The development of quantum machine learning is bridging the way to fault tolerant quantum computation by providing algorithms running on the current noisy intermediate scale quantum devices.However, it is difficult to find use-cases where quantum computers exceed their classical counterpart.The high energy physics community is experiencing a rapid growth in the amount of data physicists need to collect, store, and analyze within the more complex experiments are being conceived.Our work approaches the study of a particle physics event involving the Higgs boson from a quantum machine learning perspective.We compare quantum support vector machine with the best classical kernel method grounding our study in a new theoretical framework based on metrics observing at three different aspects: the geometry between the classical and quantum learning spaces, the dimensionality of the feature space, and the complexity of the ML models.We exploit these metrics as a compass in the parameter space because of their predictive power. Hence, we can exclude those areas where we do not expect any advantage in using quantum models and guide our study through the best parameter configurations.Indeed, how to select the number of qubits in a quantum circuits and the number of datapoints in a dataset were so far left to trial and error attempts.We observe, in a vast parameter region, that the used classical rbf kernel model overtakes the performances of the devised quantum kernels.We include in this study the projected quantum kernel - a kernel able to reduce the expressivity of the traditional fidelity quantum kernel by projecting its quantum state back to an approximate classical representation through the measurement of local quantum systems.The Higgs dataset has been proved to be low dimensional in the quantum feature space meaning that the quantum encoding selected is not enough expressive for the dataset under study.Nonetheless, the optimization of the parameters on all the kernels proposed, classical and quantum, revealed a quantum advantage for the projected kernel which well classify the Higgs boson events and surpass the classical ML model. / Utvecklingen inom kvantmaskininlärning banar vägen för nya algoritmer att lösa krävande kvantberäkningar på dagens brusfyllda kvantkomponenter. Däremot är det en utmaning att finna användningsområden för vilka algoritmer som dessa visar sig mer effektiva än sina klassiska motsvarigheter. Forskningen inom högenergifysik upplever för tillfället en drastisk ökning i mängden data att samla, lagra och analysera inom mer komplexa experiment. Detta arbete undersöker Higgsbosonen ur ett kvantmaskinsinlärningsperspektiv. Vi jämför "quantum support vector machine" med den främsta klassiska metoden med avseende på tre olika metriker: geometrin av inlärningsrummen, dimensionaliteten av egenskapsrummen, och tidskomplexiteten av maskininlärningsmetoderna. Dessa tre metriker används för att förutsäga hur problemet manifesterar sig i parameterrummet. På så vis kan vi utesluta regioner i rummet där kvantalgoritmer inte förväntas överprestera klassiska algoritmer. Det finns en godtycklighet i hur antalet qubits och antalet datapunkter bestämms, och resultatet beror på dessa parametrar.I en utbredd region av parameterrummet observerar vi dock att den klassiska rbf-kärnmodellen överpresterar de studerade kvantkärnorna. I denna studie inkluderar vi en projicerad kvantkärna - en kärna som reducerar det totala kvanttillståndet till en ungefärlig klassisk representation genom att mäta en lokal del av kvantsystemet.Den studerade Higgs-datamängden har visat sig vara av låg dimension i kvantegenskapsrummet. Men optimering av parametrarna för alla kärnor som undersökts, klassiska såväl som kvantmekaniska, visade på ett visst kvantövertag för den projicerade kärnan som klassifierar de undersöka Higgs-händelserna som överstiger de klassiska maskininlärningsmodellerna.

O problema de reconstrucão digital de imagens (Image Inpainting) possui diversas abordagens para sua resolução. Uma possibilidade consiste na sua modelagem como um problema de otimizacão contínua (lasso). Na presente dissertacão aplica-se o método do gradiente espectral projetado a esse problema. Desenvolve-se inteiramente a modelagem do problema assim como a implementacão computacional do método de otimização que o resolve. Resultados computacionais demonstram a qualidade do método para um conjunto de imagens digitais / The image inpainting problem has several resolution approaches. One possibility consists in its modeling as a continuous optimization problem. In the present dissertation we apply the spectral projected gradient method to this problem. We develop the whole modeling of the problem as well as the computational implementation of the optimization method to solve it. Computational results show the quality of the method for a set of digital images

A teoria de Compressive Sensing proporciona uma nova estratégia de aquisição e recuperação de dados com bons resultados na área de processamento de imagens. Esta teoria garante recuperar um sinal com alta probabilidade a partir de uma taxa reduzida de amostragem por debaixo do limite de Nyquist-Shanon. O problema de recuperar o sinal original a partir das amostras consiste em resolver um problema de otimização. O método de Gradiente Espectral Projetado é um método para minimizar funções suaves em conjuntos convexos que tem sido aplicado com frequência ao problema de recuperar o sinal original a partir do sinal amostrado. Este trabalho dedica-se ao estudo da aplicação do Método do Gradiente Espectral Projetado ao problema de Compressive Sensing. / The theory of compressive sensing has provided a new acquisition strategy and data recovery with good results in the image processing area. This theory guarantees to recover a signal with high probability from a reduced sampling rate below the Nyquist-Shannon limit. The problem of recovering the original signal from the samples consists in solving an optimization problem. The Spectral Projected Gradient (SPG) is a method to minimize continuous functions over convex sets which often has been applied to the problem of recovering the original signal from sampled signals. This work is dedicated to the study and application of the Spectral Projected Gradient method to Compressive Sensing problems.

Elementos tipo sanduíche, com placas de argamassa projetada, têm sido utilizados na construção de edificações em alguns países, inclusive no Brasil, apresentando boas características de resistência mecânica, térmica e acústica. De maneira geral, a aplicação desse tipo de elemento tem se restringido a obras de edificações, sendo utilizado principalmente como painéis de fechamento, portantes ou não, existindo ainda um potencial a ser explorado em obras de infra-estrutura, tais como: muros de arrimo, canais, galerias e reservatórios de água. Apesar de ser um método utilizado na construção de edificações, existem dúvidas, tais como: resistência efetiva da argamassa projetada, colaboração entre as placas resistentes em função do tipo de núcleo, modo de combater os efeitos de retração da argamassa, etc. Apresenta-se neste trabalho um estudo sobre a resistência efetiva da argamassa projetada, no qual se obteve que a sua resistência é de aproximadamente 80% da resistência à compressão de corpos-de-prova cilíndricos. Realizaram-se ainda ensaios para analisar a ligação entre elementos tipo sanduíche e seu comportamento à flexão, que comprovam o bom desempenho estrutural. Acredita-se que essa técnica de construção sanduíche possa ser aplicada em obras de infra-estrutura de interesse social, trazendo vantagens tecnológicas e econômicas em relação a sistemas tradicionais / Sandwich–type elements, with plates made of projected mortar, have been used in the construction of buildings in some countries, including Brazil, showing expressive thermical, acoustical and mechanical strength characteristics. In general, the application of this kind of element have been limited to buildings, mainly used as cladding panels, with carrying load capacity or not, and have other potential uses in infra-structural works to be explored such as bearing walls, channels, and water reservoirs. Although it is a method that have been conventionally applied in the construction of buildings, there are uncertainties in some parameters, like the effective strength of the projected mortar, interaction between the plates related to the type of core, the mode against shrinkage of the mortar etc. It is showed in this work a study concerning the effective strength of the projected mortar. As a result of a series of tests in walls made of projected mortar, it is determined that the effective strength of the projected mortar is 80% of that one measured from cylindrical specimens in compression tests. As well, some tests have been executed to analise the bending behaviour and the connections between the plates of the sandwich-type specimens, which demonstrated a relatively high structural performance. It is believed that this technical solution can be well applied to public works of social interest, and can offer technological and economical advantages in contrast to the traditional systems

Spectrally sparse signals arise in many applications of signal processing. A spectrally sparse signal is a mixture of a few undamped or damped complex sinusoids. An important problem from practice is to reconstruct such a signal from partial time domain samples. Previous convex methods have the drawback that the computation and storage costs do not scale well with respect to the signal length. This common drawback restricts their applicabilities to large and high-dimensional signals. The reconstruction of a spectrally sparse signal from partial samples can be formulated as a low-rank Hankel matrix completion problem. We develop two fast and provable non-convex solvers, FIHT and PGD. FIHT is based on Riemannian optimization while PGD is based on Burer-Monteiro factorization with projected gradient descent. Suppose the underlying spectrally sparse signal is of model order r and length n. We prove that O(r^2log^2(n)) and O(r^2log(n)) random samples are sufficient for FIHT and PGD respectively to achieve exact recovery with overwhelming probability. Every iteration, the computation and storage costs of both methods are linear with respect to signal length n. Therefore they are suitable for handling spectrally sparse signals of large size, which may be prohibited for previous convex methods. Extensive numerical experiments verify their recovery abilities as well as computation efficiency, and also show that the algorithms are robust to noise and mis-specification of the model order. Comparing the two solvers, FIHT is faster for easier problems while PGD has a better recovery ability.

Animal home range estimations are important for conservation planning and protecting the habitat of threatened species. The accuracy of home range calculations is influenced by the map projection chosen in a geographic information system (GIS) for data analysis. Different methods of projection will distort spatial data in different ways, so it is important to choose a projection that meets the needs of the research. The large number of projections in use today and the lack of distortion comparison between the various types make selecting the most appropriate projection a difficult decision. The purpose of this study is to quantify and compare the amount of area distortion in animal home range estimations when projected into a number of projected coordinate systems in order to understand how the chosen projection influences analysis. The objectives of this research are accomplished by analyzing the tracking data of four species from different regions in North and South America. The home range of each individual from the four species datasets is calculated using the Characteristic Hull Polygon method for home range estimation and then projected into eight projected coordinate systems of various scales and projection type, including equal area, conformal, equidistant, and compromise projections. A continental Albers Equal Area projection is then used as a baseline area for the calculation of a distortion measurement ratio and magnitude of distortion statistic. The distortion measurement ratio and magnitude calculations provide a measurement of the quantity of area distortion caused by a projection. Results show the amount distortion associated with each type of projection method and how the amount of distortion changes for a projection based on geographic location. These findings show how the choice of map projection can have a large influence on data analysis and illustrate the importance of using an appropriate PCS for the needs of a given study. Distorted perceptions can influence decision-making, so it is important to recognize how a map projection can influence the analysis and interpretation of spatial data.

There is the need for applying numerical methods to problems that cannot be solved analytically and as the spatial dimension of the problem is increased the need for computational recourses increase exponentially, a phenomenon known as the “curse of dimensionality”. In the Black-Scholes-Merton framework the American option pricing problem has no closed form solution and a numerical procedure has to be employed for solving a PDE. The multi-asset American option introduces challenging computational problems, since for every added asset the dimension of the PDE is increased by one. One way to deal with the curse of dimensionality is threw parallelism. Here the finite element method-of-lines is used for pricing a multi-asset American option dependent on up to four assets in a parallel environment. The problem is also solved with the PSOR method giving a accurate benchmark used for comparison. In finance the put option is one of the most fundamental derivatives since it is basically asset-value insurance and a lot of research is done in the field of quantitative finance on accurate and fast pricing techniques for the multi-dimensional case. “What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.” Norbert Wiener “As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise – by what course of calculation can these results be arrived at by the machine in the shortest time?” Charles Babbage

Elementos tipo sanduíche, com placas de argamassa projetada, têm sido utilizados na construção de edificações em alguns países, inclusive no Brasil, apresentando boas características de resistência mecânica, térmica e acústica. De maneira geral, a aplicação desse tipo de elemento tem se restringido a obras de edificações, sendo utilizado principalmente como painéis de fechamento, portantes ou não, existindo ainda um potencial a ser explorado em obras de infra-estrutura, tais como: muros de arrimo, canais, galerias e reservatórios de água. Apesar de ser um método utilizado na construção de edificações, existem dúvidas, tais como: resistência efetiva da argamassa projetada, colaboração entre as placas resistentes em função do tipo de núcleo, modo de combater os efeitos de retração da argamassa, etc. Apresenta-se neste trabalho um estudo sobre a resistência efetiva da argamassa projetada, no qual se obteve que a sua resistência é de aproximadamente 80% da resistência à compressão de corpos-de-prova cilíndricos. Realizaram-se ainda ensaios para analisar a ligação entre elementos tipo sanduíche e seu comportamento à flexão, que comprovam o bom desempenho estrutural. Acredita-se que essa técnica de construção sanduíche possa ser aplicada em obras de infra-estrutura de interesse social, trazendo vantagens tecnológicas e econômicas em relação a sistemas tradicionais / Sandwich–type elements, with plates made of projected mortar, have been used in the construction of buildings in some countries, including Brazil, showing expressive thermical, acoustical and mechanical strength characteristics. In general, the application of this kind of element have been limited to buildings, mainly used as cladding panels, with carrying load capacity or not, and have other potential uses in infra-structural works to be explored such as bearing walls, channels, and water reservoirs. Although it is a method that have been conventionally applied in the construction of buildings, there are uncertainties in some parameters, like the effective strength of the projected mortar, interaction between the plates related to the type of core, the mode against shrinkage of the mortar etc. It is showed in this work a study concerning the effective strength of the projected mortar. As a result of a series of tests in walls made of projected mortar, it is determined that the effective strength of the projected mortar is 80% of that one measured from cylindrical specimens in compression tests. As well, some tests have been executed to analise the bending behaviour and the connections between the plates of the sandwich-type specimens, which demonstrated a relatively high structural performance. It is believed that this technical solution can be well applied to public works of social interest, and can offer technological and economical advantages in contrast to the traditional systems

O problema de reconstrucão digital de imagens (Image Inpainting) possui diversas abordagens para sua resolução. Uma possibilidade consiste na sua modelagem como um problema de otimizacão contínua (lasso). Na presente dissertacão aplica-se o método do gradiente espectral projetado a esse problema. Desenvolve-se inteiramente a modelagem do problema assim como a implementacão computacional do método de otimização que o resolve. Resultados computacionais demonstram a qualidade do método para um conjunto de imagens digitais / The image inpainting problem has several resolution approaches. One possibility consists in its modeling as a continuous optimization problem. In the present dissertation we apply the spectral projected gradient method to this problem. We develop the whole modeling of the problem as well as the computational implementation of the optimization method to solve it. Computational results show the quality of the method for a set of digital images

A teoria de Compressive Sensing proporciona uma nova estratégia de aquisição e recuperação de dados com bons resultados na área de processamento de imagens. Esta teoria garante recuperar um sinal com alta probabilidade a partir de uma taxa reduzida de amostragem por debaixo do limite de Nyquist-Shanon. O problema de recuperar o sinal original a partir das amostras consiste em resolver um problema de otimização. O método de Gradiente Espectral Projetado é um método para minimizar funções suaves em conjuntos convexos que tem sido aplicado com frequência ao problema de recuperar o sinal original a partir do sinal amostrado. Este trabalho dedica-se ao estudo da aplicação do Método do Gradiente Espectral Projetado ao problema de Compressive Sensing. / The theory of compressive sensing has provided a new acquisition strategy and data recovery with good results in the image processing area. This theory guarantees to recover a signal with high probability from a reduced sampling rate below the Nyquist-Shannon limit. The problem of recovering the original signal from the samples consists in solving an optimization problem. The Spectral Projected Gradient (SPG) is a method to minimize continuous functions over convex sets which often has been applied to the problem of recovering the original signal from sampled signals. This work is dedicated to the study and application of the Spectral Projected Gradient method to Compressive Sensing problems.