O presente trabalho consiste na elaboração de uma metodologia envolvendo técnicas computacionais para proporcionar informações provenientes de avaliação de qualidade de equipamentos mamográficos. A investigação conduzida levou em conta, além da necessária determinação de parâmetros operacionais - como tensão de pico (kVp), corrente de tubo, ponto focal, dose, tempo de exposição, camada semi-redutora -, a influência das características do digitalizador usado no processo de digitalização das imagens a ser avaliadas pelo esquema computacional, seja esse um sistema de aquisição digital direta ou indireta. Dessa forma, foi elaborado um protocolo de pré-processamento da imagem para compensar os efeitos do digitalizador antes da avaliação dos parâmetros de qualidade através dela. Simultaneamente ao desenvolvimento dos softwares necessários ao esquema, foi projetado e desenvolvido um simulador radiográfico para servir como instrumento para obtenção tanto das imagens a ser processadas pelo modelo computacional, como dos dados referentes aos parâmetros operacionais. O sistema foi desenvolvido tomando um mamógrafo calibrado e um instrumento de precisão como referências e testado em outros equipamentos mamográficos em operação em clínicas e hospitais. Os resultados foram consistentes com as análises comparativas utilizando as referências, o que podem fazer do sistema uma ferramenta útil na avaliação de qualidade em mamografia. / The present work consists on developing a computational methodology to provide information regarding to mammographic equipment quality evaluation. This investigation have taken into account, beyond the required operational parameters, such as kVp, electrical current, focal point, dose, exposition time, half-value layer, the influence of the film digitizer utilized for digitization process on the images to be evaluated by the computational scheme, either this a system of direct or indirect digital acquisition. Like so, it was elaborated an image pre-processing protocol to compensate the digitization effect on digital image, before the evaluation of quality control parameters through itself. Simultaneously to the development of the necessary software to the system, a radiographic phantom was developed to be used for achievement of either the images to be processed by the computational model, as operational parameters data. The system was developed taking calibrated mammographic equipment and a precise measurement instrument as references, besides, it was tested in other mammographic equipment in operation on clinics and hospitals. Results had shown consistent with the comparative analyses using those references, which can turn this system a useful tool for evaluation of mammography quality.

Made available in DSpace on 2014-07-29T16:21:17Z (GMT). No. of bitstreams: 1 Dissertacao Luciano Lajovic Carneiro.pdf: 507309 bytes, checksum: b58c6af9d894c2d90f75adfed8ebd925 (MD5) Previous issue date: 2011-04-18 / This research aims to assess the fish biodiversity of the streams of the Tocantins and Araguaia basin and test the relative influence of local and regional processes in determining local species richness by examining the relationship between local species richness and regional species richness. For this purpose were sampled 18 streams in the basin of the Araguaia River and 16 streams in the basin of the Tocantins River in the state of Goiás using trawls. For analysis of richness observed was used and linear regression to assess the relationship of local and regional richness. The average value of diversity index of Shannon-Wiener were similar (p> 0.098) to the streams of the Tocantins (H`= 1.784) and Araguaia (H` = 2.254), uniformity also showed similar values (p> 0.962), but the average richness values were different (p = 0.039) for the basin of Tocantins S = 7.12 and S = 11.38 for Araguaia basin. Species richness of the Araguaia streams was strongly related to regional richness (r² = 0.826, p <0.0001) indicating a linear relationship and suggesting that local assemblies are unsaturated. For Tocantins streams was obtained a weak relationship (r²= 0.251, p = 0.047) and it was not possible to infer the shape of the relationship, several factors may be involved in the result. The diversity index was not an efficient descriptor of biodiversity, the test of the relationship between local and regional richness is a good predictor of ecological processes that influence species richness, has the disadvantage of the need to obtain a large amount of data. / Este trabalho objetiva avaliar a biodiversidade de peixes de riachos da bacia Tocantins e Araguaia e testar a influência relativa dos processos locais e regionais na determinação da riqueza de espécies locais através da análise da relação entre a riqueza de espécies local e a riqueza de espécies regional. Para isso, foram amostrados 18 riachos na bacia do Araguaia e 16 riachos na bacia do Tocantins no estado de Goiás utilizando redes de arrasto. Para análise da biodiversidade foi utilizada a riqueza observada e a regressão linear para avaliar a relação entre a riqueza local e regional. Foram capturados 2919 peixes (1833 da bacia do rio Araguaia e 1082 da bacia do rio Tocantins) distribuídos em cinco ordens, 20 famílias e 85 espécies. Os valores médio do índice de diversidade de Shannon-Wiener foram semelhantes (p>0,098) para os riachos da bacia do Tocantins (H`= 1,784) e Araguaia (H`= 2,254), a uniformidade também apresentou valores semelhantes (p>0,962), no entanto, a riqueza média apresentou valores distintos (p=0,039) para as bacias do Tocantins S= 7,12 e do Araguaia S= 11,38. A riqueza de espécies dos riachos do Araguaia esteve fortemente relacionada a riqueza regional (r² = 0,826; p<0,0001) indicando relação linear e sugerindo que as assembléias locais estão insaturadas. Para os riachos do Tocantins obteve-se uma relação fraca (r²= 0,251; p= 0,047), de forma que não foi possível inferir sobre a forma da relação, pois diversos fatores podem estar envolvidos no resultado obtido. O índice de diversidade não foi um descritor eficiente da biodiversidade, por outro lado, o teste da relação entre a riqueza local e regional é um bom preditor dos processos ecológicos que influenciaram a riqueza de espécies, mas tem como desvantagem a necessidade de se obter grande quantidade de dados.

The aim of this thesis is to simulate stochastic models that are driven by a fractional Brownian motion process and to apply these methods to financial applications related to yield rate and asset price modelling. Several rough volatility processes are used to model the asset price and yield dynamics. Firstly fractional processes of Cox-Ingersoll-Ross, CEV and Vasicek types are introduced as models for volatility and yield data. In this framework it holds that the Hurst parameter that determines the covariance structure of the fBM process can be directly estimated from observed data series using a least squares log-periodogram approach. The remaining parameters in the model are estimated using a combination of Maximum Likelihood estimates and expectation estimations. In the modelling and pricing of assets one model that is studied is the fractional Heston model, that is used to model an asset price process using both observed asset and volatility data. Similarly two other similar rough volatility models are also studied, which are constructed so as to have log-Normal returns. These processes which in the thesis are called the exponential models 1 and 2 have rough volatility that are characterized by the CEV and Vasicek processes. Additionally the first order Wiener Chaos Expansion is implemented and explored in two ways. Firstly the Chaos Expansion is applied to a parametric fractional stochastic model which is used to generate a Wick product process, which is found to resemble the underlying process. It is also used to generate an approximate expansion of real yield rate data using a bootstrap sampling approach. / Den här uppsatsen syftar till att simulera stokastiska modeller som drivs av fraktionell Brownsk rörelse och att använda dessa modeller i finansiella tillämpningar relaterade till räntor och finansiella tillgångar. Flera volatilitetsprocesser som är rough används för att modellera ränte- och aktiedynamiken. Först introduceras de fraktionella varianterna av Cox-Ingersoll-Ross, CEV och Vasicek processer, vilka används för att modellera volatilitet och ränteprocesser. Med detta tillvägagångssätt gäller det att Hurstparametern, vilken bestämmer covariansstrukturen för den fraktionella Brownska rörelsen, kan uppskattas direkt från observerad data med en minsta kvadrat log-periodogram-metod. Samtliga andra parametrar i modellen uppskattas med en kombination av Maximum Likelihood och uppskattning av väntevärden. I modelleringen och prissättningen av finansiella tillgångar är en model som studeras den fraktionella Hestonmodellen, som används för att modellera en tillgång baserat på både volatilitets- och aktiedata. Ytterligare två liknande modeller studeras, vilka också har volatilitet som är rough och är konstruerade så att deras avkastning är log-Normal. Dessa processer, vilka i uppsatsen är benämnda som de exponentiella modellerna 1 och 2 har volatilitet som karaktäriseras av CEV- och Vasicekprocesser. Ytterligare är Wiener's Kaosexpansion av första ordningen också implementerad och undersöks från två håll. Först används den på en parameterbestämd fraktionell stokastisk modell, vilken används för att generera en Wickproduktprocess. Expansionen används även med hjälp av en bootstrap-metod för att generera en process från observerad data.

In this thesis, we establish an analog of the Paley-Wiener Theorem for the ZS-AKNS scattering transform on a set of real potentials. We also demonstrate one application of our techniques to the study of an inverse spectral problem for a half-line Miura potential Schroedinger equation.

This study of classical and modern harmonic analysis extends the classical Wiener's approximation theorem to locally compact abelian groups. The first chapter deals with harmonic analysis on the n-dimensional Euclidean space. Included in this chapter are some properties of functions in L1(Rn) and T1(Rn), the Wiener-Levy theorem, and Wiener's approximation theorem. The second chapter introduces the notion of standard function algebra, cospectrum, and Wiener algebra. An abstract form of Wiener's approximation theorem and its generalization is obtained. The third chapter introduces the dual group of a locally compact abelian group, defines the Fourier transform of functions in L1(G), and establishes several properties of functions in L1(G) and T1(G). Wiener's approximation theorem and its generalization for L1(G) is established.

The modelling power of Itˆo integrals has a far reaching impact on a spectrum of diverse fields. For example, in mathematics of finance, its use has given insights into the relationship between call options and their non-deterministic underlying stock prices; in the study of blood clotting dynamics, its utility has helped provide an understanding of the behaviour of platelets in the blood stream; and in the investigation of experimental psychology, it has been used to build random fluctuations into deterministic models which model the dynamics of repetitive movements in humans. Finding the quadrature for these integrals using continuous groups or Lie groups has to take families of time indexed random variables, known as Wiener processes, into consideration. Adaptations of Sophus Lie’s work to stochastic ordinary differential equations (SODEs) have been done by Gaeta and Quintero [1], Wafo Soh and Mahomed [2], ¨Unal [3], Meleshko et al. [4], Fredericks and Mahomed [5], and Fredericks and Mahomed [6]. The seminal work [1] was extended in Gaeta [7]; the differential methodology of [2] and [3] were reconciled in [5]; and the integral methodology of [4] was corrected and reconciled in [5] via [6]. Symmetries of SODEs are analysed. This work focuses on maintaining the properties of the Weiner processes after the application of infinitesimal transformations. The determining equations for first-order SODEs are derived in an Itˆo calculus context. These determining equations are non-stochastic. Many methods of deriving Lie point-symmetries for Itˆo SODEs have surfaced. In the Itˆo calculus context both the formal and intuitive understanding of how to construct these symmetries has led to seemingly disparate results. The impact of Lie point-symmetries on the stock market, population growth and weather SODE models, for example, will not be understood until these different results are reconciled as has been attempted here. Extending the symmetry generator to include the infinitesimal transformation of the Wiener process for Itˆo stochastic differential equations (SDEs), has successfully been done in this thesis. The impact of this work leads to an intuitive understanding of the random time change formulae in the context of Lie point symmetries without having to consult much of the intense Itˆo calculus theory needed to derive it formerly (see Øksendal [8, 9]). Symmetries of nth-order SODEs are studied. The determining equations of these SODEs are derived in an Itˆo calculus context. These determining equations are not stochastic in nature. SODEs of this nature are normally used to model nature (e.g. earthquakes) or for testing the safety and reliability of models in construction engineering when looking at the impact of random perturbations. The symmetries of high-order multi-dimensional SODEs are found using form invariance arguments on both the instantaneous drift and diffusion properties of the SODEs. We then apply this to a generalised approximation analysis algorithm. The determining equations of SODEs are derived in an It¨o calculus context. A methodology for constructing conserved quantities with Lie symmetry infinitesimals in an Itˆo integral context is pursued as well. The basis of this construction relies on Lie bracket relations on both the instantaneous drift and diffusion operators.

La thèse porte sur l'approximation probabiliste dans un contexte fractionnaire, c'est-a-dire dans des modèles reliés d'une manière ou d'une autre au mouvement brownien fractionnaire. Le dénominateur commun de nos résultats est qu'ils proposent des conditions générales sous lesquelles une variable aléatoire de loi compliquée converge, en loi, vers une variable aléatoire de loi plus aisée. Et quand cela a été possible, nous avons aussi cherché à associer des vitesses de convergence. Les outils utilisés sont reliés a un domaine de recherche récent, appelé approche de Malliavin-Stein. En 2005, Nualart et Peccati ont découvert un théorème limite surprenant (qui porte aujourd'hui le nom de théorème du moment quatrième) pour les suites d'intégrales multiples de Wiener-Itô: pour de telles suites et après renormalisation, la convergence en loi vers la gaussienne standard se trouve être équivalente à la convergence du seul moment quatrième. Peu de temps après la publication de ce joli résultat, Peccati et Tudor l'ont étendu au cadre multivarié. Et, depuis, de nombreuses améliorations et nouveaux développements sont apparus dans la littérature, notamment un article de Nourdin et Peccati qui, pour la première fois, a combiné la méthode de Stein avec le calcul de Malliavin, offrant ainsi un cadre dans lequel il est maintenant possible d'associer une vitesse de convergence au théorème du moment quatrième. Nous nous intéressons dans cette thèse à la distance en variation totale entre les lois de deux intégrales doubles de Wiener-Itô. Nous améliorons des résultats antérieurs dus à Davydov et Martinova . Puis on étudie le comportement asymptotique des variations croisées d'un processus bidimensionnel ayant la forme d'une intégrale de Young. Finalement, on établit la convergence multivariée de certains processus de Volterra construits à partir du mouvement brownien fractionnaire. / The thesis deals with the probabilistic approximation in a fractional context, which means in models connected in one way or another to the fractional Brownian motion. The common denominator of our results is that they offer general conditions under which a random variable having a complicated law converges in law to a random variable with easier law. And when this was possible, we have also associated convergence rates. The tools are linked to a recent research field, called Malliavin-Stein approach. In 2005, Nualart and Peccati have discovered a surprising limit theorem (known as the fourth moment theorem) for series of multiple Wiener-Itô integrals: for such series and after renormalization, convergence in distribution to standard Gaussian happens to be equivalent to the convergence of the fourth moment only. Shortly after the publication of this nice result, Peccati and Tudor have extended it to the multivariate case. And since many improvements and new developments have appeared in the literature, including an article by Nourdin and Peccati which for the first time combined the method of Stein with the Malliavin calculus, providing a framework in which it is now possible to associate a rate of convergence to the fourth moment theorem. We focus in this thesis on the total variation distance between the laws of two double Wiener-Itô integrals. We improve a previous result of Davydov and Martinova. Then we study the asymptotic behavior of a two-dimensional cross-variation process that has the form of a Young integral. Finally, a multivariate convergence is established of some Volterra processes built from the fractional Brownian motion.

The ability to construct accurate mathematical models of real systems is an important part of control systems design. A block oriented systems identification approach models the unknown system as interconnected linear and nonlinear blocks. The subject of this thesis is a particular configuration of these blocks referred to as a Wiener model. The Wiener model studied here is a cascade of a one input linear block followed by a nonlinear block which then provides one output. We assume that the signal between the linear and nonlinear block is always unknown, only the Wiener model input and output can be sampled. This thesis investigates identification of the linear transfer function in a Wiener model. The question examined throughout the thesis is: given some small amount of a priori information on the nonlinear part, what can we determine about the linear part? Examples of minimal a priori information are knowledge of only one point on the nonlinear transfer characteristic, or simply that the transfer characteristic is monotonic over a certain range. Nonlinear blocks with and without memory are discussed. Several algorithms for identifying the linear transfer function of a block oriented Wiener system are presented and analyzed in detail. Linear blocks identified have both finite and infinite impulse response (i.e. FIR and IIR). Each algorithm has a carefully defined set of minimal a priori information on the nonlinearity. Also, each approach has a minimally restrictive set of assumptions on the input excitation. The universal applicability of each algorithm is established by providing rigorous proofs of identifiability and in some cases convergence. Extensive simulation testing of each algorithm has been performed. Simulation techniques and results are discussed in detail.

This research study is the result of a 3 years CIFRE PhD thesis between the Airbus design office(Aircraft Control domain) and TéSA laboratory in Toulouse. The main goal is to propose, developand validate a software solution for the detection and diagnosis of a specific type of elevator andrudder vibration, called limit cycle oscillation (LCO), based on existing signals available in flightcontrol computers on board in-series aircraft. LCO is a generic mathematical term defining aninitial condition-independent periodic mode occurring in nonconservative nonlinear systems. Thisstudy focuses on the LCO phenomenon induced by mechanical freeplays in the control surface ofa civil aircraft. The LCO consequences are local structural load augmentation, flight handlingqualities deterioration, actuator operational life reduction, cockpit and cabin comfort deteriorationand maintenance cost augmentation. The state-of-the-art for freeplay induced LCO detection anddiagnosis is based on the pilot sensitivity to vibration and to periodic freeplay check on the controlsurfaces. This study is thought to propose a data-driven solution to help LCO and freeplaydiagnosis. The goal is to improve even more aircraft availability and reduce the maintenance costsby providing to the airlines a condition monitoring signal for LCO and freeplays. For this reason,two algorithmic solutions for vibration and freeplay diagnosis are investigated in this PhD thesis. Areal time detector for LCO diagnosis is first proposed based on the theory of the generalized likeli hood ratio test (GLRT). Some variants and simplifications are also proposed to be compliantwith the industrial constraints. In a second part of this work, a mechanical freeplay detector isintroduced based on the theory of Wiener model identification. Parametric (maximum likelihoodestimator) and non parametric (kernel regression) approaches are investigated, as well as somevariants to well-known nonparametric methods. In particular, the problem of hysteresis cycleestimation (as the output nonlinearity of a Wiener model) is tackled. Moreover, the constrainedand unconstrained problems are studied. A theoretical, numerical (simulator) and experimental(flight data and laboratory) analysis is carried out to investigate the performance of the proposeddetectors and to identify limitations and industrial feasibility. The obtained numerical andexperimental results confirm that the proposed GLR test (and its variants/simplifications) is a very appealing method for LCO diagnostic in terms of performance, robustness and computationalcost. On the other hand, the proposed freeplay diagnostic algorithm is able to detect relativelylarge freeplay levels, but it does not provide consistent results for relatively small freeplay levels. Moreover, specific input types are needed to guarantee repetitive and consistent results. Further studies should be carried out in order to compare the GLRT results with a Bayesian approach and to investigate more deeply the possibilities and limitations of the proposed parametric method for Wiener model identification.

On étudie les multiplicateurs, c'est-à-dire les opérateurs bornés qui commutent avec les translations sur un espace de fonctions sur un groupe localement compact abélien G. On obtient pour tout multiplicateur un symbole essentiellement borné sur un ensemble de morphismes continus sur G, lié au spectre simultané des translations. Nous établissons aussi des résultats analogues pour les opérateurs de Wiener-Hopf (resp. Toeplitz) sur des espaces de fonctions sur R+ (resp. Z+).