Este trabalho se dedica ao estudo da interação entre princípios de seleção e jogos topológicos. Isto inclui uma abordagem não-topológica destes tópicos, com aplicações à indestrutibilidade de espaços de Lindelöf e a uma versão seletiva de d-separabilidade, dentre outros. Provamos ainda a não-equivalência consistente entre indestrutibilidade e o princípio de seleção naturalmente associado a esta propriedade, o que conduz à investigação da indestrutibilidade de espaços compactos. Finalmente, mostramos que algumas afirmações que limitam a cardinalidade de espaços de Lindelöf indestrutíveis são equiconsistentes com a existência de certos tipos de grandes cardinais. / In the present work we focus on the interplay between selection principles and topological games. This includes a nontopological approach to these topics, with applications to indestructibility of Lindelöf spaces and a selective version of d-separability, among others. We also show the consistent nonequivalence between indestructibility and the selection principle naturally associated to it, which leads to an investigation of indestructibility of compact spaces. We conclude by showing that some constraints on the cardinality of Lindelöf indestructible spaces are equiconsistent with the existence of some kinds of large cardinals.

<p>Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts.</p><p>Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems.</p><p>Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy.</p><p>Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.</p>

In this thesis, the geometric margin is used for the first time as the robustness indicator of an uncoupled cellular neural network implementing a given Boolean function. First, robust template design for uncoupled cellular neural networks implementing linearly separable Boolean functions by support vector machines is proposed. A fast sequential minimal optimization algorithm is presented to find maximal margin classifiers, which in turn determine the robust templates. Some general properties of robust templates are investigated. An improved CFC algorithm implementing an arbitrarily given Boolean function is proposed. Two illustrative examples are provided to demonstrate the validity of the proposed method.

This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time expected utility maximization with addictive consumption habit formation in incomplete markets under two independent scenarios. In the first project, we study the continuous time utility optimization problem with consumption habit formation in general incomplete semimartingale financial markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space. We establish existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living. We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable. In the second project, we examine an example of the optimal investment and consumption problem with both habit-formation and partial observations in incomplete markets driven by It\^{o} processes. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rates of return, which follow an Ornstein-Uhlenbeck process. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman(HJB) equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We provide the optimal investment and consumption policy in explicit feedback form using rigorous verification arguments. / text

abstract: Three dimensional (3-D) ultrasound is safe, inexpensive, and has been shown to drastically improve system ease-of-use, diagnostic efficiency, and patient throughput. However, its high computational complexity and resulting high power consumption has precluded its use in hand-held applications. In this dissertation, algorithm-architecture co-design techniques that aim to make hand-held 3-D ultrasound a reality are presented. First, image enhancement methods to improve signal-to-noise ratio (SNR) are proposed. These include virtual source firing techniques and a low overhead digital front-end architecture using orthogonal chirps and orthogonal Golay codes. Second, algorithm-architecture co-design techniques to reduce the power consumption of 3-D SAU imaging systems is presented. These include (i) a subaperture multiplexing strategy and the corresponding apodization method to alleviate the signal bandwidth bottleneck, and (ii) a highly efficient iterative delay calculation method to eliminate complex operations such as multiplications, divisions and square-root in delay calculation during beamforming. These techniques were used to define Sonic Millip3De, a 3-D die stacked architecture for digital beamforming in SAU systems. Sonic Millip3De produces 3-D high resolution images at 2 frames per second with system power consumption of 15W in 45nm technology. Third, a new beamforming method based on separable delay decomposition is proposed to reduce the computational complexity of the beamforming unit in an SAU system. The method is based on minimizing the root-mean-square error (RMSE) due to delay decomposition. It reduces the beamforming complexity of a SAU system by 19x while providing high image fidelity that is comparable to non-separable beamforming. The resulting modified Sonic Millip3De architecture supports a frame rate of 32 volumes per second while maintaining power consumption of 15W in 45nm technology. Next a 3-D plane-wave imaging system that utilizes both separable beamforming and coherent compounding is presented. The resulting system has computational complexity comparable to that of a non-separable non-compounding baseline system while significantly improving contrast-to-noise ratio and SNR. The modified Sonic Millip3De architecture is now capable of generating high resolution images at 1000 volumes per second with 9-fire-angle compounding. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

Vision based object recognition and localization have been studied widely in recent years. Often the initial step in such tasks is detection of interest points from a grey-level image. The current state-of-the-art algorithms in this domain, like Scale Invariant Feature Transform (SIFT) and Speeded Up Robust Features (SURF) suffer from low execution speeds on a GPU(graphic processing unit) based system. Generally the performance of these algorithms on a GPU is below real-time due to high computational complexity and data intensive nature and results in elevated power consumption. Since real-time performance is desirable in many vision based applications, hardware based feature detection is an emerging solution that exploits inherent parallelism in such algorithms to achieve significant speed gains. The efficient utilization of resources still remains a challenge that directly effects the cost of hardware. This work proposes a novel hardware architecture for scale-space extrema detection part of the SIFT algorithm. The implementation of proposed architecture for Xilinx Virtex-4 FPGA and its evaluation are also presented. The implementation is sufficiently generic and can be adapted to different design parameters efficiently according to the requirements of application. The achieved system performance exceeds real-time requirements (30 frames per second) on a 640 x 480 image. Synthesis results show efficient resource utilization when compared with the existing known implementations.

Covariant density functional theory (CDFT) is one of the modern theoretical tools for describing the nuclear structure physics of finite nuclei. Its performance is defined by underlying covariant energy density functionals (CEDFs). In this dissertation and within the framework of the CDFT, different physical properties of the ground and the excited states of rotating and non-rotating nuclei have been investigated. A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref.\ \cite{TMR.09}. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in the neutron subsystem. However, the situation is less certain in the proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level. It is shown for the first time that rotational bands which are proton unbound at zero or low spins can be transformed into proton bound ones at high spin by collective rotation of nuclear systems. This is due to strong Coriolis interaction, which acts on high-$N$ or strongly mixed M orbitals and drives the highest in energy occupied single-particle states of nucleonic configurations into the negative energy domain. Proton emission from such proton bound rotational states is suppressed by the disappearance of static pairing correlations at high spins of interest. These physical mechanisms lead to a substantial extension of the nuclear landscape beyond the spin zero proton drip line. In addition, a new phenomenon of the formation of giant proton halos in rotating nuclei emerges: it is triggered by the occupation of strongly mixed M intruder orbitals. Possible experimental fingerprints of the transition from particle bound to particle unbound part of rotational bands are discussed and compared for proton and neutron rich nuclei near and beyond respective drip lines.

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Convolution and multiplication operations in the filtering process can be optimized by minimizing the resource utilization using Field Programmable Gate Arrays (FPGA) and separable filter kernels. An FPGA architecture for separable convolution is proposed to achieve reduction of on-chip resource utilization and external memory bandwidth for a given processing rate of the convolution unit. Multiplication in integer number system can be optimized in terms of resources, operation time and power consumption by converting to logarithmic domain. To achieve this, a method altering the filter weights is proposed and implemented for error reduction. The results obtained depict significant error reduction when compared to existing methods, thereby optimizing the multiplication in terms of the above mentioned metrics. Underwater video and still images are used by many programs within National Oceanic Atmospheric and Administration (NOAA) fisheries with the objective of identifying, classifying and quantifying living marine resources. They use underwater cameras to get video recording data for manual analysis. This process of manual analysis is labour intensive, time consuming and error prone. An efficient solution for this problem is proposed which uses Gabor filters for feature extraction. The proposed method is implemented to identify two species of fish namely Epinephelus morio and Ocyurus chrysurus. The results show higher rate of detection with minimal rate of false alarms.