instance à une ontologie, alternative aux méthodes de classification classique dans l'hypothèse d'un monde ouvert. Enfin nous illustrons le fonctionnement global de notre modèle par la description de nos processus de gestion de requête utilisateur. / Autonomous robotics is successfully used in controled industrial environments where instructions follow predetermined implementation plans.Domestic robotics is the challenge of years to come and involve several new problematics : we have to move from a closed bounded world to an open one. A robot can no longer only rely on its raw sensor data as they merely show the absence or presence of things. It should also understand why objects are in its environment as well as the meaning of its tasks. Besides, it has to interact with human beings and therefore has to share their conceptualization through natural language. Indeed, each language is in its own an abstract and compact representation of the world which links up variety of concrete and abstract concepts. However, real observations are more complex than our simplified semantical representation. Thus they can come into conflict : this is the price for a finite representation of an "infinite" world.To address those challenges, we propose in this thesis a global architecture bringing together different modalities of environment representation. It allows to relate a physical representation to abstract concepts expressed in natural language. The inputs of our system are two-fold : sensor data feed the perception modality whereas textual information and human interaction are linked to the semantic modality. The novelty of our approach is in the introduction of an intermediate modality based on instances (physical realization of semantic concepts). Among other things, it allows to connect indirectly and without contradiction perceptual data to knowledge in natural langage.We propose in this context an original method to automatically generate an ontology for the description of physical objects. On the perception side, we investigate some properties of image descriptor extracted from intermediate layers of convolutional neural networks. In particular, we show their relevance for instance representation as well as their use for estimation of similarity transformation. We also propose a method to relate instances to our object-oriented ontology which, in the assumption of an open world, can be seen as an alternative to classical classification methods. Finally, the global flow of our system is illustrated through the description of user request management processes.

In this thesis, three different neural network architectures are investigated to detect the action of a shot within a football game using video data. The first architecture uses con- ventional convolution and pooling layers as feature extraction. It acts as a baseline and gives insight into the challenges faced during shot detection. The second architecture uses a pre-trained feature extractor. The last architecture uses three-dimensional convolution. All these networks are trained using short video clips extracted from football game video streams. Apart from investigating network architectures, different sampling methods are evaluated as well. This thesis shows that amongst the three evaluated methods, the ap- proach using MobileNetV2 as a feature extractor works best. However, when applying the networks to a video stream there are a multitude of challenges, such as false positives and incorrect annotations that inhibit the potential of detecting shots.

Os modelos de covariância são ferramentas geoestatísticas essenciais para mapear a continuidade espacial. A abordagem atual busca um modelo de continuidade espacial lícito com mínima ou até mesmo sem nenhuma interferência do usuário. Alinhado a essa visão moderna, é proposto obter uma tabela de covariância que visa substituir na prática o modelo tradicional explicitamente definido de covariância. Essa tabela de covariância é obtida por meio de três etapas: interpolar o conjunto de dados para preencher um grid regular, aplicar a convolução através do algoritmo da transformada rápida de Fourier e, por fim, transformar de volta para o domínio espacial. O modelo base para extrair covariância representa o ponto chave comparando com os métodos anteriores que propuseram o uso da tabela de covariância. Os resultados são satisfatórios, tanto na validação estatística do método, quanto na rapidez de obtenção de uma análise de continuidade espacial. Um estudo de caso tridimensional ilustra a aplicação prática através de krigagem e simulação geoestatística em comparação com a modelagem espacial tradicional. / Covariance models are essential geostatistical tools to map spatial continuity. The current approach pursues a licit spatial continuity model with minimum or even no user interference. Aligned with this modern view we propose to obtain a covariance table that aims at replacing in practice traditional covariance explicit defined model. This covariance table is obtained through a three steps work flow: interpolating the dataset to fill up a regular grid, auto convolute via Fast Fourier Transform algorithm and back transform to spacial domain. The base model to extract covariance represents the turning point comparing with previous methods that proposed covariance table usage. The results are satisfactory, both in the statistical validation of the method and in the speed of obtaining a spatial continuity analysis. A three dimensional case study illustrates the practical application for kriging and geostatistical simulation in comparison with traditional spatial modeling.

Este trabalho tem dois objetivos principais. O primeiro é estender o Teorema de Serre-Swan para grupoides de Lie étale. O segundo é demonstrar que, se dois grupoides de Lie étale são Morita equivalentes então a categoria dos módulos sobre as álgebras de convolução destes grupoides são equivalentes, e esta equivalência preserva a subcategoria dos módulos de tipo finito e posto constante. / In this work we have two main goals. The first one is to extend the Serre-Swan\'s theorem. Our second goal is to prove, if two étale Lie groupoids are Morita equivalence then the category of modules over its convolution algebra are Morita equivalence, and this equivalence preserve the subcategory of modules of finite type and of constant rank.

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