Sparse approximation is a Bayesian inference program with a wide number of signal processing applications, such as Compressed Sensing recovery used in medical imaging. Previous sparse coding implementations relied on digital algorithms whose power consumption and performance scale poorly with problem size, rendering them unsuitable for portable applications, and a bottleneck in high speed applications. A novel analog architecture, implementing the Locally Competitive Algorithm (LCA), was designed and programmed onto a Field Programmable Analog Arrays (FPAAs), using floating gate transistors to set the analog parameters. A network of 6 coefficients was demonstrated to converge to similar values as a digital sparse approximation algorithm, but with better power and performance scaling. A rate encoded spiking algorithm was then developed, which was shown to converge to similar values as the LCA. A second novel architecture was designed and programmed on an FPAA implementing the spiking version of the LCA with integrate and fire neurons. A network of 18 neurons converged on similar values as a digital sparse approximation algorithm, with even better performance and power efficiency than the non-spiking network. Novel algorithms were created to increase floating gate programming speed by more than two orders of magnitude, and reduce programming error from device mismatch. A new FPAA chip was designed and tested which allowed for rapid interfacing and additional improvements in accuracy. Finally, a neuromorphic chip was designed, containing 400 integrate and fire neurons, and capable of converging on a sparse approximation solution in 10 microseconds, over 1000 times faster than the best digital solution.

Ultra-wideband (UWB) technology is the next viable solution for applications in wireless personal area network (WPAN), body area network (BAN) and wireless sensor network (WSN). However, as application evolves toward a more realistic situation, wideband channel characteristics such as pulse distortion must be accounted for in channel modeling. Furthermore, application-oriented services such as ranging and localization demand fast prototyping, real-time processing of measured data, and good low signal-to-noise ratio (SNR) performance. Despite the tremendous effort being vested in devising new receivers by the global research community, channel-estimating Rake receiver is still one of the most promising receivers that can offer superior performance to the suboptimal counterparts. However, acquiring Nyquist-rate samples costs substantial power and resource consumption and is a major obstacle to the feasible implementation of the asymptotic maximum likelihood (ML) channel estimator. In this thesis, we address all three aspects of the UWB impulse radio (UWB-IR), in three separate contributions. First, we study the {\it a priori} dependency of the CLEAN deconvolution with real-world measurements, and propose a high-resolution, multi-template deconvolution algorithm to enhance the channel estimation accuracy. This algorithm is shown to supersede its predecessors in terms of accuracy, energy capture and computational speed. Secondly, we propose a {\it regularized} least squares time-of-arrival (ToA) estimator with wavelet denoising to the problem of ranging and localization with UWB-IR. We devise a threshold selection framework based on the Neyman-Pearson (NP) criterion, and show the robustness of our algorithm by comparing with other ToA algorithms in both computer simulation and ranging measurements when advanced digital signal processing (DSP) is available. Finally, we propose a low-complexity ML (LC-ML) channel estimator to fully exploit the multipath diversity with Rake receiver with sub-Nyquist rate sampling. We derive the Cram\'er-Rao Lower Bound (CRLB) for the LC-ML, and perform simulation to compare our estimator with both the $\ell_1$-norm minimization technique and the conventional ML estimator.

At low Reynolds number flows, the effect of inertia becomes negligible and the fluid motion is dominated by the effect of viscous forces. Understanding of the behaviour of low Reynolds number flows underpins the prediction of the motion of microorganisms and particle sedimentation as well as the development of micro-robots that could potentially swim inside the human body to perform targeted drug/cell delivery and non-invasive microsurgery. The work in this thesis focuses on developing an understanding in the mathematical analysis of objects moving at low Reynolds numbers. A boundary element implementation of the Method of regularized Stokeslets (MRS) is applied to analyse the low Reynolds number flow field around an object of simple shape (sphere and cube). It also showed that the results obtained by a boundary element implementation for an unbounded cube, where singularities are presented in the corners of the cube, agrees with more complex solutions methods such as a GBEM and FEM.A methodology for analysing the effect of walls by locating collocation points on the surface of the walls and the object is presented. First at all, this methodology is validated with a boundary element implementation of the method of images for a sphere at different locations. Then, the method is extended when more than one wall is presented. This methodology is applied to predict the velocity filed of a cube moving in a tow tank at low Reynolds numbers for two different cases with a supporting rod similar to an experimental set-up, and without the supporting rod as in the CFD simulations based on the FVM. The results indicate a good match between CFD and the MRS, and an excellent approximation between the MRS and experimental data from PIV measurements. The drag, thrust and torque generated by helices moving at low Reynolds numbers in an unbounded medium is analysed by the resistive force theory, a slender body theory, and a boundary element method of the MRS. The results show that the resistive force theory predict accurately the drag, thrust and torque of moving helices when the resistive force coefficients are calculated from a slender body theory approximation by calculating independently the resistive force coefficients for translation and rotation, because it is observed that the resistive force coefficients depend also of the nature of motion. Moreover, the thrust generated by helices of different pitch angles is analysed calculated by a CFD numerical simulation based on the FVM and a boundary element implementation, an compared with experimental data. The results also show an excellent prediction between the boundary element implementation, the CFD results and the experimental data. Finally, a boundary element implementation of the MRS is applied to predict swimming of a biomimetic swimmer that mimics the motion of E.coli bacteria in an unbounded medium. The results are compared with the propulsive velocity and induced angular velocity measurement by recording the motion of the biomimetic swimmer in a square tank. It is observed that special care needs to be taken when the biomimetic swimmer is modelled inside the tank, as there is an apparent increment in the calculate thrust propulsion which does not represent a real situation of the biometic swimmer which propels by a power supply. However, this increment does not represent the condition of the biomimetic swimmer and a suggested methodology based on the solution from an unbounded case and when the swimmer is moving inside the tank is presented. In addition, the prediction of the free-swimming velocity for the biomimetic swimmer agrees with the results obtained by the MRS when the resistive force coefficients are calculated from a SBT implementation. The results obtained in this work have showed that a boundary element implementation of the MRS produces results comparable with more complex numerical implementations such as GBEM, FEM, FVM, and also an excellent agreement with results obtained from experimentation. Therefore, it is a suitable and easy to apply methodology to analyse the motion of swimmers at low Reynolds numbers, such as the biomimetic swimmer modelled in this work.

Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de probabilité sur R^d. L'objectif est alors de fournir une meilleure compréhension des outils statistiques usuels sur cet espace muni de la distance de Wasserstein. Une première notion naturelle est l'analyse statistique d'ordre un, consistant en l'étude de la moyenne de Fréchet (ou barycentre). En particulier, nous nous concentrons sur le cas de données (ou observations) discrètes échantillonnées à partir de mesures de probabilité absolument continues (a.c.) par rapport à la mesure de Lebesgue. Nous introduisons ainsi un estimateur du barycentre de mesures aléatoires, pénalisé par une fonction convexe, permettant ainsi d'imposer son a.c. Un autre estimateur est régularisé par l'ajout d'entropie lors du calcul de la distance de Wasserstein. Nous nous intéressons notamment au contrôle de la variance de ces estimateurs. Grâce à ces résultats, le principe de Goldenshluger et Lepski nous permet d'obtenir une calibration automatique des paramètres de régularisation. Nous appliquons ensuite ce travail au recalage de densités multivariées, notamment pour des données de cytométrie de flux. Nous proposons également un test d'adéquation de lois capable de comparer deux distributions multivariées, efficacement en terme de temps de calcul. Enfin, nous exécutons une analyse statistique d'ordre deux dans le but d'extraire les tendances géométriques globales d'un jeu de donnée, c'est-à-dire les principaux modes de variations. Pour cela nous proposons un algorithme permettant d'effectuer une analyse en composantes principales géodésiques dans l'espace de Wasserstein. / This thesis focuses on the analysis of data in the form of probability measures on R^d. The aim is to provide a better understanding of the usual statistical tools on this space endowed with the Wasserstein distance. The first order statistical analysis is a natural notion to consider, consisting of the study of the Fréchet mean (or barycentre). In particular, we focus on the case of discrete data (or observations) sampled from absolutely continuous probability measures (a.c.) with respect to the Lebesgue measure. We thus introduce an estimator of the barycenter of random measures, penalized by a convex function, making it possible to enforce its a.c. Another estimator is regularized by adding entropy when computing the Wasserstein distance. We are particularly interested in controlling the variance of these estimators. Thanks to these results, the principle of Goldenshluger and Lepski allows us to obtain an automatic calibration of the regularization parameters. We then apply this work to the registration of multivariate densities, especially for flow cytometry data. We also propose a test statistic that can compare two multivariate distributions, efficiently in terms of computational time. Finally, we perform a second-order statistical analysis to extract the global geometric tendency of a dataset, also called the main modes of variation. For that purpose, we propose algorithms allowing to carry out a geodesic principal components analysis in the space of Wasserstein.

Apresentamos dois modelos para o elétron na eletrodinâmica clássica que incorporam alguns efeitos da eletrodinâmica quântica. No primeiro modelo, o elétron é tratado como uma partícula extensa como conseqüência das oscilações de alta-freqüência (Zitterbewegung) que sua carga elétrica realiza. Mostramos que este modelo prevê corretamente a magnitude do spin do elétron e lhe atribui o mesmo fator giromagnético previsto pela equação de Dirac sem correções radiativas. Neste modelo, a auto-energia do elétron diverge logaritmicamente como resultado da distribuição extensa de sua carga elétrica. No segundo modelo, a criação de pares virtuais em torno do elétron é levada em conta por uma generalização da lagrangeana do campo eletromagnético que respeita as simetrias da eletrodinâmica clássica. Esta generalização altera a interação entre o elétron e o campo eletromagnético em pequenas distâncias e permite que a auto-força de uma partícula puntiforme seja determinada de modo consistente. Mostramos que as soluções da equação de movimento resultante não apresentam auto-aceleração nem pré-aceleração, sendo consistentes com a causalidade. / We present two models for the electron in classical electrodynamics, which include some effects from quantum electrodynamics. In the first model, the electron is treated as an extended particle owing to the high-frequency oscillations (Zitterbewegung) of its electrical charge. We show that this model predicts correctly the magnitude of the electron spin and it gives the electron the same gyromagnetic factor as predicted by Dirac equation without radiative corrections. In this model, the electron self-energy has a logarithmic divergence due to the extended distribution of its electric charge. In the second model, virtual pair creation around the electron is taken into account by a generalization of the lagrangian for the electromagnetic field that preserves the symmetries of classical electrodynamics. This generalization changes the interaction of the electron with the electromagnetic field at small distances and allows us to evaluate the self-force of a point particle in a consistent way. We show that the solutions of the derived equation of motion do not exhibit self-acceleration nor pre-acceleration, being consistent with causality.

Este trabalho apresenta uma avaliaÃÃo da influÃncia das diferentes formas de deposiÃÃo da massa assoreada em reservatÃrios do Estado do CearÃ, e os seus impactos na vazÃo regularizada. Foram investigadas trÃs formas distintas de assoreamento, denominadas neste trabalho de alfa 1 1), alfa 2 () e alfa 3 (3). ApÃs definiÃÃo dessas formas, foram construÃdas Curvas Cota x Ãrea x Volume (CAVs) dos reservatÃrios. Com o uso do programa Simres para simulaÃÃo hidrolÃgica de reservatÃrios foi possÃvel comparar as informaÃÃes de projeto com a situaÃÃo atual dos reservatÃrios, e avaliar quanto os mesmos perderam em oferta de vazÃo regularizada. Apresenta-se tambÃm uma avaliaÃÃo do assoreamento e de seus impactos para condiÃÃes futuras (50 e 100 anos), de forma a se promover um planejamento mais preciso na gestÃo dos recursos hÃdricos. Selecionou-se cinco reservatÃrios estratÃgicos do Estado do Cearà Ãros, BanabuiÃ, Cedro, Fogareiro e Pedras Brancas, destes, existe reservatÃrios com mais de cem anos de concluÃdo. Obteve-se para os modelos alfa 1 e alfa 2 resultados semelhantes, mostrando pouca diferenÃa entre estes dois modelos, porÃm para o modelo alfa 3 os resultados sÃo bastante diferentes dos outros dois, e com impactos significativos em termos de perda de vazÃo regularizada. Os resultados mostram a importÃncia de acompanhar os reservatÃrios e ver como os mesmos estÃo assoreando. / This paper presents an evaluation of the influence of different forms of deposition silted mass of Cearà reservoirs, and their impact on the regulated flow. We investigated three different forms of silting, called this work of alpha 1 1), alpha 2 () and alpha 3 (3). After defining these forms, curves were constructed Cota x Area x Volume (VACs) reservoirs. Using the Simres program for hydrological reservoir simulation was possible to compare project information with the current situation of the reservoirs, and assess how much they lost in supply of regulated flow. Furthermore, it presents an evaluation of silting and its impact on future conditions (50 to 100 years) in order to promote a more accurate planning in the management of water resources. Was selected five strategic reservoirs of Cearà State Ãros, BanabuiÃ, Cedar, Cooker and White Stones, of whom there Shells of more than a hundred years completed. Was obtained for alpha 1 and alpha 2 models similar results, showing little difference between these two models, but for the alpha 3 model the results are quite different from the other two and with significant impact in terms of loss of regulated flow. The results show the importance of monitoring the tanks and see how they are silting.

Este trabalho foi baseado na realização de simulações computacionais 3D de parâmetros de RQD obtidos de classificação geomecânica de sondagens rotativas realizadas nas fases de investigação geológico-geotécnica e construção da barragem de Itaipu (PR), Brasil. Tais simulações foram desenvolvidas em duas áreas dispostas no entorno da barragem principal da usina, utilizando como ferramenta o programa GRASS, que executa interpolações tridimensionais pelo método numérico Spline Regularizado com Tensão (RST). Os resultados obtidos foram comparados com dados previamente interpretados e obtidos por outros métodos como os geoestatísticos e apresentaram resultados razoáveis devido as dimensões dos voxels adotados, diferenças dos métodos e distribuição espacial dos dados. / This work was based on three-dimensional computer simulations of the parameters RQD of the boreholes on geological and geotechnical research phases and construction of the Itaipu dam (PR), Brazil. These simulations were carried out in two areas arranged around the plant the main dam, using as tool the GRASS program, which performs three-dimensional interpolation by mathematical method Regularized Spline with Tension (RST) . The results were compared with data previously obtained and interpreted by other methods such as geostatistical and had reasonable results because the dimensions of the voxels adopted, differences in methods and spatial distribution of the data.

Orientador: Andréa Cristina Prokopczyk Arita / Abstract: This work presents some results of the theory of the (a,k)-regularized resolvent families, that are the main tool used in this thesis. Related with this families, one result proved in this work is the zero-one law, providing new insights on the structural properties of the theory of (a,k)-regularized resolvent families including strongly continuous semigroups, strongly continuous cosine families, integrated semigroups, among others. Moreover, an abstract nonlinear degenerate hyperbolic equation is considered, that includes the semilinear Blackstock-Crighton-Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, it is proved an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. In addition, under nonlocal initial conditions, a mild solution of the nonlinear equation is established. / Resumo: Este trabalho apresenta alguns resultados da teoria de famílias resolventes (a,k)- regularizadas, que é a principal ferramenta utilizada nesta tese. Relacionado com estas famílias, um resultado provado neste trabalho é a lei zero-um, que fornece novas percepções de propriedades estruturais da teoria de famílias resolventes (a,k)- regularizadas, incluindo os semigrupos fortemente contínuos, as famílias cosseno fortemente contínuas, os semigrupos integrados, entre outras. Além disso, uma equação hiperbólica degenerada não-linear abstrata é considerada, a qual inclui a equação semilinear de Blackstock-Crighton-Westervelt. Propondo uma nova abordagem baseada em semigrupos fortemente contínuos e famílias resolvente, é demonstrada uma representação explícita das soluções forte e branda para a linearização do modelo por uma espécie de método de variação dos parâmetros. Por fim, sob condições iniciais não-locais, uma solução branda da equação não-linear é estabelecida. / Doutor

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Measles is resurging around the world, and large outbreaks have been observed in several parts of the world. In 2019 the Philippines suffered a major measles outbreak partly due to low immunization rates in certain parts of the population. There is currently limited research on how to identify and reach pockets of unvaccinated individuals effectively. This thesis aims to find important factors associated with non-vaccination against measles using a machine learning approach, using data from the 2017 Philippine National Demographic and Health Survey. In the analyzed sample (n = 4006), 74.84% of children aged 9 months to 3 years had received their first dose of measles vaccine, and 25.16% had not. Logistic regression with all 536 candidate features was fit with the regularized regression method Elastic Net, capable of automatically selecting relevant features. The final model consists of 32 predictors, and these are related to access and contact with healthcare, the region of residence, wealth, education, religion, ethnicity, sanitary conditions, the ideal number of children, husbands’ occupation, age and weight of the child, and features relating to pre and postnatal care. Total accuracy of the final model is 79.02% [95% confidence interval: (76.37%, 81.5%)], sensitivity: 97.73%, specificity: 23.41% and area under receiver operating characteristic curve: 0.81. The results indicate that socioeconomic differences determine to a degree measles vaccination. However, the difficulty in classifying non-vaccinated children, the low specificity, using only health and demographic characteristics suggests other factors than what is available in the analyzed data, possibly vaccine hesitation, could have a large effect on measles non-vaccination. Based on the results, efforts should be made to ensure access to facility-based delivery for all mothers regardless of socioeconomic status, to improve measles vaccination rates in the Philippines.