Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2016-05-02T10:49:21Z No. of bitstreams: 1 arquivototal.pdf: 1791577 bytes, checksum: ecd7a6eb8a18230d0145c24932d9e248 (MD5) / Made available in DSpace on 2016-05-02T10:49:22Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1791577 bytes, checksum: ecd7a6eb8a18230d0145c24932d9e248 (MD5) Previous issue date: 2015-08-03 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The Hanbury Brown-Twiss experiment is very well established in quantum optics literature, so we devoted this dissertation in order to embed the parity and temporal reversal symmetry in the former experiment. Therefore, we developed the scattering matrix formalism which allow us use some techniques such as the scattering matrices' concatenation of di erent sections in terms of one matrix and the scattering problem of a parity and temporal reverse symmetric system. In this manner, we could derive the scattering matrix of a parity and temporal reverse symmetric Hanbury Brown- Twiss experiment(HBT-PT). With the possession of this matrix, we proposed a theoretical model which provides how to measure the symmetry of this system, which we called correlation functions formalism. In order to stablish the former formalism, we studied B uttiker formalism, which we veri ed how the correlation between 2 incident particles in a system relates to the noise due transport of this particles and what kind of noise we are treating in a given regime which the system is operating. Then, we found the input states in terms of the output states of two particles inciding in a multiterminal system, which we used it's scattering matrix to stablish the relation between the states. Thereat, we derived all the possibles correlations(therefore, the noise) of two incident particles in the former system. Thereby, we analysed the extreme cases of a barrier coupled to the HBT-PT experiment for the purpose of stablish which regime the experiment is symmetric adjusted, so, demonstrating the Hanbury Brown-Twiss E ect with parity and temporal reverse symmetries. / Sendo o experimento Hanbury Brown-Twiss bem estabelecido na literatura da otica quântica, dedicamos esta dissertação a embutir no mesmo experimento a questão da simetria por paridade e reversão temporal. Para tanto, abrimos mão do formalismo da matriz de espalhamento que permitiu nos utilizar tecnicas como a concatenação de matrizes de espalhamento de sec ções diferentes em termos de apenas uma matriz e o problema do espalhamento em um sistema simétrico por paridade e reversão temporal. Dessa forma, pudemos derivar a matriz de espalhamento para o experimento Hanbury Brown-Twiss com simetria de paridade e revers~ao temporal(HBT-PT). De posse dessa matriz, propusemos um modelo teórico que propicia a medição experimental a simetria desse sistema, o qual chamamos de formalismo das fun c~oes de correla c~ao. Para estabelecermos o formalismo supracitado, estudamos o formalismo de Buttiker, onde veri case como a correlaçãao entre 2 partículas incidentes em um sistema relaciona-se com o ru do devido ao transporte dessas part culas e que tipo de ru do estamos tratando, dado o regime em que o sistema está operando. Em seguida, encontramos os estados de entrada em termos dos estados de saída de 2 partículas incidindo em um sistema multiterminal, onde utilizamos a sua matriz de espalhamento para estabelecer a rela c~ao entre os estados. Com isso, derivamos todas as possíveis correlações (e, por conseguinte, o ruído) de 2 partículas incidentes nesse sistema. Assim, analisamos os casos extremos de uma barreira acoplada ao experimento HBT-PT, a m de estabelecer o regime em que o experimento está simetricamente ajustado e demonstramos o Efeito Hanbury Brown-Twiss por paridade e reversão temporal.

No description available.

The main motivation behind writing this thesis was to construct numerical methods to approximate solutions to differential equations driven by rough paths, where the solution is considered in the rough path-sense. Rough paths of inhomogeneous degree of smoothness as driving noise are considered. We also aimed to find applications of these numerical methods to stochastic differential equations. After sketching the core ideas of the Rough Paths Theory in Chapter 1, the versions of the core theorems corresponding to the inhomogeneous degree of smoothness case are stated and proved in Chapter 2 along with some auxiliary claims on the continuity of the solution in a certain sense, including an RDE-version of Gronwall's lemma. In Chapter 3, numerical schemes for approximating solutions to differential equations driven by rough paths of inhomogeneous degree of smoothness are constructed. We start with setting up some principles of approximations. Then a general class of local approximations is introduced. This class is used to construct global approximations by pasting together the local ones. A general sufficient condition on the local approximations implying global convergence is given and proved. The next step is to construct particular local approximations in finite dimensions based on solutions to ordinary differential equations derived locally and satisfying the sufficient condition for global convergence. These local approximations require strong conditions on the one-form defining the rough differential equation. Finally, we show that when the local ODE-based schemes are applied in combination with rough polynomial approximations, the conditions on the one-form can be weakened. In Chapter 4, the results of Gyurko & Lyons (2010) on path-wise approximation of solutions to stochastic differential equations are recalled and extended to the truncated signature level of the solution. Furthermore, some practical considerations related to the implementation of high order schemes are described. The effectiveness of the derived schemes is demonstrated on numerical examples. In Chapter 5, the background theory of the Kusuoka-Lyons-Victoir (KLV) family of weak approximations is recalled and linked to the results of Chapter 4. We highlight how the different versions of the KLV family are related. Finally, a numerical evaluation of the autonomous ODE-based versions of the family is carried out, focusing on SDEs in dimensions up to 4, using cubature formulas of different degrees and several high order numerical ODE solvers. We demonstrate the effectiveness and the occasional non-effectiveness of the numerical approximations in cases when the KLV family is used in its original version and also when used in combination with partial sampling methods (Monte-Carlo, TBBA) and Romberg extrapolation.

Since the end of the 20th century capital markets have undergone a fundamental change. Under the influence of globalization they have become more interconnected and more functional than before on the base of information technology. Although the financial crisis of 2008 slowed down this development and liberalization, currently markets are rising again and one of the most striking trends is their integration into multinational units. An example of Stock Exchange Cooperation in the early 21st century is the CEESEG group associating Central and Eastern European Stock Exchanges, namely, the Wiener Börse, the Prague Stock Exchange, the Ljubljana Stock Exchange and the Budapest Stock Exchange. The theme of this thesis is to analyze the example of this geographically close and, thanks to the PSE, directly related, interesting trend of Stock Exchange cooperation, the manner of its function and impact on every member Stock Exchange.

Ce mémoire aborde la synthèse de filtres H-infine d'ordre plein et d'ordre réduit pour les systèmes stochastiques à temps continu avec bruits multiplicatifs. Les bruits considérés dans l'équation d'état et dans l'équation de mesures sont des processus de Wiener.<br /><br />Les systèmes stochastiques étudiés dans ce mémoire sont écrits sous la forme d'une équation différentielle stochastique au sens d'Itô dans lesquels la dérive et la diffusion sont linéaires ou bilinéaires. Les systèmes avec plusieurs bruits multiplicatifs et les systèmes dont les mesures sont affectées par des bruits multiplicatifs sont également traités dans ce mémoire. La conception d'une commande H-infine basée sur un observateur d'ordre réduit pour les systèmes stochastiques incertains est étudiée.<br /><br />Le critère de performance considéré est le critère H-infine du signal de perturbation vers le signal d'erreur d'estimation. La stabilité retenue pour ces systèmes stochastiques dans ce travail est la stabilité exponentielle en moyenne quadratique.<br /><br />La méthode utilisée pour trouver les matrices des filtres est basée sur l'utilisation de la théorie de Lyapunov pour les équations différentielles stochastiques, la formule d'Itô et sur la résolution des Inégalités Matricielles Affines couplées à des contraintes bilinéaires qui assurent la stabilité et la performance.

Cette thèse a pour but d'étudier quelques applications des fonctions à variation bornée et des ensembles de périmètre fini. Nous nous intéressons en particulier à des applications en traitement d'images et en géométrie de dimension finie et infinie. Nous étudions tout d'abord une méthode dite Primale-Duale proposée par Appleton et Talbot pour la résolution de nombreux problèmes en traitement d'images. Nous réinterprétons cette méthode sous un oeil nouveau, ce qui aide à mieux la comprendre mathématiquement. Ceci permet par exemple de démontrer sa convergence et d'établir de nouvelles estimations a posteriori qui sont d'une grande importance pratique. Nous considérons ensuite le problème de courbure moyenne prescrite en milieu périodique. A l'aide de la théorie des ensembles de périmètre fini, nous démontrons l'existence de solutions approchées compactes de ce problème. Nous étudions également le comportement asymptotique de ces solutions lorsque leur volume tend vers l'infini. Les deux dernières parties de la thèse sont consacrées à l'étude de problèmes géométriques dans les espaces de Wiener. Nous étudions d'une part les liens entre symétrisations, semi-continuité et inégalités isopérimétriques ce qui permet d'obtenir un résultat d'approximation et de relaxation pour le périmètre dans ces espaces de dimension infinie. Nous démontrons d'autre part la convexité des solutions de certains problèmes variationnels dans ces espaces, en développant au passage l'étude de la semi-continuité et de la relaxation dans ce contexte.

<p>This project investigates a laser radar system. The system is based on the principles of time-correlated single photon counting, and by measuring the times-of-flight of reflected photons it can find range profiles and perform three-dimensional imaging of scenes. Because of the photon counting technique the resolution and precision that the system can achieve is very high compared to analog systems. These properties make the system interesting for many military applications. For example, the system can be used to interrogate non-cooperative targets at a safe distance in order to gather intelligence. However, signal processing is needed in order to extract the information from the data acquired by the system. This project focuses on the analysis of different signal processing methods.</p><p>The Wiener filter and the Richardson-Lucy algorithm are used to deconvolve the data acquired by the photon counting system. In order to find the positions of potential targets different approaches of non-linear least squares methods are tested, as well as a more unconventional method called ESPRIT. The methods are evaluated based on their ability to resolve two targets separated by some known distance and the accuracy with which they calculate the position of a single target, as well as their robustness to noise and their computational burden.</p><p>Results show that fitting a curve made of a linear combination of asymmetric super-Gaussians to the data by a method of non-linear least squares manages to accurately resolve targets separated by 1.75 cm, which is the best result of all the methods tested. The accuracy for finding the position of a single target is similar between the methods but ESPRIT has a much faster computation time.</p>

<p>Signal processing within the neurophysiological field is challenging and requires short processing time and reliable results. In this thesis, three main problems are considered.</p><p>First, a modified line source model for simulation of muscle action potentials (APs) is presented. It is formulated in continuous-time as a convolution of a muscle-fiber dependent transmembrane current and an electrode dependent weighting (impedance) function. In the discretization of the model, the Nyquist criterion is addressed. By applying anti-aliasing filtering, it is possible to decrease the discretization frequency while retaining the accuracy. Finite length muscle fibers are incorporated in the model through a simple transformation of the weighting function. The presented model is suitable for modeling large motor units.</p><p>Second, the possibility of discerning the individual AP components of the concentric needle electromyogram (EMG) is explored. Simulated motor unit APs (MUAPs) are prefiltered using Wiener filtering. The mean fiber concentration (MFC) and jitter are estimated from the prefiltered MUAPs. The results indicate that the assessment of the MFC may well benefit from the presented approach and that the jitter may be estimated from the concentric needle EMG with an accuracy comparable with traditional single fiber EMG.</p><p>Third, automatic, rather than manual, detection and discrimination of recorded C-fiber APs is addressed. The algorithm, detects the Aps reliably using a matched filter. Then, the detected APs are discriminated using multiple hypothesis tracking combined with Kalman filtering which identifies the APs originating from the same C-fiber. To improve the performance, an amplitude estimate is incorporated into the tracking algorithm. Several years of use show that the performance of the algorithm is excellent with minimal need for audit.</p>

Signal processing within the neurophysiological field is challenging and requires short processing time and reliable results. In this thesis, three main problems are considered. First, a modified line source model for simulation of muscle action potentials (APs) is presented. It is formulated in continuous-time as a convolution of a muscle-fiber dependent transmembrane current and an electrode dependent weighting (impedance) function. In the discretization of the model, the Nyquist criterion is addressed. By applying anti-aliasing filtering, it is possible to decrease the discretization frequency while retaining the accuracy. Finite length muscle fibers are incorporated in the model through a simple transformation of the weighting function. The presented model is suitable for modeling large motor units. Second, the possibility of discerning the individual AP components of the concentric needle electromyogram (EMG) is explored. Simulated motor unit APs (MUAPs) are prefiltered using Wiener filtering. The mean fiber concentration (MFC) and jitter are estimated from the prefiltered MUAPs. The results indicate that the assessment of the MFC may well benefit from the presented approach and that the jitter may be estimated from the concentric needle EMG with an accuracy comparable with traditional single fiber EMG. Third, automatic, rather than manual, detection and discrimination of recorded C-fiber APs is addressed. The algorithm, detects the Aps reliably using a matched filter. Then, the detected APs are discriminated using multiple hypothesis tracking combined with Kalman filtering which identifies the APs originating from the same C-fiber. To improve the performance, an amplitude estimate is incorporated into the tracking algorithm. Several years of use show that the performance of the algorithm is excellent with minimal need for audit.

Until recent years, terahertz (THz) waves were an undiscovered, or most importantly, an unexploited area of electromagnetic spectrum. This was due to difficulties in generation and detection of THz waves. Recent advances in hardware technology have started to open up the field to new applications such as THz imaging. This non-destructive and non-contact imaging technique can penetrate through diverse materials such that internal structures, in some cases invisible to other imaging modalities, can be visualized. Today, there are variety of techniques available to generate and detect THz waves in both pulsed and continuous fashion in two different geometries; transition, and reflection modes. In this thesis continuous wave THz imaging was employed for higher spatial resolution. However, with any new technology comes its challenges; automated processing of THz images can be quite cumbersome. Low contrast and the presence of a widely unknown type of noise make the analysis of these images difficult. In this work, there is an attempt to detect defects in composite material via segmentation by using a Terahertz imaging system. According to our knowledge, this is the first time that this type of materials are being tested under Terahertz cameras to detect manufacturing defects in aerospace industry. In addition, segmentation accuracy of THz images have been investigated by using a phantom. Beyond the defect detection for composite materials, this can establish some general knowledge about Terahertz imaging, its capabilities and limitations. To be able to segment the THz images successfully, pre-processing techniques are inevitable. In this thesis, a variety of different image processing techniques, self-developed or available from literature, have been employed for image enhancement. These methods range from filtering to contrast adjustment to fusion of phase and amplitude images by using fuzzy set theory, to just name a few. The result of pre-procssing and segmentation methods demonstrates promising outcome for future work in this field.