This thesis aims to seek interesting patterns from massive amounts of Flickr data in Sweden with pro- posed new clustering strategies. The aim can be further divided into three objectives. The first one is to acquire large amount of timestamped geolocation data from Flickr servers. The second objective is to develop effective and efficient methods to process the data. More specifically, the methods to be developed are bifold, namely, the preprocessing method to solve the “Big Data” issue encountered in the study and the new clustering method to extract spatio-temporal patterns from data. The third one is to analyze the extracted patterns with scaling analysis techniques in order to interpret human social activities underlying the Flickr Data within the urban envrionment of Sweden. During the study, the three objectives were achieved sequentially. The data employed for this study was vector points downloaded through Flickr Application Programming Interface (API). After data ac- quisition, preprocessing was performed on the raw data. The whole dataset was firstly separated by year based on the temporal information. Then data of each year was accumulated with its former year(s) so that the evovling process can be explored. After that, large datasets were splitted into small pieces and each piece was clipped, georeferenced, and rectified respectively. Then the pieces were merged together for clustering. With respect to clustering, the strategy was developed based on the Delaunay Triangula- tion (DT) and head/tail break rule. After that, the generated clusters were analyzed with scaling analysis techniques and spatio-temporal patterns were interpreted from the analysis results. It has been found that the spatial pattern of the human social activities in the urban environment of Sweden generally follows the power-law distribution and the cities defined by human social activities are evolving as time goes by. To conclude, the contributions of this research are threefold and fulfill the objectives of this study, respectively. Firstly, large amount of Flickr data is acquired and collated as a contribution to other aca- demic researches related to Flickr. Secondly, the clustering strategy based on the DT and head/tail break rule is proposed for spatio-temporal pattern seeking. Thirdly, the evolving of the cities in terms of human activities in Sweden is detected from the perspective of scaling. Future work is expected in major two aspects, namely, data and data processing. For the data aspect, the downloaded Flickr data is expected to be employed by other studies, especially those closely related to human social activities within urban environment. For the processing aspect, new algorithms are expected to either accelerate the processing process or better fit machines with super computing capacities.

The boundaries of the cities are not immutable, they can be changed. With the development of the economies and societies, the population and pollution of cities are increasing. Some urban areas are expanding with more population or other dynamics of urbanization, while other urban areas are reducing with the changing of the dynamics. Therefore, detecting urban areas or delineating the boundaries of the cities is one of the most important steps for urban studies, which is closely related to human settlements and human activities. Remote sensing data (RS) is widely used to monitor and detect land use and land cover on the surface of the earth. But the extraction of urban areas from the ordinary RS data is not easy work. The Operational Linescan System (OLS) is the sensors of the Defense Meteorological Satellite Program (DMSP). The nighttime lights from the DMSP/OLS provide worldwide remotely sensed data to analyze long-term light emissions which are closely related to human activities. But the nighttime lights imagery data contains inherent errors. Therefore, the approaches to calibrate the data and extract the urban areas from the data are complicated. The long-term objective of this thesis is to delineate the boundaries of the natural cities of the continental United States of America (USA) from 1992 to 2010 of nightlight imagery data with all the different satellites. In this thesis, the coefficients for the intercalibration of the nightlight imagery data have been calculated based on the method developed by Elvidge, et al. (2009), but the coefficients are new and available. The approach used to determine the most appropriate threshold value is very important to eliminate the possible data error. The method to offset this possible error and delineate the boundaries of the cities from nightlight imagery data is the head/tail breaks classification, which is proposed by Jiang (2012b). The head/tail breaks classification is also useful for finding the ht-index of the extracted natural cities which is developed by Jiang and Yin (2013). The ht-index is an indicator of the underlying hierarchy of the data. The results of this study can be divided into two categories. In the first, the achieved coefficients for the intercalibration of nightlight images of the continental USA are shown in a table, and the achieved data of the urban areas are stored in a data archive. In the second, the different threshold values of the uncalibrated images and the individual threshold value of the calibrated images are shown in tables, and the results of the head/tail breaks classification and power law test are also drawn. The results show that the acquired natural cities obey the power law distribution. And the results also confirm that the head/tail breaks classification is available for finding a suitable threshold value for the nightlight imagery data. Key words: cities’ boundaries; DMSP/OLS; head/tail breaks classification; nighttime lights; power law; urban areas

This thesis describes the results of the experimental investigations into some new geometrical configurations in plate-like structures materialising one-dimensional (1D) acoustic black holes for flexural waves (wedges of power-law profile) and two-dimensional (2D) acoustic black holes for flexural waves (circular indentations of power-law profile). Such acoustic black holes allow the user to reduce the amplitudes of the vibration responses of plate-like structures to a maximum effect, while not increasing the mass of the structures. This thesis also suggests some new real world practical applications for this damping technique. Initially, the effects of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power-law profile (1D black holes) were investigated, demonstrating that this method of damping is robust enough for practical applications. Then, damping of flexural vibrations in turbofan blades with trailing edges tapered according to a power-law profile has been investigated. In addition, experimental investigations into power-law profiled slots within plates have been also conducted. Another important configuration under investigation was that of circular indentations (pits) of power-law profile within the plate. In the case of quadratic or higher-order profiles, such indentations materialise 2D acoustic black holes for flexural waves. To increase the damping efficiency of power-law profiled indentations, the absorption area has been enlarged by increasing the size of the central hole in the pit, while keeping the edges sharp. The next step of investigation in this thesis was using multiple indentations of power-law profile (arrays of 2D black holes). It was shown that not only do multiple indentations of power-law profile provide substantial reduction in the damping of flexural vibrations, but also a substantial reduction in radiated sound power. The experimental results have been obtained also for a cylindrical plate incorporating a central hole of quadratic profile. They are compared to the results of numerical predictions, thus validating the results and the experimental technique. Investigations into the effects of indentations of power-law profile made in composite plates and panels and their subsequent inclusion into composite honeycomb sandwich panels are also reported. These indentations again act as 2D acoustic black holes for flexural waves and they effectively damp flexural vibrations within the panels. It was also demonstrated that these indentations can be enclosed in smooth surfaced panels and that no additional damping layer is required to induce the acoustic black hole effect in composite structures. In conclusion, it has been confirmed in this thesis that one and two-dimensional acoustic black holes represent an effective method of damping flexural vibrations and reducing the associated structure-borne sound. Furthermore, this thesis has shown that acoustic black holes can be efficiently employed in practical applications, such as trailing edges of jet engine fan blades, composite panels, and composite honeycomb sandwich structures.

Barabási-Albert random graph models are a class of evolving random graphs that are frequently used to model social networks with scale-free degree distributions. It has been shown that Barabási-Albert random graph models have asymptotic scale-free degree distributions as the size of the graph tends to infinity. Real world networks, however, have finite size so it is important to know how close the degree distribution of a Barabási-Albert random graph of a given size is to its asymptotic distribution. Stein’s method is chosen as one main method for obtaining explicit bounds for the distance between distributions. We derive a new version of Stein’s method for a class of scale-free distributions and apply the method to a Barabási-Albert random graph. We compare the evolution of a sequence of Barabási-Albert random graphs with continuous time stochastic processes motivated by Yule’s model for evolution. Through a coupling of the models we bound the total variation distance between their degree distributions. Using these bounds, we extend degree distribution bounds that we find for specific models within the scheme to find bounds for every member of the scheme. We apply the Azuma-Hoeffding inequality and Chernoff bounds to find bounds between the degree sequences of the random graph models and the given scale-free distribution. These bounds prove that the degree sequences converge completely (and therefore also converge almost surely) to our scale-free distribution. We discuss the relationship between the random graph processes and the Chinese restaurant process. Aided by the construction of an inhomogeneous Markov chain, we apply our results for the degree distribution in a Barabási-Albert random graph to a particular statistic of the Chinese restaurant process. Finally, we explore how our methods can be adapted and extended to other evolving random graph processes. We study a Bernoulli evolving random graph process, for which we bound the distance between its degree distribution and a geometric distribution and we bound the distance between the number of triangles in the graph and a normal distribution.

Picture the life of a modern person in the western world: They wake up in the morning and check their social networking sites; they drive to work on roads that connect cities to each other; they make phone calls, send emails and messages to colleagues, friends, and family around the world; they use electricity flowing through power-lines; they browse the Internet, searching for information. All of these typical daily activities rely on the structure of networks. A network, in this case, is a set of nodes (people, web pages, etc) connected by edges (physical connection, collaboration, etc). The term graph is sometimes used to represent a more abstract structure - but here we use the terms graph and network interchangeably. The field of network analysis concerns studying and understanding networks in order to solve problems in the world around us. Graph models are used in conjunction with the study of real-world networks. They are used to study how well an algorithm may do on a real-world network, and for testing properties that may further produce faster algorithms. The first piece of this dissertation is an experimental study which explores features of real data, specifically power-law distributions in degrees and spectra. In addition to a comparison between features of real data to existing results in the literature, this study resulted in a hypothesis on power-law structure in spectra of real-world networks being more reliable than that in the degrees. The theoretical contributions of this dissertation are focused primarily on generating realistic networks through existing and novel graph models. The two graph models presented are called HyperKron and the Triangle Generalized Preferential Attachment model. Both of the models incorporate higher-order structure - leading to more sophisticated properties not examined in traditional models. We use the second of our models to further validate the hypothesis on power-laws in the spectra. Due to the structure of our model, we show that the power-law in the spectra is more resilient to sub-sampling. This gives some explanation for why we see power-laws more frequently in the spectra in real world data.

Student Number : 9901877H MSc Dissertation School of Electrical and Information Engineering Faculty of Engineering and the Built Environment / algorithm. The origins of handwriting idiosyncrasies and habituation are explained using systems theory, and it is shown that the 2/3 power law governing biomechanics motion also applies to handwriting. This leads to the conclusion that it is possible to derive handwriting velocity profiles from a static image, and that a successful forgery of a signature is only possible in the event of the forger being able to generate a signature using natural ballistic motion. It is also shown that significant portion of the underlying dynamic system governing the generation of handwritten signatures can be inferred by deriving time segmented transfer function models of the x and y co-ordinate velocity profiles of a signature. The prototype algorithm consequently developed uses x and y components of pen-tip velocity profiles (vx[n] and vy[n]) to create signature representations based on autoregression-with-exogenous-input (ARX) models. Verification is accomplished using a similarity measure based on the results of a k-step ahead predictor and 5 complementary metrics. Using 350 signatures collected from 21 signers, the system’s false acceptance (FAR) and false rejection (FRR) rates were 2.19% and 27.05% respectively. This high FRR is a result of measurement inadequacies, and it is believed that the algorithm’s FRR is approximately 18%.

A turbulência clássica é um fenômeno de natureza caótica, mas de difícil estudo por ser constituída pela fusão e superposição de vórtices aleatórios, dificultando sua descrição matemática. A turbulência quântica (TQ), embora também caótica, é composta por vórtices quantizados, que favorecem o controle experimental e sua definição teórica. Embora a evidência experimental da TQ tenha sido obtida em sistemas de He líquido, sua caracterização em condensados de Bose-Einstein (BEC) ainda não foi totalmente realizada. Neste trabalho, estudamos a distribuição de momento em BECs expandidos em tempo de voo, nos regimes convencional e turbulento. Para a produção experimental da amostra quanticamente degenerada, utilizamos a técnica do resfriamento evaporativo em átomos de 87Rb, previamente resfriados em uma armadilha puramente magnética do tipo QUIC. A turbulência quântica foi produzida no sistema através de um par de bobinas de excitação capaz de produzir uma perturbação oscilatória na nuvem previamente condensada. O diagnóstico da amostra aprisionada é feito por imagem de absorção durante expansão livre da nuvem. Durante a expansão, tanto a nuvem condensada quanto a turbulenta, alcançaram um valor assintótico no aspect ratio, indicando uma evolução isotrópica. A partir deste resultado, elaboramos um método teórico capaz de determinar a projeção isotrópica da distribuição de momento, baseado na imagem produzida experimentalmente. Através de argumentos de simetria e de uma transformada integral, recuperamos a densidade de momento tridimensional da projeção, para então determinar o espectro de energia cinética da nuvem, observando uma lei de escala para um estreito intervalo de momento. A lei de escala já foi prevista teoricamente para sistemas quânticos e medida para o He superfluido, mas pela primeira vez foi evidenciada em um BEC. Desta forma, os resultados corroboram a existência da turbulência quântica em uma amostra quanticamente degenerada, introduzindo os BECs como candidatos alternativos ao He líquido superfluido no estudo deste fenômeno. / Classical turbulence is a chaotic phenomenon that requires labored work, because of its merging and overlapping of random vortices nature, which hinders its mathematical description. Quantum turbulence (QT), although chaotic, is comprised of quantized vortices that favor the experimental control and its theoretical definition. Although experimental evidence of QT has been proved in liquid helium systems, its characterization in Bose-Einstein condensates (BEC) has not been fully accomplished. In this work, we studied the momentum distribution of expanding turbulent and non-turbulent BEC. For experimental achievement of the quantum degenerated sample, we used evaporative cooling in rubidium atoms, previously cooled in a QUIC trap. Quantum turbulence was produced through a pair of excitation coils capable of producing an oscillatory perturbation in the cloud previously condensed. The diagnosis of the trapped sample is done by absorption image during free expansion of the cloud. During the expansion, both clouds achieved a asymptotic value of the aspect ratio, indicating an isotropic evolution. From this result, we have developed a theoretical method able to determine the projection of the isotropic distribution of momentum, based on the image produced experimentally. Through symmetry arguments and an integral transformation, we recovered the tridimensional momentum distribution of the projection and then determined the kinetic energy spectrum of the cloud, observing a scaling power law for a narrow range of momenta. The scaling law has been theoretically predicted for quantum systems and has been proved to liquid helium superfluid, but, in this work, was for the first time evidenced in a BEC. Thus, the results support the existence of quantum turbulence in our quantum degenerated sample, introducing the BECs as potential candidates besides liquid helium superfluid for the study of this phenomenon.

Este trabalho tem como objetivo caracterizar experimentalmente a difusão anômala de microesferas em células com alta resolução temporal. As microesferas são cobertas com um peptídeo para que elas fiquem aderidas ao citoesqueleto celular (CSK), de forma que quando o CSK se movimenta, as microesferas se movimentam junto. A grande parte dos trabalhos na literatura usa técnicas ativas, que consistem em aplicar uma perturbação na célula, para estudar a movimentação das microesferas, diferente da técnica usada neste trabalho, que é passiva. A vantagem de usar a técnica passiva é que é possível olhar a difusão das microesferas, sem haver fatores externos ativos atuando, porque o CSK já é um ambiente sujeito a forças dos próprios motores celulares, o que está relacionado com o comportamento anômalo. Ao calcular o deslocamento quadrático médio (MSD) das microesferas, os regimes aos quais as microesferas estão sujeitas, são o subdifusivo e o superdifusivo, e ambos possuem características que podem ser consideradas comportamento anômalo. Neste trabalho focamos em estudar a difusão anômala a altas frequências, usando uma câmera que pode chegar a 1000 frames por segundo (fps) para observações curtas, ou em torno de 200 fps, sustentável por longos tempos, a fim de evidenciar o comportamento anômalo. Conseguimos mostrar que a movimentação das microesferas segue uma lei de potência para deslocamentos normalizados |Z| > 3, o que indica que o fenômeno é livre de escala, corroborando com a hipótese de o citoplasma celular ter um comportamento do tipo mole. Além disso, como a análise do movimento é baseada na análise de imagem da posição das microesferas, propusemos um estudo para estimar o erro na posição das microesferas. / The aim of this master\'s thesis is to characterize experimentally anomalous diffusion of microbeads in cells with high temporal resolution. The microbeads are coated with a peptide, such that they can bound to integrins, which is a specific cell surface receptor, thus when the cytoskeleton moves the microbeads move together. The majority of works in scientific literature deals with active techniques, that consists of applying a disturbance on the cell, in order to investigate the movement of the beads, differently from the passive technique used in this work. The advantage of using the passive technique is that it makes possible to look to diffusion without having external active factors, because the cell cytoskeleton itself is an environment subjected to forces, provided by cell motors, which has been related to the anomalous behavior in the mean squared displacement. When calculating the microbeads mean squared displacement (MSD), they are subjected to the subdiffusive and supperdifusive regimes, and both have characteristics that can be considered anomalous behavior. Our goal was to study anomalous diffusion at high frequencies by using a camera that reaches up to 1000 frames per second (fps), for shorter observation times, or around 200 fps, sustainable for longer observation times, having the purpose of evidencing the anomalous behavior. We were able to show that the microbeads movement follows a power law for normalized displacements |Z| > 3, indicating that the phenomenon is scale-free, agreeing with the hypothesis that the cellular cytoplasm has a soft glassy behavior. Besides, since the movement analysis is based on the microbeads position image analysis, we have proposed a way to estimate the error in the microbeads position.

In this thesis we provide an existence result for a regularized model of viscoelastic non- newtonian fluid. We consider incompressible fluid with shear rate dependent viscosity and with Cauchy stress tensor capable to describe stress relaxation. An elastic part of the Cauchy stress tensor is governed by Oldroyd-type differential equation. In particular, we are interested in fluids with strong shear thinning effect. We prove that if the viscosity function µ (D) is such that tensor µ (D) D is p-coercive, monotone and has (p − 1)-growth for p > 6 5 and some other additional assumptions are satisfied, then there exists a solution to the system of PDEs describing the flow in a bounded domain. The proof is not simple because the convective term is not integrable with a high power. The problem is solved using Lipschitz truncation method for evolution PDEs. 1

In this dissertation, we apply Bayesian and Empirical Bayes methods for reliability growth models based on the power law process. We also apply Bayes methods for the study of microarrays, in particular, in the selection of differentially expressed genes. The power law process has been used extensively in reliability growth models. Chapter 1 reviews some basic concepts in reliability growth models. Chapter 2 shows classical inferences on the power law process. We also assess the goodness of fit of a power law process for a reliability growth model. In chapter 3 we develop Bayesian procedures for the power law process with failure truncated data, using non-informative priors for the scale and location parameters. In addition to obtaining the posterior density of parameters of the power law process, prediction inferences for the expected number of failures in some time interval and the probability of future failure times are also discussed. The prediction results for the software reliability model are illustrated. We compare our result with the result of Bar-Lev,S.K. et al. Also, posterior densities of several parametric functions are given. Chapter 4 provides Empirical Bayes for the power law process with natural conjugate priors and nonparametric priors. For the natural conjugate priors, two-hyperparameter prior and a more generalized three-hyperparameter prior are used. In chapter 5, we review some basic statistical procedures that are involved in microarray analysis. We will also present and compare several transformation and normalization methods for probe level data. The objective of chapter 6 is to select differentially expressed genes from tens of thousands of genes. Both classical methods (fold change, T-test, Wilcoxon Rank-sum Test, SAM and local Z-score and Empirical Bayes methods (EBarrays and LIMMA) are applied to obtain the results. Outputs of a typical classical method and a typical Empirical Bayes Method are discussed in detail.