[pt] Ao mesmo tempo em que a autonomia de robôs pessoais e domésticos aumenta, cresce a necessidade de interação dos mesmos com o ambiente. A interação mais básica de um robô com o ambiente é feita pela percepção deste e sua navegação. Para uma série de aplicações não é prático prover modelos geométricos válidos do ambiente a um robô antes de seu uso. O robô necessita, então, criar estes modelos enquanto se movimenta e percebe o meio em que está inserido através de sensores. Ao mesmo tempo é necessário minimizar a complexidade requerida quanto a hardware e sensores utilizados. No presente trabalho, um algoritmo iterativo baseado em entropia é proposto para planejar uma estratégia de exploração visual, permitindo a construção eficaz de um modelo em grafo do ambiente. O algoritmo se baseia na determinação da informação presente em sub-regiões de uma imagem panorâmica 2-D da localização atual do robô obtida com uma câmera fixa sobre o mesmo. Utilizando a métrica de entropia baseada na Teoria da Informação de Shannon, o algoritmo determina nós potenciais para os quais deve se prosseguir a exploração. Através de procedimento de Visual Tracking, em conjunto com a técnica SIFT (Scale Invariant Feature Transform), o algoritmo auxilia a navegação do robô para cada nó novo, onde o processo é repetido. Um procedimento baseado em transformações invariáveis a determinadas variações espaciais (desenvolvidas a partir de Fourier e Mellin) é utilizado para auxiliar o processo de guiar o robô para nós já conhecidos. Também é proposto um método baseado na técnica SIFT. Os processos relativos à obtenção de imagens, avaliação, criação do grafo, e prosseguimento dos passos citados continua até que o robô tenha mapeado o ambiente com nível pré-especificado de detalhes. O conjunto de nós e imagens obtidos são combinados de modo a se criar um modelo em grafo do ambiente. Seguindo os caminhos, nó a nó, um robô pode navegar pelo ambiente já explorado. O método é particularmente adequado para ambientes planos. As componentes do algoritmo proposto foram desenvolvidas e testadas no presente trabalho. Resultados experimentais mostrando a eficácia dos métodos propostos são apresentados. / [en] As the autonomy of personal service robotic systems increases so has their need to interact with their environment. The most basic interaction a robotic agent may have with its environment is to sense and navigate through it. For many applications it is not usually practical to provide robots in advance with valid geometric models of their environment. The robot will need to create these models by moving around and sensing the environment, while minimizing the complexity of the required sensing hardware. This work proposes an entropy-based iterative algorithm to plan the robot´s visual exploration strategy, enabling it to most efficiently build a graph model of its environment. The algorithm is based on determining the information present in sub-regions of a 2- D panoramic image of the environment from the robot´s current location using a single camera fixed on the mobile robot. Using a metric based on Shannon s information theory, the algorithm determines potential locations of nodes from which to further image the environment. Using a Visual Tracking process based on SIFT (Scale Invariant Feature Transform), the algorithm helps navigate the robot to each new node, where the imaging process is repeated. An invariant transform (based on Fourier and Mellin) and tracking process is used to guide the robot back to a previous node. Also, an SIFT based method is proposed to accomplish such task. This imaging, evaluation, branching and retracing its steps continues until the robot has mapped the environment to a pre-specified level of detail. The set of nodes and the images taken at each node are combined into a graph to model the environment. By tracing its path from node to node, a service robot can navigate around its environment. This method is particularly well suited for flat-floored environments. The components of the proposed algorithm were developed and tested. Experimental results show the effectiveness of the proposed methods.

Le thème de cette thèse est de comprendre la distribution des nombres premiers, qui est un sujet central de la théorie analytique des nombres. Plus précisément, nous allons prouver des théorèmes de type Bombieri-Vinogradov pour les nombres premiers avec un chiffre manquant dans leur développement b-adique pour un grand entier positif b. La preuve est basée sur la méthode du cercle, qui repose sur la structure de Fourier des entiers avec un chiffre manquant et les sommes exponentielles sur les nombres premiers dans les progressions arithmétiques. En combinant nos résultats avec le crible semi-linéaire, nous obtenons une borne supérieure et une borne inférieure avec le bon ordre de grandeur pour le nombre de nombres premiers de la forme p=1+m^2 + n^2 avec un chiffre manquant dans une grande base impaire b. / The theme of this thesis is to understand the distribution of prime numbers, which is a central topic in analytic number theory. More precisely, we prove Bombieri-Vinogradov type theorems for primes with a missing digit in their b-adic expansion for some large positive integer b. The proof is based on the circle method, which relies on the Fourier structure of the integers with a missing digit and the exponential sums over primes in arithmetic progressions. Combining our results with the semi-linear sieve, we obtain an upper bound and a lower bound of the correct order of magnitude for the number of primes of the form p=1+m^2+n^2 with a missing digit in a large odd base b.

We analyzed long-term temperature trends in Utah using a relatively new signal processing method called Empirical Mode Decomposition (EMD). We evaluated the available weather records in Utah and selected 52 stations, which had records longer than 60 years, for analysis. We analyzed daily temperature data, both minimum and maximums, using the EMD method that decomposes non-stationary data (data with a trend) into periodic components and the underlying trend. Most decomposition algorithms require stationary data (no trend) with constant periods and temperature data do not meet these constraints. In addition to identifying the long-term trend, we also identified other periodic processes in the data. While the immediate goal of this research is to characterize long-term temperature trends and identify periodic processes and anomalies, these techniques can be applied to any time series data to characterize trends and identify anomalies. For example, this approach could be used to evaluate flow data in a river to separate the effects of dams or other regulatory structures from natural flow or to look at other water quality data over time to characterize the underlying trends and identify anomalies, and also identify periodic fluctuations in the data. If these periodic fluctuations can be associated with physical processes, the causes or drivers might be discovered helping to better understand the system. We used EMD to separate and analyze long-term temperature trends. This provides awareness and support to better evaluate the extremities of climate change. Using these methods we will be able to define many new aspects of nonlinear and nonstationary data. This research was successful and identified several areas in which it could be extended including data reconstruction for time periods missing data. This analysis tool can be applied to various other time series records.

Long Range (LoRa) has become a key enabler technology for low power wide area networks. However, due to its ALOHA-based medium access scheme, LoRa has to cope with collisions that limit the capacity and network scalability. Collisions between randomly overlapped signals modulated with different spreading factors (SFs) result in inter-SF interference, which increases the packet loss likelihood when signal-to-interference ratio (SIR) is low. This issue cannot be resolved by channel coding since the probability of error distance is not concentrated around the adjacent symbol. In this paper, we analytically model this interference, and propose an interference cancellation method based on the idea of segmentation of the received signal. This scheme has three steps. First, the SF of the interference signal is identified, then the equivalent data symbol and complex amplitude of the interference are estimated. Finally, the estimated interference signal is subtracted from the received signal before demodulation. Unlike conventional serial interference cancellation (SIC), this scheme can directly estimate and reconstruct the non-aligned inter-SF interference without synchronization. Simulation results show that the proposed method can significantly reduce the symbol error rate (SER) under low SIR compared with the conventional demodulation. Moreover, it also shows high robustness to fractional sample timing offset (STO) and carrier frequency offset (CFO) of interference. The presented results clearly show the effectiveness of the proposed method in terms of the SER performance.

Cette thèse étudie la gestion et la couverture du risque en s’appuyant sur la Value-at-Risk (VaR) et la Value-at-Risk Conditionnelle (CVaR), comme mesures de risque. La première partie propose un modèle d’évolution de prix que nous confrontons à des données réelles issues de la bourse de Paris (Euronext PARIS). Notre modèle prend en compte les probabilités d’occurrence des pertes extrêmes et les changements de régimes observés sur les données. Notre approche consiste à détecter les différentes périodes de chaque régime par la construction d’une chaîne de Markov cachée et à estimer la queue de distribution de chaque régime par des lois puissances. Nous montrons empiriquement que ces dernières sont plus adaptées que les lois normales et les lois stables. L’estimation de la VaR est validée par plusieurs backtests et comparée aux résultats d’autres modèles classiques sur une base de 56 actifs boursiers. Dans la deuxième partie, nous supposons que les prix boursiers sont modélisés par des exponentielles de processus de Lévy. Dans un premier temps, nous développons une méthode numérique pour le calcul de la VaR et la CVaR cumulatives. Ce problème est résolu en utilisant la formalisation de Rockafellar et Uryasev, que nous évaluons numériquement par inversion de Fourier. Dans un deuxième temps, nous nous intéressons à la minimisation du risque de couverture des options européennes, sous une contrainte budgétaire sur le capital initial. En mesurant ce risque par la CVaR, nous établissons une équivalence entre ce problème et un problème de type Neyman-Pearson, pour lequel nous proposons une approximation numérique s’appuyant sur la relaxation de la contrainte / This thesis studies the risk management and hedging, based on the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR) as risk measures. The first part offers a stocks return model that we test in real data from NSYE Euronext. Our model takes into account the probability of occurrence of extreme losses and the regime switching observed in the data. Our approach is to detect the different periods of each regime by constructing a hidden Markov chain and estimate the tail of each regime distribution by power laws. We empirically show that powers laws are more suitable than Gaussian law and stable laws. The estimated VaR is validated by several backtests and compared to other conventional models results on a basis of 56 stock market assets. In the second part, we assume that stock prices are modeled by exponentials of a Lévy process. First, we develop a numerical method to compute the cumulative VaR and CVaR. This problem is solved by using the formalization of Rockafellar and Uryasev, which we numerically evaluate by Fourier inversion techniques. Secondly, we are interested in minimizing the hedging risk of European options under a budget constraint on the initial capital. By measuring this risk by CVaR, we establish an equivalence between this problem and a problem of Neyman-Pearson type, for which we propose a numerical approximation based on the constraint relaxation

La thermographie infrarouge est une méthode largement employée pour la caractérisation des propriétés thermophysiques des matériaux. L’avènement des diodes laser pratiques, peu onéreuses et aux multiples caractéristiques, étendent les possibilités métrologiques des caméras infrarouges et mettent à disposition un ensemble de nouveaux outils puissants pour la caractérisation thermique et le contrôle non desturctif. Cependant, un lot de nouvelles difficultés doit être surmonté, comme le traitement d’une grande quantité de données bruitées et la faible sensibilité de ces données aux paramètres recherchés. Cela oblige de revisiter les méthodes de traitement du signal existantes, d’adopter de nouveaux outils mathématiques sophistiqués pour la compression de données et le traitement d’informations pertinentes. Les nouvelles stratégies consistent à utiliser des transformations orthogonales du signal comme outils de compression préalable de données, de réduction et maîtrise du bruit de mesure. L’analyse de sensibilité, basée sur l’étude locale des corrélations entre les dérivées partielles du signal expérimental, complète ces nouvelles approches. L'analogie avec la théorie dans l'espace de Fourier a permis d'apporter de nouveaux éléments de réponse pour mieux cerner la «physique» des approches modales.La réponse au point source impulsionnel a été revisitée de manière numérique et expérimentale. En utilisant la séparabilité des champs de température nous avons proposé une nouvelle méthode d'inversion basée sur une double décomposition en valeurs singulières du signal expérimental. Cette méthode par rapport aux précédentes, permet de tenir compte de la diffusion bi ou tridimensionnelle et offre ainsi une meilleure exploitation du contenu spatial des images infrarouges. Des exemples numériques et expérimentaux nous ont permis de valider dans une première approche cette nouvelle méthode d'estimation pour la caractérisation de diffusivités thermiques longitudinales. Des applications dans le domaine du contrôle non destructif des matériaux sont également proposées. Une ancienne problématique qui consiste à retrouver les champs de température initiaux à partir de données bruitées a été abordée sous un nouveau jour. La nécessité de connaitre les diffusivités thermiques du matériau orthotrope et la prise en compte des transferts souvent tridimensionnels sont complexes à gérer. L'application de la double décomposition en valeurs singulières a permis d'obtenir des résultats intéressants compte tenu de la simplicité de la méthode. En effet, les méthodes modales sont basées sur des approches statistiques de traitement d'une grande quantité de données, censément plus robustes quant au bruit de mesure, comme cela a pu être observé. / Infrared thermography is a widely used method for characterization of thermophysical properties of materials. The advent of the laser diodes, which are handy, inexpensive, with a broad spectrum of characteristics, extend metrological possibilities of infrared cameras and provide a combination of new powerful tools for thermal characterization and non destructive evaluation. However, this new dynamic has also brought numerous difficulties that must be overcome, such as high volume noisy data processing and low sensitivity to estimated parameters of such data. This requires revisiting the existing methods of signal processing, adopting new sophisticated mathematical tools for data compression and processing of relevant information.New strategies consist in using orthogonal transforms of the signal as a prior data compression tools, which allow noise reduction and control over it. Correlation analysis, based on the local cerrelation study between partial derivatives of the experimental signal, completes these new strategies. A theoretical analogy in Fourier space has been performed in order to better understand the «physical» meaning of modal approaches.The response to the instantaneous point source of heat, has been revisited both numerically and experimentally. By using separable temperature fields, a new inversion technique based on a double singular value decomposition of experimental signal has been introduced. In comparison with previous methods, it takes into account two or three-dimensional heat diffusion and therefore offers a better exploitation of the spatial content of infrared images. Numerical and experimental examples have allowed us to validate in the first approach our new estimation method of longitudinal thermal diffusivities. Non destructive testing applications based on the new technique have also been introduced.An old issue, which consists in determining the initial temperature field from noisy data, has been approached in a new light. The necessity to know the thermal diffusivities of an orthotropic medium and the need to take into account often three-dimensional heat transfer, are complicated issues. The implementation of the double singular value decomposition allowed us to achieve interesting results according to its ease of use. Indeed, modal approaches are statistical methods based on high volume data processing, supposedly robust as to the measurement noise.